TSTP Solution File: SWW336+1 by CSE---1.7
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%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : SWW336+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n024.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 18:07:46 EDT 2024
% Result : Theorem 168.50s 168.37s
% Output : CNFRefutation 168.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW336+1 : TPTP v8.2.0. Released v5.2.0.
% 0.07/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jun 19 05:09:09 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.45/0.58 start to proof:theBenchmark
% 168.06/168.20 %-------------------------------------------
% 168.06/168.20 % File :CSE---1.7
% 168.06/168.20 % Problem :theBenchmark
% 168.06/168.20 % Transform :cnf
% 168.06/168.20 % Format :tptp:raw
% 168.06/168.20 % Command :java -jar mcs_scs.jar %d %s
% 168.06/168.20
% 168.06/168.20 % Result :Theorem 142.200000s
% 168.06/168.20 % Output :CNFRefutation 142.200000s
% 168.06/168.20 %-------------------------------------------
% 168.06/168.21 %------------------------------------------------------------------------------
% 168.06/168.21 % File : SWW336+1 : TPTP v8.2.0. Released v5.2.0.
% 168.06/168.21 % Domain : Software Verification
% 168.06/168.21 % Problem : Hoare's Logic with Procedures 435181, 5000 axioms selected
% 168.06/168.21 % Version : Especial.
% 168.06/168.21 % English :
% 168.06/168.21
% 168.06/168.21 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 168.06/168.21 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 168.06/168.21 % Source : [Bla11]
% 168.06/168.21 % Names : hoare_435181.5000.p [Bla11]
% 168.06/168.21
% 168.06/168.21 % Status : ContradictoryAxioms
% 168.06/168.21 % Rating : 0.69 v7.5.0, 0.75 v7.4.0, 0.87 v7.3.0, 0.79 v7.1.0, 0.78 v7.0.0, 0.80 v6.4.0, 0.77 v6.3.0, 0.83 v6.2.0, 0.92 v6.1.0, 0.93 v6.0.0, 0.91 v5.5.0, 0.93 v5.2.0
% 168.06/168.21 % Syntax : Number of formulae : 5228 (1637 unt; 0 def)
% 168.06/168.21 % Number of atoms : 12831 (4419 equ)
% 168.06/168.21 % Maximal formula atoms : 13 ( 2 avg)
% 168.06/168.21 % Number of connectives : 8611 (1008 ~; 153 |; 738 &)
% 168.06/168.21 % ( 911 <=>;5801 =>; 0 <=; 0 <~>)
% 168.06/168.21 % Maximal formula depth : 22 ( 6 avg)
% 168.06/168.21 % Maximal term depth : 19 ( 2 avg)
% 168.06/168.21 % Number of predicates : 150 ( 149 usr; 0 prp; 1-6 aty)
% 168.06/168.21 % Number of functors : 372 ( 372 usr; 47 con; 0-7 aty)
% 168.06/168.21 % Number of variables : 16569 (16415 !; 154 ?)
% 168.06/168.21 % SPC : FOF_CAX_RFO_SEQ
% 168.06/168.21
% 168.06/168.21 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 168.06/168.21 % 2011-03-01 12:08:13
% 168.06/168.21 %------------------------------------------------------------------------------
% 168.06/168.21 %----Relevant facts (4983)
% 168.06/168.21 fof(fact_ext,axiom,
% 168.06/168.21 ! [V_g_2,V_f_2] :
% 168.06/168.21 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
% 168.06/168.22 => V_f_2 = V_g_2 ) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_empty,axiom,
% 168.06/168.22 ! [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))) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_hoare__derivs_Oequations_I1_J,axiom,
% 168.06/168.22 ! [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))) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_cut,axiom,
% 168.06/168.22 ! [V_Ga_2,V_tsa_2,V_G_H_2,T_b] :
% 168.06/168.22 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_tsa_2)
% 168.06/168.22 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_G_H_2)
% 168.06/168.22 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2) ) ) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_hoare__derivs_Oinsert,axiom,
% 168.06/168.22 ! [V_tsa_2,V_t_2,V_Ga_2,T_b] :
% 168.06/168.22 ( 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))))
% 168.06/168.22 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2)
% 168.06/168.22 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),V_tsa_2)) ) ) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_derivs__insertD,axiom,
% 168.06/168.22 ! [V_tsa_2,V_t_2,V_Ga_2,T_b] :
% 168.06/168.22 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),V_tsa_2))
% 168.06/168.22 => ( 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))))
% 168.06/168.22 & c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2) ) ) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_hoare__valids__def,axiom,
% 168.06/168.22 ! [V_tsa_2,V_Ga_2,T_b] :
% 168.06/168.22 ( c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,V_tsa_2)
% 168.06/168.22 <=> ! [B_n] :
% 168.06/168.22 ( ! [B_x] :
% 168.06/168.22 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_Ga_2))
% 168.06/168.22 => c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x) )
% 168.06/168.22 => ! [B_x] :
% 168.06/168.22 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_tsa_2))
% 168.06/168.22 => c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x) ) ) ) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_ball__empty,axiom,
% 168.06/168.22 ! [V_P_2,T_b,B_x] :
% 168.06/168.22 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 168.06/168.22 => hBOOL(hAPP(V_P_2,B_x)) ) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_empty__not__insert,axiom,
% 168.06/168.22 ! [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) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_insert__not__empty,axiom,
% 168.06/168.22 ! [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)) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_doubleton__eq__iff,axiom,
% 168.06/168.22 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 168.06/168.22 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 168.06/168.22 <=> ( ( V_a_2 = V_c_2
% 168.06/168.22 & V_b_2 = V_d_2 )
% 168.06/168.22 | ( V_a_2 = V_d_2
% 168.06/168.22 & V_b_2 = V_c_2 ) ) ) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_singleton__inject,axiom,
% 168.06/168.22 ! [V_b_2,V_a_2,T_b] :
% 168.06/168.22 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
% 168.06/168.22 => V_a_2 = V_b_2 ) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_bot__apply,axiom,
% 168.06/168.22 ! [V_x_2,T_c,T_b] :
% 168.06/168.22 ( class_Orderings_Obot(T_b)
% 168.06/168.22 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_the__elem__eq,axiom,
% 168.06/168.22 ! [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 ).
% 168.06/168.22
% 168.06/168.22 fof(fact_insert__absorb2,axiom,
% 168.06/168.22 ! [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) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_insert__commute,axiom,
% 168.06/168.22 ! [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)) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_insert__code,axiom,
% 168.06/168.22 ! [V_x_2,V_A_2,V_y_2,T_b] :
% 168.06/168.22 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2))
% 168.06/168.22 <=> ( V_y_2 = V_x_2
% 168.06/168.22 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_triples__valid__Suc,axiom,
% 168.06/168.22 ! [V_n_2,V_tsa_2,T_b] :
% 168.06/168.22 ( ! [B_x] :
% 168.06/168.22 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_tsa_2))
% 168.06/168.22 => c_Hoare__Mirabelle_Otriple__valid(T_b,hAPP(c_Nat_OSuc,V_n_2),B_x) )
% 168.06/168.22 => ! [B_x] :
% 168.06/168.22 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_tsa_2))
% 168.06/168.22 => c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,B_x) ) ) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_triple__valid__Suc,axiom,
% 168.06/168.22 ! [V_t,V_n,T_a] :
% 168.06/168.22 ( c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n),V_t)
% 168.06/168.22 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n,V_t) ) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_n__not__Suc__n,axiom,
% 168.06/168.22 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_Suc__n__not__n,axiom,
% 168.06/168.22 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ).
% 168.06/168.22
% 168.06/168.22 fof(fact_nat_Oinject,axiom,
% 168.06/168.22 ! [V_nat_H_2,V_nat_2] :
% 168.06/168.22 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2)
% 168.06/168.22 <=> V_nat_2 = V_nat_H_2 ) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_Suc__inject,axiom,
% 168.06/168.22 ! [V_y,V_x] :
% 168.06/168.22 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y)
% 168.06/168.22 => V_x = V_y ) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_subset__singletonD,axiom,
% 168.06/168.22 ! [V_x_2,V_A_2,T_b] :
% 168.06/168.22 ( 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)))))
% 168.06/168.22 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.06/168.22 | V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_singletonE,axiom,
% 168.06/168.22 ! [V_a_2,V_b_2,T_b] :
% 168.06/168.22 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
% 168.06/168.22 => V_b_2 = V_a_2 ) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_singleton__iff,axiom,
% 168.06/168.22 ! [V_a_2,V_b_2,T_b] :
% 168.06/168.22 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
% 168.06/168.22 <=> V_b_2 = V_a_2 ) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_folding__one_Osingleton,axiom,
% 168.06/168.22 ! [V_x_2,V_F_2,V_f_2,T_b] :
% 168.06/168.22 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 168.06/168.22 => 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 ) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_fold1Set__sing,axiom,
% 168.06/168.22 ! [V_b_2,V_a_2,V_f_2,T_b] :
% 168.06/168.22 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_b_2))
% 168.06/168.22 <=> V_a_2 = V_b_2 ) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_insert__is__Un,axiom,
% 168.06/168.22 ! [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) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_insert__Diff__single,axiom,
% 168.06/168.22 ! [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) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_order__refl,axiom,
% 168.06/168.22 ! [V_x,T_a] :
% 168.06/168.22 ( class_Orderings_Opreorder(T_a)
% 168.06/168.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_equalityCE,axiom,
% 168.06/168.22 ! [V_c_2,T_b,V_B_2,V_A_2] :
% 168.06/168.22 ( V_A_2 = V_B_2
% 168.06/168.22 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 168.06/168.22 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) )
% 168.06/168.22 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 168.06/168.22 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_equalityI,axiom,
% 168.06/168.22 ! [V_B_2,V_A_2,T_b] :
% 168.06/168.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.06/168.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 168.06/168.22 => V_A_2 = V_B_2 ) ) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_emptyE,axiom,
% 168.06/168.22 ! [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)))) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_insertE,axiom,
% 168.06/168.22 ! [V_A_2,V_b_2,V_a_2,T_b] :
% 168.06/168.22 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
% 168.06/168.22 => ( V_a_2 != V_b_2
% 168.06/168.22 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_insertCI,axiom,
% 168.06/168.22 ! [V_b_2,V_B_2,V_a_2,T_b] :
% 168.06/168.22 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 168.06/168.22 => V_a_2 = V_b_2 )
% 168.06/168.22 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_subsetD,axiom,
% 168.06/168.22 ! [V_c_2,V_B_2,V_A_2,T_b] :
% 168.06/168.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.06/168.22 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 168.06/168.22 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_UnE,axiom,
% 168.06/168.22 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 168.06/168.22 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 168.06/168.22 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 168.06/168.22 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_UnCI,axiom,
% 168.06/168.22 ! [V_A_2,V_B_2,V_c_2,T_b] :
% 168.06/168.22 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 168.06/168.22 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
% 168.06/168.22 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_empty__subsetI,axiom,
% 168.06/168.22 ! [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)) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_DiffI,axiom,
% 168.06/168.22 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 168.06/168.22 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 168.06/168.22 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 168.06/168.22 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_DiffE,axiom,
% 168.06/168.22 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 168.06/168.22 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 168.06/168.22 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 168.06/168.22 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_subset__refl,axiom,
% 168.06/168.22 ! [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)) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_Un__upper1,axiom,
% 168.06/168.22 ! [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))) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_Un__upper2,axiom,
% 168.06/168.22 ! [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))) ).
% 168.06/168.22
% 168.06/168.22 fof(fact_Un__absorb,axiom,
% 168.06/168.22 ! [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 ).
% 168.06/168.22
% 168.06/168.22 fof(fact_Diff__subset,axiom,
% 168.06/168.22 ! [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)) ).
% 168.06/168.23
% 168.06/168.23 fof(fact_le__fun__def,axiom,
% 168.06/168.23 ! [V_g_2,V_f_2,T_b,T_c] :
% 168.06/168.23 ( class_Orderings_Oord(T_c)
% 168.06/168.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 168.06/168.23 <=> ! [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))) ) ) ).
% 168.06/168.23
% 168.06/168.23 fof(fact_mem__def,axiom,
% 168.06/168.23 ! [V_A_2,V_x_2,T_b] :
% 168.06/168.23 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.06/168.23 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 168.06/168.23
% 168.06/168.23 fof(fact_Un__commute,axiom,
% 168.06/168.23 ! [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) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_linorder__linear,axiom,
% 168.17/168.23 ! [V_y,V_x,T_a] :
% 168.17/168.23 ( class_Orderings_Olinorder(T_a)
% 168.17/168.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 168.17/168.23 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_subset__Un__eq,axiom,
% 168.17/168.23 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.17/168.23 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_set__eq__subset,axiom,
% 168.17/168.23 ! [T_b,V_B_2,V_A_2] :
% 168.17/168.23 ( V_A_2 = V_B_2
% 168.17/168.23 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.17/168.23 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_order__eq__iff,axiom,
% 168.17/168.23 ! [V_y_2,V_x_2,T_b] :
% 168.17/168.23 ( class_Orderings_Oorder(T_b)
% 168.17/168.23 => ( V_x_2 = V_y_2
% 168.17/168.23 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 168.17/168.23 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_Un__Diff__cancel,axiom,
% 168.17/168.23 ! [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) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_Un__left__absorb,axiom,
% 168.17/168.23 ! [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) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_Un__left__commute,axiom,
% 168.17/168.23 ! [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)) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_Diff__iff,axiom,
% 168.17/168.23 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 168.17/168.23 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 168.17/168.23 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 168.17/168.23 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_Un__iff,axiom,
% 168.17/168.23 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 168.17/168.23 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 168.17/168.23 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 168.17/168.23 | hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_Diff__idemp,axiom,
% 168.17/168.23 ! [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) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_Un__Diff__cancel2,axiom,
% 168.17/168.23 ! [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) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_Diff__subset__conv,axiom,
% 168.17/168.23 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 168.17/168.23 ( 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))
% 168.17/168.23 <=> 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))) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_Un__assoc,axiom,
% 168.17/168.23 ! [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)) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_Un__Diff,axiom,
% 168.17/168.23 ! [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)) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_bex__Un,axiom,
% 168.17/168.23 ! [V_P_2,V_B_2,V_A_2,T_b] :
% 168.17/168.23 ( ? [B_x] :
% 168.17/168.23 ( 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)))
% 168.17/168.23 & hBOOL(hAPP(V_P_2,B_x)) )
% 168.17/168.23 <=> ( ? [B_x] :
% 168.17/168.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.17/168.23 & hBOOL(hAPP(V_P_2,B_x)) )
% 168.17/168.23 | ? [B_x] :
% 168.17/168.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 168.17/168.23 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_ball__Un,axiom,
% 168.17/168.23 ! [V_P_2,V_B_2,V_A_2,T_b] :
% 168.17/168.23 ( ! [B_x] :
% 168.17/168.23 ( 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)))
% 168.17/168.23 => hBOOL(hAPP(V_P_2,B_x)) )
% 168.17/168.23 <=> ( ! [B_x] :
% 168.17/168.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.17/168.23 => hBOOL(hAPP(V_P_2,B_x)) )
% 168.17/168.23 & ! [B_x] :
% 168.17/168.23 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 168.17/168.23 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_equalityD1,axiom,
% 168.17/168.23 ! [T_b,V_B_2,V_A_2] :
% 168.17/168.23 ( V_A_2 = V_B_2
% 168.17/168.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_equalityD2,axiom,
% 168.17/168.23 ! [T_b,V_B_2,V_A_2] :
% 168.17/168.23 ( V_A_2 = V_B_2
% 168.17/168.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_order__eq__refl,axiom,
% 168.17/168.23 ! [V_y,V_x,T_a] :
% 168.17/168.23 ( class_Orderings_Opreorder(T_a)
% 168.17/168.23 => ( V_x = V_y
% 168.17/168.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_UnI1,axiom,
% 168.17/168.23 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 168.17/168.23 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 168.17/168.23 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_UnI2,axiom,
% 168.17/168.23 ! [V_A_2,V_B_2,V_c_2,T_b] :
% 168.17/168.23 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 168.17/168.23 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_le__funD,axiom,
% 168.17/168.23 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
% 168.17/168.23 ( class_Orderings_Oord(T_c)
% 168.17/168.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 168.17/168.23 => 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))) ) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_Un__absorb1,axiom,
% 168.17/168.23 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.17/168.23 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_Un__absorb2,axiom,
% 168.17/168.23 ! [V_A_2,V_B_2,T_b] :
% 168.17/168.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 168.17/168.23 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_eqset__imp__iff,axiom,
% 168.17/168.23 ! [V_x_2,T_b,V_B_2,V_A_2] :
% 168.17/168.23 ( V_A_2 = V_B_2
% 168.17/168.23 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.23 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_eqelem__imp__iff,axiom,
% 168.17/168.23 ! [V_A_2,T_b,V_y_2,V_x_2] :
% 168.17/168.23 ( V_x_2 = V_y_2
% 168.17/168.23 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.23 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_in__mono,axiom,
% 168.17/168.23 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 168.17/168.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.17/168.23 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.23 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_order__antisym__conv,axiom,
% 168.17/168.23 ! [V_x_2,V_y_2,T_b] :
% 168.17/168.23 ( class_Orderings_Oorder(T_b)
% 168.17/168.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
% 168.17/168.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 168.17/168.23 <=> V_x_2 = V_y_2 ) ) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_Diff__partition,axiom,
% 168.17/168.23 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.17/168.23 => 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 ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_eq__mem__trans,axiom,
% 168.17/168.23 ! [V_A_2,T_b,V_b_2,V_a_2] :
% 168.17/168.23 ( V_a_2 = V_b_2
% 168.17/168.23 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 168.17/168.23 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_ord__eq__le__trans,axiom,
% 168.17/168.23 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.23 ( class_Orderings_Oord(T_a)
% 168.17/168.23 => ( V_a = V_b
% 168.17/168.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 168.17/168.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_xt1_I3_J,axiom,
% 168.17/168.23 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.23 ( class_Orderings_Oorder(T_a)
% 168.17/168.23 => ( V_a = V_b
% 168.17/168.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b))
% 168.17/168.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_set__rev__mp,axiom,
% 168.17/168.23 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 168.17/168.23 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.17/168.23 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_set__mp,axiom,
% 168.17/168.23 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 168.17/168.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.17/168.23 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.23 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_subset__trans,axiom,
% 168.17/168.23 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 168.17/168.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.17/168.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 168.17/168.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_ord__le__eq__trans,axiom,
% 168.17/168.23 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.23 ( class_Orderings_Oord(T_a)
% 168.17/168.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 168.17/168.23 => ( V_b = V_c
% 168.17/168.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_xt1_I4_J,axiom,
% 168.17/168.23 ! [V_c,V_a,V_b,T_a] :
% 168.17/168.23 ( class_Orderings_Oorder(T_a)
% 168.17/168.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 168.17/168.23 => ( V_b = V_c
% 168.17/168.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_order__antisym,axiom,
% 168.17/168.23 ! [V_y,V_x,T_a] :
% 168.17/168.23 ( class_Orderings_Oorder(T_a)
% 168.17/168.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 168.17/168.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 168.17/168.23 => V_x = V_y ) ) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_order__trans,axiom,
% 168.17/168.23 ! [V_z,V_y,V_x,T_a] :
% 168.17/168.23 ( class_Orderings_Opreorder(T_a)
% 168.17/168.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 168.17/168.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 168.17/168.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_xt1_I5_J,axiom,
% 168.17/168.23 ! [V_x,V_y,T_a] :
% 168.17/168.23 ( class_Orderings_Oorder(T_a)
% 168.17/168.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 168.17/168.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 168.17/168.23 => V_x = V_y ) ) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_xt1_I6_J,axiom,
% 168.17/168.23 ! [V_z,V_x,V_y,T_a] :
% 168.17/168.23 ( class_Orderings_Oorder(T_a)
% 168.17/168.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 168.17/168.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 168.17/168.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_Un__least,axiom,
% 168.17/168.23 ! [V_B_2,V_C_2,V_A_2,T_b] :
% 168.17/168.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 168.17/168.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 168.17/168.23 => 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)) ) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_Un__mono,axiom,
% 168.17/168.23 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
% 168.17/168.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 168.17/168.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
% 168.17/168.23 => 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))) ) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_Diff__mono,axiom,
% 168.17/168.23 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_b] :
% 168.17/168.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 168.17/168.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_D_2),V_B_2))
% 168.17/168.23 => 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))) ) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_double__diff,axiom,
% 168.17/168.23 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 168.17/168.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.17/168.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 168.17/168.23 => 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 ) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_equalityE,axiom,
% 168.17/168.23 ! [T_b,V_B_2,V_A_2] :
% 168.17/168.23 ( V_A_2 = V_B_2
% 168.17/168.23 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.17/168.23 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_le__funE,axiom,
% 168.17/168.23 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
% 168.17/168.23 ( class_Orderings_Oord(T_c)
% 168.17/168.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 168.17/168.23 => 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))) ) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_DiffD1,axiom,
% 168.17/168.23 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 168.17/168.23 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 168.17/168.23 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_DiffD2,axiom,
% 168.17/168.23 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 168.17/168.23 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 168.17/168.23 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_linorder__le__cases,axiom,
% 168.17/168.23 ! [V_y,V_x,T_a] :
% 168.17/168.23 ( class_Orderings_Olinorder(T_a)
% 168.17/168.23 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 168.17/168.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_insert__Diff1,axiom,
% 168.17/168.23 ! [V_A_2,V_B_2,V_x_2,T_b] :
% 168.17/168.23 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 168.17/168.23 => 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) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_insert__Diff__if,axiom,
% 168.17/168.23 ! [V_A_2,V_B_2,V_x_2,T_b] :
% 168.17/168.23 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 168.17/168.23 => 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) )
% 168.17/168.23 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 168.17/168.23 => 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)) ) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_subset__insert,axiom,
% 168.17/168.23 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 168.17/168.23 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.23 => ( 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)))
% 168.17/168.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_insert__subset,axiom,
% 168.17/168.23 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 168.17/168.23 ( 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))
% 168.17/168.23 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 168.17/168.23 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_subset__insert__iff,axiom,
% 168.17/168.23 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 168.17/168.23 ( 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)))
% 168.17/168.23 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.23 => 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)) )
% 168.17/168.23 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 168.17/168.23
% 168.17/168.23 fof(fact_diff__single__insert,axiom,
% 168.17/168.23 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 168.17/168.23 ( 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))
% 168.17/168.23 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.23 => 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))) ) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_empty__fold1SetE,axiom,
% 168.17/168.24 ! [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)) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_fold1Set__nonempty,axiom,
% 168.17/168.24 ! [V_x_2,V_A_2,V_f_2,T_b] :
% 168.17/168.24 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),V_x_2))
% 168.17/168.24 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_Diff__insert__absorb,axiom,
% 168.17/168.24 ! [V_A_2,V_x_2,T_b] :
% 168.17/168.24 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.24 => 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 ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_insert__Diff,axiom,
% 168.17/168.24 ! [V_A_2,V_a_2,T_b] :
% 168.17/168.24 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.17/168.24 => 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 ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_empty__Diff,axiom,
% 168.17/168.24 ! [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)) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_Diff__empty,axiom,
% 168.17/168.24 ! [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 ).
% 168.17/168.24
% 168.17/168.24 fof(fact_Diff__cancel,axiom,
% 168.17/168.24 ! [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)) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_Un__empty__left,axiom,
% 168.17/168.24 ! [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 ).
% 168.17/168.24
% 168.17/168.24 fof(fact_Un__empty__right,axiom,
% 168.17/168.24 ! [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 ).
% 168.17/168.24
% 168.17/168.24 fof(fact_Un__empty,axiom,
% 168.17/168.24 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.24 ( 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))
% 168.17/168.24 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.24 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_Un__insert__right,axiom,
% 168.17/168.24 ! [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)) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_Un__insert__left,axiom,
% 168.17/168.24 ! [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)) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_bot__least,axiom,
% 168.17/168.24 ! [V_x,T_a] :
% 168.17/168.24 ( class_Orderings_Obot(T_a)
% 168.17/168.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_all__not__in__conv,axiom,
% 168.17/168.24 ! [V_A_2,T_b] :
% 168.17/168.24 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.17/168.24 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_ex__in__conv,axiom,
% 168.17/168.24 ! [V_A_2,T_b] :
% 168.17/168.24 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.17/168.24 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_empty__iff,axiom,
% 168.17/168.24 ! [V_c_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_equals0D,axiom,
% 168.17/168.24 ! [V_a_2,T_b,V_A_2] :
% 168.17/168.24 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.24 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_subset__empty,axiom,
% 168.17/168.24 ! [V_A_2,T_b] :
% 168.17/168.24 ( 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))))
% 168.17/168.24 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_insertI1,axiom,
% 168.17/168.24 ! [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))) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_insert__iff,axiom,
% 168.17/168.24 ! [V_A_2,V_b_2,V_a_2,T_b] :
% 168.17/168.24 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
% 168.17/168.24 <=> ( V_a_2 = V_b_2
% 168.17/168.24 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_insert__ident,axiom,
% 168.17/168.24 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 168.17/168.24 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.24 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 168.17/168.24 => ( 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)
% 168.17/168.24 <=> V_A_2 = V_B_2 ) ) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_insertI2,axiom,
% 168.17/168.24 ! [V_b_2,V_B_2,V_a_2,T_b] :
% 168.17/168.24 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 168.17/168.24 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_insert__absorb,axiom,
% 168.17/168.24 ! [V_A_2,V_a_2,T_b] :
% 168.17/168.24 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.17/168.24 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2 ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_subset__insertI,axiom,
% 168.17/168.24 ! [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))) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_subset__insertI2,axiom,
% 168.17/168.24 ! [V_b_2,V_B_2,V_A_2,T_b] :
% 168.17/168.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.17/168.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_insert__mono,axiom,
% 168.17/168.24 ! [V_a_2,V_D_2,V_C_2,T_b] :
% 168.17/168.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))
% 168.17/168.24 => 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))) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_asm,axiom,
% 168.17/168.24 ! [V_Ga_2,V_tsa_2,T_b] :
% 168.17/168.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_Ga_2))
% 168.17/168.24 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_weaken,axiom,
% 168.17/168.24 ! [V_tsa_2,V_ts_H_2,V_Ga_2,T_b] :
% 168.17/168.24 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_H_2)
% 168.17/168.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_ts_H_2))
% 168.17/168.24 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2) ) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_thin,axiom,
% 168.17/168.24 ! [V_Ga_2,V_tsa_2,V_G_H_2,T_b] :
% 168.17/168.24 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_tsa_2)
% 168.17/168.24 => ( 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))
% 168.17/168.24 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2) ) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_Diff__insert,axiom,
% 168.17/168.24 ! [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)))) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_Diff__insert2,axiom,
% 168.17/168.24 ! [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) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_sup1CI,axiom,
% 168.17/168.24 ! [T_b,V_A_2,V_x_2,V_B_2] :
% 168.17/168.24 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2))
% 168.17/168.24 => hBOOL(hAPP(V_A_2,V_x_2)) )
% 168.17/168.24 => 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)) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_sup1E,axiom,
% 168.17/168.24 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 168.17/168.24 ( 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))
% 168.17/168.24 => ( ~ hBOOL(hAPP(V_A_2,V_x_2))
% 168.17/168.24 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_minus__apply,axiom,
% 168.17/168.24 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 168.17/168.24 ( class_Groups_Ominus(T_b)
% 168.17/168.24 => 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)) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_sup__apply,axiom,
% 168.17/168.24 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 168.17/168.24 ( class_Lattices_Olattice(T_b)
% 168.17/168.24 => 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)) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_sup__bot__left,axiom,
% 168.17/168.24 ! [V_x,T_a] :
% 168.17/168.24 ( class_Lattices_Obounded__lattice__bot(T_a)
% 168.17/168.24 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_sup__bot__right,axiom,
% 168.17/168.24 ! [V_x,T_a] :
% 168.17/168.24 ( class_Lattices_Obounded__lattice__bot(T_a)
% 168.17/168.24 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_sup__eq__bot__iff,axiom,
% 168.17/168.24 ! [V_y_2,V_x_2,T_b] :
% 168.17/168.24 ( class_Lattices_Obounded__lattice__bot(T_b)
% 168.17/168.24 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_b)
% 168.17/168.24 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_b)
% 168.17/168.24 & V_y_2 = c_Orderings_Obot__class_Obot(T_b) ) ) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_le__supE,axiom,
% 168.17/168.24 ! [V_x,V_b,V_a,T_a] :
% 168.17/168.24 ( class_Lattices_Osemilattice__sup(T_a)
% 168.17/168.24 => ( 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))
% 168.17/168.24 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 168.17/168.24 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_sup__mono,axiom,
% 168.17/168.24 ! [V_d,V_b,V_c,V_a,T_a] :
% 168.17/168.24 ( class_Lattices_Osemilattice__sup(T_a)
% 168.17/168.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 168.17/168.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 168.17/168.24 => 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))) ) ) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_sup__least,axiom,
% 168.17/168.24 ! [V_z,V_x,V_y,T_a] :
% 168.17/168.24 ( class_Lattices_Osemilattice__sup(T_a)
% 168.17/168.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 168.17/168.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 168.17/168.24 => 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)) ) ) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_le__supI,axiom,
% 168.17/168.24 ! [V_b,V_x,V_a,T_a] :
% 168.17/168.24 ( class_Lattices_Osemilattice__sup(T_a)
% 168.17/168.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 168.17/168.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 168.17/168.24 => 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)) ) ) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_sup__absorb1,axiom,
% 168.17/168.24 ! [V_x,V_y,T_a] :
% 168.17/168.24 ( class_Lattices_Osemilattice__sup(T_a)
% 168.17/168.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 168.17/168.24 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_Suc__diff__le,axiom,
% 168.17/168.24 ! [V_m,V_n] :
% 168.17/168.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 168.17/168.24 => 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)) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_diff__Suc__Suc,axiom,
% 168.17/168.24 ! [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) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_Suc__diff__diff,axiom,
% 168.17/168.24 ! [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) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_Suc__n__not__le__n,axiom,
% 168.17/168.24 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_not__less__eq__eq,axiom,
% 168.17/168.24 ! [V_n_2,V_m_2] :
% 168.17/168.24 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 168.17/168.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_le__Suc__eq,axiom,
% 168.17/168.24 ! [V_n_2,V_m_2] :
% 168.17/168.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 168.17/168.24 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 168.17/168.24 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_Suc__le__mono,axiom,
% 168.17/168.24 ! [V_m_2,V_n_2] :
% 168.17/168.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),hAPP(c_Nat_OSuc,V_m_2)))
% 168.17/168.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_le__SucI,axiom,
% 168.17/168.24 ! [V_n,V_m] :
% 168.17/168.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 168.17/168.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_le__SucE,axiom,
% 168.17/168.24 ! [V_n,V_m] :
% 168.17/168.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 168.17/168.24 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 168.17/168.24 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_Suc__leD,axiom,
% 168.17/168.24 ! [V_n,V_m] :
% 168.17/168.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 168.17/168.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_eq__mem,axiom,
% 168.17/168.24 ! [V_y_2,V_x_2,T_b] :
% 168.17/168.24 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_fequal,V_y_2)))
% 168.17/168.24 <=> V_x_2 = V_y_2 ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_sup_Oidem,axiom,
% 168.17/168.24 ! [V_a,T_a] :
% 168.17/168.24 ( class_Lattices_Osemilattice__sup(T_a)
% 168.17/168.24 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_sup__idem,axiom,
% 168.17/168.24 ! [V_x,T_a] :
% 168.17/168.24 ( class_Lattices_Osemilattice__sup(T_a)
% 168.17/168.24 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_sup_Ocommute,axiom,
% 168.17/168.24 ! [V_b,V_a,T_a] :
% 168.17/168.24 ( class_Lattices_Osemilattice__sup(T_a)
% 168.17/168.24 => 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) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_inf__sup__aci_I5_J,axiom,
% 168.17/168.24 ! [V_y,V_x,T_a] :
% 168.17/168.24 ( class_Lattices_Olattice(T_a)
% 168.17/168.24 => 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) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_sup__commute,axiom,
% 168.17/168.24 ! [V_y,V_x,T_a] :
% 168.17/168.24 ( class_Lattices_Osemilattice__sup(T_a)
% 168.17/168.24 => 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) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_sup_Oleft__idem,axiom,
% 168.17/168.24 ! [V_b,V_a,T_a] :
% 168.17/168.24 ( class_Lattices_Osemilattice__sup(T_a)
% 168.17/168.24 => 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) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_inf__sup__aci_I8_J,axiom,
% 168.17/168.24 ! [V_y,V_x,T_a] :
% 168.17/168.24 ( class_Lattices_Olattice(T_a)
% 168.17/168.24 => 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) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_sup__left__idem,axiom,
% 168.17/168.24 ! [V_y,V_x,T_a] :
% 168.17/168.24 ( class_Lattices_Osemilattice__sup(T_a)
% 168.17/168.24 => 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) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_sup_Oleft__commute,axiom,
% 168.17/168.24 ! [V_c,V_a,V_b,T_a] :
% 168.17/168.24 ( class_Lattices_Osemilattice__sup(T_a)
% 168.17/168.24 => 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)) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_inf__sup__aci_I7_J,axiom,
% 168.17/168.24 ! [V_z,V_y,V_x,T_a] :
% 168.17/168.24 ( class_Lattices_Olattice(T_a)
% 168.17/168.24 => 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)) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_sup__left__commute,axiom,
% 168.17/168.24 ! [V_z,V_y,V_x,T_a] :
% 168.17/168.24 ( class_Lattices_Osemilattice__sup(T_a)
% 168.17/168.24 => 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)) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_sup_Oassoc,axiom,
% 168.17/168.24 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.24 ( class_Lattices_Osemilattice__sup(T_a)
% 168.17/168.24 => 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)) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_inf__sup__aci_I6_J,axiom,
% 168.17/168.24 ! [V_z,V_y,V_x,T_a] :
% 168.17/168.24 ( class_Lattices_Olattice(T_a)
% 168.17/168.24 => 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)) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_sup__assoc,axiom,
% 168.17/168.24 ! [V_z,V_y,V_x,T_a] :
% 168.17/168.24 ( class_Lattices_Osemilattice__sup(T_a)
% 168.17/168.24 => 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)) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_rev__predicate1D,axiom,
% 168.17/168.24 ! [V_Q_2,T_b,V_x_2,V_P_2] :
% 168.17/168.24 ( hBOOL(hAPP(V_P_2,V_x_2))
% 168.17/168.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_P_2),V_Q_2))
% 168.17/168.24 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_predicate1D,axiom,
% 168.17/168.24 ! [V_x_2,V_Q_2,V_P_2,T_b] :
% 168.17/168.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_P_2),V_Q_2))
% 168.17/168.24 => ( hBOOL(hAPP(V_P_2,V_x_2))
% 168.17/168.24 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_sup1I1,axiom,
% 168.17/168.24 ! [V_B_2,T_b,V_x_2,V_A_2] :
% 168.17/168.24 ( hBOOL(hAPP(V_A_2,V_x_2))
% 168.17/168.24 => 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)) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_sup1I2,axiom,
% 168.17/168.24 ! [V_A_2,T_b,V_x_2,V_B_2] :
% 168.17/168.24 ( hBOOL(hAPP(V_B_2,V_x_2))
% 168.17/168.24 => 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)) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_inf__sup__ord_I3_J,axiom,
% 168.17/168.24 ! [V_y,V_x,T_a] :
% 168.17/168.24 ( class_Lattices_Olattice(T_a)
% 168.17/168.24 => 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))) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_sup__ge1,axiom,
% 168.17/168.24 ! [V_y,V_x,T_a] :
% 168.17/168.24 ( class_Lattices_Osemilattice__sup(T_a)
% 168.17/168.24 => 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))) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_inf__sup__ord_I4_J,axiom,
% 168.17/168.24 ! [V_x,V_y,T_a] :
% 168.17/168.24 ( class_Lattices_Olattice(T_a)
% 168.17/168.24 => 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))) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_sup__ge2,axiom,
% 168.17/168.24 ! [V_x,V_y,T_a] :
% 168.17/168.24 ( class_Lattices_Osemilattice__sup(T_a)
% 168.17/168.24 => 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))) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_le__iff__sup,axiom,
% 168.17/168.24 ! [V_y_2,V_x_2,T_b] :
% 168.17/168.24 ( class_Lattices_Osemilattice__sup(T_b)
% 168.17/168.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 168.17/168.24 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = V_y_2 ) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_le__sup__iff,axiom,
% 168.17/168.24 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 168.17/168.24 ( class_Lattices_Osemilattice__sup(T_b)
% 168.17/168.24 => ( 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))
% 168.17/168.24 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 168.17/168.24 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_le__supI1,axiom,
% 168.17/168.24 ! [V_b,V_a,V_x,T_a] :
% 168.17/168.24 ( class_Lattices_Osemilattice__sup(T_a)
% 168.17/168.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 168.17/168.24 => 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))) ) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_le__supI2,axiom,
% 168.17/168.24 ! [V_a,V_b,V_x,T_a] :
% 168.17/168.24 ( class_Lattices_Osemilattice__sup(T_a)
% 168.17/168.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 168.17/168.24 => 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))) ) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_sup__absorb2,axiom,
% 168.17/168.24 ! [V_y,V_x,T_a] :
% 168.17/168.24 ( class_Lattices_Osemilattice__sup(T_a)
% 168.17/168.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 168.17/168.24 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_diff__eq__diff__less__eq,axiom,
% 168.17/168.24 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 168.17/168.24 ( class_Groups_Oordered__ab__group__add(T_b)
% 168.17/168.24 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2)
% 168.17/168.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 168.17/168.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2)) ) ) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_folding__one_Oremove,axiom,
% 168.17/168.24 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 168.17/168.24 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 168.17/168.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.24 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.24 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 168.17/168.24 => hAPP(V_F_2,V_A_2) = V_x_2 )
% 168.17/168.24 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 168.17/168.24 => 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)))))) ) ) ) ) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_fold1Set_Ointros,axiom,
% 168.17/168.24 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_b] :
% 168.17/168.24 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,V_a_2,V_A_2),V_x_2))
% 168.17/168.24 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.17/168.24 => 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)) ) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_psubset__insert__iff,axiom,
% 168.17/168.24 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 168.17/168.24 ( 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)))
% 168.17/168.24 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 168.17/168.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
% 168.17/168.24 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 168.17/168.24 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.24 => 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)) )
% 168.17/168.24 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_fold__graph_H_Ointros_I2_J,axiom,
% 168.17/168.24 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 168.17/168.24 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.24 => ( 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)
% 168.17/168.24 => 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)) ) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_Diff1__fold__graph,axiom,
% 168.17/168.24 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 168.17/168.24 ( 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))
% 168.17/168.24 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.24 => 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))) ) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_folding__one_Oinsert__remove,axiom,
% 168.17/168.24 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 168.17/168.24 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 168.17/168.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.24 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 168.17/168.24 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 168.17/168.24 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 168.17/168.24 => 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)))))) ) ) ) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_folding__one_Oinsert,axiom,
% 168.17/168.24 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 168.17/168.24 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 168.17/168.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.24 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.24 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.24 => 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)) ) ) ) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_nonempty__iff,axiom,
% 168.17/168.24 ! [T_b,V_A_2] :
% 168.17/168.24 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.24 <=> ? [B_x,B_B] :
% 168.17/168.24 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_B)
% 168.17/168.24 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_B)) ) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_Sup__fin_Oidem,axiom,
% 168.17/168.24 ! [V_x,T_a] :
% 168.17/168.24 ( class_Lattices_Olattice(T_a)
% 168.17/168.24 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_Powp__mono,axiom,
% 168.17/168.24 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.17/168.24 => 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))) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_finite_OemptyI,axiom,
% 168.17/168.24 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_finite_OinsertI,axiom,
% 168.17/168.24 ! [V_a_2,V_A_2,T_b] :
% 168.17/168.24 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.24 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_finite__Diff,axiom,
% 168.17/168.24 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.24 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.24 => 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))) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_le__diff__iff,axiom,
% 168.17/168.24 ! [V_n_2,V_m_2,V_k_2] :
% 168.17/168.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 168.17/168.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 168.17/168.24 => ( 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)))
% 168.17/168.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_Nat_Odiff__diff__eq,axiom,
% 168.17/168.24 ! [V_n,V_m,V_k] :
% 168.17/168.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m))
% 168.17/168.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 168.17/168.24 => 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) ) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_eq__diff__iff,axiom,
% 168.17/168.24 ! [V_n_2,V_m_2,V_k_2] :
% 168.17/168.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 168.17/168.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 168.17/168.24 => ( 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)
% 168.17/168.24 <=> V_m_2 = V_n_2 ) ) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_le__antisym,axiom,
% 168.17/168.24 ! [V_n,V_m] :
% 168.17/168.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 168.17/168.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 168.17/168.24 => V_m = V_n ) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_le__trans,axiom,
% 168.17/168.24 ! [V_k,V_j,V_i] :
% 168.17/168.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 168.17/168.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k))
% 168.17/168.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_diff__diff__cancel,axiom,
% 168.17/168.24 ! [V_n,V_i] :
% 168.17/168.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n))
% 168.17/168.24 => 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 ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_diff__le__mono,axiom,
% 168.17/168.24 ! [V_l,V_n,V_m] :
% 168.17/168.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 168.17/168.24 => 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))) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_diff__le__mono2,axiom,
% 168.17/168.24 ! [V_l,V_n,V_m] :
% 168.17/168.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 168.17/168.24 => 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))) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_eq__imp__le,axiom,
% 168.17/168.24 ! [V_n,V_m] :
% 168.17/168.24 ( V_m = V_n
% 168.17/168.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_diff__commute,axiom,
% 168.17/168.24 ! [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) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_nat__le__linear,axiom,
% 168.17/168.24 ! [V_n,V_m] :
% 168.17/168.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 168.17/168.24 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_diff__le__self,axiom,
% 168.17/168.24 ! [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)) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_le__refl,axiom,
% 168.17/168.24 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_order__less__irrefl,axiom,
% 168.17/168.24 ! [V_x,T_a] :
% 168.17/168.24 ( class_Orderings_Opreorder(T_a)
% 168.17/168.24 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_linorder__neq__iff,axiom,
% 168.17/168.24 ! [V_y_2,V_x_2,T_b] :
% 168.17/168.24 ( class_Orderings_Olinorder(T_b)
% 168.17/168.24 => ( V_x_2 != V_y_2
% 168.17/168.24 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 168.17/168.24 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_not__less__iff__gr__or__eq,axiom,
% 168.17/168.24 ! [V_y_2,V_x_2,T_b] :
% 168.17/168.24 ( class_Orderings_Olinorder(T_b)
% 168.17/168.24 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 168.17/168.24 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
% 168.17/168.24 | V_x_2 = V_y_2 ) ) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_linorder__less__linear,axiom,
% 168.17/168.24 ! [V_y,V_x,T_a] :
% 168.17/168.24 ( class_Orderings_Olinorder(T_a)
% 168.17/168.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 168.17/168.24 | V_x = V_y
% 168.17/168.24 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_linorder__antisym__conv3,axiom,
% 168.17/168.24 ! [V_x_2,V_y_2,T_b] :
% 168.17/168.24 ( class_Orderings_Olinorder(T_b)
% 168.17/168.24 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
% 168.17/168.24 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 168.17/168.24 <=> V_x_2 = V_y_2 ) ) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_linorder__neqE,axiom,
% 168.17/168.24 ! [V_y,V_x,T_a] :
% 168.17/168.24 ( class_Orderings_Olinorder(T_a)
% 168.17/168.24 => ( V_x != V_y
% 168.17/168.24 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 168.17/168.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 168.17/168.24
% 168.17/168.24 fof(fact_less__imp__neq,axiom,
% 168.17/168.24 ! [V_y,V_x,T_a] :
% 168.17/168.25 ( class_Orderings_Oorder(T_a)
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 168.17/168.25 => V_x != V_y ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_order__less__not__sym,axiom,
% 168.17/168.25 ! [V_y,V_x,T_a] :
% 168.17/168.25 ( class_Orderings_Opreorder(T_a)
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 168.17/168.25 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_order__less__imp__not__less,axiom,
% 168.17/168.25 ! [V_y,V_x,T_a] :
% 168.17/168.25 ( class_Orderings_Opreorder(T_a)
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 168.17/168.25 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_order__less__imp__not__eq,axiom,
% 168.17/168.25 ! [V_y,V_x,T_a] :
% 168.17/168.25 ( class_Orderings_Oorder(T_a)
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 168.17/168.25 => V_x != V_y ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_order__less__imp__not__eq2,axiom,
% 168.17/168.25 ! [V_y,V_x,T_a] :
% 168.17/168.25 ( class_Orderings_Oorder(T_a)
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 168.17/168.25 => V_y != V_x ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_order__less__asym_H,axiom,
% 168.17/168.25 ! [V_b,V_a,T_a] :
% 168.17/168.25 ( class_Orderings_Opreorder(T_a)
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 168.17/168.25 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_xt1_I9_J,axiom,
% 168.17/168.25 ! [V_a,V_b,T_a] :
% 168.17/168.25 ( class_Orderings_Oorder(T_a)
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 168.17/168.25 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_ord__eq__less__trans,axiom,
% 168.17/168.25 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.25 ( class_Orderings_Oord(T_a)
% 168.17/168.25 => ( V_a = V_b
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_xt1_I1_J,axiom,
% 168.17/168.25 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.25 ( class_Orderings_Oorder(T_a)
% 168.17/168.25 => ( V_a = V_b
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b))
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_psubset__trans,axiom,
% 168.17/168.25 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 168.17/168.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_ord__less__eq__trans,axiom,
% 168.17/168.25 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.25 ( class_Orderings_Oord(T_a)
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 168.17/168.25 => ( V_b = V_c
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_xt1_I2_J,axiom,
% 168.17/168.25 ! [V_c,V_a,V_b,T_a] :
% 168.17/168.25 ( class_Orderings_Oorder(T_a)
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 168.17/168.25 => ( V_b = V_c
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_order__less__trans,axiom,
% 168.17/168.25 ! [V_z,V_y,V_x,T_a] :
% 168.17/168.25 ( class_Orderings_Opreorder(T_a)
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_xt1_I10_J,axiom,
% 168.17/168.25 ! [V_z,V_x,V_y,T_a] :
% 168.17/168.25 ( class_Orderings_Oorder(T_a)
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_order__less__asym,axiom,
% 168.17/168.25 ! [V_y,V_x,T_a] :
% 168.17/168.25 ( class_Orderings_Opreorder(T_a)
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 168.17/168.25 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_linorder__cases,axiom,
% 168.17/168.25 ! [V_y,V_x,T_a] :
% 168.17/168.25 ( class_Orderings_Olinorder(T_a)
% 168.17/168.25 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 168.17/168.25 => ( V_x != V_y
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_finite,axiom,
% 168.17/168.25 ! [V_A_2,T_b] :
% 168.17/168.25 ( class_Finite__Set_Ofinite(T_b)
% 168.17/168.25 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_finite__code,axiom,
% 168.17/168.25 ! [V_A_2,T_b] :
% 168.17/168.25 ( class_Finite__Set_Ofinite(T_b)
% 168.17/168.25 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_fold__graph__imp__finite,axiom,
% 168.17/168.25 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 168.17/168.25 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
% 168.17/168.25 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_diff__eq__diff__less,axiom,
% 168.17/168.25 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 168.17/168.25 ( class_Groups_Oordered__ab__group__add(T_b)
% 168.17/168.25 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2)
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 168.17/168.25 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2)) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_fold__graph_H_Oequations_I1_J,axiom,
% 168.17/168.25 ! [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) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_fold__graph_H_Ointros_I1_J,axiom,
% 168.17/168.25 ! [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) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_less__fun__def,axiom,
% 168.17/168.25 ! [V_g_2,V_f_2,T_b,T_c] :
% 168.17/168.25 ( class_Orderings_Oord(T_c)
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 168.17/168.25 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 168.17/168.25 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_g_2),V_f_2)) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_linorder__not__less,axiom,
% 168.17/168.25 ! [V_y_2,V_x_2,T_b] :
% 168.17/168.25 ( class_Orderings_Olinorder(T_b)
% 168.17/168.25 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 168.17/168.25 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_linorder__not__le,axiom,
% 168.17/168.25 ! [V_y_2,V_x_2,T_b] :
% 168.17/168.25 ( class_Orderings_Olinorder(T_b)
% 168.17/168.25 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 168.17/168.25 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_linorder__le__less__linear,axiom,
% 168.17/168.25 ! [V_y,V_x,T_a] :
% 168.17/168.25 ( class_Orderings_Olinorder(T_a)
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 168.17/168.25 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_order__less__le,axiom,
% 168.17/168.25 ! [V_y_2,V_x_2,T_b] :
% 168.17/168.25 ( class_Orderings_Oorder(T_b)
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 168.17/168.25 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 168.17/168.25 & V_x_2 != V_y_2 ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_less__le__not__le,axiom,
% 168.17/168.25 ! [V_y_2,V_x_2,T_b] :
% 168.17/168.25 ( class_Orderings_Opreorder(T_b)
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 168.17/168.25 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 168.17/168.25 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_order__le__less,axiom,
% 168.17/168.25 ! [V_y_2,V_x_2,T_b] :
% 168.17/168.25 ( class_Orderings_Oorder(T_b)
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 168.17/168.25 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 168.17/168.25 | V_x_2 = V_y_2 ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_leI,axiom,
% 168.17/168.25 ! [V_y,V_x,T_a] :
% 168.17/168.25 ( class_Orderings_Olinorder(T_a)
% 168.17/168.25 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_not__leE,axiom,
% 168.17/168.25 ! [V_x,V_y,T_a] :
% 168.17/168.25 ( class_Orderings_Olinorder(T_a)
% 168.17/168.25 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_linorder__antisym__conv1,axiom,
% 168.17/168.25 ! [V_y_2,V_x_2,T_b] :
% 168.17/168.25 ( class_Orderings_Olinorder(T_b)
% 168.17/168.25 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 168.17/168.25 <=> V_x_2 = V_y_2 ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_order__neq__le__trans,axiom,
% 168.17/168.25 ! [V_b,V_a,T_a] :
% 168.17/168.25 ( class_Orderings_Oorder(T_a)
% 168.17/168.25 => ( V_a != V_b
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_xt1_I12_J,axiom,
% 168.17/168.25 ! [V_b,V_a,T_a] :
% 168.17/168.25 ( class_Orderings_Oorder(T_a)
% 168.17/168.25 => ( V_a != V_b
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_leD,axiom,
% 168.17/168.25 ! [V_x,V_y,T_a] :
% 168.17/168.25 ( class_Orderings_Olinorder(T_a)
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 168.17/168.25 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_order__less__imp__le,axiom,
% 168.17/168.25 ! [V_y,V_x,T_a] :
% 168.17/168.25 ( class_Orderings_Opreorder(T_a)
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_linorder__antisym__conv2,axiom,
% 168.17/168.25 ! [V_y_2,V_x_2,T_b] :
% 168.17/168.25 ( class_Orderings_Olinorder(T_b)
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 168.17/168.25 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 168.17/168.25 <=> V_x_2 = V_y_2 ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_order__le__imp__less__or__eq,axiom,
% 168.17/168.25 ! [V_y,V_x,T_a] :
% 168.17/168.25 ( class_Orderings_Oorder(T_a)
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 168.17/168.25 | V_x = V_y ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_order__le__neq__trans,axiom,
% 168.17/168.25 ! [V_b,V_a,T_a] :
% 168.17/168.25 ( class_Orderings_Oorder(T_a)
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 168.17/168.25 => ( V_a != V_b
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_xt1_I11_J,axiom,
% 168.17/168.25 ! [V_a,V_b,T_a] :
% 168.17/168.25 ( class_Orderings_Oorder(T_a)
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 168.17/168.25 => ( V_a != V_b
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_order__less__le__trans,axiom,
% 168.17/168.25 ! [V_z,V_y,V_x,T_a] :
% 168.17/168.25 ( class_Orderings_Opreorder(T_a)
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_xt1_I7_J,axiom,
% 168.17/168.25 ! [V_z,V_x,V_y,T_a] :
% 168.17/168.25 ( class_Orderings_Oorder(T_a)
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_order__le__less__trans,axiom,
% 168.17/168.25 ! [V_z,V_y,V_x,T_a] :
% 168.17/168.25 ( class_Orderings_Opreorder(T_a)
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_xt1_I8_J,axiom,
% 168.17/168.25 ! [V_z,V_x,V_y,T_a] :
% 168.17/168.25 ( class_Orderings_Oorder(T_a)
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_psubsetD,axiom,
% 168.17/168.25 ! [V_c_2,V_B_2,V_A_2,T_b] :
% 168.17/168.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_not__psubset__empty,axiom,
% 168.17/168.25 ! [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)))) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_less__supI2,axiom,
% 168.17/168.25 ! [V_a,V_b,V_x,T_a] :
% 168.17/168.25 ( class_Lattices_Osemilattice__sup(T_a)
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 168.17/168.25 => 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))) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_less__supI1,axiom,
% 168.17/168.25 ! [V_b,V_a,V_x,T_a] :
% 168.17/168.25 ( class_Lattices_Osemilattice__sup(T_a)
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 168.17/168.25 => 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))) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_psubset__eq,axiom,
% 168.17/168.25 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.17/168.25 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.17/168.25 & V_A_2 != V_B_2 ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_subset__iff__psubset__eq,axiom,
% 168.17/168.25 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.17/168.25 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.17/168.25 | V_A_2 = V_B_2 ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_psubset__imp__subset,axiom,
% 168.17/168.25 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_psubset__subset__trans,axiom,
% 168.17/168.25 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 168.17/168.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_subset__psubset__trans,axiom,
% 168.17/168.25 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 168.17/168.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_finite_Oequations_I1_J,axiom,
% 168.17/168.25 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_finite__insert,axiom,
% 168.17/168.25 ! [V_A_2,V_a_2,T_b] :
% 168.17/168.25 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)))
% 168.17/168.25 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_finite__subset,axiom,
% 168.17/168.25 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.17/168.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.25 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_rev__finite__subset,axiom,
% 168.17/168.25 ! [V_A_2,V_B_2,T_b] :
% 168.17/168.25 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.17/168.25 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_finite__UnI,axiom,
% 168.17/168.25 ! [V_Ga_2,V_F_2,T_b] :
% 168.17/168.25 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 168.17/168.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2))
% 168.17/168.25 => 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))) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_finite__Un,axiom,
% 168.17/168.25 ! [V_Ga_2,V_F_2,T_b] :
% 168.17/168.25 ( 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)))
% 168.17/168.25 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 168.17/168.25 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_finite__Diff2,axiom,
% 168.17/168.25 ! [V_A_2,V_B_2,T_b] :
% 168.17/168.25 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.25 => ( 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)))
% 168.17/168.25 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_fold__graph_Oequations_I1_J,axiom,
% 168.17/168.25 ! [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)) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_fold__graph_OemptyI,axiom,
% 168.17/168.25 ! [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)) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_empty__fold__graphE,axiom,
% 168.17/168.25 ! [V_x_2,V_z_2,V_f_2,T_c,T_b] :
% 168.17/168.25 ( 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))
% 168.17/168.25 => V_x_2 = V_z_2 ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_finite__Diff__insert,axiom,
% 168.17/168.25 ! [V_B_2,V_a_2,V_A_2,T_b] :
% 168.17/168.25 ( 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))))
% 168.17/168.25 <=> 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))) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_fold__graph_OinsertI,axiom,
% 168.17/168.25 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 168.17/168.25 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.25 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 168.17/168.25 => 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))) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_diff__eq__diff__eq,axiom,
% 168.17/168.25 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 168.17/168.25 ( class_Groups_Oab__group__add(T_b)
% 168.17/168.25 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2)
% 168.17/168.25 => ( V_a_2 = V_b_2
% 168.17/168.25 <=> V_c_2 = V_d_2 ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_folding__image__simple_Oremove,axiom,
% 168.17/168.25 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 168.17/168.25 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 168.17/168.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 168.17/168.25 => 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)))))) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_folding__image__simple_Oinsert__remove,axiom,
% 168.17/168.25 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 168.17/168.25 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 168.17/168.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 168.17/168.25 => 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)))))) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_Sup__fin_Oremove,axiom,
% 168.17/168.25 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.25 ( class_Lattices_Olattice(T_b)
% 168.17/168.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.25 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 168.17/168.25 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = V_x_2 )
% 168.17/168.25 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 168.17/168.25 => 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)))))) ) ) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_fold__graph_H_Oequations_I2_J,axiom,
% 168.17/168.25 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_c,T_b] :
% 168.17/168.25 ( 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))
% 168.17/168.25 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.25 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 )
% 168.17/168.25 | ? [B_x,B_y] :
% 168.17/168.25 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y)
% 168.17/168.25 & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a2_2))
% 168.17/168.25 & 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) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_folding__one_Oclosed,axiom,
% 168.17/168.25 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 168.17/168.25 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 168.17/168.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.25 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.25 => ( ! [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))))))
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_finite__empty__induct,axiom,
% 168.17/168.25 ! [V_P_2,V_A_2,T_b] :
% 168.17/168.25 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.25 => ( hBOOL(hAPP(V_P_2,V_A_2))
% 168.17/168.25 => ( ! [B_a,B_A] :
% 168.17/168.25 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_A))
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
% 168.17/168.25 => ( hBOOL(hAPP(V_P_2,B_A))
% 168.17/168.25 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),B_A),hAPP(hAPP(c_Set_Oinsert(T_b),B_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) )
% 168.17/168.25 => hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_folding__one__idem_Ounion__idem,axiom,
% 168.17/168.25 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 168.17/168.25 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 168.17/168.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.25 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.25 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.25 => 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)) ) ) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_finite__subset__induct,axiom,
% 168.17/168.25 ! [V_P_2,V_A_2,V_F_2,T_b] :
% 168.17/168.25 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_A_2))
% 168.17/168.25 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 168.17/168.25 => ( ! [B_a,B_F] :
% 168.17/168.25 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F))
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 168.17/168.25 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_F))
% 168.17/168.25 => ( hBOOL(hAPP(V_P_2,B_F))
% 168.17/168.25 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F))) ) ) ) )
% 168.17/168.25 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_folding__one__idem_Osubset__idem,axiom,
% 168.17/168.25 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 168.17/168.25 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 168.17/168.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.25 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 168.17/168.25 => 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) ) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_folding__one__idem_Oinsert__idem,axiom,
% 168.17/168.25 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 168.17/168.25 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 168.17/168.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.25 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.25 => 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)) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_Sup__fin_Oinsert__remove,axiom,
% 168.17/168.25 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.25 ( class_Lattices_Olattice(T_b)
% 168.17/168.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.25 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 168.17/168.25 => 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 )
% 168.17/168.25 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 168.17/168.25 => 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)))))) ) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_lessI,axiom,
% 168.17/168.25 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_Suc__mono,axiom,
% 168.17/168.25 ! [V_n,V_m] :
% 168.17/168.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_folding__one__idem_Oidem,axiom,
% 168.17/168.25 ! [V_x_2,V_F_2,V_f_2,T_b] :
% 168.17/168.25 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 168.17/168.25 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_not__less__eq,axiom,
% 168.17/168.25 ! [V_n_2,V_m_2] :
% 168.17/168.25 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 168.17/168.25 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_less__Suc__eq,axiom,
% 168.17/168.25 ! [V_n_2,V_m_2] :
% 168.17/168.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 168.17/168.25 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 168.17/168.25 | V_m_2 = V_n_2 ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_Suc__less__eq,axiom,
% 168.17/168.25 ! [V_n_2,V_m_2] :
% 168.17/168.25 ( 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)))
% 168.17/168.25 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_not__less__less__Suc__eq,axiom,
% 168.17/168.25 ! [V_m_2,V_n_2] :
% 168.17/168.25 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 168.17/168.25 <=> V_n_2 = V_m_2 ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_less__antisym,axiom,
% 168.17/168.25 ! [V_m,V_n] :
% 168.17/168.25 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m)))
% 168.17/168.25 => V_m = V_n ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_less__SucI,axiom,
% 168.17/168.25 ! [V_n,V_m] :
% 168.17/168.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_Suc__lessI,axiom,
% 168.17/168.25 ! [V_n,V_m] :
% 168.17/168.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 168.17/168.25 => ( hAPP(c_Nat_OSuc,V_m) != V_n
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_less__trans__Suc,axiom,
% 168.17/168.25 ! [V_k,V_j,V_i] :
% 168.17/168.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_less__SucE,axiom,
% 168.17/168.25 ! [V_n,V_m] :
% 168.17/168.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 168.17/168.25 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 168.17/168.25 => V_m = V_n ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_Suc__lessD,axiom,
% 168.17/168.25 ! [V_n,V_m] :
% 168.17/168.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_Suc__less__SucD,axiom,
% 168.17/168.25 ! [V_n,V_m] :
% 168.17/168.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)))
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_nat__less__le,axiom,
% 168.17/168.25 ! [V_n_2,V_m_2] :
% 168.17/168.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 168.17/168.25 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 168.17/168.25 & V_m_2 != V_n_2 ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_le__eq__less__or__eq,axiom,
% 168.17/168.25 ! [V_n_2,V_m_2] :
% 168.17/168.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 168.17/168.25 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 168.17/168.25 | V_m_2 = V_n_2 ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_less__imp__le__nat,axiom,
% 168.17/168.25 ! [V_n,V_m] :
% 168.17/168.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_le__neq__implies__less,axiom,
% 168.17/168.25 ! [V_n,V_m] :
% 168.17/168.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 168.17/168.25 => ( V_m != V_n
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_less__or__eq__imp__le,axiom,
% 168.17/168.25 ! [V_n,V_m] :
% 168.17/168.25 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 168.17/168.25 | V_m = V_n )
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_less__imp__diff__less,axiom,
% 168.17/168.25 ! [V_n,V_k,V_j] :
% 168.17/168.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_n)),V_k)) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_diff__less__mono2,axiom,
% 168.17/168.25 ! [V_l,V_n,V_m] :
% 168.17/168.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l))
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_n)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_m))) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_folding__image__simple_Oempty,axiom,
% 168.17/168.25 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 168.17/168.25 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 168.17/168.25 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_Suc__le__lessD,axiom,
% 168.17/168.25 ! [V_n,V_m] :
% 168.17/168.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_le__less__Suc__eq,axiom,
% 168.17/168.25 ! [V_n_2,V_m_2] :
% 168.17/168.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 168.17/168.25 <=> V_n_2 = V_m_2 ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_Suc__leI,axiom,
% 168.17/168.25 ! [V_n,V_m] :
% 168.17/168.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_le__imp__less__Suc,axiom,
% 168.17/168.25 ! [V_n,V_m] :
% 168.17/168.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_Suc__le__eq,axiom,
% 168.17/168.25 ! [V_n_2,V_m_2] :
% 168.17/168.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 168.17/168.25 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_less__Suc__eq__le,axiom,
% 168.17/168.25 ! [V_n_2,V_m_2] :
% 168.17/168.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 168.17/168.25 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_less__eq__Suc__le,axiom,
% 168.17/168.25 ! [V_m_2,V_n_2] :
% 168.17/168.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 168.17/168.25 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_diff__less__Suc,axiom,
% 168.17/168.25 ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),hAPP(c_Nat_OSuc,V_m))) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_diff__less__mono,axiom,
% 168.17/168.25 ! [V_c,V_b,V_a] :
% 168.17/168.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b))
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a))
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a),V_c)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_b),V_c))) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_less__diff__iff,axiom,
% 168.17/168.25 ! [V_n_2,V_m_2,V_k_2] :
% 168.17/168.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_k_2)))
% 168.17/168.25 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_Sup__fin_Osingleton,axiom,
% 168.17/168.25 ! [V_x_2,T_b] :
% 168.17/168.25 ( class_Lattices_Olattice(T_b)
% 168.17/168.25 => 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 ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_Sup__fin_Oin__idem,axiom,
% 168.17/168.25 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.25 ( class_Lattices_Olattice(T_b)
% 168.17/168.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.25 => 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) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_folding__one__idem_Oin__idem,axiom,
% 168.17/168.25 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 168.17/168.25 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 168.17/168.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.25 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_Sup__fin_Oinsert__idem,axiom,
% 168.17/168.25 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.25 ( class_Lattices_Olattice(T_b)
% 168.17/168.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.25 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.25 => 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)) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_Sup__fin_Osubset__idem,axiom,
% 168.17/168.25 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.25 ( class_Lattices_Olattice(T_b)
% 168.17/168.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.25 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 168.17/168.25 => 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) ) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_Sup__fin_Ounion__idem,axiom,
% 168.17/168.25 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.25 ( class_Lattices_Olattice(T_b)
% 168.17/168.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.25 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.25 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.25 => 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)) ) ) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_folding__image__simple_Oinsert,axiom,
% 168.17/168.25 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 168.17/168.25 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 168.17/168.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 168.17/168.25 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 168.17/168.25 => 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)) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_Sup__fin_Oinsert,axiom,
% 168.17/168.25 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.25 ( class_Lattices_Olattice(T_b)
% 168.17/168.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.25 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.25 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.25 => 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)) ) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_Sup__fin_Oclosed,axiom,
% 168.17/168.25 ! [V_A_2,T_b] :
% 168.17/168.25 ( class_Lattices_Olattice(T_b)
% 168.17/168.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.25 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.25 => ( ! [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))))))
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_insert__fold1SetE,axiom,
% 168.17/168.25 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_b] :
% 168.17/168.25 ( 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))
% 168.17/168.25 => ~ ! [B_a,B_A] :
% 168.17/168.25 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
% 168.17/168.25 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_x_2))
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_fold1Set_Oequations,axiom,
% 168.17/168.25 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_b] :
% 168.17/168.25 ( 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))
% 168.17/168.25 <=> ? [B_a,B_A] :
% 168.17/168.25 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
% 168.17/168.25 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_a3_2))
% 168.17/168.25 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_card__Suc__Diff1,axiom,
% 168.17/168.25 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.25 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.25 => 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) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_setsum__diff1__ring,axiom,
% 168.17/168.25 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 168.17/168.25 ( class_Rings_Oring(T_c)
% 168.17/168.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.17/168.25 => 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)) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_setsum__diff1,axiom,
% 168.17/168.25 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 168.17/168.25 ( class_Groups_Oab__group__add(T_c)
% 168.17/168.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.25 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.17/168.25 => 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)) )
% 168.17/168.25 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.17/168.25 => 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) ) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_fold__graph__permute__diff,axiom,
% 168.17/168.25 ! [V_a_2,V_x_2,V_A_2,V_b_2,T_b] :
% 168.17/168.25 ( class_Groups_Oab__semigroup__mult(T_b)
% 168.17/168.25 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_b_2,V_A_2),V_x_2))
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.17/168.25 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 168.17/168.25 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_a_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_x_2)) ) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_Sup__fin_Ounion__disjoint,axiom,
% 168.17/168.25 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.25 ( class_Lattices_Olattice(T_b)
% 168.17/168.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.25 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.25 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.25 => ( 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))
% 168.17/168.25 => 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)) ) ) ) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_Sup__fin_Ounion__inter,axiom,
% 168.17/168.25 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.25 ( class_Lattices_Olattice(T_b)
% 168.17/168.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.25 => ( 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))
% 168.17/168.25 => 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)) ) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_folding__image__simple__idem_Ounion__idem,axiom,
% 168.17/168.25 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 168.17/168.25 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 168.17/168.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 168.17/168.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 168.17/168.25 => 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)) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_inf1I,axiom,
% 168.17/168.25 ! [T_b,V_B_2,V_x_2,V_A_2] :
% 168.17/168.25 ( hBOOL(hAPP(V_A_2,V_x_2))
% 168.17/168.25 => ( hBOOL(hAPP(V_B_2,V_x_2))
% 168.17/168.25 => 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)) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_inf1E,axiom,
% 168.17/168.25 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 168.17/168.25 ( 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))
% 168.17/168.25 => ~ ( hBOOL(hAPP(V_A_2,V_x_2))
% 168.17/168.25 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_IntI,axiom,
% 168.17/168.25 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 168.17/168.25 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_IntE,axiom,
% 168.17/168.25 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 168.17/168.25 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 168.17/168.25 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 168.17/168.25 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_finite__Int,axiom,
% 168.17/168.25 ! [V_Ga_2,V_F_2,T_b] :
% 168.17/168.25 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 168.17/168.25 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) )
% 168.17/168.25 => 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))) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_less__not__refl,axiom,
% 168.17/168.25 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_nat__neq__iff,axiom,
% 168.17/168.25 ! [V_n_2,V_m_2] :
% 168.17/168.25 ( V_m_2 != V_n_2
% 168.17/168.25 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 168.17/168.25 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_linorder__neqE__nat,axiom,
% 168.17/168.25 ! [V_y,V_x] :
% 168.17/168.25 ( V_x != V_y
% 168.17/168.25 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_less__irrefl__nat,axiom,
% 168.17/168.25 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_less__not__refl2,axiom,
% 168.17/168.25 ! [V_m,V_n] :
% 168.17/168.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 168.17/168.25 => V_m != V_n ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_less__not__refl3,axiom,
% 168.17/168.25 ! [V_t,V_s] :
% 168.17/168.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t))
% 168.17/168.25 => V_s != V_t ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_nat__less__cases,axiom,
% 168.17/168.25 ! [V_P_2,V_n_2,V_m_2] :
% 168.17/168.25 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 168.17/168.25 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 168.17/168.25 => ( ( V_m_2 = V_n_2
% 168.17/168.25 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 168.17/168.25 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 168.17/168.25 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 168.17/168.25 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_times_Oidem,axiom,
% 168.17/168.25 ! [V_a,T_a] :
% 168.17/168.25 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 168.17/168.25 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_mult__idem,axiom,
% 168.17/168.25 ! [V_x,T_a] :
% 168.17/168.25 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 168.17/168.25 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_inf_Oidem,axiom,
% 168.17/168.25 ! [V_a,T_a] :
% 168.17/168.25 ( class_Lattices_Osemilattice__inf(T_a)
% 168.17/168.25 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_inf__idem,axiom,
% 168.17/168.25 ! [V_x,T_a] :
% 168.17/168.25 ( class_Lattices_Osemilattice__inf(T_a)
% 168.17/168.25 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_inf_Ocommute,axiom,
% 168.17/168.25 ! [V_b,V_a,T_a] :
% 168.17/168.25 ( class_Lattices_Osemilattice__inf(T_a)
% 168.17/168.25 => 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) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_inf__sup__aci_I1_J,axiom,
% 168.17/168.25 ! [V_y,V_x,T_a] :
% 168.17/168.25 ( class_Lattices_Olattice(T_a)
% 168.17/168.25 => 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) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_inf__commute,axiom,
% 168.17/168.25 ! [V_y,V_x,T_a] :
% 168.17/168.25 ( class_Lattices_Osemilattice__inf(T_a)
% 168.17/168.25 => 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) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_mult__left__idem,axiom,
% 168.17/168.25 ! [V_b,V_a,T_a] :
% 168.17/168.25 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 168.17/168.25 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_inf_Oleft__idem,axiom,
% 168.17/168.25 ! [V_b,V_a,T_a] :
% 168.17/168.25 ( class_Lattices_Osemilattice__inf(T_a)
% 168.17/168.25 => 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) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_inf__sup__aci_I4_J,axiom,
% 168.17/168.25 ! [V_y,V_x,T_a] :
% 168.17/168.25 ( class_Lattices_Olattice(T_a)
% 168.17/168.25 => 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) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_inf__left__idem,axiom,
% 168.17/168.25 ! [V_y,V_x,T_a] :
% 168.17/168.25 ( class_Lattices_Osemilattice__inf(T_a)
% 168.17/168.25 => 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) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_inf_Oleft__commute,axiom,
% 168.17/168.25 ! [V_c,V_a,V_b,T_a] :
% 168.17/168.25 ( class_Lattices_Osemilattice__inf(T_a)
% 168.17/168.25 => 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)) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_inf__sup__aci_I3_J,axiom,
% 168.17/168.25 ! [V_z,V_y,V_x,T_a] :
% 168.17/168.25 ( class_Lattices_Olattice(T_a)
% 168.17/168.25 => 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)) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_inf__left__commute,axiom,
% 168.17/168.25 ! [V_z,V_y,V_x,T_a] :
% 168.17/168.25 ( class_Lattices_Osemilattice__inf(T_a)
% 168.17/168.25 => 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)) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_inf_Oassoc,axiom,
% 168.17/168.25 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.25 ( class_Lattices_Osemilattice__inf(T_a)
% 168.17/168.25 => 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)) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_inf__sup__aci_I2_J,axiom,
% 168.17/168.25 ! [V_z,V_y,V_x,T_a] :
% 168.17/168.25 ( class_Lattices_Olattice(T_a)
% 168.17/168.25 => 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)) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_inf__assoc,axiom,
% 168.17/168.25 ! [V_z,V_y,V_x,T_a] :
% 168.17/168.25 ( class_Lattices_Osemilattice__inf(T_a)
% 168.17/168.25 => 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)) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_inf__apply,axiom,
% 168.17/168.25 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 168.17/168.25 ( class_Lattices_Olattice(T_b)
% 168.17/168.25 => 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)) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_inf1D1,axiom,
% 168.17/168.25 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 168.17/168.25 ( 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))
% 168.17/168.25 => hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_inf1D2,axiom,
% 168.17/168.25 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 168.17/168.25 ( 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))
% 168.17/168.25 => hBOOL(hAPP(V_B_2,V_x_2)) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_Int__absorb,axiom,
% 168.17/168.25 ! [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 ).
% 168.17/168.25
% 168.17/168.25 fof(fact_Int__commute,axiom,
% 168.17/168.25 ! [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) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_Int__left__absorb,axiom,
% 168.17/168.25 ! [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) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_Int__left__commute,axiom,
% 168.17/168.25 ! [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)) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_Int__assoc,axiom,
% 168.17/168.25 ! [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)) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_Inf__fin_Oidem,axiom,
% 168.17/168.25 ! [V_x,T_a] :
% 168.17/168.25 ( class_Lattices_Olattice(T_a)
% 168.17/168.25 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 168.17/168.25 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.25 ( class_Groups_Oab__semigroup__mult(T_a)
% 168.17/168.25 => 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)) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_folding__image__simple__idem_Oidem,axiom,
% 168.17/168.25 ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 168.17/168.25 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 168.17/168.25 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_le__infE,axiom,
% 168.17/168.25 ! [V_b,V_a,V_x,T_a] :
% 168.17/168.25 ( class_Lattices_Osemilattice__inf(T_a)
% 168.17/168.25 => ( 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)))
% 168.17/168.25 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 168.17/168.25 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_inf__mono,axiom,
% 168.17/168.25 ! [V_d,V_b,V_c,V_a,T_a] :
% 168.17/168.25 ( class_Lattices_Osemilattice__inf(T_a)
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 168.17/168.25 => 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))) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_inf__greatest,axiom,
% 168.17/168.25 ! [V_z,V_y,V_x,T_a] :
% 168.17/168.25 ( class_Lattices_Osemilattice__inf(T_a)
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 168.17/168.25 => 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))) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_le__infI,axiom,
% 168.17/168.25 ! [V_b,V_a,V_x,T_a] :
% 168.17/168.25 ( class_Lattices_Osemilattice__inf(T_a)
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 168.17/168.25 => 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))) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_inf__absorb2,axiom,
% 168.17/168.25 ! [V_x,V_y,T_a] :
% 168.17/168.25 ( class_Lattices_Osemilattice__inf(T_a)
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 168.17/168.25 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_inf__absorb1,axiom,
% 168.17/168.25 ! [V_y,V_x,T_a] :
% 168.17/168.25 ( class_Lattices_Osemilattice__inf(T_a)
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 168.17/168.25 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_le__infI2,axiom,
% 168.17/168.25 ! [V_a,V_x,V_b,T_a] :
% 168.17/168.25 ( class_Lattices_Osemilattice__inf(T_a)
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 168.17/168.25 => 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)) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_le__infI1,axiom,
% 168.17/168.25 ! [V_b,V_x,V_a,T_a] :
% 168.17/168.25 ( class_Lattices_Osemilattice__inf(T_a)
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 168.17/168.25 => 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)) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_le__inf__iff,axiom,
% 168.17/168.25 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 168.17/168.25 ( class_Lattices_Osemilattice__inf(T_b)
% 168.17/168.25 => ( 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)))
% 168.17/168.25 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 168.17/168.25 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_le__iff__inf,axiom,
% 168.17/168.25 ! [V_y_2,V_x_2,T_b] :
% 168.17/168.25 ( class_Lattices_Osemilattice__inf(T_b)
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 168.17/168.25 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = V_x_2 ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_inf__le2,axiom,
% 168.17/168.25 ! [V_y,V_x,T_a] :
% 168.17/168.25 ( class_Lattices_Osemilattice__inf(T_a)
% 168.17/168.25 => 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)) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_inf__sup__ord_I2_J,axiom,
% 168.17/168.25 ! [V_y,V_x,T_a] :
% 168.17/168.25 ( class_Lattices_Olattice(T_a)
% 168.17/168.25 => 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)) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_inf__le1,axiom,
% 168.17/168.25 ! [V_y,V_x,T_a] :
% 168.17/168.25 ( class_Lattices_Osemilattice__inf(T_a)
% 168.17/168.25 => 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)) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_inf__sup__ord_I1_J,axiom,
% 168.17/168.25 ! [V_y,V_x,T_a] :
% 168.17/168.25 ( class_Lattices_Olattice(T_a)
% 168.17/168.25 => 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)) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_less__infI1,axiom,
% 168.17/168.25 ! [V_b,V_x,V_a,T_a] :
% 168.17/168.25 ( class_Lattices_Osemilattice__inf(T_a)
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 168.17/168.25 => 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)) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_less__infI2,axiom,
% 168.17/168.25 ! [V_a,V_x,V_b,T_a] :
% 168.17/168.25 ( class_Lattices_Osemilattice__inf(T_a)
% 168.17/168.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 168.17/168.25 => 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)) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_inf__bot__left,axiom,
% 168.17/168.25 ! [V_x,T_a] :
% 168.17/168.25 ( class_Lattices_Obounded__lattice__bot(T_a)
% 168.17/168.25 => 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) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_inf__bot__right,axiom,
% 168.17/168.25 ! [V_x,T_a] :
% 168.17/168.25 ( class_Lattices_Obounded__lattice__bot(T_a)
% 168.17/168.25 => 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) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_sup__inf__distrib2,axiom,
% 168.17/168.25 ! [V_x,V_z,V_y,T_a] :
% 168.17/168.25 ( class_Lattices_Odistrib__lattice(T_a)
% 168.17/168.25 => 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)) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_inf__sup__distrib2,axiom,
% 168.17/168.25 ! [V_x,V_z,V_y,T_a] :
% 168.17/168.25 ( class_Lattices_Odistrib__lattice(T_a)
% 168.17/168.25 => 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)) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_sup__inf__distrib1,axiom,
% 168.17/168.25 ! [V_z,V_y,V_x,T_a] :
% 168.17/168.25 ( class_Lattices_Odistrib__lattice(T_a)
% 168.17/168.25 => 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)) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_inf__sup__distrib1,axiom,
% 168.17/168.25 ! [V_z,V_y,V_x,T_a] :
% 168.17/168.25 ( class_Lattices_Odistrib__lattice(T_a)
% 168.17/168.25 => 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)) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_sup__inf__absorb,axiom,
% 168.17/168.25 ! [V_y,V_x,T_a] :
% 168.17/168.25 ( class_Lattices_Olattice(T_a)
% 168.17/168.25 => 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 ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_inf__sup__absorb,axiom,
% 168.17/168.25 ! [V_y,V_x,T_a] :
% 168.17/168.25 ( class_Lattices_Olattice(T_a)
% 168.17/168.25 => 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 ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_Int__iff,axiom,
% 168.17/168.25 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 168.17/168.25 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 168.17/168.25 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 168.17/168.25 & hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_IntD1,axiom,
% 168.17/168.25 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 168.17/168.25 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_IntD2,axiom,
% 168.17/168.25 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 168.17/168.25 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 168.17/168.25 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_Int__empty__left,axiom,
% 168.17/168.25 ! [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)) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_Int__empty__right,axiom,
% 168.17/168.25 ! [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)) ).
% 168.17/168.25
% 168.17/168.25 fof(fact_disjoint__iff__not__equal,axiom,
% 168.17/168.26 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.26 ( 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))
% 168.17/168.26 <=> ! [B_x] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.17/168.26 => ! [B_xa] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_B_2))
% 168.17/168.26 => B_x != B_xa ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_insert__inter__insert,axiom,
% 168.17/168.26 ! [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)) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Int__lower1,axiom,
% 168.17/168.26 ! [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)) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Int__lower2,axiom,
% 168.17/168.26 ! [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)) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Int__absorb2,axiom,
% 168.17/168.26 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.17/168.26 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Int__absorb1,axiom,
% 168.17/168.26 ! [V_A_2,V_B_2,T_b] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 168.17/168.26 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Int__greatest,axiom,
% 168.17/168.26 ! [V_B_2,V_A_2,V_C_2,T_b] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2))
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2))
% 168.17/168.26 => 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))) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Int__mono,axiom,
% 168.17/168.26 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
% 168.17/168.26 => 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))) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Int__Un__distrib,axiom,
% 168.17/168.26 ! [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)) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Un__Int__distrib,axiom,
% 168.17/168.26 ! [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)) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Int__Un__distrib2,axiom,
% 168.17/168.26 ! [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)) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Un__Int__distrib2,axiom,
% 168.17/168.26 ! [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)) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Un__Int__crazy,axiom,
% 168.17/168.26 ! [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)) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Suc__mult__cancel1,axiom,
% 168.17/168.26 ! [V_n_2,V_m_2,V_k_2] :
% 168.17/168.26 ( 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)
% 168.17/168.26 <=> V_m_2 = V_n_2 ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Suc__mult__less__cancel1,axiom,
% 168.17/168.26 ! [V_n_2,V_m_2,V_k_2] :
% 168.17/168.26 ( 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)))
% 168.17/168.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Diff__Int__distrib,axiom,
% 168.17/168.26 ! [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)) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Int__Diff,axiom,
% 168.17/168.26 ! [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)) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Diff__Int__distrib2,axiom,
% 168.17/168.26 ! [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)) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Diff__Int2,axiom,
% 168.17/168.26 ! [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) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_mult__le__mono,axiom,
% 168.17/168.26 ! [V_l,V_k,V_j,V_i] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 168.17/168.26 => 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))) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_mult__le__mono2,axiom,
% 168.17/168.26 ! [V_k,V_j,V_i] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 168.17/168.26 => 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))) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_mult__le__mono1,axiom,
% 168.17/168.26 ! [V_k,V_j,V_i] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 168.17/168.26 => 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))) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_le__cube,axiom,
% 168.17/168.26 ! [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)))) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_le__square,axiom,
% 168.17/168.26 ! [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))) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_diff__mult__distrib,axiom,
% 168.17/168.26 ! [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)) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_diff__mult__distrib2,axiom,
% 168.17/168.26 ! [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)) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_card__Diff__subset__Int,axiom,
% 168.17/168.26 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.26 ( 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)))
% 168.17/168.26 => 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))) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_distrib__inf__le,axiom,
% 168.17/168.26 ! [V_z,V_y,V_x,T_a] :
% 168.17/168.26 ( class_Lattices_Olattice(T_a)
% 168.17/168.26 => 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)))) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_distrib__sup__le,axiom,
% 168.17/168.26 ! [V_z,V_y,V_x,T_a] :
% 168.17/168.26 ( class_Lattices_Olattice(T_a)
% 168.17/168.26 => 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)))) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Int__insert__left__if1,axiom,
% 168.17/168.26 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 168.17/168.26 => 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)) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Int__insert__right__if1,axiom,
% 168.17/168.26 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.17/168.26 => 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)) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Int__insert__left__if0,axiom,
% 168.17/168.26 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 168.17/168.26 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 168.17/168.26 => 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) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Int__insert__right__if0,axiom,
% 168.17/168.26 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 168.17/168.26 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.17/168.26 => 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) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Int__insert__left,axiom,
% 168.17/168.26 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 168.17/168.26 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 168.17/168.26 => 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)) )
% 168.17/168.26 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 168.17/168.26 => 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) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Int__insert__right,axiom,
% 168.17/168.26 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 168.17/168.26 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.17/168.26 => 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)) )
% 168.17/168.26 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.17/168.26 => 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) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Diff__triv,axiom,
% 168.17/168.26 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.26 ( 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))
% 168.17/168.26 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Diff__disjoint,axiom,
% 168.17/168.26 ! [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)) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Un__Int__assoc__eq,axiom,
% 168.17/168.26 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 168.17/168.26 ( 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))
% 168.17/168.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_psubset__card__mono,axiom,
% 168.17/168.26 ! [V_A_2,V_B_2,T_b] :
% 168.17/168.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.17/168.26 => 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))) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Diff__Int,axiom,
% 168.17/168.26 ! [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)) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Diff__Un,axiom,
% 168.17/168.26 ! [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)) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Un__Diff__Int,axiom,
% 168.17/168.26 ! [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 ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Suc__mult__le__cancel1,axiom,
% 168.17/168.26 ! [V_n_2,V_m_2,V_k_2] :
% 168.17/168.26 ( 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)))
% 168.17/168.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_card__insert__le,axiom,
% 168.17/168.26 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => 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)))) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_card__mono,axiom,
% 168.17/168.26 ! [V_A_2,V_B_2,T_b] :
% 168.17/168.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.17/168.26 => 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))) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_card__seteq,axiom,
% 168.17/168.26 ! [V_A_2,V_B_2,T_b] :
% 168.17/168.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.17/168.26 => ( 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)))
% 168.17/168.26 => V_A_2 = V_B_2 ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_inf__Sup__absorb,axiom,
% 168.17/168.26 ! [V_a_2,V_A_2,T_b] :
% 168.17/168.26 ( class_Lattices_Olattice(T_b)
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.17/168.26 => 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 ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_card__psubset,axiom,
% 168.17/168.26 ! [V_A_2,V_B_2,T_b] :
% 168.17/168.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.17/168.26 => ( 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)))
% 168.17/168.26 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_fold__graph__insert__swap,axiom,
% 168.17/168.26 ! [V_z_2,V_y_2,V_A_2,V_b_2,T_b] :
% 168.17/168.26 ( class_Groups_Oab__semigroup__mult(T_b)
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_b_2,V_A_2),V_y_2))
% 168.17/168.26 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 168.17/168.26 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_z_2),V_y_2))) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_folding__image__simple_Ounion__inter,axiom,
% 168.17/168.26 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 168.17/168.26 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 168.17/168.26 => 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)) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_setsum__diff,axiom,
% 168.17/168.26 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 168.17/168.26 ( class_Groups_Oab__group__add(T_c)
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 168.17/168.26 => 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)) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_setsum__diff__nat,axiom,
% 168.17/168.26 ! [V_f_2,V_A_2,V_B_2,T_b] :
% 168.17/168.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 168.17/168.26 => 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)) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_card__insert__disjoint,axiom,
% 168.17/168.26 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.26 => 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)) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_card__insert__if,axiom,
% 168.17/168.26 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.26 => 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) )
% 168.17/168.26 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.26 => 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)) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_card__Diff__subset,axiom,
% 168.17/168.26 ! [V_A_2,V_B_2,T_b] :
% 168.17/168.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 168.17/168.26 => 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)) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_diff__card__le__card__Diff,axiom,
% 168.17/168.26 ! [V_A_2,V_B_2,T_b] :
% 168.17/168.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.26 => 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)))) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_folding__one_Ounion__inter,axiom,
% 168.17/168.26 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 168.17/168.26 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.26 => ( 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))
% 168.17/168.26 => 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)) ) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_folding__one_Ounion__disjoint,axiom,
% 168.17/168.26 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 168.17/168.26 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.26 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.26 => ( 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))
% 168.17/168.26 => 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)) ) ) ) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_folding__image__simple_Ounion__disjoint,axiom,
% 168.17/168.26 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 168.17/168.26 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 168.17/168.26 => ( 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))
% 168.17/168.26 => 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)) ) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_setsum__diff1__nat,axiom,
% 168.17/168.26 ! [V_f_2,V_A_2,V_a_2,T_b] :
% 168.17/168.26 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.17/168.26 => 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)) )
% 168.17/168.26 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.17/168.26 => 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) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_card__Diff1__less,axiom,
% 168.17/168.26 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.26 => 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))) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_card__Diff2__less,axiom,
% 168.17/168.26 ! [V_y_2,V_x_2,V_A_2,T_b] :
% 168.17/168.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 168.17/168.26 => 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))) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_card__insert,axiom,
% 168.17/168.26 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => 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)))))) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_card__Diff1__le,axiom,
% 168.17/168.26 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => 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))) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_folding__image__simple__idem_Oin__idem,axiom,
% 168.17/168.26 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 168.17/168.26 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 168.17/168.26 => 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) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom,
% 168.17/168.26 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 168.17/168.26 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 168.17/168.26 => 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)) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_folding__image__simple__idem_Osubset__idem,axiom,
% 168.17/168.26 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 168.17/168.26 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))
% 168.17/168.26 => 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) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_card__Diff__singleton__if,axiom,
% 168.17/168.26 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.26 => 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)) )
% 168.17/168.26 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.26 => 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) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_card__Diff__singleton,axiom,
% 168.17/168.26 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.26 => 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)) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_termination__basic__simps_I5_J,axiom,
% 168.17/168.26 ! [V_y,V_x] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 168.17/168.26 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Inf__fin_Oremove,axiom,
% 168.17/168.26 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.26 ( class_Lattices_Olattice(T_b)
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.26 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 168.17/168.26 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = V_x_2 )
% 168.17/168.26 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 168.17/168.26 => 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)))))) ) ) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_card__Diff__insert,axiom,
% 168.17/168.26 ! [V_B_2,V_a_2,V_A_2,T_b] :
% 168.17/168.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.17/168.26 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 168.17/168.26 => 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)) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_setsum__strict__mono,axiom,
% 168.17/168.26 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
% 168.17/168.26 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 168.17/168.26 & class_Groups_Oordered__cancel__ab__semigroup__add(T_c) )
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.26 => ( ! [B_x] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.17/168.26 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 168.17/168.26 => 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))) ) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_setsum__diff1_H,axiom,
% 168.17/168.26 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 168.17/168.26 ( class_Groups_Ocomm__monoid__add(T_c)
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.17/168.26 => 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)))))) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_setsum_Oremove,axiom,
% 168.17/168.26 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 168.17/168.26 ( class_Groups_Ocomm__monoid__add(T_c)
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.26 => 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)))))) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Inf__fin_Ounion__inter,axiom,
% 168.17/168.26 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.26 ( class_Lattices_Olattice(T_b)
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.26 => ( 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))
% 168.17/168.26 => 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)) ) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Inf__fin_Ounion__disjoint,axiom,
% 168.17/168.26 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.26 ( class_Lattices_Olattice(T_b)
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.26 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.26 => ( 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))
% 168.17/168.26 => 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)) ) ) ) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_nat__mult__1,axiom,
% 168.17/168.26 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ).
% 168.17/168.26
% 168.17/168.26 fof(fact_nat__1__eq__mult__iff,axiom,
% 168.17/168.26 ! [V_n_2,V_m_2] :
% 168.17/168.26 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
% 168.17/168.26 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 168.17/168.26 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_nat__mult__1__right,axiom,
% 168.17/168.26 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 168.17/168.26
% 168.17/168.26 fof(fact_nat__mult__commute,axiom,
% 168.17/168.26 ! [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) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_add__mult__distrib2,axiom,
% 168.17/168.26 ! [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)) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_nat__mult__eq__1__iff,axiom,
% 168.17/168.26 ! [V_n_2,V_m_2] :
% 168.17/168.26 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 168.17/168.26 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 168.17/168.26 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_nat__mult__assoc,axiom,
% 168.17/168.26 ! [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)) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_add__mult__distrib,axiom,
% 168.17/168.26 ! [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)) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_add__right__imp__eq,axiom,
% 168.17/168.26 ! [V_c,V_a,V_b,T_a] :
% 168.17/168.26 ( class_Groups_Ocancel__semigroup__add(T_a)
% 168.17/168.26 => ( 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)
% 168.17/168.26 => V_b = V_c ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_add__imp__eq,axiom,
% 168.17/168.26 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.26 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 168.17/168.26 => ( 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)
% 168.17/168.26 => V_b = V_c ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_add__left__imp__eq,axiom,
% 168.17/168.26 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.26 ( class_Groups_Ocancel__semigroup__add(T_a)
% 168.17/168.26 => ( 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)
% 168.17/168.26 => V_b = V_c ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_add__right__cancel,axiom,
% 168.17/168.26 ! [V_c_2,V_a_2,V_b_2,T_b] :
% 168.17/168.26 ( class_Groups_Ocancel__semigroup__add(T_b)
% 168.17/168.26 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)
% 168.17/168.26 <=> V_b_2 = V_c_2 ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_add__left__cancel,axiom,
% 168.17/168.26 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 168.17/168.26 ( class_Groups_Ocancel__semigroup__add(T_b)
% 168.17/168.26 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)
% 168.17/168.26 <=> V_b_2 = V_c_2 ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 168.17/168.26 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.26 ( class_Groups_Oab__semigroup__add(T_a)
% 168.17/168.26 => 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)) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_one__reorient,axiom,
% 168.17/168.26 ! [V_x_2,T_b] :
% 168.17/168.26 ( class_Groups_Oone(T_b)
% 168.17/168.26 => ( c_Groups_Oone__class_Oone(T_b) = V_x_2
% 168.17/168.26 <=> V_x_2 = c_Groups_Oone__class_Oone(T_b) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Suc__eq__plus1,axiom,
% 168.17/168.26 ! [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)) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Suc__eq__plus1__left,axiom,
% 168.17/168.26 ! [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) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_termination__basic__simps_I1_J,axiom,
% 168.17/168.26 ! [V_z,V_y,V_x] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 168.17/168.26 => 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))) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_termination__basic__simps_I2_J,axiom,
% 168.17/168.26 ! [V_y,V_z,V_x] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z))
% 168.17/168.26 => 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))) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_termination__basic__simps_I3_J,axiom,
% 168.17/168.26 ! [V_z,V_y,V_x] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y))
% 168.17/168.26 => 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))) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_termination__basic__simps_I4_J,axiom,
% 168.17/168.26 ! [V_y,V_z,V_x] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z))
% 168.17/168.26 => 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))) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_add__le__cancel__right,axiom,
% 168.17/168.26 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 168.17/168.26 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2)))
% 168.17/168.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_add__le__cancel__left,axiom,
% 168.17/168.26 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 168.17/168.26 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2)))
% 168.17/168.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_add__right__mono,axiom,
% 168.17/168.26 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.26 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 168.17/168.26 => 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))) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_add__left__mono,axiom,
% 168.17/168.26 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.26 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 168.17/168.26 => 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))) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_add__mono,axiom,
% 168.17/168.26 ! [V_d,V_c,V_b,V_a,T_a] :
% 168.17/168.26 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 168.17/168.26 => 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))) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_add__le__imp__le__right,axiom,
% 168.17/168.26 ! [V_b,V_c,V_a,T_a] :
% 168.17/168.26 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 168.17/168.26 => ( 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)))
% 168.17/168.26 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_add__le__imp__le__left,axiom,
% 168.17/168.26 ! [V_b,V_a,V_c,T_a] :
% 168.17/168.26 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 168.17/168.26 => ( 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)))
% 168.17/168.26 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_add__less__cancel__right,axiom,
% 168.17/168.26 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 168.17/168.26 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2)))
% 168.17/168.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_add__less__cancel__left,axiom,
% 168.17/168.26 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 168.17/168.26 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2)))
% 168.17/168.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_add__strict__right__mono,axiom,
% 168.17/168.26 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.26 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 168.17/168.26 => 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))) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_add__strict__left__mono,axiom,
% 168.17/168.26 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.26 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 168.17/168.26 => 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))) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_add__strict__mono,axiom,
% 168.17/168.26 ! [V_d,V_c,V_b,V_a,T_a] :
% 168.17/168.26 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 168.17/168.26 => 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))) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_add__less__imp__less__right,axiom,
% 168.17/168.26 ! [V_b,V_c,V_a,T_a] :
% 168.17/168.26 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 168.17/168.26 => ( 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)))
% 168.17/168.26 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_add__less__imp__less__left,axiom,
% 168.17/168.26 ! [V_b,V_a,V_c,T_a] :
% 168.17/168.26 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 168.17/168.26 => ( 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)))
% 168.17/168.26 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_diff__add__cancel,axiom,
% 168.17/168.26 ! [V_b,V_a,T_a] :
% 168.17/168.26 ( class_Groups_Ogroup__add(T_a)
% 168.17/168.26 => 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 ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_add__diff__cancel,axiom,
% 168.17/168.26 ! [V_b,V_a,T_a] :
% 168.17/168.26 ( class_Groups_Ogroup__add(T_a)
% 168.17/168.26 => 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 ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_mult_Ocomm__neutral,axiom,
% 168.17/168.26 ! [V_a,T_a] :
% 168.17/168.26 ( class_Groups_Ocomm__monoid__mult(T_a)
% 168.17/168.26 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_mult__1__right,axiom,
% 168.17/168.26 ! [V_a,T_a] :
% 168.17/168.26 ( class_Groups_Omonoid__mult(T_a)
% 168.17/168.26 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_mult__1,axiom,
% 168.17/168.26 ! [V_a,T_a] :
% 168.17/168.26 ( class_Groups_Ocomm__monoid__mult(T_a)
% 168.17/168.26 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_mult__1__left,axiom,
% 168.17/168.26 ! [V_a,T_a] :
% 168.17/168.26 ( class_Groups_Omonoid__mult(T_a)
% 168.17/168.26 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_add__Suc__right,axiom,
% 168.17/168.26 ! [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)) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_add__Suc,axiom,
% 168.17/168.26 ! [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)) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_add__Suc__shift,axiom,
% 168.17/168.26 ! [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)) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_mult__Suc,axiom,
% 168.17/168.26 ! [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)) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_mult__Suc__right,axiom,
% 168.17/168.26 ! [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)) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_add__lessD1,axiom,
% 168.17/168.26 ! [V_k,V_j,V_i] :
% 168.17/168.26 ( 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))
% 168.17/168.26 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_less__add__eq__less,axiom,
% 168.17/168.26 ! [V_n,V_m,V_l,V_k] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 168.17/168.26 => ( 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)
% 168.17/168.26 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_add__less__mono,axiom,
% 168.17/168.26 ! [V_l,V_k,V_j,V_i] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 168.17/168.26 => 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))) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_add__less__mono1,axiom,
% 168.17/168.26 ! [V_k,V_j,V_i] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 168.17/168.26 => 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))) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_trans__less__add2,axiom,
% 168.17/168.26 ! [V_m,V_j,V_i] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 168.17/168.26 => 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))) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_trans__less__add1,axiom,
% 168.17/168.26 ! [V_m,V_j,V_i] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 168.17/168.26 => 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))) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_nat__add__left__cancel__less,axiom,
% 168.17/168.26 ! [V_n_2,V_m_2,V_k_2] :
% 168.17/168.26 ( 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)))
% 168.17/168.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_not__add__less2,axiom,
% 168.17/168.26 ! [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)) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_not__add__less1,axiom,
% 168.17/168.26 ! [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)) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_le__add2,axiom,
% 168.17/168.26 ! [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))) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_le__add1,axiom,
% 168.17/168.26 ! [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))) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_le__iff__add,axiom,
% 168.17/168.26 ! [V_n_2,V_m_2] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 168.17/168.26 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_nat__add__left__cancel__le,axiom,
% 168.17/168.26 ! [V_n_2,V_m_2,V_k_2] :
% 168.17/168.26 ( 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)))
% 168.17/168.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_trans__le__add1,axiom,
% 168.17/168.26 ! [V_m,V_j,V_i] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 168.17/168.26 => 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))) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_trans__le__add2,axiom,
% 168.17/168.26 ! [V_m,V_j,V_i] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 168.17/168.26 => 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))) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_add__le__mono1,axiom,
% 168.17/168.26 ! [V_k,V_j,V_i] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 168.17/168.26 => 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))) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_add__le__mono,axiom,
% 168.17/168.26 ! [V_l,V_k,V_j,V_i] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 168.17/168.26 => 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))) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_add__leD2,axiom,
% 168.17/168.26 ! [V_n,V_k,V_m] :
% 168.17/168.26 ( 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))
% 168.17/168.26 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_add__leD1,axiom,
% 168.17/168.26 ! [V_n,V_k,V_m] :
% 168.17/168.26 ( 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))
% 168.17/168.26 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_add__leE,axiom,
% 168.17/168.26 ! [V_n,V_k,V_m] :
% 168.17/168.26 ( 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))
% 168.17/168.26 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 168.17/168.26 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_diff__add__inverse2,axiom,
% 168.17/168.26 ! [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 ).
% 168.17/168.26
% 168.17/168.26 fof(fact_diff__add__inverse,axiom,
% 168.17/168.26 ! [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 ).
% 168.17/168.26
% 168.17/168.26 fof(fact_diff__diff__left,axiom,
% 168.17/168.26 ! [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)) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_diff__cancel,axiom,
% 168.17/168.26 ! [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) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_diff__cancel2,axiom,
% 168.17/168.26 ! [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) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_card_Oinsert,axiom,
% 168.17/168.26 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.26 => 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)) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_add__less__le__mono,axiom,
% 168.17/168.26 ! [V_d,V_c,V_b,V_a,T_a] :
% 168.17/168.26 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 168.17/168.26 => 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))) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_add__le__less__mono,axiom,
% 168.17/168.26 ! [V_d,V_c,V_b,V_a,T_a] :
% 168.17/168.26 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 168.17/168.26 => 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))) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_less__iff__Suc__add,axiom,
% 168.17/168.26 ! [V_n_2,V_m_2] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 168.17/168.26 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_less__add__Suc2,axiom,
% 168.17/168.26 ! [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)))) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_less__add__Suc1,axiom,
% 168.17/168.26 ! [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)))) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_less__diff__conv,axiom,
% 168.17/168.26 ! [V_k_2,V_j_2,V_i_2] :
% 168.17/168.26 ( 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)))
% 168.17/168.26 <=> 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)) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_add__diff__inverse,axiom,
% 168.17/168.26 ! [V_n,V_m] :
% 168.17/168.26 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 168.17/168.26 => 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 ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_diff__diff__right,axiom,
% 168.17/168.26 ! [V_i,V_j,V_k] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 168.17/168.26 => 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) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_le__diff__conv,axiom,
% 168.17/168.26 ! [V_i_2,V_k_2,V_j_2] :
% 168.17/168.26 ( 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))
% 168.17/168.26 <=> 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))) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_le__add__diff,axiom,
% 168.17/168.26 ! [V_m,V_n,V_k] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 168.17/168.26 => 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))) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_le__add__diff__inverse,axiom,
% 168.17/168.26 ! [V_m,V_n] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 168.17/168.26 => 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 ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_add__diff__assoc,axiom,
% 168.17/168.26 ! [V_i,V_j,V_k] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 168.17/168.26 => 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) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_le__diff__conv2,axiom,
% 168.17/168.26 ! [V_i_2,V_j_2,V_k_2] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2))
% 168.17/168.26 => ( 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)))
% 168.17/168.26 <=> 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)) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_le__add__diff__inverse2,axiom,
% 168.17/168.26 ! [V_m,V_n] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 168.17/168.26 => 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 ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_le__imp__diff__is__add,axiom,
% 168.17/168.26 ! [V_k_2,V_j_2,V_i_2] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 168.17/168.26 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2
% 168.17/168.26 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_diff__add__assoc,axiom,
% 168.17/168.26 ! [V_i,V_j,V_k] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 168.17/168.26 => 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)) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_add__diff__assoc2,axiom,
% 168.17/168.26 ! [V_i,V_j,V_k] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 168.17/168.26 => 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) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_diff__add__assoc2,axiom,
% 168.17/168.26 ! [V_i,V_j,V_k] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 168.17/168.26 => 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) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_diff__Suc__1,axiom,
% 168.17/168.26 ! [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 ).
% 168.17/168.26
% 168.17/168.26 fof(fact_diff__Suc__eq__diff__pred,axiom,
% 168.17/168.26 ! [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) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Inf__fin_Osingleton,axiom,
% 168.17/168.26 ! [V_x_2,T_b] :
% 168.17/168.26 ( class_Lattices_Olattice(T_b)
% 168.17/168.26 => 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 ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_card_Oinsert__remove,axiom,
% 168.17/168.26 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => 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)))))) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_card_Oremove,axiom,
% 168.17/168.26 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.26 => 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)))))) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_diff__Suc__diff__eq1,axiom,
% 168.17/168.26 ! [V_m,V_j,V_k] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 168.17/168.26 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(c_Nat_OSuc,V_j)) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_diff__Suc__diff__eq2,axiom,
% 168.17/168.26 ! [V_m,V_j,V_k] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 168.17/168.26 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))),V_m) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_j)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_sup__Inf__absorb,axiom,
% 168.17/168.26 ! [V_a_2,V_A_2,T_b] :
% 168.17/168.26 ( class_Lattices_Olattice(T_b)
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.17/168.26 => 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 ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Inf__fin_Oin__idem,axiom,
% 168.17/168.26 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.26 ( class_Lattices_Olattice(T_b)
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.26 => 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) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_setsum_Oinsert,axiom,
% 168.17/168.26 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 168.17/168.26 ( class_Groups_Ocomm__monoid__add(T_c)
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.26 => 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)) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_setsum__insert,axiom,
% 168.17/168.26 ! [V_f_2,V_a_2,V_F_2,T_b,T_c] :
% 168.17/168.26 ( class_Groups_Ocomm__monoid__add(T_c)
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 168.17/168.26 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_F_2))
% 168.17/168.26 => 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)) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_setsum__Un__Int,axiom,
% 168.17/168.26 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 168.17/168.26 ( class_Groups_Ocomm__monoid__add(T_c)
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.26 => 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)) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_setsum__Un__nat,axiom,
% 168.17/168.26 ! [V_f_2,V_B_2,V_A_2,T_b] :
% 168.17/168.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.26 => 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))) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_card__Un__Int,axiom,
% 168.17/168.26 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.26 => 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))) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_card_Ounion__inter,axiom,
% 168.17/168.26 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.26 => 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)) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Inf__fin_Oinsert__idem,axiom,
% 168.17/168.26 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.26 ( class_Lattices_Olattice(T_b)
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.26 => 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)) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Inf__fin_Osubset__idem,axiom,
% 168.17/168.26 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.26 ( class_Lattices_Olattice(T_b)
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 168.17/168.26 => 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) ) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Inf__fin_Ounion__idem,axiom,
% 168.17/168.26 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.26 ( class_Lattices_Olattice(T_b)
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.26 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.26 => 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)) ) ) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Inf__le__Sup,axiom,
% 168.17/168.26 ! [V_A_2,T_b] :
% 168.17/168.26 ( class_Lattices_Olattice(T_b)
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.26 => 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))) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_setsum_Oinsert__remove,axiom,
% 168.17/168.26 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
% 168.17/168.26 ( class_Groups_Ocomm__monoid__add(T_c)
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => 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)))))) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_setsum__Un__disjoint,axiom,
% 168.17/168.26 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 168.17/168.26 ( class_Groups_Ocomm__monoid__add(T_c)
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.26 => ( 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))
% 168.17/168.26 => 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)) ) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_setsum__Un,axiom,
% 168.17/168.26 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 168.17/168.26 ( class_Groups_Oab__group__add(T_c)
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.26 => 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))) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_card__Un__disjoint,axiom,
% 168.17/168.26 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.26 => ( 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))
% 168.17/168.26 => 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)) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Inf__fin_Oinsert,axiom,
% 168.17/168.26 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.26 ( class_Lattices_Olattice(T_b)
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.26 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.26 => 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)) ) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Inf__fin_Oinsert__remove,axiom,
% 168.17/168.26 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.26 ( class_Lattices_Olattice(T_b)
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 168.17/168.26 => 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 )
% 168.17/168.26 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 168.17/168.26 => 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)))))) ) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_nat__less__add__iff2,axiom,
% 168.17/168.26 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
% 168.17/168.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2))) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_nat__less__add__iff1,axiom,
% 168.17/168.26 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
% 168.17/168.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2)),V_n_2)) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_less__add__iff2,axiom,
% 168.17/168.26 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 168.17/168.26 ( class_Rings_Oordered__ring(T_b)
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
% 168.17/168.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_less__add__iff1,axiom,
% 168.17/168.26 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 168.17/168.26 ( class_Rings_Oordered__ring(T_b)
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
% 168.17/168.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_le__add__iff2,axiom,
% 168.17/168.26 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 168.17/168.26 ( class_Rings_Oordered__ring(T_b)
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
% 168.17/168.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_le__add__iff1,axiom,
% 168.17/168.26 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 168.17/168.26 ( class_Rings_Oordered__ring(T_b)
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
% 168.17/168.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_nat__eq__add__iff2,axiom,
% 168.17/168.26 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 168.17/168.26 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)
% 168.17/168.26 <=> V_m_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_nat__diff__add__eq2,axiom,
% 168.17/168.26 ! [V_n,V_m,V_u,V_j,V_i] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 168.17/168.26 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_i)),V_u)),V_n)) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_nat__le__add__iff2,axiom,
% 168.17/168.26 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
% 168.17/168.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2))) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_nat__eq__add__iff1,axiom,
% 168.17/168.26 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 168.17/168.26 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)
% 168.17/168.26 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2) = V_n_2 ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_nat__add__right__cancel,axiom,
% 168.17/168.26 ! [V_n_2,V_k_2,V_m_2] :
% 168.17/168.26 ( 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)
% 168.17/168.26 <=> V_m_2 = V_n_2 ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_nat__add__left__cancel,axiom,
% 168.17/168.26 ! [V_n_2,V_m_2,V_k_2] :
% 168.17/168.26 ( 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)
% 168.17/168.26 <=> V_m_2 = V_n_2 ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_nat__add__assoc,axiom,
% 168.17/168.26 ! [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)) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_nat__add__left__commute,axiom,
% 168.17/168.26 ! [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)) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_nat__add__commute,axiom,
% 168.17/168.26 ! [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) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_linorder__neqE__linordered__idom,axiom,
% 168.17/168.26 ! [V_y,V_x,T_a] :
% 168.17/168.26 ( class_Rings_Olinordered__idom(T_a)
% 168.17/168.26 => ( V_x != V_y
% 168.17/168.26 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 168.17/168.26 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_left__add__mult__distrib,axiom,
% 168.17/168.26 ! [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) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_combine__common__factor,axiom,
% 168.17/168.26 ! [V_c,V_b,V_e,V_a,T_a] :
% 168.17/168.26 ( class_Rings_Osemiring(T_a)
% 168.17/168.26 => 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) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_comm__semiring__class_Odistrib,axiom,
% 168.17/168.26 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.26 ( class_Rings_Ocomm__semiring(T_a)
% 168.17/168.26 => 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)) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_less__add__one,axiom,
% 168.17/168.26 ! [V_a,T_a] :
% 168.17/168.26 ( class_Rings_Olinordered__semidom(T_a)
% 168.17/168.26 => 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)))) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_less__1__mult,axiom,
% 168.17/168.26 ! [V_n,V_m,T_a] :
% 168.17/168.26 ( class_Rings_Olinordered__semidom(T_a)
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m))
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n))
% 168.17/168.26 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n))) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_eq__add__iff2,axiom,
% 168.17/168.26 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 168.17/168.26 ( class_Rings_Oring(T_b)
% 168.17/168.26 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)
% 168.17/168.26 <=> V_c_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_eq__add__iff1,axiom,
% 168.17/168.26 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 168.17/168.26 ( class_Rings_Oring(T_b)
% 168.17/168.26 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)
% 168.17/168.26 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2) = V_d_2 ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_nat__le__add__iff1,axiom,
% 168.17/168.26 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
% 168.17/168.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2)),V_n_2)) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_nat__diff__add__eq1,axiom,
% 168.17/168.26 ! [V_n,V_m,V_u,V_i,V_j] :
% 168.17/168.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 168.17/168.26 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u)),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u)),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_u)),V_m)),V_n) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 168.17/168.26 ! [V_m,T_a] :
% 168.17/168.26 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.17/168.26 => 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) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 168.17/168.26 ! [V_a,V_m,T_a] :
% 168.17/168.26 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.17/168.26 => 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) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 168.17/168.26 ! [V_m,V_a,T_a] :
% 168.17/168.26 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.17/168.26 => 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) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_Inf__fin_Oclosed,axiom,
% 168.17/168.26 ! [V_A_2,T_b] :
% 168.17/168.26 ( class_Lattices_Olattice(T_b)
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.26 => ( ! [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))))))
% 168.17/168.26 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 168.17/168.26 ! [V_a,T_a] :
% 168.17/168.26 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.17/168.26 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 168.17/168.26 ! [V_a,T_a] :
% 168.17/168.26 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.17/168.26 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_crossproduct__eq,axiom,
% 168.17/168.26 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_b] :
% 168.17/168.26 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 168.17/168.26 => ( 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))
% 168.17/168.26 <=> ( V_w_2 = V_x_2
% 168.17/168.26 | V_y_2 = V_z_2 ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 168.17/168.26 ! [V_b,V_m,V_a,T_a] :
% 168.17/168.26 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.17/168.26 => 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) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 168.17/168.26 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.26 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.17/168.26 => 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)) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 168.17/168.26 ! [V_c,V_a,T_a] :
% 168.17/168.26 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.17/168.26 => 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) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 168.17/168.26 ! [V_d,V_c,V_a,T_a] :
% 168.17/168.26 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.17/168.26 => 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)) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 168.17/168.26 ! [V_d,V_c,V_a,T_a] :
% 168.17/168.26 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.17/168.26 => 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) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 168.17/168.26 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.26 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.17/168.26 => 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)) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 168.17/168.26 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.26 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.17/168.26 => 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) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 168.17/168.26 ! [V_d,V_c,V_b,V_a,T_a] :
% 168.17/168.26 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.17/168.26 => 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)) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 168.17/168.26 ! [V_b,V_a,T_a] :
% 168.17/168.26 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.17/168.26 => 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) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 168.17/168.26 ! [V_ry,V_rx,V_lx,T_a] :
% 168.17/168.26 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.17/168.26 => 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)) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 168.17/168.26 ! [V_ry,V_rx,V_lx,T_a] :
% 168.17/168.26 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.17/168.26 => 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) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 168.17/168.26 ! [V_rx,V_ly,V_lx,T_a] :
% 168.17/168.26 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.17/168.26 => 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)) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 168.17/168.26 ! [V_rx,V_ly,V_lx,T_a] :
% 168.17/168.26 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.17/168.26 => 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) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 168.17/168.26 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 168.17/168.26 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.17/168.26 => 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))) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 168.17/168.26 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 168.17/168.26 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.17/168.26 => 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)) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 168.17/168.26 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 168.17/168.26 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.17/168.26 => 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)) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 168.17/168.26 ! [V_z,V_y,V_x,T_a] :
% 168.17/168.26 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.17/168.26 => 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)) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_crossproduct__noteq,axiom,
% 168.17/168.26 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 168.17/168.26 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 168.17/168.26 => ( ( V_a_2 != V_b_2
% 168.17/168.26 & V_c_2 != V_d_2 )
% 168.17/168.26 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_d_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2)) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_fold__Un__disjoint,axiom,
% 168.17/168.26 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 168.17/168.26 ( class_Groups_Ocomm__monoid__mult(T_c)
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.26 => ( 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))
% 168.17/168.26 => 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)) ) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_fold1__Un,axiom,
% 168.17/168.26 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.26 ( class_Groups_Oab__semigroup__mult(T_b)
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.26 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.26 => ( 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))
% 168.17/168.26 => 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)) ) ) ) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom,
% 168.17/168.26 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 168.17/168.26 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 168.17/168.26 => ( ! [B_x] :
% 168.17/168.26 ( 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)))
% 168.17/168.26 => hAPP(V_g_2,B_x) = V_z_2 )
% 168.17/168.26 => 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)) ) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_fold1__insert,axiom,
% 168.17/168.26 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.26 ( class_Groups_Oab__semigroup__mult(T_b)
% 168.17/168.26 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.26 => 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)) ) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_fold__image__Un__Int,axiom,
% 168.17/168.26 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 168.17/168.26 ( class_Groups_Ocomm__monoid__mult(T_c)
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.26 => 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))) ) ) ) ).
% 168.17/168.26
% 168.17/168.26 fof(fact_setprod_Oremove,axiom,
% 168.17/168.26 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 168.17/168.26 ( class_Groups_Ocomm__monoid__mult(T_c)
% 168.17/168.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.26 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.27 => 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)))))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_convex__bound__lt,axiom,
% 168.17/168.27 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 168.17/168.27 ( class_Rings_Olinordered__semiring__1__strict(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 168.17/168.27 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 168.17/168.27 => 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)) ) ) ) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_card__Plus,axiom,
% 168.17/168.27 ! [V_B_2,T_c,V_A_2,T_b] :
% 168.17/168.27 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 168.17/168.27 => 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)) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_Inf__fin_Oeq__fold_H,axiom,
% 168.17/168.27 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.27 ( class_Lattices_Olattice(T_b)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.27 => 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) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_less__zeroE,axiom,
% 168.17/168.27 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_le0,axiom,
% 168.17/168.27 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_zero__less__Suc,axiom,
% 168.17/168.27 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_n))) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_setprod__zero__iff,axiom,
% 168.17/168.27 ! [V_f_2,V_A_2,T_b,T_c] :
% 168.17/168.27 ( ( class_Rings_Ocomm__semiring__1(T_c)
% 168.17/168.27 & class_Rings_Ono__zero__divisors(T_c) )
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => ( 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)
% 168.17/168.27 <=> ? [B_x] :
% 168.17/168.27 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.17/168.27 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_setprod__zero,axiom,
% 168.17/168.27 ! [V_f_2,V_A_2,T_b,T_c] :
% 168.17/168.27 ( class_Rings_Ocomm__semiring__1(T_c)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => ( ? [B_x] :
% 168.17/168.27 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.17/168.27 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 168.17/168.27 => 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) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_zero__reorient,axiom,
% 168.17/168.27 ! [V_x_2,T_b] :
% 168.17/168.27 ( class_Groups_Ozero(T_b)
% 168.17/168.27 => ( c_Groups_Ozero__class_Ozero(T_b) = V_x_2
% 168.17/168.27 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_setprod__pos__nat__iff,axiom,
% 168.17/168.27 ! [V_f_2,V_S_2,T_b] :
% 168.17/168.27 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 168.17/168.27 => ( 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)))
% 168.17/168.27 <=> ! [B_x] :
% 168.17/168.27 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 168.17/168.27 => 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))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_fold__empty,axiom,
% 168.17/168.27 ! [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 ).
% 168.17/168.27
% 168.17/168.27 fof(fact_add__0__left,axiom,
% 168.17/168.27 ! [V_a,T_a] :
% 168.17/168.27 ( class_Groups_Omonoid__add(T_a)
% 168.17/168.27 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_add__0,axiom,
% 168.17/168.27 ! [V_a,T_a] :
% 168.17/168.27 ( class_Groups_Ocomm__monoid__add(T_a)
% 168.17/168.27 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_double__zero__sym,axiom,
% 168.17/168.27 ! [V_a_2,T_b] :
% 168.17/168.27 ( class_Groups_Olinordered__ab__group__add(T_b)
% 168.17/168.27 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)
% 168.17/168.27 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_add__0__right,axiom,
% 168.17/168.27 ! [V_a,T_a] :
% 168.17/168.27 ( class_Groups_Omonoid__add(T_a)
% 168.17/168.27 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_add_Ocomm__neutral,axiom,
% 168.17/168.27 ! [V_a,T_a] :
% 168.17/168.27 ( class_Groups_Ocomm__monoid__add(T_a)
% 168.17/168.27 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_add__0__iff,axiom,
% 168.17/168.27 ! [V_a_2,V_b_2,T_b] :
% 168.17/168.27 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 168.17/168.27 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2)
% 168.17/168.27 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 168.17/168.27 ! [V_a,T_a] :
% 168.17/168.27 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.17/168.27 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 168.17/168.27 ! [V_a,T_a] :
% 168.17/168.27 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.17/168.27 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_divisors__zero,axiom,
% 168.17/168.27 ! [V_b,V_a,T_a] :
% 168.17/168.27 ( class_Rings_Ono__zero__divisors(T_a)
% 168.17/168.27 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.27 => ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.27 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_no__zero__divisors,axiom,
% 168.17/168.27 ! [V_b,V_a,T_a] :
% 168.17/168.27 ( class_Rings_Ono__zero__divisors(T_a)
% 168.17/168.27 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.27 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.27 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__eq__0__iff,axiom,
% 168.17/168.27 ! [V_b_2,V_a_2,T_b] :
% 168.17/168.27 ( class_Rings_Oring__no__zero__divisors(T_b)
% 168.17/168.27 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
% 168.17/168.27 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
% 168.17/168.27 | V_b_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__zero__right,axiom,
% 168.17/168.27 ! [V_a,T_a] :
% 168.17/168.27 ( class_Rings_Omult__zero(T_a)
% 168.17/168.27 => 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) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__zero__left,axiom,
% 168.17/168.27 ! [V_a,T_a] :
% 168.17/168.27 ( class_Rings_Omult__zero(T_a)
% 168.17/168.27 => 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) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 168.17/168.27 ! [V_a,T_a] :
% 168.17/168.27 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.17/168.27 => 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) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 168.17/168.27 ! [V_a,T_a] :
% 168.17/168.27 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.17/168.27 => 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) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_right__minus__eq,axiom,
% 168.17/168.27 ! [V_b_2,V_a_2,T_b] :
% 168.17/168.27 ( class_Groups_Ogroup__add(T_b)
% 168.17/168.27 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
% 168.17/168.27 <=> V_a_2 = V_b_2 ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_eq__iff__diff__eq__0,axiom,
% 168.17/168.27 ! [V_b_2,V_a_2,T_b] :
% 168.17/168.27 ( class_Groups_Oab__group__add(T_b)
% 168.17/168.27 => ( V_a_2 = V_b_2
% 168.17/168.27 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_diff__self,axiom,
% 168.17/168.27 ! [V_a,T_a] :
% 168.17/168.27 ( class_Groups_Ogroup__add(T_a)
% 168.17/168.27 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_diff__0__right,axiom,
% 168.17/168.27 ! [V_a,T_a] :
% 168.17/168.27 ( class_Groups_Ogroup__add(T_a)
% 168.17/168.27 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_zero__neq__one,axiom,
% 168.17/168.27 ! [T_a] :
% 168.17/168.27 ( class_Rings_Ozero__neq__one(T_a)
% 168.17/168.27 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_one__neq__zero,axiom,
% 168.17/168.27 ! [T_a] :
% 168.17/168.27 ( class_Rings_Ozero__neq__one(T_a)
% 168.17/168.27 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_fold__image__empty,axiom,
% 168.17/168.27 ! [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 ).
% 168.17/168.27
% 168.17/168.27 fof(fact_Suc__neq__Zero,axiom,
% 168.17/168.27 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_Zero__neq__Suc,axiom,
% 168.17/168.27 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_nat_Osimps_I3_J,axiom,
% 168.17/168.27 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_Suc__not__Zero,axiom,
% 168.17/168.27 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_nat_Osimps_I2_J,axiom,
% 168.17/168.27 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_Zero__not__Suc,axiom,
% 168.17/168.27 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_not__less0,axiom,
% 168.17/168.27 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_neq0__conv,axiom,
% 168.17/168.27 ! [V_n_2] :
% 168.17/168.27 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_less__nat__zero__code,axiom,
% 168.17/168.27 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_gr__implies__not0,axiom,
% 168.17/168.27 ! [V_n,V_m] :
% 168.17/168.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 168.17/168.27 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_gr0I,axiom,
% 168.17/168.27 ! [V_n] :
% 168.17/168.27 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_add__eq__self__zero,axiom,
% 168.17/168.27 ! [V_n,V_m] :
% 168.17/168.27 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m
% 168.17/168.27 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_add__is__0,axiom,
% 168.17/168.27 ! [V_n_2,V_m_2] :
% 168.17/168.27 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.27 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.27 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_Nat_Oadd__0__right,axiom,
% 168.17/168.27 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 168.17/168.27
% 168.17/168.27 fof(fact_plus__nat_Oadd__0,axiom,
% 168.17/168.27 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 168.17/168.27
% 168.17/168.27 fof(fact_le__0__eq,axiom,
% 168.17/168.27 ! [V_n_2] :
% 168.17/168.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 168.17/168.27 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 168.17/168.27 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_diffs0__imp__equal,axiom,
% 168.17/168.27 ! [V_n,V_m] :
% 168.17/168.27 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.27 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.27 => V_m = V_n ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_diff__self__eq__0,axiom,
% 168.17/168.27 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_minus__nat_Odiff__0,axiom,
% 168.17/168.27 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 168.17/168.27
% 168.17/168.27 fof(fact_diff__0__eq__0,axiom,
% 168.17/168.27 ! [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) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_nat__mult__eq__cancel__disj,axiom,
% 168.17/168.27 ! [V_n_2,V_m_2,V_k_2] :
% 168.17/168.27 ( 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)
% 168.17/168.27 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.27 | V_m_2 = V_n_2 ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__cancel2,axiom,
% 168.17/168.27 ! [V_n_2,V_k_2,V_m_2] :
% 168.17/168.27 ( 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)
% 168.17/168.27 <=> ( V_m_2 = V_n_2
% 168.17/168.27 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__cancel1,axiom,
% 168.17/168.27 ! [V_n_2,V_m_2,V_k_2] :
% 168.17/168.27 ( 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)
% 168.17/168.27 <=> ( V_m_2 = V_n_2
% 168.17/168.27 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__is__0,axiom,
% 168.17/168.27 ! [V_n_2,V_m_2] :
% 168.17/168.27 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.27 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.27 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__0__right,axiom,
% 168.17/168.27 ! [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) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__0,axiom,
% 168.17/168.27 ! [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) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_setprod_OF__eq,axiom,
% 168.17/168.27 ! [V_g_2,V_A_2,T_b,T_c] :
% 168.17/168.27 ( class_Groups_Ocomm__monoid__mult(T_c)
% 168.17/168.27 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => 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) )
% 168.17/168.27 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => 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) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_setprod_Oeq__fold,axiom,
% 168.17/168.27 ! [V_g_2,V_A_2,T_b,T_c] :
% 168.17/168.27 ( class_Groups_Ocomm__monoid__mult(T_c)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => 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) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_fold1__eq__fold__idem,axiom,
% 168.17/168.27 ! [V_a_2,V_A_2,T_b] :
% 168.17/168.27 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => 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) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_setsum_OF__eq,axiom,
% 168.17/168.27 ! [V_g_2,V_A_2,T_b,T_c] :
% 168.17/168.27 ( class_Groups_Ocomm__monoid__add(T_c)
% 168.17/168.27 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => 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) )
% 168.17/168.27 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => 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) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_setsum_Oeq__fold,axiom,
% 168.17/168.27 ! [V_g_2,V_A_2,T_b,T_c] :
% 168.17/168.27 ( class_Groups_Ocomm__monoid__add(T_c)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => 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) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_setprod_Oempty,axiom,
% 168.17/168.27 ! [V_g_2,T_c,T_b] :
% 168.17/168.27 ( class_Groups_Ocomm__monoid__mult(T_b)
% 168.17/168.27 => 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) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_setprod__empty,axiom,
% 168.17/168.27 ! [V_f_2,T_c,T_b] :
% 168.17/168.27 ( class_Groups_Ocomm__monoid__mult(T_b)
% 168.17/168.27 => 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) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_setprod__infinite,axiom,
% 168.17/168.27 ! [V_f_2,V_A_2,T_b,T_c] :
% 168.17/168.27 ( class_Groups_Ocomm__monoid__mult(T_c)
% 168.17/168.27 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => 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) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_setprod_Oinfinite,axiom,
% 168.17/168.27 ! [V_g_2,V_A_2,T_b,T_c] :
% 168.17/168.27 ( class_Groups_Ocomm__monoid__mult(T_c)
% 168.17/168.27 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => 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) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_setprod__eq__1__iff,axiom,
% 168.17/168.27 ! [V_f_2,V_F_2,T_b] :
% 168.17/168.27 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 168.17/168.27 => ( 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)
% 168.17/168.27 <=> ! [B_x] :
% 168.17/168.27 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
% 168.17/168.27 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_finite__Plus__iff,axiom,
% 168.17/168.27 ! [V_B_2,V_A_2,T_c,T_b] :
% 168.17/168.27 ( 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)))
% 168.17/168.27 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_finite__Plus,axiom,
% 168.17/168.27 ! [V_B_2,T_c,V_A_2,T_b] :
% 168.17/168.27 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 168.17/168.27 => 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))) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_finite__PlusD_I1_J,axiom,
% 168.17/168.27 ! [V_B_2,V_A_2,T_c,T_b] :
% 168.17/168.27 ( 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)))
% 168.17/168.27 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_finite__PlusD_I2_J,axiom,
% 168.17/168.27 ! [V_B_2,V_A_2,T_c,T_b] :
% 168.17/168.27 ( 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)))
% 168.17/168.27 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_card__Plus__conv__if,axiom,
% 168.17/168.27 ! [V_B_2,T_c,V_A_2,T_b] :
% 168.17/168.27 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) )
% 168.17/168.27 => 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)) )
% 168.17/168.27 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) )
% 168.17/168.27 => 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) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_fold1__eq__fold,axiom,
% 168.17/168.27 ! [V_a_2,V_A_2,T_b] :
% 168.17/168.27 ( class_Groups_Oab__semigroup__mult(T_b)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.17/168.27 => 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) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 168.17/168.27 ! [V_a_2,T_b] :
% 168.17/168.27 ( class_Groups_Olinordered__ab__group__add(T_b)
% 168.17/168.27 => ( 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)))
% 168.17/168.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 168.17/168.27 ! [V_a_2,T_b] :
% 168.17/168.27 ( class_Groups_Olinordered__ab__group__add(T_b)
% 168.17/168.27 => ( 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)))
% 168.17/168.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_add__nonneg__nonneg,axiom,
% 168.17/168.27 ! [V_b,V_a,T_a] :
% 168.17/168.27 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 168.17/168.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_add__nonneg__eq__0__iff,axiom,
% 168.17/168.27 ! [V_y_2,V_x_2,T_b] :
% 168.17/168.27 ( class_Groups_Oordered__comm__monoid__add(T_b)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_x_2))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_y_2))
% 168.17/168.27 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_b)
% 168.17/168.27 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 168.17/168.27 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_add__increasing,axiom,
% 168.17/168.27 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.27 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 168.17/168.27 => 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))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_add__increasing2,axiom,
% 168.17/168.27 ! [V_a,V_b,V_c,T_a] :
% 168.17/168.27 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 168.17/168.27 => 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))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_add__nonpos__nonpos,axiom,
% 168.17/168.27 ! [V_b,V_a,T_a] :
% 168.17/168.27 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.27 => 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))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_zero__le__square,axiom,
% 168.17/168.27 ! [V_a,T_a] :
% 168.17/168.27 ( class_Rings_Olinordered__ring(T_a)
% 168.17/168.27 => 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))) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_zero__le__mult__iff,axiom,
% 168.17/168.27 ! [V_b_2,V_a_2,T_b] :
% 168.17/168.27 ( class_Rings_Olinordered__ring__strict(T_b)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)))
% 168.17/168.27 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 168.17/168.27 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 168.17/168.27 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 168.17/168.27 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__le__0__iff,axiom,
% 168.17/168.27 ! [V_b_2,V_a_2,T_b] :
% 168.17/168.27 ( class_Rings_Olinordered__ring__strict(T_b)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 168.17/168.27 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 168.17/168.27 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 168.17/168.27 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 168.17/168.27 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__nonneg__nonneg,axiom,
% 168.17/168.27 ! [V_b,V_a,T_a] :
% 168.17/168.27 ( class_Rings_Oordered__cancel__semiring(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 168.17/168.27 => 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))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__nonneg__nonpos,axiom,
% 168.17/168.27 ! [V_b,V_a,T_a] :
% 168.17/168.27 ( class_Rings_Oordered__cancel__semiring(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.27 => 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))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__nonneg__nonpos2,axiom,
% 168.17/168.27 ! [V_b,V_a,T_a] :
% 168.17/168.27 ( class_Rings_Oordered__cancel__semiring(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.27 => 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))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__nonpos__nonneg,axiom,
% 168.17/168.27 ! [V_b,V_a,T_a] :
% 168.17/168.27 ( class_Rings_Oordered__cancel__semiring(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 168.17/168.27 => 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))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__nonpos__nonpos,axiom,
% 168.17/168.27 ! [V_b,V_a,T_a] :
% 168.17/168.27 ( class_Rings_Oordered__ring(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.27 => 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))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__right__mono,axiom,
% 168.17/168.27 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.27 ( class_Rings_Oordered__semiring(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 168.17/168.27 => 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))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__left__mono,axiom,
% 168.17/168.27 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.27 ( class_Rings_Oordered__semiring(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 168.17/168.27 => 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))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_comm__mult__left__mono,axiom,
% 168.17/168.27 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.27 ( class_Rings_Oordered__comm__semiring(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 168.17/168.27 => 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))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__right__mono__neg,axiom,
% 168.17/168.27 ! [V_c,V_a,V_b,T_a] :
% 168.17/168.27 ( class_Rings_Oordered__ring(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.27 => 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))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__left__mono__neg,axiom,
% 168.17/168.27 ! [V_c,V_a,V_b,T_a] :
% 168.17/168.27 ( class_Rings_Oordered__ring(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.27 => 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))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__mono_H,axiom,
% 168.17/168.27 ! [V_d,V_c,V_b,V_a,T_a] :
% 168.17/168.27 ( class_Rings_Oordered__semiring(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 168.17/168.27 => 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))) ) ) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__mono,axiom,
% 168.17/168.27 ! [V_d,V_c,V_b,V_a,T_a] :
% 168.17/168.27 ( class_Rings_Oordered__semiring(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 168.17/168.27 => 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))) ) ) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_split__mult__pos__le,axiom,
% 168.17/168.27 ! [V_b,V_a,T_a] :
% 168.17/168.27 ( class_Rings_Oordered__ring(T_a)
% 168.17/168.27 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 168.17/168.27 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) )
% 168.17/168.27 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.27 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 168.17/168.27 => 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))) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_split__mult__neg__le,axiom,
% 168.17/168.27 ! [V_b,V_a,T_a] :
% 168.17/168.27 ( class_Rings_Oordered__cancel__semiring(T_a)
% 168.17/168.27 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 168.17/168.27 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) )
% 168.17/168.27 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.27 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) )
% 168.17/168.27 => 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))) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_pos__add__strict,axiom,
% 168.17/168.27 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.27 ( class_Rings_Olinordered__semidom(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 168.17/168.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 168.17/168.27 ! [V_a_2,T_b] :
% 168.17/168.27 ( class_Groups_Olinordered__ab__group__add(T_b)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)))
% 168.17/168.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 168.17/168.27 ! [V_a_2,T_b] :
% 168.17/168.27 ( class_Groups_Olinordered__ab__group__add(T_b)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 168.17/168.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_add__pos__pos,axiom,
% 168.17/168.27 ! [V_b,V_a,T_a] :
% 168.17/168.27 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 168.17/168.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_add__neg__neg,axiom,
% 168.17/168.27 ! [V_b,V_a,T_a] :
% 168.17/168.27 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__strict__left__mono__neg,axiom,
% 168.17/168.27 ! [V_c,V_a,V_b,T_a] :
% 168.17/168.27 ( class_Rings_Olinordered__ring__strict(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.27 => 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))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__strict__right__mono__neg,axiom,
% 168.17/168.27 ! [V_c,V_a,V_b,T_a] :
% 168.17/168.27 ( class_Rings_Olinordered__ring__strict(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.27 => 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))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_comm__mult__strict__left__mono,axiom,
% 168.17/168.27 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.27 ( class_Rings_Olinordered__comm__semiring__strict(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 168.17/168.27 => 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))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__strict__left__mono,axiom,
% 168.17/168.27 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.27 ( class_Rings_Olinordered__semiring__strict(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 168.17/168.27 => 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))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__strict__right__mono,axiom,
% 168.17/168.27 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.27 ( class_Rings_Olinordered__semiring__strict(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 168.17/168.27 => 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))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__neg__neg,axiom,
% 168.17/168.27 ! [V_b,V_a,T_a] :
% 168.17/168.27 ( class_Rings_Olinordered__ring__strict(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__neg__pos,axiom,
% 168.17/168.27 ! [V_b,V_a,T_a] :
% 168.17/168.27 ( class_Rings_Olinordered__semiring__strict(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 168.17/168.27 => 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))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__less__cancel__left__neg,axiom,
% 168.17/168.27 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 168.17/168.27 ( class_Rings_Olinordered__ring__strict(T_b)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
% 168.17/168.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_zero__less__mult__pos2,axiom,
% 168.17/168.27 ! [V_a,V_b,T_a] :
% 168.17/168.27 ( class_Rings_Olinordered__semiring__strict(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 168.17/168.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_zero__less__mult__pos,axiom,
% 168.17/168.27 ! [V_b,V_a,T_a] :
% 168.17/168.27 ( class_Rings_Olinordered__semiring__strict(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 168.17/168.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__pos__neg2,axiom,
% 168.17/168.27 ! [V_b,V_a,T_a] :
% 168.17/168.27 ( class_Rings_Olinordered__semiring__strict(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.27 => 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))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__pos__neg,axiom,
% 168.17/168.27 ! [V_b,V_a,T_a] :
% 168.17/168.27 ( class_Rings_Olinordered__semiring__strict(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.27 => 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))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__pos__pos,axiom,
% 168.17/168.27 ! [V_b,V_a,T_a] :
% 168.17/168.27 ( class_Rings_Olinordered__semiring__strict(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 168.17/168.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__less__cancel__left__pos,axiom,
% 168.17/168.27 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 168.17/168.27 ( class_Rings_Olinordered__ring__strict(T_b)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
% 168.17/168.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__less__cancel__left__disj,axiom,
% 168.17/168.27 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 168.17/168.27 ( class_Rings_Olinordered__ring__strict(T_b)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
% 168.17/168.27 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 168.17/168.27 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
% 168.17/168.27 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 168.17/168.27 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__less__cancel__right__disj,axiom,
% 168.17/168.27 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 168.17/168.27 ( class_Rings_Olinordered__ring__strict(T_b)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2)))
% 168.17/168.27 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 168.17/168.27 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
% 168.17/168.27 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 168.17/168.27 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_not__square__less__zero,axiom,
% 168.17/168.27 ! [V_a,T_a] :
% 168.17/168.27 ( class_Rings_Olinordered__ring(T_a)
% 168.17/168.27 => ~ 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))) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_le__iff__diff__le__0,axiom,
% 168.17/168.27 ! [V_b_2,V_a_2,T_b] :
% 168.17/168.27 ( class_Groups_Oordered__ab__group__add(T_b)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 168.17/168.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_less__iff__diff__less__0,axiom,
% 168.17/168.27 ! [V_b_2,V_a_2,T_b] :
% 168.17/168.27 ( class_Groups_Oordered__ab__group__add(T_b)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 168.17/168.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_sum__squares__eq__zero__iff,axiom,
% 168.17/168.27 ! [V_y_2,V_x_2,T_b] :
% 168.17/168.27 ( class_Rings_Olinordered__ring__strict(T_b)
% 168.17/168.27 => ( 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)
% 168.17/168.27 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 168.17/168.27 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_add__scale__eq__noteq,axiom,
% 168.17/168.27 ! [V_d,V_c,V_b,V_a,V_r,T_a] :
% 168.17/168.27 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 168.17/168.27 => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.27 => ( ( V_a = V_b
% 168.17/168.27 & V_c != V_d )
% 168.17/168.27 => 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)) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_not__one__le__zero,axiom,
% 168.17/168.27 ! [T_a] :
% 168.17/168.27 ( class_Rings_Olinordered__semidom(T_a)
% 168.17/168.27 => ~ 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))) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_zero__le__one,axiom,
% 168.17/168.27 ! [T_a] :
% 168.17/168.27 ( class_Rings_Olinordered__semidom(T_a)
% 168.17/168.27 => 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))) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_not__one__less__zero,axiom,
% 168.17/168.27 ! [T_a] :
% 168.17/168.27 ( class_Rings_Olinordered__semidom(T_a)
% 168.17/168.27 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_zero__less__one,axiom,
% 168.17/168.27 ! [T_a] :
% 168.17/168.27 ( class_Rings_Olinordered__semidom(T_a)
% 168.17/168.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_setsum_Oempty,axiom,
% 168.17/168.27 ! [V_g_2,T_c,T_b] :
% 168.17/168.27 ( class_Groups_Ocomm__monoid__add(T_b)
% 168.17/168.27 => 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) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_setsum__empty,axiom,
% 168.17/168.27 ! [V_f_2,T_c,T_b] :
% 168.17/168.27 ( class_Groups_Ocomm__monoid__add(T_b)
% 168.17/168.27 => 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) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_setsum__infinite,axiom,
% 168.17/168.27 ! [V_f_2,V_A_2,T_b,T_c] :
% 168.17/168.27 ( class_Groups_Ocomm__monoid__add(T_c)
% 168.17/168.27 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => 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) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_setsum_Oinfinite,axiom,
% 168.17/168.27 ! [V_g_2,V_A_2,T_b,T_c] :
% 168.17/168.27 ( class_Groups_Ocomm__monoid__add(T_c)
% 168.17/168.27 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => 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) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_gr0__conv__Suc,axiom,
% 168.17/168.27 ! [V_n_2] :
% 168.17/168.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 168.17/168.27 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_less__Suc0,axiom,
% 168.17/168.27 ! [V_n_2] :
% 168.17/168.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
% 168.17/168.27 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_less__Suc__eq__0__disj,axiom,
% 168.17/168.27 ! [V_n_2,V_m_2] :
% 168.17/168.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 168.17/168.27 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.27 | ? [B_j] :
% 168.17/168.27 ( V_m_2 = hAPP(c_Nat_OSuc,B_j)
% 168.17/168.27 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_one__is__add,axiom,
% 168.17/168.27 ! [V_n_2,V_m_2] :
% 168.17/168.27 ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)
% 168.17/168.27 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 168.17/168.27 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 168.17/168.27 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.27 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_add__is__1,axiom,
% 168.17/168.27 ! [V_n_2,V_m_2] :
% 168.17/168.27 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 168.17/168.27 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 168.17/168.27 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 168.17/168.27 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.27 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_add__gr__0,axiom,
% 168.17/168.27 ! [V_n_2,V_m_2] :
% 168.17/168.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)))
% 168.17/168.27 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 168.17/168.27 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_card_Oempty,axiom,
% 168.17/168.27 ! [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) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_card__infinite,axiom,
% 168.17/168.27 ! [V_A_2,T_b] :
% 168.17/168.27 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__eq__1__iff,axiom,
% 168.17/168.27 ! [V_n_2,V_m_2] :
% 168.17/168.27 ( 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))
% 168.17/168.27 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 168.17/168.27 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_diff__less,axiom,
% 168.17/168.27 ! [V_m,V_n] :
% 168.17/168.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 168.17/168.27 => 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)) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_zero__less__diff,axiom,
% 168.17/168.27 ! [V_m_2,V_n_2] :
% 168.17/168.27 ( 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)))
% 168.17/168.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_nat__mult__less__cancel1,axiom,
% 168.17/168.27 ! [V_n_2,V_m_2,V_k_2] :
% 168.17/168.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 168.17/168.27 => ( 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)))
% 168.17/168.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_nat__mult__eq__cancel1,axiom,
% 168.17/168.27 ! [V_n_2,V_m_2,V_k_2] :
% 168.17/168.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 168.17/168.27 => ( 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)
% 168.17/168.27 <=> V_m_2 = V_n_2 ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_nat__0__less__mult__iff,axiom,
% 168.17/168.27 ! [V_n_2,V_m_2] :
% 168.17/168.27 ( 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)))
% 168.17/168.27 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 168.17/168.27 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__less__cancel1,axiom,
% 168.17/168.27 ! [V_n_2,V_m_2,V_k_2] :
% 168.17/168.27 ( 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)))
% 168.17/168.27 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 168.17/168.27 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__less__cancel2,axiom,
% 168.17/168.27 ! [V_n_2,V_k_2,V_m_2] :
% 168.17/168.27 ( 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)))
% 168.17/168.27 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 168.17/168.27 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__less__mono1,axiom,
% 168.17/168.27 ! [V_k,V_j,V_i] :
% 168.17/168.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 168.17/168.27 => 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))) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__less__mono2,axiom,
% 168.17/168.27 ! [V_k,V_j,V_i] :
% 168.17/168.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 168.17/168.27 => 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))) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_diff__add__0,axiom,
% 168.17/168.27 ! [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) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_fold1__singleton,axiom,
% 168.17/168.27 ! [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 ).
% 168.17/168.27
% 168.17/168.27 fof(fact_fold1__singleton__def,axiom,
% 168.17/168.27 ! [V_a_2,V_f_2,T_b,V_g_2] :
% 168.17/168.27 ( V_g_2 = c_Finite__Set_Ofold1(T_b,V_f_2)
% 168.17/168.27 => 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 ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_diff__is__0__eq_H,axiom,
% 168.17/168.27 ! [V_n,V_m] :
% 168.17/168.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 168.17/168.27 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_diff__is__0__eq,axiom,
% 168.17/168.27 ! [V_n_2,V_m_2] :
% 168.17/168.27 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_One__nat__def,axiom,
% 168.17/168.27 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__eq__self__implies__10,axiom,
% 168.17/168.27 ! [V_n,V_m] :
% 168.17/168.27 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
% 168.17/168.27 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 168.17/168.27 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_setsum__eq__0__iff,axiom,
% 168.17/168.27 ! [V_f_2,V_F_2,T_b] :
% 168.17/168.27 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 168.17/168.27 => ( 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)
% 168.17/168.27 <=> ! [B_x] :
% 168.17/168.27 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
% 168.17/168.27 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_folding__image__simple_Oeq__fold__g,axiom,
% 168.17/168.27 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 168.17/168.27 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 168.17/168.27 => 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) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_folding__one_Oeq__fold,axiom,
% 168.17/168.27 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 168.17/168.27 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_union__fold__insert,axiom,
% 168.17/168.27 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.27 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => 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) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_fold__sup__insert,axiom,
% 168.17/168.27 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 168.17/168.27 ( class_Lattices_Osemilattice__sup(T_b)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),V_A_2)) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_fold__inf__insert,axiom,
% 168.17/168.27 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 168.17/168.27 ( class_Lattices_Osemilattice__inf(T_b)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),V_A_2)) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_add__nonpos__neg,axiom,
% 168.17/168.27 ! [V_b,V_a,T_a] :
% 168.17/168.27 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_add__neg__nonpos,axiom,
% 168.17/168.27 ! [V_b,V_a,T_a] :
% 168.17/168.27 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_add__strict__increasing2,axiom,
% 168.17/168.27 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.27 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 168.17/168.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_add__strict__increasing,axiom,
% 168.17/168.27 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.27 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 168.17/168.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_add__nonneg__pos,axiom,
% 168.17/168.27 ! [V_b,V_a,T_a] :
% 168.17/168.27 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 168.17/168.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_add__pos__nonneg,axiom,
% 168.17/168.27 ! [V_b,V_a,T_a] :
% 168.17/168.27 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 168.17/168.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__left__le__imp__le,axiom,
% 168.17/168.27 ! [V_b,V_a,V_c,T_a] :
% 168.17/168.27 ( class_Rings_Olinordered__semiring__strict(T_a)
% 168.17/168.27 => ( 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)))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 168.17/168.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__right__le__imp__le,axiom,
% 168.17/168.27 ! [V_b,V_c,V_a,T_a] :
% 168.17/168.27 ( class_Rings_Olinordered__semiring__strict(T_a)
% 168.17/168.27 => ( 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)))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 168.17/168.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__less__imp__less__left,axiom,
% 168.17/168.27 ! [V_b,V_a,V_c,T_a] :
% 168.17/168.27 ( class_Rings_Olinordered__semiring__strict(T_a)
% 168.17/168.27 => ( 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)))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 168.17/168.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__left__less__imp__less,axiom,
% 168.17/168.27 ! [V_b,V_a,V_c,T_a] :
% 168.17/168.27 ( class_Rings_Olinordered__semiring(T_a)
% 168.17/168.27 => ( 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)))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 168.17/168.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__less__imp__less__right,axiom,
% 168.17/168.27 ! [V_b,V_c,V_a,T_a] :
% 168.17/168.27 ( class_Rings_Olinordered__semiring__strict(T_a)
% 168.17/168.27 => ( 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)))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 168.17/168.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__right__less__imp__less,axiom,
% 168.17/168.27 ! [V_b,V_c,V_a,T_a] :
% 168.17/168.27 ( class_Rings_Olinordered__semiring(T_a)
% 168.17/168.27 => ( 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)))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 168.17/168.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__le__less__imp__less,axiom,
% 168.17/168.27 ! [V_d,V_c,V_b,V_a,T_a] :
% 168.17/168.27 ( class_Rings_Olinordered__semiring__strict(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 168.17/168.27 => 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))) ) ) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__less__le__imp__less,axiom,
% 168.17/168.27 ! [V_d,V_c,V_b,V_a,T_a] :
% 168.17/168.27 ( class_Rings_Olinordered__semiring__strict(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 168.17/168.27 => 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))) ) ) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__strict__mono_H,axiom,
% 168.17/168.27 ! [V_d,V_c,V_b,V_a,T_a] :
% 168.17/168.27 ( class_Rings_Olinordered__semiring__strict(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 168.17/168.27 => 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))) ) ) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__strict__mono,axiom,
% 168.17/168.27 ! [V_d,V_c,V_b,V_a,T_a] :
% 168.17/168.27 ( class_Rings_Olinordered__semiring__strict(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 168.17/168.27 => 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))) ) ) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__le__cancel__left__neg,axiom,
% 168.17/168.27 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 168.17/168.27 ( class_Rings_Olinordered__ring__strict(T_b)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
% 168.17/168.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__le__cancel__left__pos,axiom,
% 168.17/168.27 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 168.17/168.27 ( class_Rings_Olinordered__ring__strict(T_b)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
% 168.17/168.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_sum__squares__ge__zero,axiom,
% 168.17/168.27 ! [V_y,V_x,T_a] :
% 168.17/168.27 ( class_Rings_Olinordered__ring(T_a)
% 168.17/168.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)))) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_sum__squares__le__zero__iff,axiom,
% 168.17/168.27 ! [V_y_2,V_x_2,T_b] :
% 168.17/168.27 ( class_Rings_Olinordered__ring__strict(T_b)
% 168.17/168.27 => ( 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)))
% 168.17/168.27 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 168.17/168.27 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_not__sum__squares__lt__zero,axiom,
% 168.17/168.27 ! [V_y,V_x,T_a] :
% 168.17/168.27 ( class_Rings_Olinordered__ring(T_a)
% 168.17/168.27 => ~ 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))) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_sum__squares__gt__zero__iff,axiom,
% 168.17/168.27 ! [V_y_2,V_x_2,T_b] :
% 168.17/168.27 ( class_Rings_Olinordered__ring__strict(T_b)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_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))))
% 168.17/168.27 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
% 168.17/168.27 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__right__le__one__le,axiom,
% 168.17/168.27 ! [V_y,V_x,T_a] :
% 168.17/168.27 ( class_Rings_Olinordered__idom(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 168.17/168.27 => 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)) ) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__left__le__one__le,axiom,
% 168.17/168.27 ! [V_y,V_x,T_a] :
% 168.17/168.27 ( class_Rings_Olinordered__idom(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 168.17/168.27 => 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)) ) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_zero__less__two,axiom,
% 168.17/168.27 ! [T_a] :
% 168.17/168.27 ( class_Rings_Olinordered__semidom(T_a)
% 168.17/168.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)))) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_card__eq__0__iff,axiom,
% 168.17/168.27 ! [V_A_2,T_b] :
% 168.17/168.27 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.27 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.27 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_card__ge__0__finite,axiom,
% 168.17/168.27 ! [V_A_2,T_b] :
% 168.17/168.27 ( 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)))
% 168.17/168.27 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_diff__Suc__less,axiom,
% 168.17/168.27 ! [V_i,V_n] :
% 168.17/168.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 168.17/168.27 => 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)) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_Suc__pred,axiom,
% 168.17/168.27 ! [V_n] :
% 168.17/168.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 168.17/168.27 => 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 ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_n__less__m__mult__n,axiom,
% 168.17/168.27 ! [V_m,V_n] :
% 168.17/168.27 ( 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))
% 168.17/168.27 => ( 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))
% 168.17/168.27 => 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))) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_n__less__n__mult__m,axiom,
% 168.17/168.27 ! [V_m,V_n] :
% 168.17/168.27 ( 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))
% 168.17/168.27 => ( 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))
% 168.17/168.27 => 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))) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_one__less__mult,axiom,
% 168.17/168.27 ! [V_m,V_n] :
% 168.17/168.27 ( 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))
% 168.17/168.27 => ( 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))
% 168.17/168.27 => 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))) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_nat__diff__split__asm,axiom,
% 168.17/168.27 ! [V_b_2,V_a_2,V_P_2] :
% 168.17/168.27 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 168.17/168.27 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 168.17/168.27 & ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 168.17/168.27 | ? [B_d] :
% 168.17/168.27 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 168.17/168.27 & ~ hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_nat__diff__split,axiom,
% 168.17/168.27 ! [V_b_2,V_a_2,V_P_2] :
% 168.17/168.27 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 168.17/168.27 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 168.17/168.27 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 168.17/168.27 & ! [B_d] :
% 168.17/168.27 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 168.17/168.27 => hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_one__le__mult__iff,axiom,
% 168.17/168.27 ! [V_n_2,V_m_2] :
% 168.17/168.27 ( 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)))
% 168.17/168.27 <=> ( 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))
% 168.17/168.27 & 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)) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_nat__mult__le__cancel1,axiom,
% 168.17/168.27 ! [V_n_2,V_m_2,V_k_2] :
% 168.17/168.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 168.17/168.27 => ( 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)))
% 168.17/168.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__le__cancel1,axiom,
% 168.17/168.27 ! [V_n_2,V_m_2,V_k_2] :
% 168.17/168.27 ( 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)))
% 168.17/168.27 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 168.17/168.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__le__cancel2,axiom,
% 168.17/168.27 ! [V_n_2,V_k_2,V_m_2] :
% 168.17/168.27 ( 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)))
% 168.17/168.27 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 168.17/168.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom,
% 168.17/168.27 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_b] :
% 168.17/168.27 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => 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) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_setprod_Oinsert,axiom,
% 168.17/168.27 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 168.17/168.27 ( class_Groups_Ocomm__monoid__mult(T_c)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.27 => 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)) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_setprod__insert,axiom,
% 168.17/168.27 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 168.17/168.27 ( class_Groups_Ocomm__monoid__mult(T_c)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.17/168.27 => 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)) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_setsum__eq__Suc0__iff,axiom,
% 168.17/168.27 ! [V_f_2,V_A_2,T_b] :
% 168.17/168.27 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => ( 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))
% 168.17/168.27 <=> ? [B_x] :
% 168.17/168.27 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.17/168.27 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 168.17/168.27 & ! [B_xa] :
% 168.17/168.27 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 168.17/168.27 => ( B_x != B_xa
% 168.17/168.27 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_setprod_Ounion__inter,axiom,
% 168.17/168.27 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 168.17/168.27 ( class_Groups_Ocomm__monoid__mult(T_c)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.27 => 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)) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_setprod__Un__Int,axiom,
% 168.17/168.27 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 168.17/168.27 ( class_Groups_Ocomm__monoid__mult(T_c)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.27 => 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)) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_setsum__eq__1__iff,axiom,
% 168.17/168.27 ! [V_f_2,V_A_2,T_b] :
% 168.17/168.27 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => ( 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)
% 168.17/168.27 <=> ? [B_x] :
% 168.17/168.27 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.17/168.27 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 168.17/168.27 & ! [B_xa] :
% 168.17/168.27 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 168.17/168.27 => ( B_x != B_xa
% 168.17/168.27 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_Sup__fin_OF__eq,axiom,
% 168.17/168.27 ! [V_A_2,T_b] :
% 168.17/168.27 ( class_Lattices_Olattice(T_b)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => 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) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_Inf__fin_OF__eq,axiom,
% 168.17/168.27 ! [V_A_2,T_b] :
% 168.17/168.27 ( class_Lattices_Olattice(T_b)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => 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) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_sup__le__fold__sup,axiom,
% 168.17/168.27 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 168.17/168.27 ( class_Lattices_Osemilattice__sup(T_b)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.17/168.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),V_A_2))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_fold__inf__le__inf,axiom,
% 168.17/168.27 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 168.17/168.27 ( class_Lattices_Osemilattice__inf(T_b)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.17/168.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),V_b_2))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom,
% 168.17/168.27 ! [V_a_2,V_A_2,T_b] :
% 168.17/168.27 ( class_Lattices_Olattice(T_b)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => 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) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom,
% 168.17/168.27 ! [V_a_2,V_A_2,T_b] :
% 168.17/168.27 ( class_Lattices_Olattice(T_b)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => 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) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_convex__bound__le,axiom,
% 168.17/168.27 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 168.17/168.27 ( class_Rings_Olinordered__semiring__1(T_a)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 168.17/168.27 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 168.17/168.27 => 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)) ) ) ) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_folding__one_Oeq__fold_H,axiom,
% 168.17/168.27 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 168.17/168.27 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.27 => 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) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_fold__image__insert,axiom,
% 168.17/168.27 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_b,T_c] :
% 168.17/168.27 ( class_Groups_Oab__semigroup__mult(T_c)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.17/168.27 => 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)) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_setprod_Oinsert__remove,axiom,
% 168.17/168.27 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
% 168.17/168.27 ( class_Groups_Ocomm__monoid__mult(T_c)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => 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)))))) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_setprod__Un__disjoint,axiom,
% 168.17/168.27 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 168.17/168.27 ( class_Groups_Ocomm__monoid__mult(T_c)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.27 => ( 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))
% 168.17/168.27 => 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)) ) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_setprod_Ounion__disjoint,axiom,
% 168.17/168.27 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 168.17/168.27 ( class_Groups_Ocomm__monoid__mult(T_c)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.27 => ( 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))
% 168.17/168.27 => 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)) ) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_card__gt__0__iff,axiom,
% 168.17/168.27 ! [V_A_2,T_b] :
% 168.17/168.27 ( 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)))
% 168.17/168.27 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.27 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_fold1__belowI,axiom,
% 168.17/168.27 ! [V_a_2,V_A_2,T_b] :
% 168.17/168.27 ( class_Lattices_Osemilattice__inf(T_b)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.17/168.27 => 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)) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_below__fold1__iff,axiom,
% 168.17/168.27 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.27 ( class_Lattices_Osemilattice__inf(T_b)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.27 => ( 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)))
% 168.17/168.27 <=> ! [B_x] :
% 168.17/168.27 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.17/168.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_fold1__insert__idem,axiom,
% 168.17/168.27 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.27 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 168.17/168.27 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => 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)) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_fold1__Un2,axiom,
% 168.17/168.27 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.27 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.27 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.27 => 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)) ) ) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_Suc__pred_H,axiom,
% 168.17/168.27 ! [V_n] :
% 168.17/168.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 168.17/168.27 => 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))) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_Suc__diff__1,axiom,
% 168.17/168.27 ! [V_n] :
% 168.17/168.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 168.17/168.27 => 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 ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_add__eq__if,axiom,
% 168.17/168.27 ! [V_n,V_m] :
% 168.17/168.27 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.27 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n )
% 168.17/168.27 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.27 => 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)) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_mult__eq__if,axiom,
% 168.17/168.27 ! [V_n,V_m] :
% 168.17/168.27 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.27 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 168.17/168.27 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.27 => 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)) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_Sup__fin_Oeq__fold_H,axiom,
% 168.17/168.27 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.27 ( class_Lattices_Olattice(T_b)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.27 => 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) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_semilattice__big_OF__eq,axiom,
% 168.17/168.27 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 168.17/168.27 ( c_Big__Operators_Osemilattice__big(T_b,V_f_2,V_F_2)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_even__less__0__iff,axiom,
% 168.17/168.27 ! [V_a_2,T_b] :
% 168.17/168.27 ( class_Rings_Olinordered__idom(T_b)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 168.17/168.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_fun__left__comm_Ofold__rec,axiom,
% 168.17/168.27 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 168.17/168.27 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.27 => 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)))))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_comm__monoid__big_OF__eq,axiom,
% 168.17/168.27 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 168.17/168.27 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 168.17/168.27 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 168.17/168.27 => 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) )
% 168.17/168.27 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 168.17/168.27 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_setsum__mono2,axiom,
% 168.17/168.27 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 168.17/168.27 ( class_Groups_Oordered__comm__monoid__add(T_c)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.17/168.27 => ( ! [B_b] :
% 168.17/168.27 ( 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)))
% 168.17/168.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_b))) )
% 168.17/168.27 => 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))) ) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_Plus__eq__empty__conv,axiom,
% 168.17/168.27 ! [V_B_2,V_A_2,T_c,T_b] :
% 168.17/168.27 ( 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))
% 168.17/168.27 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.27 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_fun__left__comm_Ofold__insert__remove,axiom,
% 168.17/168.27 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 168.17/168.27 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => 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)))))) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_card_Ounion__inter__neutral,axiom,
% 168.17/168.27 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.27 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.27 => ( ( ? [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)))
% 168.17/168.27 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 168.17/168.27 => 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)) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_fold__image__Un__one,axiom,
% 168.17/168.27 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 168.17/168.27 ( class_Groups_Ocomm__monoid__mult(T_c)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 168.17/168.27 => ( ! [B_x] :
% 168.17/168.27 ( 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)))
% 168.17/168.27 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 168.17/168.27 => 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)) ) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_bot__nat__def,axiom,
% 168.17/168.27 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_fun__left__comm_Ofun__left__comm,axiom,
% 168.17/168.27 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 168.17/168.27 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 168.17/168.27 => 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)) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_fun__left__comm,axiom,
% 168.17/168.27 ! [T_b] :
% 168.17/168.27 ( class_Groups_Oab__semigroup__mult(T_b)
% 168.17/168.27 => c_Finite__Set_Ofun__left__comm(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_fun__left__comm_Ofold__graph__determ,axiom,
% 168.17/168.27 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 168.17/168.27 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 168.17/168.27 => V_y_2 = V_x_2 ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_fun__left__comm_Ofold__fun__comm,axiom,
% 168.17/168.27 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 168.17/168.27 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => 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) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_fun__left__comm_Ofold__equality,axiom,
% 168.17/168.27 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 168.17/168.27 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 168.17/168.27 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_comm__monoid__big_Oinfinite,axiom,
% 168.17/168.27 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 168.17/168.27 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 168.17/168.27 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 168.17/168.27 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_fun__left__comm_Ofold__graph__fold,axiom,
% 168.17/168.27 ! [V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 168.17/168.27 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => 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))) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_fun__left__comm_Ofold__insert2,axiom,
% 168.17/168.27 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 168.17/168.27 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.27 => 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) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_fun__left__comm_Ofold__insert,axiom,
% 168.17/168.27 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 168.17/168.27 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.27 => 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)) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_double__eq__0__iff,axiom,
% 168.17/168.27 ! [V_a_2,T_b] :
% 168.17/168.27 ( class_Groups_Olinordered__ab__group__add(T_b)
% 168.17/168.27 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 168.17/168.27 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom,
% 168.17/168.27 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 168.17/168.27 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.17/168.27 => ? [B_y_H] :
% 168.17/168.27 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H)
% 168.17/168.27 & 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)) ) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_fold1__in,axiom,
% 168.17/168.27 ! [V_A_2,T_b] :
% 168.17/168.27 ( class_Groups_Oab__semigroup__mult(T_b)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.27 => ( ! [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))))))
% 168.17/168.27 => 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)) ) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_setprod__Un__one,axiom,
% 168.17/168.27 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 168.17/168.27 ( class_Groups_Ocomm__monoid__mult(T_c)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 168.17/168.27 => ( ! [B_x] :
% 168.17/168.27 ( 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)))
% 168.17/168.27 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 168.17/168.27 => 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)) ) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_setprod_Ounion__inter__neutral,axiom,
% 168.17/168.27 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 168.17/168.27 ( class_Groups_Ocomm__monoid__mult(T_c)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.27 => ( ! [B_x] :
% 168.17/168.27 ( 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)))
% 168.17/168.27 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 168.17/168.27 => 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)) ) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_setsum__Un__zero,axiom,
% 168.17/168.27 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 168.17/168.27 ( class_Groups_Ocomm__monoid__add(T_c)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 168.17/168.27 => ( ! [B_x] :
% 168.17/168.27 ( 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)))
% 168.17/168.27 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 168.17/168.27 => 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)) ) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_setsum_Ounion__inter__neutral,axiom,
% 168.17/168.27 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 168.17/168.27 ( class_Groups_Ocomm__monoid__add(T_c)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.27 => ( ! [B_x] :
% 168.17/168.27 ( 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)))
% 168.17/168.27 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 168.17/168.27 => 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)) ) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_card__Suc__eq,axiom,
% 168.17/168.27 ! [V_k_2,V_A_2,T_b] :
% 168.17/168.27 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Nat_OSuc,V_k_2)
% 168.17/168.27 <=> ? [B_b,B_B] :
% 168.17/168.27 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_b),B_B)
% 168.17/168.27 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_b),B_B))
% 168.17/168.27 & hAPP(c_Finite__Set_Ocard(T_b),B_B) = V_k_2
% 168.17/168.27 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.27 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_setsum__mono3,axiom,
% 168.17/168.27 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 168.17/168.27 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 168.17/168.27 & class_Groups_Oordered__ab__semigroup__add(T_c) )
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.17/168.27 => ( ! [B_x] :
% 168.17/168.27 ( 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)))
% 168.17/168.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 168.17/168.27 => 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))) ) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_Ints__odd__less__0,axiom,
% 168.17/168.27 ! [V_a_2,T_b] :
% 168.17/168.27 ( class_Rings_Olinordered__idom(T_b)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 168.17/168.27 => ( 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)))
% 168.17/168.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_setprod__diff1,axiom,
% 168.17/168.27 ! [V_a_2,V_f_2,V_A_2,T_b,T_c] :
% 168.17/168.27 ( class_Fields_Ofield(T_c)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_c)
% 168.17/168.27 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.17/168.27 => 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)) )
% 168.17/168.27 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.17/168.27 => 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) ) ) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_ex__least__nat__less,axiom,
% 168.17/168.27 ! [V_n_2,V_P_2] :
% 168.17/168.27 ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 168.17/168.27 => ( hBOOL(hAPP(V_P_2,V_n_2))
% 168.17/168.27 => ? [B_k] :
% 168.17/168.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2))
% 168.17/168.27 & ! [B_i] :
% 168.17/168.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k))
% 168.17/168.27 => ~ hBOOL(hAPP(V_P_2,B_i)) )
% 168.17/168.27 & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_setprod__mono__one__right,axiom,
% 168.17/168.27 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 168.17/168.27 ( class_Groups_Ocomm__monoid__mult(T_c)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 168.17/168.27 => ( ! [B_x] :
% 168.17/168.27 ( 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)))
% 168.17/168.27 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 168.17/168.27 => 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) ) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_setprod__mono__one__left,axiom,
% 168.17/168.27 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 168.17/168.27 ( class_Groups_Ocomm__monoid__mult(T_c)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 168.17/168.27 => ( ! [B_x] :
% 168.17/168.27 ( 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)))
% 168.17/168.27 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 168.17/168.27 => 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) ) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_setsum__mono__zero__right,axiom,
% 168.17/168.27 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 168.17/168.27 ( class_Groups_Ocomm__monoid__add(T_c)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 168.17/168.27 => ( ! [B_x] :
% 168.17/168.27 ( 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)))
% 168.17/168.27 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 168.17/168.27 => 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) ) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_setsum__mono__zero__left,axiom,
% 168.17/168.27 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 168.17/168.27 ( class_Groups_Ocomm__monoid__add(T_c)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 168.17/168.27 => ( ! [B_x] :
% 168.17/168.27 ( 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)))
% 168.17/168.27 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 168.17/168.27 => 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) ) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_Sup__fold__sup,axiom,
% 168.17/168.27 ! [V_A_2,T_b] :
% 168.17/168.27 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => 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) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_divide__zero,axiom,
% 168.17/168.27 ! [V_a,T_a] :
% 168.17/168.27 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 168.17/168.27 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_divide__zero__left,axiom,
% 168.17/168.27 ! [V_a,T_a] :
% 168.17/168.27 ( class_Rings_Odivision__ring(T_a)
% 168.17/168.27 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_add__divide__distrib,axiom,
% 168.17/168.27 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.27 ( class_Rings_Odivision__ring(T_a)
% 168.17/168.27 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_times__divide__eq__right,axiom,
% 168.17/168.27 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.27 ( class_Rings_Odivision__ring(T_a)
% 168.17/168.27 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_diff__divide__distrib,axiom,
% 168.17/168.27 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.27 ( class_Rings_Odivision__ring(T_a)
% 168.17/168.27 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_divide__1,axiom,
% 168.17/168.27 ! [V_a,T_a] :
% 168.17/168.27 ( class_Rings_Odivision__ring(T_a)
% 168.17/168.27 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_finite__UnionD,axiom,
% 168.17/168.27 ! [V_A_2,T_b] :
% 168.17/168.27 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))
% 168.17/168.27 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_eq__divide__imp,axiom,
% 168.17/168.27 ! [V_b,V_a,V_c,T_a] :
% 168.17/168.27 ( class_Rings_Odivision__ring(T_a)
% 168.17/168.27 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.27 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b
% 168.17/168.27 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_divide__eq__imp,axiom,
% 168.17/168.27 ! [V_a,V_b,V_c,T_a] :
% 168.17/168.27 ( class_Rings_Odivision__ring(T_a)
% 168.17/168.27 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.27 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)
% 168.17/168.27 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_nonzero__divide__eq__eq,axiom,
% 168.17/168.27 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 168.17/168.27 ( class_Rings_Odivision__ring(T_b)
% 168.17/168.27 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 168.17/168.27 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2
% 168.17/168.27 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_nonzero__eq__divide__eq,axiom,
% 168.17/168.27 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 168.17/168.27 ( class_Rings_Odivision__ring(T_b)
% 168.17/168.27 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 168.17/168.27 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
% 168.17/168.27 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2 ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_divide__self__if,axiom,
% 168.17/168.27 ! [V_a,T_a] :
% 168.17/168.27 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 168.17/168.27 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.27 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) )
% 168.17/168.27 & ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.27 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_divide__self,axiom,
% 168.17/168.27 ! [V_a,T_a] :
% 168.17/168.27 ( class_Rings_Odivision__ring(T_a)
% 168.17/168.27 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.27 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_right__inverse__eq,axiom,
% 168.17/168.27 ! [V_a_2,V_b_2,T_b] :
% 168.17/168.27 ( class_Rings_Odivision__ring(T_b)
% 168.17/168.27 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_b)
% 168.17/168.27 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_b)
% 168.17/168.27 <=> V_a_2 = V_b_2 ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_Ints__0,axiom,
% 168.17/168.27 ! [T_b] :
% 168.17/168.27 ( class_Rings_Oring__1(T_b)
% 168.17/168.27 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_Ints__add,axiom,
% 168.17/168.27 ! [V_b_2,V_a_2,T_b] :
% 168.17/168.27 ( class_Rings_Oring__1(T_b)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 168.17/168.27 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_Ints__mult,axiom,
% 168.17/168.27 ! [V_b_2,V_a_2,T_b] :
% 168.17/168.27 ( class_Rings_Oring__1(T_b)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 168.17/168.27 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_Ints__diff,axiom,
% 168.17/168.27 ! [V_b_2,V_a_2,T_b] :
% 168.17/168.27 ( class_Rings_Oring__1(T_b)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 168.17/168.27 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_Ints__1,axiom,
% 168.17/168.27 ! [T_b] :
% 168.17/168.27 ( class_Rings_Oring__1(T_b)
% 168.17/168.27 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_Ints__double__eq__0__iff,axiom,
% 168.17/168.27 ! [V_a_2,T_b] :
% 168.17/168.27 ( class_Int_Oring__char__0(T_b)
% 168.17/168.27 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 168.17/168.27 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 168.17/168.27 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_sup__Sup__fold__sup,axiom,
% 168.17/168.27 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.27 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 168.17/168.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.27 => 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) ) ) ).
% 168.17/168.27
% 168.17/168.27 fof(fact_Sup__fin__Sup,axiom,
% 168.17/168.27 ! [V_A_2,T_b] :
% 168.17/168.27 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.28 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Ints__odd__nonzero,axiom,
% 168.17/168.28 ! [V_a_2,T_b] :
% 168.17/168.28 ( class_Int_Oring__char__0(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 168.17/168.28 => 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) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_le__divide__eq,axiom,
% 168.17/168.28 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 168.17/168.28 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
% 168.17/168.28 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) )
% 168.17/168.28 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 168.17/168.28 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) )
% 168.17/168.28 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_divide__le__eq,axiom,
% 168.17/168.28 ! [V_a_2,V_c_2,V_b_2,T_b] :
% 168.17/168.28 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
% 168.17/168.28 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) )
% 168.17/168.28 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 168.17/168.28 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) )
% 168.17/168.28 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_pos__le__divide__eq,axiom,
% 168.17/168.28 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 168.17/168.28 ( class_Fields_Olinordered__field(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
% 168.17/168.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_pos__divide__le__eq,axiom,
% 168.17/168.28 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 168.17/168.28 ( class_Fields_Olinordered__field(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
% 168.17/168.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_mult__imp__div__pos__le,axiom,
% 168.17/168.28 ! [V_z,V_x,V_y,T_a] :
% 168.17/168.28 ( class_Fields_Olinordered__field(T_a)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 168.17/168.28 => ( 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)))
% 168.17/168.28 => 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)) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_mult__imp__le__div__pos,axiom,
% 168.17/168.28 ! [V_x,V_z,V_y,T_a] :
% 168.17/168.28 ( class_Fields_Olinordered__field(T_a)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 168.17/168.28 => ( 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))
% 168.17/168.28 => 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))) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_neg__le__divide__eq,axiom,
% 168.17/168.28 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 168.17/168.28 ( class_Fields_Olinordered__field(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
% 168.17/168.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_neg__divide__le__eq,axiom,
% 168.17/168.28 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 168.17/168.28 ( class_Fields_Olinordered__field(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
% 168.17/168.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_times__divide__times__eq,axiom,
% 168.17/168.28 ! [V_w,V_z,V_y,V_x,T_a] :
% 168.17/168.28 ( class_Fields_Ofield__inverse__zero(T_a)
% 168.17/168.28 => 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)) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zero__le__divide__iff,axiom,
% 168.17/168.28 ! [V_b_2,V_a_2,T_b] :
% 168.17/168.28 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)))
% 168.17/168.28 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 168.17/168.28 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 168.17/168.28 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 168.17/168.28 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_divide__le__0__iff,axiom,
% 168.17/168.28 ! [V_b_2,V_a_2,T_b] :
% 168.17/168.28 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 168.17/168.28 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 168.17/168.28 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 168.17/168.28 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 168.17/168.28 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_divide__right__mono,axiom,
% 168.17/168.28 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.28 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 168.17/168.28 => 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))) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_divide__right__mono__neg,axiom,
% 168.17/168.28 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.28 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.28 => 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))) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zero__less__divide__iff,axiom,
% 168.17/168.28 ! [V_b_2,V_a_2,T_b] :
% 168.17/168.28 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)))
% 168.17/168.28 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 168.17/168.28 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 168.17/168.28 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 168.17/168.28 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_divide__less__0__iff,axiom,
% 168.17/168.28 ! [V_b_2,V_a_2,T_b] :
% 168.17/168.28 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 168.17/168.28 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 168.17/168.28 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 168.17/168.28 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 168.17/168.28 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_divide__pos__pos,axiom,
% 168.17/168.28 ! [V_y,V_x,T_a] :
% 168.17/168.28 ( class_Fields_Olinordered__field(T_a)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 168.17/168.28 => 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))) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_divide__pos__neg,axiom,
% 168.17/168.28 ! [V_y,V_x,T_a] :
% 168.17/168.28 ( class_Fields_Olinordered__field(T_a)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.28 => 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))) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_divide__neg__pos,axiom,
% 168.17/168.28 ! [V_y,V_x,T_a] :
% 168.17/168.28 ( class_Fields_Olinordered__field(T_a)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 168.17/168.28 => 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))) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_divide__neg__neg,axiom,
% 168.17/168.28 ! [V_y,V_x,T_a] :
% 168.17/168.28 ( class_Fields_Olinordered__field(T_a)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.28 => 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))) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_divide__strict__right__mono,axiom,
% 168.17/168.28 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.28 ( class_Fields_Olinordered__field(T_a)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 168.17/168.28 => 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))) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_divide__strict__right__mono__neg,axiom,
% 168.17/168.28 ! [V_c,V_a,V_b,T_a] :
% 168.17/168.28 ( class_Fields_Olinordered__field(T_a)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.28 => 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))) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_frac__eq__eq,axiom,
% 168.17/168.28 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_b] :
% 168.17/168.28 ( class_Fields_Ofield(T_b)
% 168.17/168.28 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
% 168.17/168.28 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_b)
% 168.17/168.28 => ( 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)
% 168.17/168.28 <=> 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) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_mult__divide__mult__cancel__left,axiom,
% 168.17/168.28 ! [V_b,V_a,V_c,T_a] :
% 168.17/168.28 ( class_Fields_Ofield__inverse__zero(T_a)
% 168.17/168.28 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.28 => 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) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_mult__divide__mult__cancel__right,axiom,
% 168.17/168.28 ! [V_b,V_a,V_c,T_a] :
% 168.17/168.28 ( class_Fields_Ofield__inverse__zero(T_a)
% 168.17/168.28 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.28 => 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) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_divide__eq__eq,axiom,
% 168.17/168.28 ! [V_a_2,V_c_2,V_b_2,T_b] :
% 168.17/168.28 ( class_Fields_Ofield__inverse__zero(T_b)
% 168.17/168.28 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2
% 168.17/168.28 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 168.17/168.28 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) )
% 168.17/168.28 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 168.17/168.28 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_eq__divide__eq,axiom,
% 168.17/168.28 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 168.17/168.28 ( class_Fields_Ofield__inverse__zero(T_b)
% 168.17/168.28 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
% 168.17/168.28 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 168.17/168.28 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2 )
% 168.17/168.28 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 168.17/168.28 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_divide__nonpos__neg,axiom,
% 168.17/168.28 ! [V_y,V_x,T_a] :
% 168.17/168.28 ( class_Fields_Olinordered__field(T_a)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.28 => 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))) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_divide__nonpos__pos,axiom,
% 168.17/168.28 ! [V_y,V_x,T_a] :
% 168.17/168.28 ( class_Fields_Olinordered__field(T_a)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 168.17/168.28 => 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))) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_frac__le,axiom,
% 168.17/168.28 ! [V_z,V_w,V_y,V_x,T_a] :
% 168.17/168.28 ( class_Fields_Olinordered__field(T_a)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 168.17/168.28 => 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))) ) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_frac__less,axiom,
% 168.17/168.28 ! [V_z,V_w,V_y,V_x,T_a] :
% 168.17/168.28 ( class_Fields_Olinordered__field(T_a)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 168.17/168.28 => 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))) ) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_frac__less2,axiom,
% 168.17/168.28 ! [V_z,V_w,V_y,V_x,T_a] :
% 168.17/168.28 ( class_Fields_Olinordered__field(T_a)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z))
% 168.17/168.28 => 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))) ) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_divide__nonneg__neg,axiom,
% 168.17/168.28 ! [V_y,V_x,T_a] :
% 168.17/168.28 ( class_Fields_Olinordered__field(T_a)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.28 => 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))) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_divide__nonneg__pos,axiom,
% 168.17/168.28 ! [V_y,V_x,T_a] :
% 168.17/168.28 ( class_Fields_Olinordered__field(T_a)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 168.17/168.28 => 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))) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_divide__strict__left__mono__neg,axiom,
% 168.17/168.28 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.28 ( class_Fields_Olinordered__field(T_a)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
% 168.17/168.28 => 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))) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_divide__strict__left__mono,axiom,
% 168.17/168.28 ! [V_c,V_a,V_b,T_a] :
% 168.17/168.28 ( class_Fields_Olinordered__field(T_a)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
% 168.17/168.28 => 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))) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_neg__divide__less__eq,axiom,
% 168.17/168.28 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 168.17/168.28 ( class_Fields_Olinordered__field(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
% 168.17/168.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_neg__less__divide__eq,axiom,
% 168.17/168.28 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 168.17/168.28 ( class_Fields_Olinordered__field(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
% 168.17/168.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_mult__imp__less__div__pos,axiom,
% 168.17/168.28 ! [V_x,V_z,V_y,T_a] :
% 168.17/168.28 ( class_Fields_Olinordered__field(T_a)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 168.17/168.28 => ( 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))
% 168.17/168.28 => 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))) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_mult__imp__div__pos__less,axiom,
% 168.17/168.28 ! [V_z,V_x,V_y,T_a] :
% 168.17/168.28 ( class_Fields_Olinordered__field(T_a)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 168.17/168.28 => ( 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)))
% 168.17/168.28 => 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)) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_pos__divide__less__eq,axiom,
% 168.17/168.28 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 168.17/168.28 ( class_Fields_Olinordered__field(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
% 168.17/168.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_pos__less__divide__eq,axiom,
% 168.17/168.28 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 168.17/168.28 ( class_Fields_Olinordered__field(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
% 168.17/168.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_divide__less__eq,axiom,
% 168.17/168.28 ! [V_a_2,V_c_2,V_b_2,T_b] :
% 168.17/168.28 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
% 168.17/168.28 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) )
% 168.17/168.28 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 168.17/168.28 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) )
% 168.17/168.28 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_less__divide__eq,axiom,
% 168.17/168.28 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 168.17/168.28 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
% 168.17/168.28 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) )
% 168.17/168.28 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 168.17/168.28 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) )
% 168.17/168.28 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_add__num__frac,axiom,
% 168.17/168.28 ! [V_x,V_z,V_y,T_a] :
% 168.17/168.28 ( class_Fields_Ofield__inverse__zero(T_a)
% 168.17/168.28 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.28 => 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) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_add__divide__eq__iff,axiom,
% 168.17/168.28 ! [V_y,V_x,V_z,T_a] :
% 168.17/168.28 ( class_Fields_Ofield(T_a)
% 168.17/168.28 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.28 => 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) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_add__frac__num,axiom,
% 168.17/168.28 ! [V_z,V_x,V_y,T_a] :
% 168.17/168.28 ( class_Fields_Ofield__inverse__zero(T_a)
% 168.17/168.28 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.28 => 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) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_divide__add__eq__iff,axiom,
% 168.17/168.28 ! [V_y,V_x,V_z,T_a] :
% 168.17/168.28 ( class_Fields_Ofield(T_a)
% 168.17/168.28 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.28 => 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) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_add__frac__eq,axiom,
% 168.17/168.28 ! [V_w,V_x,V_z,V_y,T_a] :
% 168.17/168.28 ( class_Fields_Ofield(T_a)
% 168.17/168.28 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.28 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.28 => 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)) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_diff__divide__eq__iff,axiom,
% 168.17/168.28 ! [V_y,V_x,V_z,T_a] :
% 168.17/168.28 ( class_Fields_Ofield(T_a)
% 168.17/168.28 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.28 => 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) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_divide__diff__eq__iff,axiom,
% 168.17/168.28 ! [V_y,V_x,V_z,T_a] :
% 168.17/168.28 ( class_Fields_Ofield(T_a)
% 168.17/168.28 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.28 => 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) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_diff__frac__eq,axiom,
% 168.17/168.28 ! [V_w,V_x,V_z,V_y,T_a] :
% 168.17/168.28 ( class_Fields_Ofield(T_a)
% 168.17/168.28 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.28 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.28 => 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)) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_less__half__sum,axiom,
% 168.17/168.28 ! [V_b,V_a,T_a] :
% 168.17/168.28 ( class_Fields_Olinordered__field(T_a)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 168.17/168.28 => 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))))) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_gt__half__sum,axiom,
% 168.17/168.28 ! [V_b,V_a,T_a] :
% 168.17/168.28 ( class_Fields_Olinordered__field(T_a)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 168.17/168.28 => 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)) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_divide__left__mono__neg,axiom,
% 168.17/168.28 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.28 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
% 168.17/168.28 => 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))) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_divide__left__mono,axiom,
% 168.17/168.28 ! [V_c,V_a,V_b,T_a] :
% 168.17/168.28 ( class_Fields_Olinordered__field(T_a)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
% 168.17/168.28 => 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))) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_UnionI,axiom,
% 168.17/168.28 ! [V_A_2,V_C_2,V_X_2,T_b] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2))
% 168.17/168.28 => 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))) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Sup__binary,axiom,
% 168.17/168.28 ! [V_b_2,V_a_2,T_b] :
% 168.17/168.28 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 168.17/168.28 => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),V_b_2) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Union__mono,axiom,
% 168.17/168.28 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.28 ( 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))
% 168.17/168.28 => 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))) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Union__Int__subset,axiom,
% 168.17/168.28 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),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)))) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Union__disjoint,axiom,
% 168.17/168.28 ! [V_A_2,V_C_2,T_b] :
% 168.17/168.28 ( 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))
% 168.17/168.28 <=> ! [B_x] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_C_2))
% 168.17/168.28 => 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)) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Sup__insert,axiom,
% 168.17/168.28 ! [V_A_2,V_a_2,T_b] :
% 168.17/168.28 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 168.17/168.28 => 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)) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Sup__singleton,axiom,
% 168.17/168.28 ! [V_a_2,T_b] :
% 168.17/168.28 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 168.17/168.28 => 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 ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Sup__empty,axiom,
% 168.17/168.28 ! [T_b] :
% 168.17/168.28 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 168.17/168.28 => 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) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Sup__le__iff,axiom,
% 168.17/168.28 ! [V_b_2,V_A_2,T_b] :
% 168.17/168.28 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)),V_b_2))
% 168.17/168.28 <=> ! [B_x] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_less__Sup__iff,axiom,
% 168.17/168.28 ! [V_S_2,V_a_2,T_b] :
% 168.17/168.28 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 168.17/168.28 & class_Orderings_Olinorder(T_b) )
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_S_2)))
% 168.17/168.28 <=> ? [B_x] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 168.17/168.28 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),B_x)) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Union__empty,axiom,
% 168.17/168.28 ! [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)) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Union__upper,axiom,
% 168.17/168.28 ! [V_A_2,V_B_2,T_b] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 168.17/168.28 => 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))) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Un__eq__Union,axiom,
% 168.17/168.28 ! [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))))) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Union__insert,axiom,
% 168.17/168.28 ! [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)) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Union__Un__distrib,axiom,
% 168.17/168.28 ! [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)) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Sup__upper,axiom,
% 168.17/168.28 ! [V_A_2,V_x_2,T_b] :
% 168.17/168.28 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.28 => 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))) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_setprod__Un,axiom,
% 168.17/168.28 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 168.17/168.28 ( class_Fields_Ofield(T_c)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.28 => ( ! [B_x] :
% 168.17/168.28 ( 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)))
% 168.17/168.28 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c) )
% 168.17/168.28 => 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))) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_finite__Union,axiom,
% 168.17/168.28 ! [V_A_2,T_b] :
% 168.17/168.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2))
% 168.17/168.28 => ( ! [B_M] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_M),V_A_2))
% 168.17/168.28 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_M)) )
% 168.17/168.28 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_field__le__mult__one__interval,axiom,
% 168.17/168.28 ! [V_y,V_x,T_a] :
% 168.17/168.28 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 168.17/168.28 => ( ! [B_z] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a)))
% 168.17/168.28 => 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)) ) )
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_setprod__pos__nat,axiom,
% 168.17/168.28 ! [V_f_2,V_S_2,T_b] :
% 168.17/168.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 168.17/168.28 => ( ! [B_x] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 168.17/168.28 => 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))) )
% 168.17/168.28 => 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))) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom,
% 168.17/168.28 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_c,T_b] :
% 168.17/168.28 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 168.17/168.28 => ( 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))
% 168.17/168.28 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.28 => ~ ! [B_y] :
% 168.17/168.28 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y)
% 168.17/168.28 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom,
% 168.17/168.28 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 168.17/168.28 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => 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)) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom,
% 168.17/168.28 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 168.17/168.28 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => 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) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom,
% 168.17/168.28 ! [V_z_2,V_x_2,V_f_2,T_c,T_b] :
% 168.17/168.28 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 168.17/168.28 => 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) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_fun__left__comm__idem__insert,axiom,
% 168.17/168.28 ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_fun__left__comm__idem,axiom,
% 168.17/168.28 ! [T_b] :
% 168.17/168.28 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 168.17/168.28 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_fun__left__comm__idem__sup,axiom,
% 168.17/168.28 ! [T_b] :
% 168.17/168.28 ( class_Lattices_Osemilattice__sup(T_b)
% 168.17/168.28 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_fun__left__comm__idem__inf,axiom,
% 168.17/168.28 ! [T_b] :
% 168.17/168.28 ( class_Lattices_Osemilattice__inf(T_b)
% 168.17/168.28 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_insert__partition,axiom,
% 168.17/168.28 ! [V_F_2,V_x_2,T_b] :
% 168.17/168.28 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2))
% 168.17/168.28 => ( ! [B_x] :
% 168.17/168.28 ( 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)))
% 168.17/168.28 => ! [B_xa] :
% 168.17/168.28 ( 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)))
% 168.17/168.28 => ( B_x != B_xa
% 168.17/168.28 => 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)) ) ) )
% 168.17/168.28 => 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)) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_setsum__SucD,axiom,
% 168.17/168.28 ! [V_n_2,V_A_2,V_f_2,T_b] :
% 168.17/168.28 ( 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)
% 168.17/168.28 => ? [B_x] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.17/168.28 & 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))) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_card__partition,axiom,
% 168.17/168.28 ! [V_k_2,V_C_2,T_b] :
% 168.17/168.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_C_2))
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
% 168.17/168.28 => ( ! [B_c] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c),V_C_2))
% 168.17/168.28 => hAPP(c_Finite__Set_Ocard(T_b),B_c) = V_k_2 )
% 168.17/168.28 => ( ! [B_c1] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c1),V_C_2))
% 168.17/168.28 => ! [B_c2] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c2),V_C_2))
% 168.17/168.28 => ( B_c1 != B_c2
% 168.17/168.28 => 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)) ) ) )
% 168.17/168.28 => 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)) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_fold__image__1,axiom,
% 168.17/168.28 ! [V_f_2,V_S_2,T_b,T_c] :
% 168.17/168.28 ( class_Groups_Ocomm__monoid__mult(T_c)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 168.17/168.28 => ( ! [B_x] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 168.17/168.28 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 168.17/168.28 => 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) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_card_Oneutral,axiom,
% 168.17/168.28 ! [V_A_2,T_b] :
% 168.17/168.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.17/168.28 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 168.17/168.28 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_fold__image__cong,axiom,
% 168.17/168.28 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 168.17/168.28 ( class_Groups_Oab__semigroup__mult(T_c)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => ( ! [B_x] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.17/168.28 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) )
% 168.17/168.28 => 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) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_inf__le__fold__inf,axiom,
% 168.17/168.28 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 168.17/168.28 ( class_Lattices_Osemilattice__inf(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => ( ! [B_x] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_c_2),V_A_2))) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_fold__sup__le__sup,axiom,
% 168.17/168.28 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 168.17/168.28 ( class_Lattices_Osemilattice__sup(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => ( ! [B_x] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_c_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_b_2),V_c_2))) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_expand__Suc,axiom,
% 168.17/168.28 ! [V_v] :
% 168.17/168.28 ( 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)))
% 168.17/168.28 => 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))) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_UnionE,axiom,
% 168.17/168.28 ! [V_C_2,V_A_2,T_b] :
% 168.17/168.28 ( 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)))
% 168.17/168.28 => ~ ! [B_X] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X))
% 168.17/168.28 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_setprod__pos,axiom,
% 168.17/168.28 ! [V_f_2,V_A_2,T_b,T_c] :
% 168.17/168.28 ( class_Rings_Olinordered__semidom(T_c)
% 168.17/168.28 => ( ! [B_x] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2))) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_setprod__nonneg,axiom,
% 168.17/168.28 ! [V_f_2,V_A_2,T_b,T_c] :
% 168.17/168.28 ( class_Rings_Olinordered__semidom(T_c)
% 168.17/168.28 => ( ! [B_x] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2))) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_finite__induct,axiom,
% 168.17/168.28 ! [V_P_2,V_F_2,T_b] :
% 168.17/168.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 168.17/168.28 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 168.17/168.28 => ( ! [B_x,B_F] :
% 168.17/168.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F))
% 168.17/168.28 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_F))
% 168.17/168.28 => ( hBOOL(hAPP(V_P_2,B_F))
% 168.17/168.28 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_F))) ) ) )
% 168.17/168.28 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_fold1__antimono,axiom,
% 168.17/168.28 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.28 => 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))) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__number__of,axiom,
% 168.17/168.28 ! [V_v,V_u,T_b] :
% 168.17/168.28 ( ( class_Int_Onumber(T_b)
% 168.17/168.28 & class_Orderings_Oord(T_b) )
% 168.17/168.28 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)))
% 168.17/168.28 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u) )
% 168.17/168.28 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)))
% 168.17/168.28 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_number__of__reorient,axiom,
% 168.17/168.28 ! [V_x_2,V_w_2,T_b] :
% 168.17/168.28 ( class_Int_Onumber(T_b)
% 168.17/168.28 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = V_x_2
% 168.17/168.28 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_eq__number__of,axiom,
% 168.17/168.28 ! [V_y_2,V_x_2,T_b] :
% 168.17/168.28 ( ( class_Int_Onumber__ring(T_b)
% 168.17/168.28 & class_Int_Oring__char__0(T_b) )
% 168.17/168.28 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 168.17/168.28 <=> V_x_2 = V_y_2 ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_Oinf_Oidem,axiom,
% 168.17/168.28 ! [V_a,T_a] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_a)
% 168.17/168.28 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_Oinf_Ocommute,axiom,
% 168.17/168.28 ! [V_b,V_a,T_a] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_a)
% 168.17/168.28 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_a) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_Oinf__commute,axiom,
% 168.17/168.28 ! [V_y,V_x,T_a] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_a)
% 168.17/168.28 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_x) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_Oinf_Oleft__idem,axiom,
% 168.17/168.28 ! [V_b,V_a,T_a] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_a)
% 168.17/168.28 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_Oinf__left__idem,axiom,
% 168.17/168.28 ! [V_y,V_x,T_a] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_a)
% 168.17/168.28 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_Oinf_Oleft__commute,axiom,
% 168.17/168.28 ! [V_c,V_a,V_b,T_a] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_a)
% 168.17/168.28 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_c)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_c)) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_Oinf__left__commute,axiom,
% 168.17/168.28 ! [V_z,V_y,V_x,T_a] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_a)
% 168.17/168.28 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z)) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_Oinf_Oassoc,axiom,
% 168.17/168.28 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_a)
% 168.17/168.28 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_c)) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_Oinf__assoc,axiom,
% 168.17/168.28 ! [V_z,V_y,V_x,T_a] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_a)
% 168.17/168.28 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Min_Oidem,axiom,
% 168.17/168.28 ! [V_x,T_a] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_a)
% 168.17/168.28 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__le__iff__disj,axiom,
% 168.17/168.28 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)),V_z_2))
% 168.17/168.28 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 168.17/168.28 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_Ole__infE,axiom,
% 168.17/168.28 ! [V_b,V_a,V_x,T_a] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_a)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)))
% 168.17/168.28 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 168.17/168.28 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_Oinf__mono,axiom,
% 168.17/168.28 ! [V_d,V_b,V_c,V_a,T_a] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_a)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_c),V_d))) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_Oinf__greatest,axiom,
% 168.17/168.28 ! [V_z,V_y,V_x,T_a] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_a)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z))) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_Ole__infI,axiom,
% 168.17/168.28 ! [V_b,V_a,V_x,T_a] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_a)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b))) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_Oinf__absorb2,axiom,
% 168.17/168.28 ! [V_x,V_y,T_a] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_a)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 168.17/168.28 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_Oinf__absorb1,axiom,
% 168.17/168.28 ! [V_y,V_x,T_a] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_a)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 168.17/168.28 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_Ole__infI2,axiom,
% 168.17/168.28 ! [V_a,V_x,V_b,T_a] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_a)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_Ole__infI1,axiom,
% 168.17/168.28 ! [V_b,V_x,V_a,T_a] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_a)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_Ole__inf__iff,axiom,
% 168.17/168.28 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_y_2),V_z_2)))
% 168.17/168.28 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 168.17/168.28 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_Ole__iff__inf,axiom,
% 168.17/168.28 ! [V_y_2,V_x_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 168.17/168.28 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2) = V_x_2 ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_Oinf__le2,axiom,
% 168.17/168.28 ! [V_y,V_x,T_a] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_a)
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_y)) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_Oinf__le1,axiom,
% 168.17/168.28 ! [V_y,V_x,T_a] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_a)
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_x)) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_Oless__infI1,axiom,
% 168.17/168.28 ! [V_b,V_x,V_a,T_a] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_a)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_Oless__infI2,axiom,
% 168.17/168.28 ! [V_a,V_x,V_b,T_a] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_a)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__less__iff__conj,axiom,
% 168.17/168.28 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)))
% 168.17/168.28 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
% 168.17/168.28 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__less__iff__disj,axiom,
% 168.17/168.28 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)),V_z_2))
% 168.17/168.28 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
% 168.17/168.28 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_le__number__of,axiom,
% 168.17/168.28 ! [V_y_2,V_x_2,T_b] :
% 168.17/168.28 ( ( class_Int_Onumber__ring(T_b)
% 168.17/168.28 & class_Rings_Olinordered__idom(T_b) )
% 168.17/168.28 => ( 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)))
% 168.17/168.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_less__number__of,axiom,
% 168.17/168.28 ! [V_y_2,V_x_2,T_b] :
% 168.17/168.28 ( ( class_Int_Onumber__ring(T_b)
% 168.17/168.28 & class_Rings_Olinordered__idom(T_b) )
% 168.17/168.28 => ( 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)))
% 168.17/168.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__add__distrib__left,axiom,
% 168.17/168.28 ! [V_z,V_y,V_x,T_a] :
% 168.17/168.28 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 168.17/168.28 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__diff__distrib__left,axiom,
% 168.17/168.28 ! [V_z,V_y,V_x,T_a] :
% 168.17/168.28 ( class_Groups_Oordered__ab__group__add(T_a)
% 168.17/168.28 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z)) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_number__of__add,axiom,
% 168.17/168.28 ! [V_w,V_v,T_a] :
% 168.17/168.28 ( class_Int_Onumber__ring(T_a)
% 168.17/168.28 => 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)) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_add__number__of__eq,axiom,
% 168.17/168.28 ! [V_w,V_v,T_a] :
% 168.17/168.28 ( class_Int_Onumber__ring(T_a)
% 168.17/168.28 => 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)) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_add__number__of__left,axiom,
% 168.17/168.28 ! [V_z,V_w,V_v,T_a] :
% 168.17/168.28 ( class_Int_Onumber__ring(T_a)
% 168.17/168.28 => 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) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_number__of__mult,axiom,
% 168.17/168.28 ! [V_w,V_v,T_a] :
% 168.17/168.28 ( class_Int_Onumber__ring(T_a)
% 168.17/168.28 => 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)) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_arith__simps_I32_J,axiom,
% 168.17/168.28 ! [V_w,V_v,T_a] :
% 168.17/168.28 ( class_Int_Onumber__ring(T_a)
% 168.17/168.28 => 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)) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_mult__number__of__left,axiom,
% 168.17/168.28 ! [V_z,V_w,V_v,T_a] :
% 168.17/168.28 ( class_Int_Onumber__ring(T_a)
% 168.17/168.28 => 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) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_number__of__diff,axiom,
% 168.17/168.28 ! [V_w,V_v,T_a] :
% 168.17/168.28 ( class_Int_Onumber__ring(T_a)
% 168.17/168.28 => 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)) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_inf__min,axiom,
% 168.17/168.28 ! [T_b] :
% 168.17/168.28 ( ( class_Lattices_Osemilattice__inf(T_b)
% 168.17/168.28 & class_Orderings_Olinorder(T_b) )
% 168.17/168.28 => c_Lattices_Osemilattice__inf__class_Oinf(T_b) = c_Orderings_Oord__class_Omin(T_b) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__0R,axiom,
% 168.17/168.28 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__0L,axiom,
% 168.17/168.28 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__Suc__Suc,axiom,
% 168.17/168.28 ! [V_n,V_m] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m),V_n)) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__diff,axiom,
% 168.17/168.28 ! [V_n,V_i,V_m] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_i)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_i)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m),V_n)),V_i) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom,
% 168.17/168.28 ! [T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_le__number__of__eq__not__less,axiom,
% 168.17/168.28 ! [V_w_2,V_v_2,T_b] :
% 168.17/168.28 ( ( class_Int_Onumber(T_b)
% 168.17/168.28 & class_Orderings_Olinorder(T_b) )
% 168.17/168.28 => ( 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)))
% 168.17/168.28 <=> ~ 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))) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_right__distrib__number__of,axiom,
% 168.17/168.28 ! [V_c,V_b,V_v,T_b] :
% 168.17/168.28 ( ( class_Int_Onumber(T_b)
% 168.17/168.28 & class_Rings_Osemiring(T_b) )
% 168.17/168.28 => 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)) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_left__distrib__number__of,axiom,
% 168.17/168.28 ! [V_v,V_b,V_a,T_b] :
% 168.17/168.28 ( ( class_Int_Onumber(T_b)
% 168.17/168.28 & class_Rings_Osemiring(T_b) )
% 168.17/168.28 => 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))) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_add__number__of__diff1,axiom,
% 168.17/168.28 ! [V_c,V_w,V_v,T_a] :
% 168.17/168.28 ( class_Int_Onumber__ring(T_a)
% 168.17/168.28 => 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) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_right__diff__distrib__number__of,axiom,
% 168.17/168.28 ! [V_c,V_b,V_v,T_b] :
% 168.17/168.28 ( ( class_Int_Onumber(T_b)
% 168.17/168.28 & class_Rings_Oring(T_b) )
% 168.17/168.28 => 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)) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_left__diff__distrib__number__of,axiom,
% 168.17/168.28 ! [V_v,V_b,V_a,T_b] :
% 168.17/168.28 ( ( class_Int_Onumber(T_b)
% 168.17/168.28 & class_Rings_Oring(T_b) )
% 168.17/168.28 => 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))) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Ints__number__of,axiom,
% 168.17/168.28 ! [V_w_2,T_b] :
% 168.17/168.28 ( class_Int_Onumber__ring(T_b)
% 168.17/168.28 => 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))) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_divide__eq__eq__number__of1,axiom,
% 168.17/168.28 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 168.17/168.28 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 168.17/168.28 & class_Int_Onumber(T_b) )
% 168.17/168.28 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) = V_a_2
% 168.17/168.28 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
% 168.17/168.28 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) )
% 168.17/168.28 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
% 168.17/168.28 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_divide__eq__eq__number__of,axiom,
% 168.17/168.28 ! [V_w_2,V_c_2,V_b_2,T_b] :
% 168.17/168.28 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 168.17/168.28 & class_Int_Onumber(T_b) )
% 168.17/168.28 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)
% 168.17/168.28 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 168.17/168.28 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2) )
% 168.17/168.28 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 168.17/168.28 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_eq__divide__eq__number__of,axiom,
% 168.17/168.28 ! [V_c_2,V_b_2,V_w_2,T_b] :
% 168.17/168.28 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 168.17/168.28 & class_Int_Onumber(T_b) )
% 168.17/168.28 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
% 168.17/168.28 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 168.17/168.28 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2) = V_b_2 )
% 168.17/168.28 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 168.17/168.28 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_eq__divide__eq__number__of1,axiom,
% 168.17/168.28 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 168.17/168.28 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 168.17/168.28 & class_Int_Onumber(T_b) )
% 168.17/168.28 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))
% 168.17/168.28 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
% 168.17/168.28 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) = V_b_2 )
% 168.17/168.28 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
% 168.17/168.28 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_Ofold__inf__insert,axiom,
% 168.17/168.28 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),V_A_2)) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_divide__less__eq__number__of1,axiom,
% 168.17/168.28 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 168.17/168.28 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 168.17/168.28 & class_Int_Onumber(T_b) )
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2))
% 168.17/168.28 <=> ( ( 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)))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) )
% 168.17/168.28 & ( ~ 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)))
% 168.17/168.28 => ( ( 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)))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) )
% 168.17/168.28 & ( ~ 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)))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_divide__less__eq__number__of,axiom,
% 168.17/168.28 ! [V_w_2,V_c_2,V_b_2,T_b] :
% 168.17/168.28 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 168.17/168.28 & class_Int_Onumber(T_b) )
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 168.17/168.28 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) )
% 168.17/168.28 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 168.17/168.28 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) )
% 168.17/168.28 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 168.17/168.28 => 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))) ) ) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_less__divide__eq__number__of,axiom,
% 168.17/168.28 ! [V_c_2,V_b_2,V_w_2,T_b] :
% 168.17/168.28 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 168.17/168.28 & class_Int_Onumber(T_b) )
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
% 168.17/168.28 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) )
% 168.17/168.28 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 168.17/168.28 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) )
% 168.17/168.28 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 168.17/168.28 => 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))) ) ) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_less__divide__eq__number__of1,axiom,
% 168.17/168.28 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 168.17/168.28 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 168.17/168.28 & class_Int_Onumber(T_b) )
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
% 168.17/168.28 <=> ( ( 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)))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) )
% 168.17/168.28 & ( ~ 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)))
% 168.17/168.28 => ( ( 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)))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) )
% 168.17/168.28 & ( ~ 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)))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_Ofold__inf__le__inf,axiom,
% 168.17/168.28 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),V_b_2))) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_Ofold1__belowI,axiom,
% 168.17/168.28 ! [V_a_2,V_A_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.17/168.28 => 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)) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_fold1__below__iff,axiom,
% 168.17/168.28 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.28 => ( 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))
% 168.17/168.28 <=> ? [B_x] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.17/168.28 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_x_2)) ) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_Obelow__fold1__iff,axiom,
% 168.17/168.28 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.28 => ( 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)))
% 168.17/168.28 <=> ! [B_x] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_strict__below__fold1__iff,axiom,
% 168.17/168.28 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.28 => ( 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)))
% 168.17/168.28 <=> ! [B_x] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_fold1__strict__below__iff,axiom,
% 168.17/168.28 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.28 => ( 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))
% 168.17/168.28 <=> ? [B_x] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.17/168.28 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_x_2)) ) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_divide__le__eq__number__of1,axiom,
% 168.17/168.28 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 168.17/168.28 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 168.17/168.28 & class_Int_Onumber(T_b) )
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2))
% 168.17/168.28 <=> ( ( 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)))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) )
% 168.17/168.28 & ( ~ 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)))
% 168.17/168.28 => ( ( 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)))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) )
% 168.17/168.28 & ( ~ 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)))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_divide__le__eq__number__of,axiom,
% 168.17/168.28 ! [V_w_2,V_c_2,V_b_2,T_b] :
% 168.17/168.28 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 168.17/168.28 & class_Int_Onumber(T_b) )
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 168.17/168.28 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) )
% 168.17/168.28 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 168.17/168.28 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) )
% 168.17/168.28 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 168.17/168.28 => 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))) ) ) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_le__divide__eq__number__of,axiom,
% 168.17/168.28 ! [V_c_2,V_b_2,V_w_2,T_b] :
% 168.17/168.28 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 168.17/168.28 & class_Int_Onumber(T_b) )
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
% 168.17/168.28 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) )
% 168.17/168.28 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 168.17/168.28 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) )
% 168.17/168.28 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 168.17/168.28 => 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))) ) ) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_le__divide__eq__number__of1,axiom,
% 168.17/168.28 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 168.17/168.28 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 168.17/168.28 & class_Int_Onumber(T_b) )
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
% 168.17/168.28 <=> ( ( 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)))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) )
% 168.17/168.28 & ( ~ 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)))
% 168.17/168.28 => ( ( 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)))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) )
% 168.17/168.28 & ( ~ 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)))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__ord__min,axiom,
% 168.17/168.28 ! [T_b] :
% 168.17/168.28 ( class_Orderings_Oord(T_b)
% 168.17/168.28 => c_Orderings_Oord__class_Omin(T_b) = c_Orderings_Oord_Omin(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Min_Oremove,axiom,
% 168.17/168.28 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.28 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 168.17/168.28 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 )
% 168.17/168.28 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 168.17/168.28 => 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)))))) ) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_OInf__fin_Oremove,axiom,
% 168.17/168.28 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.28 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 168.17/168.28 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = V_x_2 )
% 168.17/168.28 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 168.17/168.28 => 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)))))) ) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Min_Oeq__fold_H,axiom,
% 168.17/168.28 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.28 => 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) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Min_Ounion__inter,axiom,
% 168.17/168.28 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.28 => ( 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))
% 168.17/168.28 => 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)) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Min_Ounion__disjoint,axiom,
% 168.17/168.28 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.28 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.28 => ( 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))
% 168.17/168.28 => 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)) ) ) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Min_Oinsert__remove,axiom,
% 168.17/168.28 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 168.17/168.28 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 168.17/168.28 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 168.17/168.28 => 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)))))) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_inf__nat__def,axiom,
% 168.17/168.28 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_plus__numeral__code_I9_J,axiom,
% 168.17/168.28 ! [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)) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_less__number__of__int__code,axiom,
% 168.17/168.28 ! [V_l_2,V_k_2] :
% 168.17/168.28 ( 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)))
% 168.17/168.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_less__eq__number__of__int__code,axiom,
% 168.17/168.28 ! [V_l_2,V_k_2] :
% 168.17/168.28 ( 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)))
% 168.17/168.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_times__numeral__code_I5_J,axiom,
% 168.17/168.28 ! [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)) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zmult__assoc,axiom,
% 168.17/168.28 ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_z3)) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zmult__commute,axiom,
% 168.17/168.28 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zdiff__zmult__distrib2,axiom,
% 168.17/168.28 ! [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)) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zdiff__zmult__distrib,axiom,
% 168.17/168.28 ! [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)) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zle__refl,axiom,
% 168.17/168.28 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zle__linear,axiom,
% 168.17/168.28 ! [V_w,V_z] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 168.17/168.28 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zle__trans,axiom,
% 168.17/168.28 ! [V_k,V_j,V_i] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zle__antisym,axiom,
% 168.17/168.28 ! [V_w,V_z] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z))
% 168.17/168.28 => V_z = V_w ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zless__linear,axiom,
% 168.17/168.28 ! [V_y,V_x] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y))
% 168.17/168.28 | V_x = V_y
% 168.17/168.28 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zless__le,axiom,
% 168.17/168.28 ! [V_w_2,V_z_2] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2))
% 168.17/168.28 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2))
% 168.17/168.28 & V_z_2 != V_w_2 ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zadd__assoc,axiom,
% 168.17/168.28 ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z2),V_z3)) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zadd__left__commute,axiom,
% 168.17/168.28 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_y),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_z)) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zadd__commute,axiom,
% 168.17/168.28 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),V_z) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zadd__left__mono,axiom,
% 168.17/168.28 ! [V_k,V_j,V_i] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 168.17/168.28 => 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))) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zmult__1,axiom,
% 168.17/168.28 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zmult__1__right,axiom,
% 168.17/168.28 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zadd__zmult__distrib2,axiom,
% 168.17/168.28 ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zadd__zmult__distrib,axiom,
% 168.17/168.28 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z1),V_z2)),V_w) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zless__add1__eq,axiom,
% 168.17/168.28 ! [V_z_2,V_w_2] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
% 168.17/168.28 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 168.17/168.28 | V_w_2 = V_z_2 ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zadd__strict__right__mono,axiom,
% 168.17/168.28 ! [V_k,V_j,V_i] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_j),V_k))) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zle__add1__eq__le,axiom,
% 168.17/168.28 ! [V_z_2,V_w_2] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
% 168.17/168.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zle__diff1__eq,axiom,
% 168.17/168.28 ! [V_z_2,V_w_2] :
% 168.17/168.28 ( 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))))
% 168.17/168.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_add1__zle__eq,axiom,
% 168.17/168.28 ! [V_z_2,V_w_2] :
% 168.17/168.28 ( 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))
% 168.17/168.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zless__imp__add1__zle,axiom,
% 168.17/168.28 ! [V_z,V_w] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z))
% 168.17/168.28 => 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)) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zadd__zless__mono,axiom,
% 168.17/168.28 ! [V_z,V_z_H,V_w,V_w_H] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 168.17/168.28 => 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))) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_le__imp__0__less,axiom,
% 168.17/168.28 ! [V_z] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 168.17/168.28 => 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))) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_int__one__le__iff__zero__less,axiom,
% 168.17/168.28 ! [V_z_2] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))
% 168.17/168.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_pos__zmult__eq__1__iff,axiom,
% 168.17/168.28 ! [V_n_2,V_m_2] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2))
% 168.17/168.28 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 168.17/168.28 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 168.17/168.28 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_odd__less__0,axiom,
% 168.17/168.28 ! [V_z_2] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)),V_z_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_int__0__less__1,axiom,
% 168.17/168.28 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_odd__nonzero,axiom,
% 168.17/168.28 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)),V_z) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zadd__0,axiom,
% 168.17/168.28 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zadd__0__right,axiom,
% 168.17/168.28 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ).
% 168.17/168.28
% 168.17/168.28 fof(fact_less__bin__lemma,axiom,
% 168.17/168.28 ! [V_l_2,V_k_2] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
% 168.17/168.28 <=> 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))) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zmult__zless__mono2,axiom,
% 168.17/168.28 ! [V_k,V_j,V_i] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j))) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Min_Osingleton,axiom,
% 168.17/168.28 ! [V_x_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => 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 ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_OInf__fin_Oin__idem,axiom,
% 168.17/168.28 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.28 => 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) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Min__le,axiom,
% 168.17/168.28 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.28 => 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)) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_OInf__fin_Osingleton,axiom,
% 168.17/168.28 ! [V_x_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => 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 ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Min__in,axiom,
% 168.17/168.28 ! [V_A_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Min_Oin__idem,axiom,
% 168.17/168.28 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.28 => 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) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_OInf__fin_OF__eq,axiom,
% 168.17/168.28 ! [V_A_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => 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) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Min_OF__eq,axiom,
% 168.17/168.28 ! [V_A_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => 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) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom,
% 168.17/168.28 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.28 => 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)) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_OInf__fin_Osubset__idem,axiom,
% 168.17/168.28 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 168.17/168.28 => 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) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_OInf__fin_Ounion__idem,axiom,
% 168.17/168.28 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.28 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.28 => 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)) ) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Min__antimono,axiom,
% 168.17/168.28 ! [V_N_2,V_M_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
% 168.17/168.28 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 168.17/168.28 => 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))) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom,
% 168.17/168.28 ! [V_a_2,V_A_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => 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) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Min__insert,axiom,
% 168.17/168.28 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.28 => 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)) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Min_Osubset__idem,axiom,
% 168.17/168.28 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 168.17/168.28 => 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) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Min__Un,axiom,
% 168.17/168.28 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.28 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.28 => 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)) ) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Min_Oeq__fold__idem_H,axiom,
% 168.17/168.28 ! [V_a_2,V_A_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => 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) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_OInf__fin_Oinsert,axiom,
% 168.17/168.28 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.28 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.28 => 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)) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom,
% 168.17/168.28 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 168.17/168.28 => 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 )
% 168.17/168.28 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 168.17/168.28 => 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)))))) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom,
% 168.17/168.28 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.28 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.28 => ( 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))
% 168.17/168.28 => 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)) ) ) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_OInf__fin_Ounion__inter,axiom,
% 168.17/168.28 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.28 => ( 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))
% 168.17/168.28 => 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)) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom,
% 168.17/168.28 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.28 => 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) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Min_Oinsert,axiom,
% 168.17/168.28 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.28 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.28 => 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)) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zdiv__mono2__neg__lemma,axiom,
% 168.17/168.28 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 168.17/168.28 ( 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)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_unique__quotient__lemma__neg,axiom,
% 168.17/168.28 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 168.17/168.28 ( 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)))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zdiv__mono2__lemma,axiom,
% 168.17/168.28 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 168.17/168.28 ( 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)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_unique__quotient__lemma,axiom,
% 168.17/168.28 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 168.17/168.28 ( 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)))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_q__neg__lemma,axiom,
% 168.17/168.28 ! [V_r_H,V_q_H,V_b_H] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_q__pos__lemma,axiom,
% 168.17/168.28 ! [V_r_H,V_q_H,V_b_H] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H)))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_self__quotient__aux1,axiom,
% 168.17/168.28 ! [V_q,V_r,V_a] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 168.17/168.28 => ( 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))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_number__of__is__id,axiom,
% 168.17/168.28 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ).
% 168.17/168.28
% 168.17/168.28 fof(fact_int__0__neq__1,axiom,
% 168.17/168.28 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_self__quotient__aux2,axiom,
% 168.17/168.28 ! [V_q,V_r,V_a] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 168.17/168.28 => ( 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))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 168.17/168.28 ! [V_y,V_x] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y))) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 168.17/168.28 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))) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 168.17/168.28 ! [V_y,V_x] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y))) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_min__max_OInf__fin_Oclosed,axiom,
% 168.17/168.28 ! [V_A_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.28 => ( ! [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))))))
% 168.17/168.28 => 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)) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Min_Oclosed,axiom,
% 168.17/168.28 ! [V_A_2,T_b] :
% 168.17/168.28 ( class_Orderings_Olinorder(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.28 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.28 => ( ! [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))))))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 168.17/168.28 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))) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_of__nat__number__of__lemma,axiom,
% 168.17/168.28 ! [V_v,T_a] :
% 168.17/168.28 ( class_Int_Onumber__ring(T_a)
% 168.17/168.28 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 168.17/168.28 => 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) )
% 168.17/168.28 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 168.17/168.28 => 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) ) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_of__nat__eq__iff,axiom,
% 168.17/168.28 ! [V_n_2,V_m_2,T_b] :
% 168.17/168.28 ( class_Nat_Osemiring__char__0(T_b)
% 168.17/168.28 => ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)
% 168.17/168.28 <=> V_m_2 = V_n_2 ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_transfer__int__nat__numerals_I1_J,axiom,
% 168.17/168.28 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
% 168.17/168.28 ! [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))) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom,
% 168.17/168.28 ! [V_P_2] :
% 168.17/168.28 ( ? [B_x] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 168.17/168.28 & hBOOL(hAPP(V_P_2,B_x)) )
% 168.17/168.28 <=> ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom,
% 168.17/168.28 ! [V_P_2] :
% 168.17/168.28 ( ! [B_x] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 168.17/168.28 => hBOOL(hAPP(V_P_2,B_x)) )
% 168.17/168.28 <=> ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_transfer__int__nat__relations_I2_J,axiom,
% 168.17/168.28 ! [V_y_2,V_x_2] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))
% 168.17/168.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_transfer__int__nat__relations_I3_J,axiom,
% 168.17/168.28 ! [V_y_2,V_x_2] :
% 168.17/168.28 ( 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)))
% 168.17/168.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
% 168.17/168.28 ! [V_y,V_x] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x),V_y)) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
% 168.17/168.28 ! [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)) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_transfer__int__nat__numerals_I2_J,axiom,
% 168.17/168.28 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)) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_int__eq__0__conv,axiom,
% 168.17/168.28 ! [V_n_2] :
% 168.17/168.28 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.28 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_int__0,axiom,
% 168.17/168.28 hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zero__zle__int,axiom,
% 168.17/168.28 ! [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))) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_int__less__0__conv,axiom,
% 168.17/168.28 ! [V_k] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zless__int,axiom,
% 168.17/168.28 ! [V_n_2,V_m_2] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)))
% 168.17/168.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zle__int,axiom,
% 168.17/168.28 ! [V_n_2,V_m_2] :
% 168.17/168.28 ( 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)))
% 168.17/168.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zadd__int,axiom,
% 168.17/168.28 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zadd__int__left,axiom,
% 168.17/168.28 ! [V_z,V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n))),V_z) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zle__iff__zadd,axiom,
% 168.17/168.28 ! [V_z_2,V_w_2] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))
% 168.17/168.28 <=> ? [B_n] : V_z_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_of__nat__0__le__iff,axiom,
% 168.17/168.28 ! [V_n,T_a] :
% 168.17/168.28 ( class_Rings_Olinordered__semidom(T_a)
% 168.17/168.28 => 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))) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zero__le__imp__of__nat,axiom,
% 168.17/168.28 ! [V_m,T_a] :
% 168.17/168.28 ( class_Rings_Olinordered__semidom(T_a)
% 168.17/168.28 => 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))) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_of__nat__less__0__iff,axiom,
% 168.17/168.28 ! [V_m,T_a] :
% 168.17/168.28 ( class_Rings_Olinordered__semidom(T_a)
% 168.17/168.28 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_int__mult,axiom,
% 168.17/168.28 ! [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)) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zmult__int,axiom,
% 168.17/168.28 ! [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)) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_of__nat__0,axiom,
% 168.17/168.28 ! [T_a] :
% 168.17/168.28 ( class_Rings_Osemiring__1(T_a)
% 168.17/168.28 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_of__nat__less__imp__less,axiom,
% 168.17/168.28 ! [V_n,V_m,T_a] :
% 168.17/168.28 ( class_Rings_Olinordered__semidom(T_a)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_less__imp__of__nat__less,axiom,
% 168.17/168.28 ! [V_n,V_m,T_a] :
% 168.17/168.28 ( class_Rings_Olinordered__semidom(T_a)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n))) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_of__nat__less__iff,axiom,
% 168.17/168.28 ! [V_n_2,V_m_2,T_b] :
% 168.17/168.28 ( class_Rings_Olinordered__semidom(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)))
% 168.17/168.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_int__1,axiom,
% 168.17/168.28 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) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_of__nat__le__iff,axiom,
% 168.17/168.28 ! [V_n_2,V_m_2,T_b] :
% 168.17/168.28 ( class_Rings_Olinordered__semidom(T_b)
% 168.17/168.28 => ( 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)))
% 168.17/168.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_of__nat__add,axiom,
% 168.17/168.28 ! [V_n,V_m,T_a] :
% 168.17/168.28 ( class_Rings_Osemiring__1(T_a)
% 168.17/168.28 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_of__nat__mult,axiom,
% 168.17/168.28 ! [V_n,V_m,T_a] :
% 168.17/168.28 ( class_Rings_Osemiring__1(T_a)
% 168.17/168.28 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_of__nat__1,axiom,
% 168.17/168.28 ! [T_a] :
% 168.17/168.28 ( class_Rings_Osemiring__1(T_a)
% 168.17/168.28 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_Ints__of__nat,axiom,
% 168.17/168.28 ! [V_n_2,T_b] :
% 168.17/168.28 ( class_Rings_Oring__1(T_b)
% 168.17/168.28 => 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))) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_int__le__0__conv,axiom,
% 168.17/168.28 ! [V_n_2] :
% 168.17/168.28 ( 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)))
% 168.17/168.28 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_int__Suc0__eq__1,axiom,
% 168.17/168.28 hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zless__iff__Suc__zadd,axiom,
% 168.17/168.28 ! [V_z_2,V_w_2] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 168.17/168.28 <=> ? [B_n] : V_z_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,B_n))) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_int__Suc,axiom,
% 168.17/168.28 ! [V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_m)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zdiff__int,axiom,
% 168.17/168.28 ! [V_m,V_n] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 168.17/168.28 => 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)) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_of__nat__Suc,axiom,
% 168.17/168.28 ! [V_m,T_a] :
% 168.17/168.28 ( class_Rings_Osemiring__1(T_a)
% 168.17/168.28 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Nat_OSuc,V_m)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_m)) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_of__nat__diff,axiom,
% 168.17/168.28 ! [V_m,V_n,T_a] :
% 168.17/168.28 ( class_Rings_Oring__1(T_a)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 168.17/168.28 => 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)) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zero__less__int__conv,axiom,
% 168.17/168.28 ! [V_n_2] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)))
% 168.17/168.28 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_zmult__zless__mono2__lemma,axiom,
% 168.17/168.28 ! [V_k,V_j,V_i] :
% 168.17/168.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 168.17/168.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_k)),V_j))) ) ) ).
% 168.17/168.28
% 168.17/168.28 fof(fact_of__nat__0__less__iff,axiom,
% 168.17/168.28 ! [V_n_2,T_b] :
% 168.17/168.28 ( class_Rings_Olinordered__semidom(T_b)
% 168.17/168.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_zdiff__int__split,axiom,
% 168.17/168.29 ! [V_y_2,V_x_2,V_P_2] :
% 168.17/168.29 ( hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2))))
% 168.17/168.29 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2))
% 168.17/168.29 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))) )
% 168.17/168.29 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 168.17/168.29 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_setsum__bounded,axiom,
% 168.17/168.29 ! [V_K_2,V_f_2,V_A_2,T_b,T_c] :
% 168.17/168.29 ( ( class_Groups_Oordered__ab__semigroup__add(T_c)
% 168.17/168.29 & class_Rings_Osemiring__1(T_c) )
% 168.17/168.29 => ( ! [B_i] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2))
% 168.17/168.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_i)),V_K_2)) )
% 168.17/168.29 => 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))) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_tsub__def,axiom,
% 168.17/168.29 ! [V_x,V_y] :
% 168.17/168.29 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 168.17/168.29 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) )
% 168.17/168.29 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 168.17/168.29 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_of__nat__number__of__eq,axiom,
% 168.17/168.29 ! [V_v,T_a] :
% 168.17/168.29 ( class_Int_Onumber__ring(T_a)
% 168.17/168.29 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 168.17/168.29 => 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) )
% 168.17/168.29 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 168.17/168.29 => 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) ) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_mult__nat__number__of,axiom,
% 168.17/168.29 ! [V_v_H,V_v] :
% 168.17/168.29 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 168.17/168.29 => 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) )
% 168.17/168.29 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 168.17/168.29 => 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)) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_nat__number__of__mult__left,axiom,
% 168.17/168.29 ! [V_k,V_v_H,V_v] :
% 168.17/168.29 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 168.17/168.29 => 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) )
% 168.17/168.29 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 168.17/168.29 => 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) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_min__max_Oinf__le__fold__inf,axiom,
% 168.17/168.29 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 168.17/168.29 ( class_Orderings_Olinorder(T_b)
% 168.17/168.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.29 => ( ! [B_x] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.17/168.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
% 168.17/168.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_c_2),V_A_2))) ) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_not__neg__int,axiom,
% 168.17/168.29 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_transfer__int__nat__relations_I1_J,axiom,
% 168.17/168.29 ! [V_y_2,V_x_2] :
% 168.17/168.29 ( 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)
% 168.17/168.29 <=> V_x_2 = V_y_2 ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_int__int__eq,axiom,
% 168.17/168.29 ! [V_n_2,V_m_2] :
% 168.17/168.29 ( 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)
% 168.17/168.29 <=> V_m_2 = V_n_2 ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_not__neg__number__of__Pls,axiom,
% 168.17/168.29 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_Pls__def,axiom,
% 168.17/168.29 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_rel__simps_I19_J,axiom,
% 168.17/168.29 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_rel__simps_I2_J,axiom,
% 168.17/168.29 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_add__Pls,axiom,
% 168.17/168.29 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ).
% 168.17/168.29
% 168.17/168.29 fof(fact_add__Pls__right,axiom,
% 168.17/168.29 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 168.17/168.29
% 168.17/168.29 fof(fact_mult__Pls,axiom,
% 168.17/168.29 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ).
% 168.17/168.29
% 168.17/168.29 fof(fact_diff__bin__simps_I1_J,axiom,
% 168.17/168.29 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 168.17/168.29
% 168.17/168.29 fof(fact_not__neg__0,axiom,
% 168.17/168.29 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_not__neg__1,axiom,
% 168.17/168.29 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_number__of__Pls,axiom,
% 168.17/168.29 ! [T_a] :
% 168.17/168.29 ( class_Int_Onumber__ring(T_a)
% 168.17/168.29 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_semiring__norm_I112_J,axiom,
% 168.17/168.29 ! [T_a] :
% 168.17/168.29 ( class_Int_Onumber__ring(T_a)
% 168.17/168.29 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_add__numeral__0__right,axiom,
% 168.17/168.29 ! [V_a,T_a] :
% 168.17/168.29 ( class_Int_Onumber__ring(T_a)
% 168.17/168.29 => 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 ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_add__numeral__0,axiom,
% 168.17/168.29 ! [V_a,T_a] :
% 168.17/168.29 ( class_Int_Onumber__ring(T_a)
% 168.17/168.29 => 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 ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_number__of2,axiom,
% 168.17/168.29 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))) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_bin__less__0__simps_I1_J,axiom,
% 168.17/168.29 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_semiring__norm_I113_J,axiom,
% 168.17/168.29 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_nat__number__of__Pls,axiom,
% 168.17/168.29 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_zero__is__num__zero,axiom,
% 168.17/168.29 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_not__neg__eq__ge__0,axiom,
% 168.17/168.29 ! [V_x_2] :
% 168.17/168.29 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_neg__def,axiom,
% 168.17/168.29 ! [V_Z_2] :
% 168.17/168.29 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
% 168.17/168.29 ! [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)) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_divide__Numeral0,axiom,
% 168.17/168.29 ! [V_x,T_a] :
% 168.17/168.29 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 168.17/168.29 & class_Int_Onumber__ring(T_a) )
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_eq__0__number__of,axiom,
% 168.17/168.29 ! [V_v_2] :
% 168.17/168.29 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_eq__number__of__0,axiom,
% 168.17/168.29 ! [V_v_2] :
% 168.17/168.29 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_less__nat__number__of,axiom,
% 168.17/168.29 ! [V_v_H_2,V_v_2] :
% 168.17/168.29 ( 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)))
% 168.17/168.29 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2))
% 168.17/168.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) )
% 168.17/168.29 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_le__nat__number__of,axiom,
% 168.17/168.29 ! [V_v_H_2,V_v_2] :
% 168.17/168.29 ( 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)))
% 168.17/168.29 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2))
% 168.17/168.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_neg__imp__number__of__eq__0,axiom,
% 168.17/168.29 ! [V_v] :
% 168.17/168.29 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 168.17/168.29 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_int__nat__number__of,axiom,
% 168.17/168.29 ! [V_v] :
% 168.17/168.29 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 168.17/168.29 => 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) )
% 168.17/168.29 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 168.17/168.29 => 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) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_le__special_I1_J,axiom,
% 168.17/168.29 ! [V_y_2,T_b] :
% 168.17/168.29 ( ( class_Int_Onumber__ring(T_b)
% 168.17/168.29 & class_Rings_Olinordered__idom(T_b) )
% 168.17/168.29 => ( 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)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_le__special_I3_J,axiom,
% 168.17/168.29 ! [V_x_2,T_b] :
% 168.17/168.29 ( ( class_Int_Onumber__ring(T_b)
% 168.17/168.29 & class_Rings_Olinordered__idom(T_b) )
% 168.17/168.29 => ( 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)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_less__special_I1_J,axiom,
% 168.17/168.29 ! [V_y_2,T_b] :
% 168.17/168.29 ( ( class_Int_Onumber__ring(T_b)
% 168.17/168.29 & class_Rings_Olinordered__idom(T_b) )
% 168.17/168.29 => ( 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)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_less__special_I3_J,axiom,
% 168.17/168.29 ! [V_x_2,T_b] :
% 168.17/168.29 ( ( class_Int_Onumber__ring(T_b)
% 168.17/168.29 & class_Rings_Olinordered__idom(T_b) )
% 168.17/168.29 => ( 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)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_less__0__number__of,axiom,
% 168.17/168.29 ! [V_v_2] :
% 168.17/168.29 ( 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)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_add__nat__number__of,axiom,
% 168.17/168.29 ! [V_v_H,V_v] :
% 168.17/168.29 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 168.17/168.29 => 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) )
% 168.17/168.29 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 168.17/168.29 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 168.17/168.29 => 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) )
% 168.17/168.29 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 168.17/168.29 => 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)) ) ) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_eq__nat__number__of,axiom,
% 168.17/168.29 ! [V_v_H_2,V_v_2] :
% 168.17/168.29 ( 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)
% 168.17/168.29 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 168.17/168.29 => 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))) )
% 168.17/168.29 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 168.17/168.29 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 168.17/168.29 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 168.17/168.29 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 168.17/168.29 => V_v_2 = V_v_H_2 ) ) ) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_nat__number__of__add__left,axiom,
% 168.17/168.29 ! [V_k,V_v_H,V_v] :
% 168.17/168.29 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 168.17/168.29 => 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) )
% 168.17/168.29 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 168.17/168.29 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 168.17/168.29 => 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) )
% 168.17/168.29 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 168.17/168.29 => 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) ) ) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
% 168.17/168.29 ! [V_y,V_x] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 168.17/168.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 168.17/168.29 => 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))) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_tsub__eq,axiom,
% 168.17/168.29 ! [V_x,V_y] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 168.17/168.29 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_Suc__nat__number__of__add,axiom,
% 168.17/168.29 ! [V_n,V_v] :
% 168.17/168.29 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 168.17/168.29 => 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) )
% 168.17/168.29 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 168.17/168.29 => 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) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_Suc__nat__number__of,axiom,
% 168.17/168.29 ! [V_v] :
% 168.17/168.29 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 168.17/168.29 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 168.17/168.29 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 168.17/168.29 => 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)) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_nat__number__of__add__1,axiom,
% 168.17/168.29 ! [V_v] :
% 168.17/168.29 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 168.17/168.29 => 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) )
% 168.17/168.29 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 168.17/168.29 => 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)) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_nat__1__add__number__of,axiom,
% 168.17/168.29 ! [V_v] :
% 168.17/168.29 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 168.17/168.29 => 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) )
% 168.17/168.29 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 168.17/168.29 => 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)) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_nat__number__of__diff__1,axiom,
% 168.17/168.29 ! [V_v] :
% 168.17/168.29 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 168.17/168.29 => 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) )
% 168.17/168.29 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 168.17/168.29 => 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)) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_Nats__number__of,axiom,
% 168.17/168.29 ! [V_w_2,T_b] :
% 168.17/168.29 ( class_Int_Onumber__ring(T_b)
% 168.17/168.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2))
% 168.17/168.29 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_Suc__diff__number__of,axiom,
% 168.17/168.29 ! [V_m,V_v] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v))
% 168.17/168.29 => 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))) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_succ__pred,axiom,
% 168.17/168.29 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ).
% 168.17/168.29
% 168.17/168.29 fof(fact_le__iff__pred__less,axiom,
% 168.17/168.29 ! [V_l_2,V_k_2] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_pred__def,axiom,
% 168.17/168.29 ! [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)) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_succ__def,axiom,
% 168.17/168.29 ! [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)) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_Nats__0,axiom,
% 168.17/168.29 ! [T_b] :
% 168.17/168.29 ( class_Rings_Osemiring__1(T_b)
% 168.17/168.29 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_Nats__add,axiom,
% 168.17/168.29 ! [V_b_2,V_a_2,T_b] :
% 168.17/168.29 ( class_Rings_Osemiring__1(T_b)
% 168.17/168.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 168.17/168.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 168.17/168.29 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_Nats__mult,axiom,
% 168.17/168.29 ! [V_b_2,V_a_2,T_b] :
% 168.17/168.29 ( class_Rings_Osemiring__1(T_b)
% 168.17/168.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 168.17/168.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 168.17/168.29 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_Nats__1,axiom,
% 168.17/168.29 ! [T_b] :
% 168.17/168.29 ( class_Rings_Osemiring__1(T_b)
% 168.17/168.29 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_of__nat__in__Nats,axiom,
% 168.17/168.29 ! [V_n_2,T_b] :
% 168.17/168.29 ( class_Rings_Osemiring__1(T_b)
% 168.17/168.29 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_number__of__succ,axiom,
% 168.17/168.29 ! [V_k,T_a] :
% 168.17/168.29 ( class_Int_Onumber__ring(T_a)
% 168.17/168.29 => 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)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_neg__number__of__pred__iff__0,axiom,
% 168.17/168.29 ! [V_v_2] :
% 168.17/168.29 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))))
% 168.17/168.29 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_decr__mult__lemma,axiom,
% 168.17/168.29 ! [V_k_2,V_P_2,V_d_2] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 168.17/168.29 => ( ! [B_x] :
% 168.17/168.29 ( hBOOL(hAPP(V_P_2,B_x))
% 168.17/168.29 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) )
% 168.17/168.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 168.17/168.29 => ! [B_x] :
% 168.17/168.29 ( hBOOL(hAPP(V_P_2,B_x))
% 168.17/168.29 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_incr__mult__lemma,axiom,
% 168.17/168.29 ! [V_k_2,V_P_2,V_d_2] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 168.17/168.29 => ( ! [B_x] :
% 168.17/168.29 ( hBOOL(hAPP(V_P_2,B_x))
% 168.17/168.29 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) )
% 168.17/168.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 168.17/168.29 => ! [B_x] :
% 168.17/168.29 ( hBOOL(hAPP(V_P_2,B_x))
% 168.17/168.29 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_zero__less__imp__eq__int,axiom,
% 168.17/168.29 ! [V_k] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 168.17/168.29 => ? [B_n] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 168.17/168.29 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_decr__lemma,axiom,
% 168.17/168.29 ! [V_z,V_x,V_d] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 168.17/168.29 => 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)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_incr__lemma,axiom,
% 168.17/168.29 ! [V_x,V_z,V_d] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 168.17/168.29 => 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)))) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_Min__eqI,axiom,
% 168.17/168.29 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.29 ( class_Orderings_Olinorder(T_b)
% 168.17/168.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.29 => ( ! [B_y] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 168.17/168.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_y)) )
% 168.17/168.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.29 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) ) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_Suc__diff__eq__diff__pred,axiom,
% 168.17/168.29 ! [V_m,V_n] :
% 168.17/168.29 ( 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))
% 168.17/168.29 => 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)))) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_rel__simps_I51_J,axiom,
% 168.17/168.29 ! [V_l_2,V_k_2] :
% 168.17/168.29 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2)
% 168.17/168.29 <=> V_k_2 = V_l_2 ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_abs__idempotent,axiom,
% 168.17/168.29 ! [V_a,T_a] :
% 168.17/168.29 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_abs__le__D1,axiom,
% 168.17/168.29 ! [V_b,V_a,T_a] :
% 168.17/168.29 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 168.17/168.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 168.17/168.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_abs__ge__self,axiom,
% 168.17/168.29 ! [V_a,T_a] :
% 168.17/168.29 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 168.17/168.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_abs__zero,axiom,
% 168.17/168.29 ! [T_a] :
% 168.17/168.29 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 168.17/168.29 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_abs__eq__0,axiom,
% 168.17/168.29 ! [V_a_2,T_b] :
% 168.17/168.29 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 168.17/168.29 => ( hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 168.17/168.29 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_abs__add__abs,axiom,
% 168.17/168.29 ! [V_b,V_a,T_a] :
% 168.17/168.29 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 168.17/168.29 => 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)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_abs__mult,axiom,
% 168.17/168.29 ! [V_b,V_a,T_a] :
% 168.17/168.29 ( class_Rings_Olinordered__idom(T_a)
% 168.17/168.29 => 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)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_abs__mult__self,axiom,
% 168.17/168.29 ! [V_a,T_a] :
% 168.17/168.29 ( class_Rings_Olinordered__idom(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_abs__minus__commute,axiom,
% 168.17/168.29 ! [V_b,V_a,T_a] :
% 168.17/168.29 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 168.17/168.29 => 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)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_abs__one,axiom,
% 168.17/168.29 ! [T_a] :
% 168.17/168.29 ( class_Rings_Olinordered__idom(T_a)
% 168.17/168.29 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_abs__of__nat,axiom,
% 168.17/168.29 ! [V_n,T_a] :
% 168.17/168.29 ( class_Rings_Olinordered__idom(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_abs__divide,axiom,
% 168.17/168.29 ! [V_b,V_a,T_a] :
% 168.17/168.29 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 168.17/168.29 => 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)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_abs__int__eq,axiom,
% 168.17/168.29 ! [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) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_less__eq__int__code_I16_J,axiom,
% 168.17/168.29 ! [V_k2_2,V_k1_2] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_rel__simps_I34_J,axiom,
% 168.17/168.29 ! [V_l_2,V_k_2] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_less__int__code_I16_J,axiom,
% 168.17/168.29 ! [V_k2_2,V_k1_2] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_rel__simps_I17_J,axiom,
% 168.17/168.29 ! [V_l_2,V_k_2] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_rel__simps_I39_J,axiom,
% 168.17/168.29 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_rel__simps_I46_J,axiom,
% 168.17/168.29 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ).
% 168.17/168.29
% 168.17/168.29 fof(fact_abs__ge__zero,axiom,
% 168.17/168.29 ! [V_a,T_a] :
% 168.17/168.29 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 168.17/168.29 => 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))) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_abs__le__zero__iff,axiom,
% 168.17/168.29 ! [V_a_2,T_b] :
% 168.17/168.29 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 168.17/168.29 => ( 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)))
% 168.17/168.29 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_abs__of__nonneg,axiom,
% 168.17/168.29 ! [V_a,T_a] :
% 168.17/168.29 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 168.17/168.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 168.17/168.29 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_abs__of__pos,axiom,
% 168.17/168.29 ! [V_a,T_a] :
% 168.17/168.29 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 168.17/168.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 168.17/168.29 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_zero__less__abs__iff,axiom,
% 168.17/168.29 ! [V_a_2,T_b] :
% 168.17/168.29 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 168.17/168.29 => ( 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)))
% 168.17/168.29 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_abs__not__less__zero,axiom,
% 168.17/168.29 ! [V_a,T_a] :
% 168.17/168.29 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 168.17/168.29 => ~ 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))) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_abs__triangle__ineq,axiom,
% 168.17/168.29 ! [V_b,V_a,T_a] :
% 168.17/168.29 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 168.17/168.29 => 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)))) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_abs__mult__less,axiom,
% 168.17/168.29 ! [V_d,V_b,V_c,V_a,T_a] :
% 168.17/168.29 ( class_Rings_Olinordered__idom(T_a)
% 168.17/168.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c))
% 168.17/168.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d))
% 168.17/168.29 => 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))) ) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_abs__triangle__ineq2__sym,axiom,
% 168.17/168.29 ! [V_b,V_a,T_a] :
% 168.17/168.29 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 168.17/168.29 => 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)))) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_abs__triangle__ineq2,axiom,
% 168.17/168.29 ! [V_b,V_a,T_a] :
% 168.17/168.29 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 168.17/168.29 => 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)))) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_abs__triangle__ineq3,axiom,
% 168.17/168.29 ! [V_b,V_a,T_a] :
% 168.17/168.29 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 168.17/168.29 => 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)))) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_nonzero__abs__divide,axiom,
% 168.17/168.29 ! [V_a,V_b,T_a] :
% 168.17/168.29 ( class_Fields_Olinordered__field(T_a)
% 168.17/168.29 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.29 => 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)) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_bin__less__0__simps_I4_J,axiom,
% 168.17/168.29 ! [V_w_2] :
% 168.17/168.29 ( 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)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_abs__zmult__eq__1,axiom,
% 168.17/168.29 ! [V_n,V_m] :
% 168.17/168.29 ( 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)
% 168.17/168.29 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_rel__simps_I22_J,axiom,
% 168.17/168.29 ! [V_k_2] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_rel__simps_I12_J,axiom,
% 168.17/168.29 ! [V_k_2] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_Bit1__def,axiom,
% 168.17/168.29 ! [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) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_neg__number__of__Bit1,axiom,
% 168.17/168.29 ! [V_w_2] :
% 168.17/168.29 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2))))
% 168.17/168.29 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_succ__Pls,axiom,
% 168.17/168.29 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_abs__mult__pos,axiom,
% 168.17/168.29 ! [V_y,V_x,T_a] :
% 168.17/168.29 ( class_Rings_Olinordered__idom(T_a)
% 168.17/168.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 168.17/168.29 => 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)) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_abs__eq__mult,axiom,
% 168.17/168.29 ! [V_b,V_a,T_a] :
% 168.17/168.29 ( class_Rings_Oordered__ring__abs(T_a)
% 168.17/168.29 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 168.17/168.29 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) )
% 168.17/168.29 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 168.17/168.29 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 168.17/168.29 => 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)) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_abs__diff__triangle__ineq,axiom,
% 168.17/168.29 ! [V_d,V_c,V_b,V_a,T_a] :
% 168.17/168.29 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 168.17/168.29 => 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))))) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_abs__triangle__ineq4,axiom,
% 168.17/168.29 ! [V_b,V_a,T_a] :
% 168.17/168.29 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 168.17/168.29 => 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)))) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_abs__div__pos,axiom,
% 168.17/168.29 ! [V_x,V_y,T_a] :
% 168.17/168.29 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 168.17/168.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 168.17/168.29 => 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)) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_number__of__Bit1,axiom,
% 168.17/168.29 ! [V_w,T_a] :
% 168.17/168.29 ( class_Int_Onumber__ring(T_a)
% 168.17/168.29 => 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)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_zabs__less__one__iff,axiom,
% 168.17/168.29 ! [V_z_2] :
% 168.17/168.29 ( 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)))
% 168.17/168.29 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_mult__numeral__1__right,axiom,
% 168.17/168.29 ! [V_a,T_a] :
% 168.17/168.29 ( class_Int_Onumber__ring(T_a)
% 168.17/168.29 => 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 ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_mult__numeral__1,axiom,
% 168.17/168.29 ! [V_a,T_a] :
% 168.17/168.29 ( class_Int_Onumber__ring(T_a)
% 168.17/168.29 => 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 ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_numeral__1__eq__1,axiom,
% 168.17/168.29 ! [T_a] :
% 168.17/168.29 ( class_Int_Onumber__ring(T_a)
% 168.17/168.29 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_semiring__norm_I110_J,axiom,
% 168.17/168.29 ! [T_a] :
% 168.17/168.29 ( class_Int_Onumber__ring(T_a)
% 168.17/168.29 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_rel__simps_I29_J,axiom,
% 168.17/168.29 ! [V_k_2] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_rel__simps_I5_J,axiom,
% 168.17/168.29 ! [V_k_2] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_divide__Numeral1,axiom,
% 168.17/168.29 ! [V_x,T_a] :
% 168.17/168.29 ( ( class_Fields_Ofield(T_a)
% 168.17/168.29 & class_Int_Onumber__ring(T_a) )
% 168.17/168.29 => 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 ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_divide__numeral__1,axiom,
% 168.17/168.29 ! [V_a,T_a] :
% 168.17/168.29 ( ( class_Fields_Ofield(T_a)
% 168.17/168.29 & class_Int_Onumber__ring(T_a) )
% 168.17/168.29 => 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 ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_one__is__num__one,axiom,
% 168.17/168.29 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_Numeral1__eq1__nat,axiom,
% 168.17/168.29 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_nat__numeral__1__eq__1,axiom,
% 168.17/168.29 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_numeral__3__eq__3,axiom,
% 168.17/168.29 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)))) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_numeral__1__eq__Suc__0,axiom,
% 168.17/168.29 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)) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
% 168.17/168.29 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))))) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_Suc3__eq__add__3,axiom,
% 168.17/168.29 ! [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) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_transfer__int__nat__numerals_I4_J,axiom,
% 168.17/168.29 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)))) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_le__special_I4_J,axiom,
% 168.17/168.29 ! [V_x_2,T_b] :
% 168.17/168.29 ( ( class_Int_Onumber__ring(T_b)
% 168.17/168.29 & class_Rings_Olinordered__idom(T_b) )
% 168.17/168.29 => ( 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)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_le__special_I2_J,axiom,
% 168.17/168.29 ! [V_y_2,T_b] :
% 168.17/168.29 ( ( class_Int_Onumber__ring(T_b)
% 168.17/168.29 & class_Rings_Olinordered__idom(T_b) )
% 168.17/168.29 => ( 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)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_less__special_I4_J,axiom,
% 168.17/168.29 ! [V_x_2,T_b] :
% 168.17/168.29 ( ( class_Int_Onumber__ring(T_b)
% 168.17/168.29 & class_Rings_Olinordered__idom(T_b) )
% 168.17/168.29 => ( 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)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_less__special_I2_J,axiom,
% 168.17/168.29 ! [V_y_2,T_b] :
% 168.17/168.29 ( ( class_Int_Onumber__ring(T_b)
% 168.17/168.29 & class_Rings_Olinordered__idom(T_b) )
% 168.17/168.29 => ( 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)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_add__special_I2_J,axiom,
% 168.17/168.29 ! [V_w,T_a] :
% 168.17/168.29 ( class_Int_Onumber__ring(T_a)
% 168.17/168.29 => 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)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_add__special_I3_J,axiom,
% 168.17/168.29 ! [V_v,T_a] :
% 168.17/168.29 ( class_Int_Onumber__ring(T_a)
% 168.17/168.29 => 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))) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_one__code__numeral__code,axiom,
% 168.17/168.29 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)) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_diff__special_I2_J,axiom,
% 168.17/168.29 ! [V_v,T_a] :
% 168.17/168.29 ( class_Int_Onumber__ring(T_a)
% 168.17/168.29 => 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)))) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_diff__special_I1_J,axiom,
% 168.17/168.29 ! [V_w,T_a] :
% 168.17/168.29 ( class_Int_Onumber__ring(T_a)
% 168.17/168.29 => 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))) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_less__2__cases,axiom,
% 168.17/168.29 ! [V_n] :
% 168.17/168.29 ( 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)))))
% 168.17/168.29 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.29 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_half__gt__zero,axiom,
% 168.17/168.29 ! [V_r,T_a] :
% 168.17/168.29 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 168.17/168.29 & class_Int_Onumber__ring(T_a) )
% 168.17/168.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r))
% 168.17/168.29 => 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)))))) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_half__gt__zero__iff,axiom,
% 168.17/168.29 ! [V_r_2,T_b] :
% 168.17/168.29 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 168.17/168.29 & class_Int_Onumber__ring(T_b) )
% 168.17/168.29 => ( 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))))))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_r_2)) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_negative__zle,axiom,
% 168.17/168.29 ! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m))) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_negative__zless,axiom,
% 168.17/168.29 ! [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))) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_arith__simps_I30_J,axiom,
% 168.17/168.29 ! [V_w,T_a] :
% 168.17/168.29 ( class_Int_Onumber__ring(T_a)
% 168.17/168.29 => 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)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_number__of__minus,axiom,
% 168.17/168.29 ! [V_w,T_a] :
% 168.17/168.29 ( class_Int_Onumber__ring(T_a)
% 168.17/168.29 => 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)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_code__numeral__zero__minus__one,axiom,
% 168.17/168.29 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) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_neg__equal__iff__equal,axiom,
% 168.17/168.29 ! [V_b_2,V_a_2,T_b] :
% 168.17/168.29 ( class_Groups_Ogroup__add(T_b)
% 168.17/168.29 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 168.17/168.29 <=> V_a_2 = V_b_2 ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_minus__equation__iff,axiom,
% 168.17/168.29 ! [V_b_2,V_a_2,T_b] :
% 168.17/168.29 ( class_Groups_Ogroup__add(T_b)
% 168.17/168.29 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_b_2
% 168.17/168.29 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) = V_a_2 ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_equation__minus__iff,axiom,
% 168.17/168.29 ! [V_b_2,V_a_2,T_b] :
% 168.17/168.29 ( class_Groups_Ogroup__add(T_b)
% 168.17/168.29 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 168.17/168.29 <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_minus__minus,axiom,
% 168.17/168.29 ! [V_a,T_a] :
% 168.17/168.29 ( class_Groups_Ogroup__add(T_a)
% 168.17/168.29 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_compl__eq__compl__iff,axiom,
% 168.17/168.29 ! [V_y_2,V_x_2,T_b] :
% 168.17/168.29 ( class_Lattices_Oboolean__algebra(T_b)
% 168.17/168.29 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)
% 168.17/168.29 <=> V_x_2 = V_y_2 ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_uminus__apply,axiom,
% 168.17/168.29 ! [V_x_2,V_A_2,T_c,T_b] :
% 168.17/168.29 ( class_Groups_Ouminus(T_b)
% 168.17/168.29 => 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)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_double__compl,axiom,
% 168.17/168.29 ! [V_x,T_a] :
% 168.17/168.29 ( class_Lattices_Oboolean__algebra(T_a)
% 168.17/168.29 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_rel__simps_I48_J,axiom,
% 168.17/168.29 ! [V_l_2,V_k_2] :
% 168.17/168.29 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2)
% 168.17/168.29 <=> V_k_2 = V_l_2 ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_minus__Bit0,axiom,
% 168.17/168.29 ! [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)) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_zminus__zminus,axiom,
% 168.17/168.29 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ).
% 168.17/168.29
% 168.17/168.29 fof(fact_minus__number__of__mult,axiom,
% 168.17/168.29 ! [V_z,V_w,T_a] :
% 168.17/168.29 ( class_Int_Onumber__ring(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_compl__le__compl__iff,axiom,
% 168.17/168.29 ! [V_y_2,V_x_2,T_b] :
% 168.17/168.29 ( class_Lattices_Oboolean__algebra(T_b)
% 168.17/168.29 => ( 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)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_compl__mono,axiom,
% 168.17/168.29 ! [V_y,V_x,T_a] :
% 168.17/168.29 ( class_Lattices_Oboolean__algebra(T_a)
% 168.17/168.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 168.17/168.29 => 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))) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_le__minus__iff,axiom,
% 168.17/168.29 ! [V_b_2,V_a_2,T_b] :
% 168.17/168.29 ( class_Groups_Oordered__ab__group__add(T_b)
% 168.17/168.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_minus__le__iff,axiom,
% 168.17/168.29 ! [V_b_2,V_a_2,T_b] :
% 168.17/168.29 ( class_Groups_Oordered__ab__group__add(T_b)
% 168.17/168.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_neg__le__iff__le,axiom,
% 168.17/168.29 ! [V_a_2,V_b_2,T_b] :
% 168.17/168.29 ( class_Groups_Oordered__ab__group__add(T_b)
% 168.17/168.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_le__imp__neg__le,axiom,
% 168.17/168.29 ! [V_b,V_a,T_a] :
% 168.17/168.29 ( class_Groups_Oordered__ab__group__add(T_a)
% 168.17/168.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 168.17/168.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a))) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_neg__equal__zero,axiom,
% 168.17/168.29 ! [V_a_2,T_b] :
% 168.17/168.29 ( class_Groups_Olinordered__ab__group__add(T_b)
% 168.17/168.29 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_a_2
% 168.17/168.29 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_neg__equal__0__iff__equal,axiom,
% 168.17/168.29 ! [V_a_2,T_b] :
% 168.17/168.29 ( class_Groups_Ogroup__add(T_b)
% 168.17/168.29 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 168.17/168.29 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_equal__neg__zero,axiom,
% 168.17/168.29 ! [V_a_2,T_b] :
% 168.17/168.29 ( class_Groups_Olinordered__ab__group__add(T_b)
% 168.17/168.29 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
% 168.17/168.29 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_neg__0__equal__iff__equal,axiom,
% 168.17/168.29 ! [V_a_2,T_b] :
% 168.17/168.29 ( class_Groups_Ogroup__add(T_b)
% 168.17/168.29 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
% 168.17/168.29 <=> c_Groups_Ozero__class_Ozero(T_b) = V_a_2 ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_minus__zero,axiom,
% 168.17/168.29 ! [T_a] :
% 168.17/168.29 ( class_Groups_Ogroup__add(T_a)
% 168.17/168.29 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_less__minus__iff,axiom,
% 168.17/168.29 ! [V_b_2,V_a_2,T_b] :
% 168.17/168.29 ( class_Groups_Oordered__ab__group__add(T_b)
% 168.17/168.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_minus__less__iff,axiom,
% 168.17/168.29 ! [V_b_2,V_a_2,T_b] :
% 168.17/168.29 ( class_Groups_Oordered__ab__group__add(T_b)
% 168.17/168.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_neg__less__iff__less,axiom,
% 168.17/168.29 ! [V_a_2,V_b_2,T_b] :
% 168.17/168.29 ( class_Groups_Oordered__ab__group__add(T_b)
% 168.17/168.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_minus__add__cancel,axiom,
% 168.17/168.29 ! [V_b,V_a,T_a] :
% 168.17/168.29 ( class_Groups_Ogroup__add(T_a)
% 168.17/168.29 => 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 ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_add__minus__cancel,axiom,
% 168.17/168.29 ! [V_b,V_a,T_a] :
% 168.17/168.29 ( class_Groups_Ogroup__add(T_a)
% 168.17/168.29 => 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 ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_minus__add,axiom,
% 168.17/168.29 ! [V_b,V_a,T_a] :
% 168.17/168.29 ( class_Groups_Ogroup__add(T_a)
% 168.17/168.29 => 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)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_minus__add__distrib,axiom,
% 168.17/168.29 ! [V_b,V_a,T_a] :
% 168.17/168.29 ( class_Groups_Oab__group__add(T_a)
% 168.17/168.29 => 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)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_square__eq__iff,axiom,
% 168.17/168.29 ! [V_b_2,V_a_2,T_b] :
% 168.17/168.29 ( class_Rings_Oidom(T_b)
% 168.17/168.29 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_b_2)
% 168.17/168.29 <=> ( V_a_2 = V_b_2
% 168.17/168.29 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) ) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_minus__mult__minus,axiom,
% 168.17/168.29 ! [V_b,V_a,T_a] :
% 168.17/168.29 ( class_Rings_Oring(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_minus__mult__commute,axiom,
% 168.17/168.29 ! [V_b,V_a,T_a] :
% 168.17/168.29 ( class_Rings_Oring(T_a)
% 168.17/168.29 => 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)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_minus__mult__left,axiom,
% 168.17/168.29 ! [V_b,V_a,T_a] :
% 168.17/168.29 ( class_Rings_Oring(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_minus__mult__right,axiom,
% 168.17/168.29 ! [V_b,V_a,T_a] :
% 168.17/168.29 ( class_Rings_Oring(T_a)
% 168.17/168.29 => 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)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_minus__diff__eq,axiom,
% 168.17/168.29 ! [V_b,V_a,T_a] :
% 168.17/168.29 ( class_Groups_Oab__group__add(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_rel__simps_I31_J,axiom,
% 168.17/168.29 ! [V_l_2,V_k_2] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_less__eq__int__code_I13_J,axiom,
% 168.17/168.29 ! [V_k2_2,V_k1_2] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_rel__simps_I14_J,axiom,
% 168.17/168.29 ! [V_l_2,V_k_2] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_less__int__code_I13_J,axiom,
% 168.17/168.29 ! [V_k2_2,V_k1_2] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_zminus__0,axiom,
% 168.17/168.29 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) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_rel__simps_I44_J,axiom,
% 168.17/168.29 ! [V_k_2] :
% 168.17/168.29 ( c_Int_OBit0(V_k_2) = c_Int_OPls
% 168.17/168.29 <=> V_k_2 = c_Int_OPls ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_rel__simps_I38_J,axiom,
% 168.17/168.29 ! [V_l_2] :
% 168.17/168.29 ( c_Int_OPls = c_Int_OBit0(V_l_2)
% 168.17/168.29 <=> c_Int_OPls = V_l_2 ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_Bit0__Pls,axiom,
% 168.17/168.29 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ).
% 168.17/168.29
% 168.17/168.29 fof(fact_rel__simps_I50_J,axiom,
% 168.17/168.29 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_rel__simps_I49_J,axiom,
% 168.17/168.29 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_add__Bit0__Bit0,axiom,
% 168.17/168.29 ! [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)) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_Bit0__def,axiom,
% 168.17/168.29 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_minus__divide__left,axiom,
% 168.17/168.29 ! [V_b,V_a,T_a] :
% 168.17/168.29 ( class_Rings_Odivision__ring(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_minus__divide__divide,axiom,
% 168.17/168.29 ! [V_b,V_a,T_a] :
% 168.17/168.29 ( class_Fields_Ofield__inverse__zero(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_minus__divide__right,axiom,
% 168.17/168.29 ! [V_b,V_a,T_a] :
% 168.17/168.29 ( class_Fields_Ofield__inverse__zero(T_a)
% 168.17/168.29 => 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)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_mult__Bit0,axiom,
% 168.17/168.29 ! [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)) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_abs__minus__cancel,axiom,
% 168.17/168.29 ! [V_a,T_a] :
% 168.17/168.29 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_minus__Pls,axiom,
% 168.17/168.29 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ).
% 168.17/168.29
% 168.17/168.29 fof(fact_zminus__zadd__distrib,axiom,
% 168.17/168.29 ! [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)) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_minus__numeral__code_I5_J,axiom,
% 168.17/168.29 ! [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)) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_diff__bin__simps_I7_J,axiom,
% 168.17/168.29 ! [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)) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_zmult__zminus,axiom,
% 168.17/168.29 ! [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)) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_minus__le__self__iff,axiom,
% 168.17/168.29 ! [V_a_2,T_b] :
% 168.17/168.29 ( class_Groups_Olinordered__ab__group__add(T_b)
% 168.17/168.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_neg__le__0__iff__le,axiom,
% 168.17/168.29 ! [V_a_2,T_b] :
% 168.17/168.29 ( class_Groups_Oordered__ab__group__add(T_b)
% 168.17/168.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_le__minus__self__iff,axiom,
% 168.17/168.29 ! [V_a_2,T_b] :
% 168.17/168.29 ( class_Groups_Olinordered__ab__group__add(T_b)
% 168.17/168.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_neg__0__le__iff__le,axiom,
% 168.17/168.29 ! [V_a_2,T_b] :
% 168.17/168.29 ( class_Groups_Oordered__ab__group__add(T_b)
% 168.17/168.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_less__minus__self__iff,axiom,
% 168.17/168.29 ! [V_a_2,T_b] :
% 168.17/168.29 ( class_Rings_Olinordered__idom(T_b)
% 168.17/168.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_neg__less__nonneg,axiom,
% 168.17/168.29 ! [V_a_2,T_b] :
% 168.17/168.29 ( class_Groups_Olinordered__ab__group__add(T_b)
% 168.17/168.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_neg__less__0__iff__less,axiom,
% 168.17/168.29 ! [V_a_2,T_b] :
% 168.17/168.29 ( class_Groups_Oordered__ab__group__add(T_b)
% 168.17/168.29 => ( 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)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_neg__0__less__iff__less,axiom,
% 168.17/168.29 ! [V_a_2,T_b] :
% 168.17/168.29 ( class_Groups_Oordered__ab__group__add(T_b)
% 168.17/168.29 => ( 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)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_minus__unique,axiom,
% 168.17/168.29 ! [V_b,V_a,T_a] :
% 168.17/168.29 ( class_Groups_Ogroup__add(T_a)
% 168.17/168.29 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.29 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_ab__left__minus,axiom,
% 168.17/168.29 ! [V_a,T_a] :
% 168.17/168.29 ( class_Groups_Oab__group__add(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_left__minus,axiom,
% 168.17/168.29 ! [V_a,T_a] :
% 168.17/168.29 ( class_Groups_Ogroup__add(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_eq__neg__iff__add__eq__0,axiom,
% 168.17/168.29 ! [V_b_2,V_a_2,T_b] :
% 168.17/168.29 ( class_Groups_Ogroup__add(T_b)
% 168.17/168.29 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 168.17/168.29 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_right__minus,axiom,
% 168.17/168.29 ! [V_a,T_a] :
% 168.17/168.29 ( class_Groups_Ogroup__add(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_diff__0,axiom,
% 168.17/168.29 ! [V_a,T_a] :
% 168.17/168.29 ( class_Groups_Ogroup__add(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
% 168.17/168.29 ! [V_y,V_x,T_a] :
% 168.17/168.29 ( class_Rings_Ocomm__ring__1(T_a)
% 168.17/168.29 => 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)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_diff__minus__eq__add,axiom,
% 168.17/168.29 ! [V_b,V_a,T_a] :
% 168.17/168.29 ( class_Groups_Ogroup__add(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_ab__diff__minus,axiom,
% 168.17/168.29 ! [V_b,V_a,T_a] :
% 168.17/168.29 ( class_Groups_Oab__group__add(T_a)
% 168.17/168.29 => 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)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_diff__def,axiom,
% 168.17/168.29 ! [V_b,V_a,T_a] :
% 168.17/168.29 ( class_Groups_Ogroup__add(T_a)
% 168.17/168.29 => 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)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
% 168.17/168.29 ! [V_x,T_a] :
% 168.17/168.29 ( class_Rings_Ocomm__ring__1(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_square__eq__1__iff,axiom,
% 168.17/168.29 ! [V_x_2,T_b] :
% 168.17/168.29 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 168.17/168.29 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_b)
% 168.17/168.29 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_b)
% 168.17/168.29 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_inf__compl__bot,axiom,
% 168.17/168.29 ! [V_x,T_a] :
% 168.17/168.29 ( class_Lattices_Oboolean__algebra(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_compl__inf__bot,axiom,
% 168.17/168.29 ! [V_x,T_a] :
% 168.17/168.29 ( class_Lattices_Oboolean__algebra(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_diff__eq,axiom,
% 168.17/168.29 ! [V_y,V_x,T_a] :
% 168.17/168.29 ( class_Lattices_Oboolean__algebra(T_a)
% 168.17/168.29 => 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)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_compl__inf,axiom,
% 168.17/168.29 ! [V_y,V_x,T_a] :
% 168.17/168.29 ( class_Lattices_Oboolean__algebra(T_a)
% 168.17/168.29 => 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)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_compl__sup,axiom,
% 168.17/168.29 ! [V_y,V_x,T_a] :
% 168.17/168.29 ( class_Lattices_Oboolean__algebra(T_a)
% 168.17/168.29 => 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)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_nonzero__minus__divide__divide,axiom,
% 168.17/168.29 ! [V_a,V_b,T_a] :
% 168.17/168.29 ( class_Rings_Odivision__ring(T_a)
% 168.17/168.29 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.29 => 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) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_nonzero__minus__divide__right,axiom,
% 168.17/168.29 ! [V_a,V_b,T_a] :
% 168.17/168.29 ( class_Rings_Odivision__ring(T_a)
% 168.17/168.29 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.29 => 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)) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_abs__ge__minus__self,axiom,
% 168.17/168.29 ! [V_a,T_a] :
% 168.17/168.29 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 168.17/168.29 => 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))) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_abs__le__iff,axiom,
% 168.17/168.29 ! [V_b_2,V_a_2,T_b] :
% 168.17/168.29 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 168.17/168.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2))
% 168.17/168.29 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 168.17/168.29 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) ) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_abs__leI,axiom,
% 168.17/168.29 ! [V_b,V_a,T_a] :
% 168.17/168.29 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 168.17/168.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 168.17/168.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))
% 168.17/168.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_abs__le__D2,axiom,
% 168.17/168.29 ! [V_b,V_a,T_a] :
% 168.17/168.29 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 168.17/168.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 168.17/168.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_abs__less__iff,axiom,
% 168.17/168.29 ! [V_b_2,V_a_2,T_b] :
% 168.17/168.29 ( class_Rings_Olinordered__idom(T_b)
% 168.17/168.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2))
% 168.17/168.29 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 168.17/168.29 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) ) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_bin__less__0__simps_I3_J,axiom,
% 168.17/168.29 ! [V_w_2] :
% 168.17/168.29 ( 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)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_rel__simps_I27_J,axiom,
% 168.17/168.29 ! [V_k_2] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_rel__simps_I21_J,axiom,
% 168.17/168.29 ! [V_k_2] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_less__eq__int__code_I14_J,axiom,
% 168.17/168.29 ! [V_k2_2,V_k1_2] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_rel__simps_I32_J,axiom,
% 168.17/168.29 ! [V_l_2,V_k_2] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_rel__simps_I10_J,axiom,
% 168.17/168.29 ! [V_k_2] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_rel__simps_I4_J,axiom,
% 168.17/168.29 ! [V_k_2] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_less__int__code_I15_J,axiom,
% 168.17/168.29 ! [V_k2_2,V_k1_2] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_rel__simps_I16_J,axiom,
% 168.17/168.29 ! [V_l_2,V_k_2] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_add__Bit0__Bit1,axiom,
% 168.17/168.29 ! [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)) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_add__Bit1__Bit0,axiom,
% 168.17/168.29 ! [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)) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_zadd__zminus__inverse2,axiom,
% 168.17/168.29 ! [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) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_negative__eq__positive,axiom,
% 168.17/168.29 ! [V_m_2,V_n_2] :
% 168.17/168.29 ( 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)
% 168.17/168.29 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.29 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_diff__bin__simps_I3_J,axiom,
% 168.17/168.29 ! [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)) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_diff__bin__simps_I10_J,axiom,
% 168.17/168.29 ! [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)) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_diff__bin__simps_I9_J,axiom,
% 168.17/168.29 ! [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)) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_not__int__zless__negative,axiom,
% 168.17/168.29 ! [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)))) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_diff__int__def,axiom,
% 168.17/168.29 ! [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)) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_diff__int__def__symmetric,axiom,
% 168.17/168.29 ! [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) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_Ints__minus,axiom,
% 168.17/168.29 ! [V_a_2,T_b] :
% 168.17/168.29 ( class_Rings_Oring__1(T_b)
% 168.17/168.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 168.17/168.29 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_neg__number__of__Bit0,axiom,
% 168.17/168.29 ! [V_w_2] :
% 168.17/168.29 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2))))
% 168.17/168.29 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_pred__Bit1,axiom,
% 168.17/168.29 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_pred__Bit0,axiom,
% 168.17/168.29 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_minus__Bit1,axiom,
% 168.17/168.29 ! [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))) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_succ__Bit0,axiom,
% 168.17/168.29 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_succ__Bit1,axiom,
% 168.17/168.29 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_number__of__Bit0,axiom,
% 168.17/168.29 ! [V_w,T_a] :
% 168.17/168.29 ( class_Int_Onumber__ring(T_a)
% 168.17/168.29 => 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)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_abs__minus__le__zero,axiom,
% 168.17/168.29 ! [V_a,T_a] :
% 168.17/168.29 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 168.17/168.29 => 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))) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_abs__of__nonpos,axiom,
% 168.17/168.29 ! [V_a,T_a] :
% 168.17/168.29 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 168.17/168.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.29 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_abs__if,axiom,
% 168.17/168.29 ! [V_a,T_a] :
% 168.17/168.29 ( class_Groups_Oabs__if(T_a)
% 168.17/168.29 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.29 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) )
% 168.17/168.29 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.29 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_abs__of__neg,axiom,
% 168.17/168.29 ! [V_a,T_a] :
% 168.17/168.29 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 168.17/168.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.29 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_rel__simps_I15_J,axiom,
% 168.17/168.29 ! [V_l_2,V_k_2] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_less__int__code_I14_J,axiom,
% 168.17/168.29 ! [V_k2_2,V_k1_2] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_rel__simps_I33_J,axiom,
% 168.17/168.29 ! [V_l_2,V_k_2] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_less__eq__int__code_I15_J,axiom,
% 168.17/168.29 ! [V_k2_2,V_k1_2] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_diff__number__of__eq,axiom,
% 168.17/168.29 ! [V_w,V_v,T_a] :
% 168.17/168.29 ( class_Int_Onumber__ring(T_a)
% 168.17/168.29 => 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))) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_mult__Bit1,axiom,
% 168.17/168.29 ! [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) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_int__zle__neg,axiom,
% 168.17/168.29 ! [V_m_2,V_n_2] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2))))
% 168.17/168.29 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.29 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_negative__zle__0,axiom,
% 168.17/168.29 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_minus__numeral__code_I6_J,axiom,
% 168.17/168.29 ! [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))) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_zabs__def,axiom,
% 168.17/168.29 ! [V_i] :
% 168.17/168.29 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.29 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) )
% 168.17/168.29 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.29 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_neg__zminus__int,axiom,
% 168.17/168.29 ! [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))))) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_diff__bin__simps_I8_J,axiom,
% 168.17/168.29 ! [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)) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_add__Bit1__Bit1,axiom,
% 168.17/168.29 ! [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))) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_zero__code__numeral__code,axiom,
% 168.17/168.29 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) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_double__number__of__Bit0,axiom,
% 168.17/168.29 ! [V_w,T_a] :
% 168.17/168.29 ( class_Int_Onumber__ring(T_a)
% 168.17/168.29 => 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)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_abs__number__of,axiom,
% 168.17/168.29 ! [V_x,T_a] :
% 168.17/168.29 ( ( class_Int_Onumber__ring(T_a)
% 168.17/168.29 & class_Rings_Olinordered__idom(T_a) )
% 168.17/168.29 => ( ( 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)))
% 168.17/168.29 => 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)) )
% 168.17/168.29 & ( ~ 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)))
% 168.17/168.29 => 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) ) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_add__number__of__diff2,axiom,
% 168.17/168.29 ! [V_w,V_c,V_v,T_a] :
% 168.17/168.29 ( class_Int_Onumber__ring(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_number__of1,axiom,
% 168.17/168.29 ! [V_n] :
% 168.17/168.29 ( 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)))
% 168.17/168.29 => ( 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))))
% 168.17/168.29 & 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)))) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_number__of__pred,axiom,
% 168.17/168.29 ! [V_w,T_a] :
% 168.17/168.29 ( class_Int_Onumber__ring(T_a)
% 168.17/168.29 => 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)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_not__zle__0__negative,axiom,
% 168.17/168.29 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n))))) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_negative__zless__0,axiom,
% 168.17/168.29 ! [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))) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_mult__2__right,axiom,
% 168.17/168.29 ! [V_z,T_a] :
% 168.17/168.29 ( class_Int_Onumber__ring(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_mult__2,axiom,
% 168.17/168.29 ! [V_z,T_a] :
% 168.17/168.29 ( class_Int_Onumber__ring(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_one__add__one__is__two,axiom,
% 168.17/168.29 ! [T_a] :
% 168.17/168.29 ( class_Int_Onumber__ring(T_a)
% 168.17/168.29 => 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))) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_semiring__norm_I115_J,axiom,
% 168.17/168.29 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))) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_numeral__2__eq__2,axiom,
% 168.17/168.29 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))) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
% 168.17/168.29 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))))) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_add__2__eq__Suc_H,axiom,
% 168.17/168.29 ! [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)) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_add__2__eq__Suc,axiom,
% 168.17/168.29 ! [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)) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_nat__mult__2__right,axiom,
% 168.17/168.29 ! [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) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_nat__mult__2,axiom,
% 168.17/168.29 ! [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) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_transfer__int__nat__numerals_I3_J,axiom,
% 168.17/168.29 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)))) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_nat__1__add__1,axiom,
% 168.17/168.29 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))) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_eq__special_I2_J,axiom,
% 168.17/168.29 ! [V_y_2,T_b] :
% 168.17/168.29 ( class_Int_Onumber__ring(T_b)
% 168.17/168.29 => ( c_Groups_Oone__class_Oone(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 168.17/168.29 <=> 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)))) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_eq__special_I4_J,axiom,
% 168.17/168.29 ! [V_x_2,T_b] :
% 168.17/168.29 ( class_Int_Onumber__ring(T_b)
% 168.17/168.29 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Oone__class_Oone(T_b)
% 168.17/168.29 <=> 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))))) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_zmod__number__of__Bit1,axiom,
% 168.17/168.29 ! [V_v,V_w] :
% 168.17/168.29 ( ( 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)))
% 168.17/168.29 => 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)) )
% 168.17/168.29 & ( ~ 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)))
% 168.17/168.29 => 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)) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_neg__zmod__mult__2,axiom,
% 168.17/168.29 ! [V_b,V_a] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.29 => 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)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_pos__zmod__mult__2,axiom,
% 168.17/168.29 ! [V_b,V_a] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 168.17/168.29 => 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))) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_pos__zdiv__mult__2,axiom,
% 168.17/168.29 ! [V_b,V_a] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_ComplI,axiom,
% 168.17/168.29 ! [V_A_2,V_c_2,T_b] :
% 168.17/168.29 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 168.17/168.29 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_mod__mod__trivial,axiom,
% 168.17/168.29 ! [V_b,V_a,T_a] :
% 168.17/168.29 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_DIVISION__BY__ZERO,axiom,
% 168.17/168.29 ! [V_a] :
% 168.17/168.29 ( 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)
% 168.17/168.29 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_mod__div__trivial,axiom,
% 168.17/168.29 ! [V_b,V_a,T_a] :
% 168.17/168.29 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_zmod__zdiv__trivial,axiom,
% 168.17/168.29 ! [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) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_zdiv__zadd1__eq,axiom,
% 168.17/168.29 ! [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)) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_semiring__div__class_Omod__div__equality_H,axiom,
% 168.17/168.29 ! [V_b,V_a,T_a] :
% 168.17/168.29 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.29 => 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 ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_mod__div__equality2,axiom,
% 168.17/168.29 ! [V_a,V_b,T_a] :
% 168.17/168.29 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.29 => 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 ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_mod__div__equality,axiom,
% 168.17/168.29 ! [V_b,V_a,T_a] :
% 168.17/168.29 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.29 => 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 ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_div__mod__equality2,axiom,
% 168.17/168.29 ! [V_c,V_a,V_b,T_a] :
% 168.17/168.29 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_div__mod__equality,axiom,
% 168.17/168.29 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.29 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_zdiv__zmod__equality2,axiom,
% 168.17/168.29 ! [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) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_zdiv__zmod__equality,axiom,
% 168.17/168.29 ! [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) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_zdiv__zmult1__eq,axiom,
% 168.17/168.29 ! [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)) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_zmod__zdiv__equality,axiom,
% 168.17/168.29 ! [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)) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_zmult__div__cancel,axiom,
% 168.17/168.29 ! [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)) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_zmod__zdiv__equality_H,axiom,
% 168.17/168.29 ! [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)) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_mod__self,axiom,
% 168.17/168.29 ! [V_a,T_a] :
% 168.17/168.29 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.29 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_mod__by__0,axiom,
% 168.17/168.29 ! [V_a,T_a] :
% 168.17/168.29 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.29 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_mod__0,axiom,
% 168.17/168.29 ! [V_a,T_a] :
% 168.17/168.29 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.29 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_mod__add__self2,axiom,
% 168.17/168.29 ! [V_b,V_a,T_a] :
% 168.17/168.29 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_mod__add__self1,axiom,
% 168.17/168.29 ! [V_a,V_b,T_a] :
% 168.17/168.29 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_mod__add__right__eq,axiom,
% 168.17/168.29 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.29 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_mod__add__left__eq,axiom,
% 168.17/168.29 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.29 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_mod__add__eq,axiom,
% 168.17/168.29 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.29 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_zmod__simps_I2_J,axiom,
% 168.17/168.29 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.29 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_zmod__simps_I1_J,axiom,
% 168.17/168.29 ! [V_b,V_c,V_a,T_a] :
% 168.17/168.29 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_mod__add__cong,axiom,
% 168.17/168.29 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 168.17/168.29 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.29 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 168.17/168.29 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 168.17/168.29 => 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) ) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_mod__mult__cong,axiom,
% 168.17/168.29 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 168.17/168.29 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.29 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 168.17/168.29 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 168.17/168.29 => 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) ) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_zmod__simps_I4_J,axiom,
% 168.17/168.29 ! [V_b,V_c,V_a,T_a] :
% 168.17/168.29 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_mod__mult__mult2,axiom,
% 168.17/168.29 ! [V_b,V_c,V_a,T_a] :
% 168.17/168.29 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_mod__mult__mult1,axiom,
% 168.17/168.29 ! [V_b,V_a,V_c,T_a] :
% 168.17/168.29 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.29 => 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)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_mod__mult__eq,axiom,
% 168.17/168.29 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.29 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_mod__mult__left__eq,axiom,
% 168.17/168.29 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.29 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_mod__mult__right__eq,axiom,
% 168.17/168.29 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.29 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_mod__diff__cong,axiom,
% 168.17/168.29 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 168.17/168.29 ( class_Divides_Oring__div(T_a)
% 168.17/168.29 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 168.17/168.29 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 168.17/168.29 => 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) ) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_mod__diff__eq,axiom,
% 168.17/168.29 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.29 ( class_Divides_Oring__div(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_mod__diff__left__eq,axiom,
% 168.17/168.29 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.29 ( class_Divides_Oring__div(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_mod__diff__right__eq,axiom,
% 168.17/168.29 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.29 ( class_Divides_Oring__div(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_mod__minus__eq,axiom,
% 168.17/168.29 ! [V_b,V_a,T_a] :
% 168.17/168.29 ( class_Divides_Oring__div(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_mod__minus__cong,axiom,
% 168.17/168.29 ! [V_a_H,V_b,V_a,T_a] :
% 168.17/168.29 ( class_Divides_Oring__div(T_a)
% 168.17/168.29 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b)
% 168.17/168.29 => 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) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_Compl__iff,axiom,
% 168.17/168.29 ! [V_A_2,V_c_2,T_b] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 168.17/168.29 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_ComplD,axiom,
% 168.17/168.29 ! [V_A_2,V_c_2,T_b] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 168.17/168.29 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_ComplE,axiom,
% 168.17/168.29 ! [V_A_2,V_c_2,T_b] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 168.17/168.29 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_zdiv__zero,axiom,
% 168.17/168.29 ! [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) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_zmod__self,axiom,
% 168.17/168.29 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_zmod__zero,axiom,
% 168.17/168.29 ! [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) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_Compl__subset__Compl__iff,axiom,
% 168.17/168.29 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.29 ( 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)))
% 168.17/168.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_Compl__anti__mono,axiom,
% 168.17/168.29 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.17/168.29 => 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))) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_zdiv__zminus2,axiom,
% 168.17/168.29 ! [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) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_zdiv__zminus__zminus,axiom,
% 168.17/168.29 ! [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) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_zmod__zmult1__eq,axiom,
% 168.17/168.29 ! [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) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_zmod__simps_I3_J,axiom,
% 168.17/168.29 ! [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) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_zdiff__zmod__left,axiom,
% 168.17/168.29 ! [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) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_zdiff__zmod__right,axiom,
% 168.17/168.29 ! [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) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_zmod__zminus2,axiom,
% 168.17/168.29 ! [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)) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_zmod__zminus__zminus,axiom,
% 168.17/168.29 ! [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)) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_zminus__zmod,axiom,
% 168.17/168.29 ! [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) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_div__by__0,axiom,
% 168.17/168.29 ! [V_a,T_a] :
% 168.17/168.29 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_div__0,axiom,
% 168.17/168.29 ! [V_a,T_a] :
% 168.17/168.29 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_div__by__1,axiom,
% 168.17/168.29 ! [V_a,T_a] :
% 168.17/168.29 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.29 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_mod__mult__self1__is__0,axiom,
% 168.17/168.29 ! [V_a,V_b,T_a] :
% 168.17/168.29 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_mod__mult__self2__is__0,axiom,
% 168.17/168.29 ! [V_b,V_a,T_a] :
% 168.17/168.29 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_zmod__zmult2__eq,axiom,
% 168.17/168.29 ! [V_b,V_a,V_c] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 168.17/168.29 => 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)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_mod__mult__self2,axiom,
% 168.17/168.29 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.29 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_mod__mult__self1,axiom,
% 168.17/168.29 ! [V_b,V_c,V_a,T_a] :
% 168.17/168.29 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.29 => 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) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_mod__by__1,axiom,
% 168.17/168.29 ! [V_a,T_a] :
% 168.17/168.29 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.29 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_zdiv__zminus1__eq__if,axiom,
% 168.17/168.29 ! [V_a,V_b] :
% 168.17/168.29 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.29 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.29 => 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)) )
% 168.17/168.29 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.29 => 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)) ) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_zdiv__zminus2__eq__if,axiom,
% 168.17/168.29 ! [V_a,V_b] :
% 168.17/168.29 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.29 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.29 => 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)) )
% 168.17/168.29 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.29 => 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)) ) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_iszero__def,axiom,
% 168.17/168.29 ! [V_z_2,T_b] :
% 168.17/168.29 ( class_Rings_Osemiring__1(T_b)
% 168.17/168.29 => ( c_Int_Oiszero(T_b,V_z_2)
% 168.17/168.29 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_iszero__0,axiom,
% 168.17/168.29 ! [T_a] :
% 168.17/168.29 ( class_Rings_Osemiring__1(T_a)
% 168.17/168.29 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
% 168.17/168.29 ! [V_y,V_x] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 168.17/168.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 168.17/168.29 => 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))) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_not__iszero__1,axiom,
% 168.17/168.29 ! [T_a] :
% 168.17/168.29 ( class_Rings_Osemiring__1(T_a)
% 168.17/168.29 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_div__neg__pos__less0,axiom,
% 168.17/168.29 ! [V_b,V_a] :
% 168.17/168.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 168.17/168.29 => 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))) ) ) ).
% 168.17/168.29
% 168.17/168.29 fof(fact_neg__imp__zdiv__neg__iff,axiom,
% 168.17/168.30 ! [V_a_2,V_b_2] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_pos__imp__zdiv__neg__iff,axiom,
% 168.17/168.30 ! [V_a_2,V_b_2] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zdiv__self,axiom,
% 168.17/168.30 ! [V_a] :
% 168.17/168.30 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.30 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_subset__Compl__self__eq,axiom,
% 168.17/168.30 ! [V_A_2,T_b] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 168.17/168.30 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
% 168.17/168.30 ! [V_y,V_x] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 168.17/168.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y))) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zmod__le__nonneg__dividend,axiom,
% 168.17/168.30 ! [V_k,V_m] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
% 168.17/168.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_k)),V_m)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_neg__mod__bound,axiom,
% 168.17/168.30 ! [V_a,V_b] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_pos__mod__bound,axiom,
% 168.17/168.30 ! [V_a,V_b] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 168.17/168.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_Compl__disjoint,axiom,
% 168.17/168.30 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_Compl__disjoint2,axiom,
% 168.17/168.30 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zdiv__number__of__Bit0,axiom,
% 168.17/168.30 ! [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)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zmod__eq__0__iff,axiom,
% 168.17/168.30 ! [V_d_2,V_m_2] :
% 168.17/168.30 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.30 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_Compl__Int,axiom,
% 168.17/168.30 ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_Compl__Un,axiom,
% 168.17/168.30 ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zmod__zminus2__not__zero,axiom,
% 168.17/168.30 ! [V_l,V_k] :
% 168.17/168.30 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.30 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zmod__zminus1__not__zero,axiom,
% 168.17/168.30 ! [V_l,V_k] :
% 168.17/168.30 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k),V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.30 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_Compl__Diff__eq,axiom,
% 168.17/168.30 ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_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) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_Diff__eq,axiom,
% 168.17/168.30 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_Diff__Compl,axiom,
% 168.17/168.30 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_div__mult__mult1,axiom,
% 168.17/168.30 ! [V_b,V_a,V_c,T_a] :
% 168.17/168.30 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.30 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.30 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_div__mult__mult2,axiom,
% 168.17/168.30 ! [V_b,V_a,V_c,T_a] :
% 168.17/168.30 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.30 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.30 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_div__mult__self1__is__id,axiom,
% 168.17/168.30 ! [V_a,V_b,T_a] :
% 168.17/168.30 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.30 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.30 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)),V_b) = V_a ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_div__mult__self2__is__id,axiom,
% 168.17/168.30 ! [V_a,V_b,T_a] :
% 168.17/168.30 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.30 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.30 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_b) = V_a ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_div__mult__mult1__if,axiom,
% 168.17/168.30 ! [V_b,V_a,V_c,T_a] :
% 168.17/168.30 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.30 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.30 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = c_Groups_Ozero__class_Ozero(T_a) )
% 168.17/168.30 & ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.30 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_div__self,axiom,
% 168.17/168.30 ! [V_a,T_a] :
% 168.17/168.30 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.30 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.30 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_split__pos__lemma,axiom,
% 168.17/168.30 ! [V_n_2,V_P_2,V_k_2] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 168.17/168.30 <=> ! [B_i,B_j] :
% 168.17/168.30 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 168.17/168.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 168.17/168.30 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) )
% 168.17/168.30 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_split__neg__lemma,axiom,
% 168.17/168.30 ! [V_n_2,V_P_2,V_k_2] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 168.17/168.30 <=> ! [B_i,B_j] :
% 168.17/168.30 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 168.17/168.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.30 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) )
% 168.17/168.30 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zdiv__eq__0__iff,axiom,
% 168.17/168.30 ! [V_k_2,V_i_2] :
% 168.17/168.30 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.30 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.30 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2))
% 168.17/168.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) )
% 168.17/168.30 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
% 168.17/168.30 ! [V_a_2,V_b_2] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)))
% 168.17/168.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_pos__imp__zdiv__pos__iff,axiom,
% 168.17/168.30 ! [V_i_2,V_k_2] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2)))
% 168.17/168.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
% 168.17/168.30 ! [V_b_2,V_a_2] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)))
% 168.17/168.30 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2))
% 168.17/168.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zdiv__mono2,axiom,
% 168.17/168.30 ! [V_b,V_b_H,V_a] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 168.17/168.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H))) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_div__nonneg__neg__le0,axiom,
% 168.17/168.30 ! [V_b,V_a] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_div__pos__pos__trivial,axiom,
% 168.17/168.30 ! [V_b,V_a] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 168.17/168.30 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
% 168.17/168.30 ! [V_a_2,V_b_2] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)))
% 168.17/168.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_div__nonpos__pos__le0,axiom,
% 168.17/168.30 ! [V_b,V_a] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 168.17/168.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zdiv__mono2__neg,axiom,
% 168.17/168.30 ! [V_b,V_b_H,V_a] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 168.17/168.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_div__neg__neg__trivial,axiom,
% 168.17/168.30 ! [V_b,V_a] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 168.17/168.30 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zdiv__mono1,axiom,
% 168.17/168.30 ! [V_b,V_a_H,V_a] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 168.17/168.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b))) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zdiv__mono1__neg,axiom,
% 168.17/168.30 ! [V_b,V_a_H,V_a] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_int__div__less__self,axiom,
% 168.17/168.30 ! [V_k,V_x] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k))
% 168.17/168.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_k)),V_x)) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zdiv__zmult2__eq,axiom,
% 168.17/168.30 ! [V_b,V_a,V_c] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 168.17/168.30 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),V_c) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_pos__mod__sign,axiom,
% 168.17/168.30 ! [V_a,V_b] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 168.17/168.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_pos__mod__conj,axiom,
% 168.17/168.30 ! [V_a,V_b] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))
% 168.17/168.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b)) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_mod__pos__pos__trivial,axiom,
% 168.17/168.30 ! [V_b,V_a] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 168.17/168.30 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_neg__mod__sign,axiom,
% 168.17/168.30 ! [V_a,V_b] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_neg__mod__conj,axiom,
% 168.17/168.30 ! [V_a,V_b] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_mod__neg__neg__trivial,axiom,
% 168.17/168.30 ! [V_b,V_a] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 168.17/168.30 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_disjoint__eq__subset__Compl,axiom,
% 168.17/168.30 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.30 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2))) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zmod__zminus1__eq__if,axiom,
% 168.17/168.30 ! [V_b,V_a] :
% 168.17/168.30 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.30 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 168.17/168.30 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.30 => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zmod__zminus2__eq__if,axiom,
% 168.17/168.30 ! [V_b,V_a] :
% 168.17/168.30 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.30 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 168.17/168.30 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.30 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_div__mult__self2,axiom,
% 168.17/168.30 ! [V_c,V_a,V_b,T_a] :
% 168.17/168.30 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.30 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.30 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_div__mult__self1,axiom,
% 168.17/168.30 ! [V_c,V_a,V_b,T_a] :
% 168.17/168.30 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.30 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.30 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_div__add__self1,axiom,
% 168.17/168.30 ! [V_a,V_b,T_a] :
% 168.17/168.30 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.30 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.30 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_div__add__self2,axiom,
% 168.17/168.30 ! [V_a,V_b,T_a] :
% 168.17/168.30 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.30 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.30 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_iszero__Numeral0,axiom,
% 168.17/168.30 ! [T_a] :
% 168.17/168.30 ( class_Int_Onumber__ring(T_a)
% 168.17/168.30 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_iszero__number__of__Bit1,axiom,
% 168.17/168.30 ! [V_w,T_a] :
% 168.17/168.30 ( ( class_Int_Onumber__ring(T_a)
% 168.17/168.30 & class_Int_Oring__char__0(T_a) )
% 168.17/168.30 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_iszero__number__of__Bit0,axiom,
% 168.17/168.30 ! [V_w_2,T_b] :
% 168.17/168.30 ( ( class_Int_Onumber__ring(T_b)
% 168.17/168.30 & class_Int_Oring__char__0(T_b) )
% 168.17/168.30 => ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(V_w_2)))
% 168.17/168.30 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_mod__pos__neg__trivial,axiom,
% 168.17/168.30 ! [V_b,V_a] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.30 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_split__zdiv,axiom,
% 168.17/168.30 ! [V_k_2,V_n_2,V_P_2] :
% 168.17/168.30 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)))
% 168.17/168.30 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.30 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 168.17/168.30 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 168.17/168.30 => ! [B_i] :
% 168.17/168.30 ( ? [B_j] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 168.17/168.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 168.17/168.30 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) )
% 168.17/168.30 => hBOOL(hAPP(V_P_2,B_i)) ) )
% 168.17/168.30 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.30 => ! [B_i] :
% 168.17/168.30 ( ? [B_j] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 168.17/168.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.30 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) )
% 168.17/168.30 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_divmod__int__rel__div__eq,axiom,
% 168.17/168.30 ! [V_r_1,V_y,V_b_1,V_a_1] :
% 168.17/168.30 ( V_a_1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_y)),V_r_1)
% 168.17/168.30 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1))
% 168.17/168.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) )
% 168.17/168.30 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1))
% 168.17/168.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 168.17/168.30 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.30 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_split__zmod,axiom,
% 168.17/168.30 ! [V_k_2,V_n_2,V_P_2] :
% 168.17/168.30 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 168.17/168.30 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.30 => hBOOL(hAPP(V_P_2,V_n_2)) )
% 168.17/168.30 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 168.17/168.30 => ! [B_i,B_j] :
% 168.17/168.30 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 168.17/168.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 168.17/168.30 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) )
% 168.17/168.30 => hBOOL(hAPP(V_P_2,B_j)) ) )
% 168.17/168.30 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.30 => ! [B_i,B_j] :
% 168.17/168.30 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 168.17/168.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.30 & V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),B_i)),B_j) )
% 168.17/168.30 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zmult2__lemma__aux3,axiom,
% 168.17/168.30 ! [V_q,V_b,V_r,V_c] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 168.17/168.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r))) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zmult2__lemma__aux4,axiom,
% 168.17/168.30 ! [V_q,V_b,V_r,V_c] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 168.17/168.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c))) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zmult2__lemma__aux1,axiom,
% 168.17/168.30 ! [V_q,V_r,V_b,V_c] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r))) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zmult2__lemma__aux2,axiom,
% 168.17/168.30 ! [V_q,V_r,V_b,V_c] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_divmod__int__rel__mod__eq,axiom,
% 168.17/168.30 ! [V_y,V_q_1,V_b_1,V_a_1] :
% 168.17/168.30 ( V_a_1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_1),V_q_1)),V_y)
% 168.17/168.30 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 168.17/168.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) )
% 168.17/168.30 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y))
% 168.17/168.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 168.17/168.30 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.30 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zmod__number__of__Bit0,axiom,
% 168.17/168.30 ! [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))) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_not__iszero__Numeral1,axiom,
% 168.17/168.30 ! [T_a] :
% 168.17/168.30 ( class_Int_Onumber__ring(T_a)
% 168.17/168.30 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_eq__number__of__eq,axiom,
% 168.17/168.30 ! [V_y_2,V_x_2,T_b] :
% 168.17/168.30 ( class_Int_Onumber__ring(T_b)
% 168.17/168.30 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 168.17/168.30 <=> 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)))) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zdiv__number__of__Bit1,axiom,
% 168.17/168.30 ! [V_v,V_w] :
% 168.17/168.30 ( ( 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)))
% 168.17/168.30 => 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)) )
% 168.17/168.30 & ( ~ 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)))
% 168.17/168.30 => 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)) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_eq__special_I1_J,axiom,
% 168.17/168.30 ! [V_y_2,T_b] :
% 168.17/168.30 ( class_Int_Onumber__ring(T_b)
% 168.17/168.30 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 168.17/168.30 <=> 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)))) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_eq__special_I3_J,axiom,
% 168.17/168.30 ! [V_x_2,T_b] :
% 168.17/168.30 ( class_Int_Onumber__ring(T_b)
% 168.17/168.30 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Ozero__class_Ozero(T_b)
% 168.17/168.30 <=> 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)))) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_neg__zdiv__mult__2,axiom,
% 168.17/168.30 ! [V_b,V_a] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.30 => 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) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_nat__of__aux__code,axiom,
% 168.17/168.30 ! [V_n,V_i] :
% 168.17/168.30 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 168.17/168.30 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n )
% 168.17/168.30 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 168.17/168.30 => 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)) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_z3div__def,axiom,
% 168.17/168.30 ! [V_k,V_l] :
% 168.17/168.30 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 168.17/168.30 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) )
% 168.17/168.30 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 168.17/168.30 => c_SMT_Oz3div(V_k,V_l) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l))) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_z3mod__def,axiom,
% 168.17/168.30 ! [V_k,V_l] :
% 168.17/168.30 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 168.17/168.30 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) )
% 168.17/168.30 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 168.17/168.30 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l)) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_of__nat__double,axiom,
% 168.17/168.30 ! [V_x,T_a] :
% 168.17/168.30 ( class_Rings_Osemiring__1(T_a)
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 168.17/168.30 => 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))) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__minus1__odd,axiom,
% 168.17/168.30 ! [V_n,T_a] :
% 168.17/168.30 ( class_Rings_Oring__1(T_a)
% 168.17/168.30 => 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)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_odd__power__less__zero,axiom,
% 168.17/168.30 ! [V_n,V_a,T_a] :
% 168.17/168.30 ( class_Rings_Olinordered__idom(T_a)
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.30 => 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))) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_Compl__eq__Compl__iff,axiom,
% 168.17/168.30 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.30 ( 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)
% 168.17/168.30 <=> V_A_2 = V_B_2 ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_double__complement,axiom,
% 168.17/168.30 ! [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 ).
% 168.17/168.30
% 168.17/168.30 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom,
% 168.17/168.30 ! [V_n,V_x] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 168.17/168.30 => 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)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_nat__power__eq,axiom,
% 168.17/168.30 ! [V_n,V_z] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 168.17/168.30 => 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) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_div__add1__eq,axiom,
% 168.17/168.30 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_c)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_c)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c))),V_c)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_div__mult1__eq,axiom,
% 168.17/168.30 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_b),V_c))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_b,V_c))),V_c)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_mod__mult2__eq,axiom,
% 168.17/168.30 ! [V_c,V_b,V_a] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b),V_c))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_b)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_div__mod__equality_H,axiom,
% 168.17/168.30 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_mult__div__cancel,axiom,
% 168.17/168.30 ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_Divides_Omod__div__equality_H,axiom,
% 168.17/168.30 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_n)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom,
% 168.17/168.30 ! [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)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zpower__int,axiom,
% 168.17/168.30 ! [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)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_int__power,axiom,
% 168.17/168.30 ! [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) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 168.17/168.30 ! [V_q,V_y,V_x,T_a] :
% 168.17/168.30 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.17/168.30 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_q) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_q)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_div__le__dividend,axiom,
% 168.17/168.30 ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_m)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_div__le__mono,axiom,
% 168.17/168.30 ! [V_k,V_n,V_m] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 168.17/168.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n),V_k))) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_mod__Suc__eq__Suc__mod,axiom,
% 168.17/168.30 ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_div__mult2__eq,axiom,
% 168.17/168.30 ! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b)),V_c) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_mod__less,axiom,
% 168.17/168.30 ! [V_n,V_m] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 168.17/168.30 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_mod__less__eq__dividend,axiom,
% 168.17/168.30 ! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_m)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_mod__mult__distrib,axiom,
% 168.17/168.30 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_k) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_mod__mult__distrib2,axiom,
% 168.17/168.30 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_nat__int,axiom,
% 168.17/168.30 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ).
% 168.17/168.30
% 168.17/168.30 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 168.17/168.30 ! [V_q,V_p,V_x,T_a] :
% 168.17/168.30 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.17/168.30 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zpower__zpower,axiom,
% 168.17/168.30 ! [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)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 168.17/168.30 ! [V_x,T_a] :
% 168.17/168.30 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.17/168.30 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zpower__zmod,axiom,
% 168.17/168.30 ! [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) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__nat__number__of,axiom,
% 168.17/168.30 ! [V_n,V_v] :
% 168.17/168.30 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 168.17/168.30 => 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) )
% 168.17/168.30 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 168.17/168.30 => 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)) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__nat__number__of__number__of,axiom,
% 168.17/168.30 ! [V_w,V_v] :
% 168.17/168.30 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 168.17/168.30 => 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)) )
% 168.17/168.30 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 168.17/168.30 => 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))) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom,
% 168.17/168.30 ! [V_y,V_x] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 168.17/168.30 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_nat__div__distrib,axiom,
% 168.17/168.30 ! [V_y,V_x] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 168.17/168.30 => hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom,
% 168.17/168.30 ! [V_y,V_x] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 168.17/168.30 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,V_x),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_nat__mod__distrib,axiom,
% 168.17/168.30 ! [V_y,V_x] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 168.17/168.30 => hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,V_x),hAPP(c_Int_Onat,V_y)) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_div__1,axiom,
% 168.17/168.30 ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = V_m ).
% 168.17/168.30
% 168.17/168.30 fof(fact_div__less,axiom,
% 168.17/168.30 ! [V_n,V_m] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 168.17/168.30 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_nat__mult__div__cancel__disj,axiom,
% 168.17/168.30 ! [V_n,V_m,V_k] :
% 168.17/168.30 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.30 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 168.17/168.30 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.30 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
% 168.17/168.30 ! [V_q,V_x,T_a] :
% 168.17/168.30 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.17/168.30 => 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)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
% 168.17/168.30 ! [V_q,V_x,T_a] :
% 168.17/168.30 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.17/168.30 => 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)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
% 168.17/168.30 ! [V_q,V_x,T_a] :
% 168.17/168.30 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.17/168.30 => 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)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_transfer__nat__int__numerals_I1_J,axiom,
% 168.17/168.30 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_nat__0,axiom,
% 168.17/168.30 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_mod__1,axiom,
% 168.17/168.30 ! [V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_mod__Suc,axiom,
% 168.17/168.30 ! [V_n,V_m] :
% 168.17/168.30 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n
% 168.17/168.30 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 168.17/168.30 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n
% 168.17/168.30 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_mod__less__divisor,axiom,
% 168.17/168.30 ! [V_m,V_n] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 168.17/168.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 168.17/168.30 ! [V_x,T_a] :
% 168.17/168.30 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.17/168.30 => 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) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 168.17/168.30 ! [V_q,V_p,V_x,T_a] :
% 168.17/168.30 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.17/168.30 => 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)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_ex__nat,axiom,
% 168.17/168.30 ! [V_P_2] :
% 168.17/168.30 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 168.17/168.30 <=> ? [B_x] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 168.17/168.30 & hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_all__nat,axiom,
% 168.17/168.30 ! [V_P_2] :
% 168.17/168.30 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 168.17/168.30 <=> ! [B_x] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 168.17/168.30 => hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_transfer__nat__int__relations_I1_J,axiom,
% 168.17/168.30 ! [V_y_2,V_x_2] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 168.17/168.30 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2)
% 168.17/168.30 <=> V_x_2 = V_y_2 ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_eq__nat__nat__iff,axiom,
% 168.17/168.30 ! [V_z_H_2,V_z_2] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2))
% 168.17/168.30 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2)
% 168.17/168.30 <=> V_z_2 = V_z_H_2 ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_mod__eq__0__iff,axiom,
% 168.17/168.30 ! [V_d_2,V_m_2] :
% 168.17/168.30 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.30 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 168.17/168.30 ! [V_n,V_x] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 168.17/168.30 => 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))) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_mod__geq,axiom,
% 168.17/168.30 ! [V_n,V_m] :
% 168.17/168.30 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 168.17/168.30 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_mod__if,axiom,
% 168.17/168.30 ! [V_n,V_m] :
% 168.17/168.30 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 168.17/168.30 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m )
% 168.17/168.30 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 168.17/168.30 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_mod__mult__self3,axiom,
% 168.17/168.30 ! [V_m,V_n,V_k] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),V_m),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_le__mod__geq,axiom,
% 168.17/168.30 ! [V_m,V_n] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 168.17/168.30 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),V_n) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom,
% 168.17/168.30 ! [V_y,V_x] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_x),V_y)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zdiv__int,axiom,
% 168.17/168.30 ! [V_b,V_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_a)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_b)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_nat__number__of__def,axiom,
% 168.17/168.30 ! [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)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_nat__number__of,axiom,
% 168.17/168.30 ! [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) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zpower__zadd__distrib,axiom,
% 168.17/168.30 ! [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)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_transfer__nat__int__numerals_I2_J,axiom,
% 168.17/168.30 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom,
% 168.17/168.30 ! [V_y,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_y)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zmod__int,axiom,
% 168.17/168.30 ! [V_b,V_a] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_a,V_b)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_b)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_neg__nat,axiom,
% 168.17/168.30 ! [V_z] :
% 168.17/168.30 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 168.17/168.30 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_not__neg__nat,axiom,
% 168.17/168.30 ! [V_z] :
% 168.17/168.30 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 168.17/168.30 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_Ints__power,axiom,
% 168.17/168.30 ! [V_n_2,V_a_2,T_b] :
% 168.17/168.30 ( class_Rings_Oring__1(T_b)
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 168.17/168.30 => 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))) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_div__nat__number__of,axiom,
% 168.17/168.30 ! [V_v_H,V_v] :
% 168.17/168.30 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 168.17/168.30 => 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) )
% 168.17/168.30 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 168.17/168.30 => 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))) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_mod__nat__number__of,axiom,
% 168.17/168.30 ! [V_v_H,V_v] :
% 168.17/168.30 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 168.17/168.30 => 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) )
% 168.17/168.30 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 168.17/168.30 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 168.17/168.30 => 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) )
% 168.17/168.30 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 168.17/168.30 => 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))) ) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_one__div__nat__number__of,axiom,
% 168.17/168.30 ! [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))) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_div__le__mono2,axiom,
% 168.17/168.30 ! [V_k,V_n,V_m] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 168.17/168.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_k),V_n)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_k),V_m))) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_nat__mult__div__cancel1,axiom,
% 168.17/168.30 ! [V_n,V_m,V_k] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 168.17/168.30 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_div__mult__self1__is__m,axiom,
% 168.17/168.30 ! [V_m,V_n] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 168.17/168.30 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)),V_n) = V_m ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_div__mult__self__is__m,axiom,
% 168.17/168.30 ! [V_m,V_n] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 168.17/168.30 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_n) = V_m ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_div__less__dividend,axiom,
% 168.17/168.30 ! [V_m,V_n] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 168.17/168.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_m)) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_nat__0__iff,axiom,
% 168.17/168.30 ! [V_i_2] :
% 168.17/168.30 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_nat__le__0,axiom,
% 168.17/168.30 ! [V_z] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.30 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zless__nat__conj,axiom,
% 168.17/168.30 ! [V_z_2,V_w_2] :
% 168.17/168.30 ( 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)))
% 168.17/168.30 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 168.17/168.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_nat__mono__iff,axiom,
% 168.17/168.30 ! [V_w_2,V_z_2] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 168.17/168.30 => ( 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)))
% 168.17/168.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_mod__le__divisor,axiom,
% 168.17/168.30 ! [V_m,V_n] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 168.17/168.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_transfer__nat__int__relations_I3_J,axiom,
% 168.17/168.30 ! [V_y_2,V_x_2] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 168.17/168.30 => ( 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)))
% 168.17/168.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_nat__1,axiom,
% 168.17/168.30 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_mod__mult__self4,axiom,
% 168.17/168.30 ! [V_m,V_n,V_k] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),V_m)),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_int__nat__eq,axiom,
% 168.17/168.30 ! [V_z] :
% 168.17/168.30 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 168.17/168.30 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z )
% 168.17/168.30 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 168.17/168.30 => 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) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_int__eq__iff,axiom,
% 168.17/168.30 ! [V_z_2,V_m_2] :
% 168.17/168.30 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2
% 168.17/168.30 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2)
% 168.17/168.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_nat__0__le,axiom,
% 168.17/168.30 ! [V_z] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 168.17/168.30 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zless__nat__eq__int__zless,axiom,
% 168.17/168.30 ! [V_z_2,V_m_2] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2)))
% 168.17/168.30 <=> 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)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_nat__zminus__int,axiom,
% 168.17/168.30 ! [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) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zero__le__zpower__abs,axiom,
% 168.17/168.30 ! [V_n,V_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),V_n))) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_nat__abs__mult__distrib,axiom,
% 168.17/168.30 ! [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))) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_one__mod__nat__number__of,axiom,
% 168.17/168.30 ! [V_v_H] :
% 168.17/168.30 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 168.17/168.30 => 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)) )
% 168.17/168.30 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 168.17/168.30 => 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))) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_div__if,axiom,
% 168.17/168.30 ! [V_m,V_n] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 168.17/168.30 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 168.17/168.30 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 168.17/168.30 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 168.17/168.30 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_div__geq,axiom,
% 168.17/168.30 ! [V_m,V_n] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 168.17/168.30 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 168.17/168.30 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_split__div,axiom,
% 168.17/168.30 ! [V_k_2,V_n_2,V_P_2] :
% 168.17/168.30 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2)))
% 168.17/168.30 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.30 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 168.17/168.30 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.30 => ! [B_i,B_j] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 168.17/168.30 => ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)
% 168.17/168.30 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zero__less__nat__eq,axiom,
% 168.17/168.30 ! [V_z_2] :
% 168.17/168.30 ( 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)))
% 168.17/168.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_transfer__nat__int__relations_I2_J,axiom,
% 168.17/168.30 ! [V_y_2,V_x_2] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 168.17/168.30 => ( 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)))
% 168.17/168.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_nat__less__eq__zless,axiom,
% 168.17/168.30 ! [V_z_2,V_w_2] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 168.17/168.30 => ( 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)))
% 168.17/168.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_nat__eq__iff,axiom,
% 168.17/168.30 ! [V_m_2,V_w_2] :
% 168.17/168.30 ( hAPP(c_Int_Onat,V_w_2) = V_m_2
% 168.17/168.30 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 168.17/168.30 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 168.17/168.30 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 168.17/168.30 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_nat__eq__iff2,axiom,
% 168.17/168.30 ! [V_w_2,V_m_2] :
% 168.17/168.30 ( V_m_2 = hAPP(c_Int_Onat,V_w_2)
% 168.17/168.30 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 168.17/168.30 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 168.17/168.30 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 168.17/168.30 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_nat__le__eq__zle,axiom,
% 168.17/168.30 ! [V_z_2,V_w_2] :
% 168.17/168.30 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 168.17/168.30 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
% 168.17/168.30 => ( 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)))
% 168.17/168.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_split__nat,axiom,
% 168.17/168.30 ! [V_i_2,V_P_2] :
% 168.17/168.30 ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2)))
% 168.17/168.30 <=> ( ! [B_n] :
% 168.17/168.30 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)
% 168.17/168.30 => hBOOL(hAPP(V_P_2,B_n)) )
% 168.17/168.30 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.30 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_mod__lemma,axiom,
% 168.17/168.30 ! [V_q,V_b,V_r,V_c] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b))
% 168.17/168.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c))),V_r)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c))) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_split__mod,axiom,
% 168.17/168.30 ! [V_k_2,V_n_2,V_P_2] :
% 168.17/168.30 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))
% 168.17/168.30 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.30 => hBOOL(hAPP(V_P_2,V_n_2)) )
% 168.17/168.30 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.30 => ! [B_i,B_j] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 168.17/168.30 => ( V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),B_i)),B_j)
% 168.17/168.30 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom,
% 168.17/168.30 ! [V_y,V_x] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 168.17/168.30 => 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)) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_nat__add__distrib,axiom,
% 168.17/168.30 ! [V_z_H,V_z] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 168.17/168.30 => 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)) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power3__eq__cube,axiom,
% 168.17/168.30 ! [V_a,T_a] :
% 168.17/168.30 ( class_Groups_Omonoid__mult(T_a)
% 168.17/168.30 => 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) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_int__eq__iff__number__of,axiom,
% 168.17/168.30 ! [V_v_2,V_m_2] :
% 168.17/168.30 ( 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)
% 168.17/168.30 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))
% 168.17/168.30 & 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))) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom,
% 168.17/168.30 ! [V_y,V_x] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 168.17/168.30 => 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)) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_nat__mult__distrib,axiom,
% 168.17/168.30 ! [V_z_H,V_z] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 168.17/168.30 => 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)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_nat__diff__distrib,axiom,
% 168.17/168.30 ! [V_z,V_z_H] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 168.17/168.30 => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z),V_z_H)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z)),hAPP(c_Int_Onat,V_z_H)) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_Suc__times__mod__eq,axiom,
% 168.17/168.30 ! [V_m,V_k] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k))
% 168.17/168.30 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),V_k) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_transfer__nat__int__numerals_I4_J,axiom,
% 168.17/168.30 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)))) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__eq__if,axiom,
% 168.17/168.30 ! [V_p,V_m] :
% 168.17/168.30 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.30 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 168.17/168.30 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.30 => 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)))) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zero__less__zpower__abs__iff,axiom,
% 168.17/168.30 ! [V_n_2,V_x_2] :
% 168.17/168.30 ( 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)))
% 168.17/168.30 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.30 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom,
% 168.17/168.30 ! [V_y,V_x] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 168.17/168.30 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_x)),hAPP(c_Int_Onat,V_y)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_le__div__geq,axiom,
% 168.17/168.30 ! [V_m,V_n] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 168.17/168.30 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_split__div__lemma,axiom,
% 168.17/168.30 ! [V_m_2,V_q_2,V_n_2] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 168.17/168.30 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_q_2)),V_m_2))
% 168.17/168.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_q_2)))) )
% 168.17/168.30 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_split__div_H,axiom,
% 168.17/168.30 ! [V_n_2,V_m_2,V_P_2] :
% 168.17/168.30 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2)))
% 168.17/168.30 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.30 & hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 168.17/168.30 | ? [B_q] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),B_q)),V_m_2))
% 168.17/168.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,B_q))))
% 168.17/168.30 & hBOOL(hAPP(V_P_2,B_q)) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_Suc__div__eq__add3__div__number__of,axiom,
% 168.17/168.30 ! [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)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_Suc__div__eq__add3__div,axiom,
% 168.17/168.30 ! [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) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_div__Suc__eq__div__add3,axiom,
% 168.17/168.30 ! [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)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_div2__Suc__Suc,axiom,
% 168.17/168.30 ! [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))))) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_add__self__div__2,axiom,
% 168.17/168.30 ! [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 ).
% 168.17/168.30
% 168.17/168.30 fof(fact_one__less__nat__eq,axiom,
% 168.17/168.30 ! [V_z_2] :
% 168.17/168.30 ( 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)))
% 168.17/168.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_nat__less__iff,axiom,
% 168.17/168.30 ! [V_m_2,V_w_2] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2))
% 168.17/168.30 <=> 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))) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_Suc__nat__eq__nat__zadd1,axiom,
% 168.17/168.30 ! [V_z] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 168.17/168.30 => 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)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom,
% 168.17/168.30 ! [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)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_Suc__mod__eq__add3__mod,axiom,
% 168.17/168.30 ! [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) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_mod__Suc__eq__mod__add3,axiom,
% 168.17/168.30 ! [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)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zero__power2,axiom,
% 168.17/168.30 ! [T_a] :
% 168.17/168.30 ( class_Rings_Osemiring__1(T_a)
% 168.17/168.30 => 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) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zero__eq__power2,axiom,
% 168.17/168.30 ! [V_a_2,T_b] :
% 168.17/168.30 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 168.17/168.30 => ( 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)
% 168.17/168.30 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
% 168.17/168.30 ! [V_x,T_a] :
% 168.17/168.30 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.17/168.30 => 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)))) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power2__eq__square,axiom,
% 168.17/168.30 ! [V_a,T_a] :
% 168.17/168.30 ( class_Groups_Omonoid__mult(T_a)
% 168.17/168.30 => 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) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_mod2__Suc__Suc,axiom,
% 168.17/168.30 ! [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)))) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_one__power2,axiom,
% 168.17/168.30 ! [T_a] :
% 168.17/168.30 ( class_Rings_Osemiring__1(T_a)
% 168.17/168.30 => 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) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_transfer__nat__int__numerals_I3_J,axiom,
% 168.17/168.30 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)))) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power2__minus,axiom,
% 168.17/168.30 ! [V_a,T_a] :
% 168.17/168.30 ( class_Rings_Oring__1(T_a)
% 168.17/168.30 => 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)))) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_nat__mult__distrib__neg,axiom,
% 168.17/168.30 ! [V_z_H,V_z] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.30 => 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))) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__even__eq,axiom,
% 168.17/168.30 ! [V_n,V_a,T_a] :
% 168.17/168.30 ( class_Groups_Omonoid__mult(T_a)
% 168.17/168.30 => 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)))) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power2__abs,axiom,
% 168.17/168.30 ! [V_a,T_a] :
% 168.17/168.30 ( class_Rings_Olinordered__idom(T_a)
% 168.17/168.30 => 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)))) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_abs__power2,axiom,
% 168.17/168.30 ! [V_a,T_a] :
% 168.17/168.30 ( class_Rings_Olinordered__idom(T_a)
% 168.17/168.30 => 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)))) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zero__le__power2,axiom,
% 168.17/168.30 ! [V_a,T_a] :
% 168.17/168.30 ( class_Rings_Olinordered__idom(T_a)
% 168.17/168.30 => 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)))))) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power2__le__imp__le,axiom,
% 168.17/168.30 ! [V_y,V_x,T_a] :
% 168.17/168.30 ( class_Rings_Olinordered__semidom(T_a)
% 168.17/168.30 => ( 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))))))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 168.17/168.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power2__eq__imp__eq,axiom,
% 168.17/168.30 ! [V_y,V_x,T_a] :
% 168.17/168.30 ( class_Rings_Olinordered__semidom(T_a)
% 168.17/168.30 => ( 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))))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 168.17/168.30 => V_x = V_y ) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zero__less__power2,axiom,
% 168.17/168.30 ! [V_a_2,T_b] :
% 168.17/168.30 ( class_Rings_Olinordered__idom(T_b)
% 168.17/168.30 => ( 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))))))
% 168.17/168.30 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power2__less__0,axiom,
% 168.17/168.30 ! [V_a,T_a] :
% 168.17/168.30 ( class_Rings_Olinordered__idom(T_a)
% 168.17/168.30 => ~ 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))) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_sum__power2__eq__zero__iff,axiom,
% 168.17/168.30 ! [V_y_2,V_x_2,T_b] :
% 168.17/168.30 ( class_Rings_Olinordered__idom(T_b)
% 168.17/168.30 => ( 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)
% 168.17/168.30 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 168.17/168.30 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_nat__2,axiom,
% 168.17/168.30 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))) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power2__eq__square__number__of,axiom,
% 168.17/168.30 ! [V_w,T_b] :
% 168.17/168.30 ( ( class_Groups_Omonoid__mult(T_b)
% 168.17/168.30 & class_Int_Onumber(T_b) )
% 168.17/168.30 => 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)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power2__eq__1__iff,axiom,
% 168.17/168.30 ! [V_a_2,T_b] :
% 168.17/168.30 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 168.17/168.30 => ( 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)
% 168.17/168.30 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_b)
% 168.17/168.30 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
% 168.17/168.30 ! [V_n,V_x,T_a] :
% 168.17/168.30 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.17/168.30 => 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)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__minus__even,axiom,
% 168.17/168.30 ! [V_n,V_a,T_a] :
% 168.17/168.30 ( class_Rings_Oring__1(T_a)
% 168.17/168.30 => 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)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_div__2__gt__zero,axiom,
% 168.17/168.30 ! [V_n] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 168.17/168.30 => 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)))))) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power2__less__imp__less,axiom,
% 168.17/168.30 ! [V_y,V_x,T_a] :
% 168.17/168.30 ( class_Rings_Olinordered__semidom(T_a)
% 168.17/168.30 => ( 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))))))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 168.17/168.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_sum__power2__le__zero__iff,axiom,
% 168.17/168.30 ! [V_y_2,V_x_2,T_b] :
% 168.17/168.30 ( class_Rings_Olinordered__idom(T_b)
% 168.17/168.30 => ( 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)))
% 168.17/168.30 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 168.17/168.30 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_sum__power2__ge__zero,axiom,
% 168.17/168.30 ! [V_y,V_x,T_a] :
% 168.17/168.30 ( class_Rings_Olinordered__idom(T_a)
% 168.17/168.30 => 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))))))) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_not__sum__power2__lt__zero,axiom,
% 168.17/168.30 ! [V_y,V_x,T_a] :
% 168.17/168.30 ( class_Rings_Olinordered__idom(T_a)
% 168.17/168.30 => ~ 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))) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_sum__power2__gt__zero__iff,axiom,
% 168.17/168.30 ! [V_y_2,V_x_2,T_b] :
% 168.17/168.30 ( class_Rings_Olinordered__idom(T_b)
% 168.17/168.30 => ( 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)))))))
% 168.17/168.30 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
% 168.17/168.30 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power2__sum,axiom,
% 168.17/168.30 ! [V_y,V_x,T_a] :
% 168.17/168.30 ( class_Int_Onumber__ring(T_a)
% 168.17/168.30 => 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)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zero__le__even__power_H,axiom,
% 168.17/168.30 ! [V_n,V_a,T_a] :
% 168.17/168.30 ( class_Rings_Olinordered__idom(T_a)
% 168.17/168.30 => 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)))) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__odd__eq,axiom,
% 168.17/168.30 ! [V_n,V_a,T_a] :
% 168.17/168.30 ( class_Groups_Omonoid__mult(T_a)
% 168.17/168.30 => 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))))) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
% 168.17/168.30 ! [V_n,V_x,T_a] :
% 168.17/168.30 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.17/168.30 => 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))) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_mod2__gr__0,axiom,
% 168.17/168.30 ! [V_m_2] :
% 168.17/168.30 ( 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))))))
% 168.17/168.30 <=> 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) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__minus1__even,axiom,
% 168.17/168.30 ! [V_n,T_a] :
% 168.17/168.30 ( class_Rings_Oring__1(T_a)
% 168.17/168.30 => 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) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_int__power__div__base,axiom,
% 168.17/168.30 ! [V_k,V_m] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 168.17/168.30 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),V_m)),V_k) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_Suc__n__div__2__gt__zero,axiom,
% 168.17/168.30 ! [V_n] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 168.17/168.30 => 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)))))) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power2__diff,axiom,
% 168.17/168.30 ! [V_y,V_x,T_a] :
% 168.17/168.30 ( class_Int_Onumber__ring(T_a)
% 168.17/168.30 => 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)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_odd__0__le__power__imp__0__le,axiom,
% 168.17/168.30 ! [V_n,V_a,T_a] :
% 168.17/168.30 ( class_Rings_Olinordered__idom(T_a)
% 168.17/168.30 => ( 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)))))
% 168.17/168.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_int__of__code,axiom,
% 168.17/168.30 ! [V_k] :
% 168.17/168.30 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 168.17/168.30 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 168.17/168.30 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 168.17/168.30 => ( ( 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)
% 168.17/168.30 => 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)))))) )
% 168.17/168.30 & ( 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)
% 168.17/168.30 => 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)) ) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__strict__mono,axiom,
% 168.17/168.30 ! [V_n,V_b,V_a,T_a] :
% 168.17/168.30 ( class_Rings_Olinordered__semidom(T_a)
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 168.17/168.30 => 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))) ) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__diff,axiom,
% 168.17/168.30 ! [V_m,V_n,V_a,T_a] :
% 168.17/168.30 ( class_Fields_Ofield(T_a)
% 168.17/168.30 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 168.17/168.30 => 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)) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_one__less__power,axiom,
% 168.17/168.30 ! [V_n,V_a,T_a] :
% 168.17/168.30 ( class_Rings_Olinordered__semidom(T_a)
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 168.17/168.30 => 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))) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__increasing__iff,axiom,
% 168.17/168.30 ! [V_y_2,V_x_2,V_b_2,T_b] :
% 168.17/168.30 ( class_Rings_Olinordered__semidom(T_b)
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2)))
% 168.17/168.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_field__power__not__zero,axiom,
% 168.17/168.30 ! [V_n,V_a,T_a] :
% 168.17/168.30 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 168.17/168.30 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.30 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_nat__power__eq__Suc__0__iff,axiom,
% 168.17/168.30 ! [V_m_2,V_x_2] :
% 168.17/168.30 ( 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))
% 168.17/168.30 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.30 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__Suc__0,axiom,
% 168.17/168.30 ! [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)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_nat__power__less__imp__less,axiom,
% 168.17/168.30 ! [V_n,V_m,V_i] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i))
% 168.17/168.30 => ( 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)))
% 168.17/168.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_nat__zero__less__power__iff,axiom,
% 168.17/168.30 ! [V_n_2,V_x_2] :
% 168.17/168.30 ( 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)))
% 168.17/168.30 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2))
% 168.17/168.30 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__mult__distrib,axiom,
% 168.17/168.30 ! [V_n,V_b,V_a,T_a] :
% 168.17/168.30 ( class_Groups_Ocomm__monoid__mult(T_a)
% 168.17/168.30 => 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)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__commutes,axiom,
% 168.17/168.30 ! [V_n,V_a,T_a] :
% 168.17/168.30 ( class_Groups_Omonoid__mult(T_a)
% 168.17/168.30 => 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)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__one,axiom,
% 168.17/168.30 ! [V_n,T_a] :
% 168.17/168.30 ( class_Groups_Omonoid__mult(T_a)
% 168.17/168.30 => 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) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_of__nat__power,axiom,
% 168.17/168.30 ! [V_n,V_m,T_a] :
% 168.17/168.30 ( class_Rings_Osemiring__1(T_a)
% 168.17/168.30 => 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) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__mult,axiom,
% 168.17/168.30 ! [V_n,V_m,V_a,T_a] :
% 168.17/168.30 ( class_Groups_Omonoid__mult(T_a)
% 168.17/168.30 => 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) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__divide,axiom,
% 168.17/168.30 ! [V_n,V_b,V_a,T_a] :
% 168.17/168.30 ( class_Fields_Ofield__inverse__zero(T_a)
% 168.17/168.30 => 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)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__abs,axiom,
% 168.17/168.30 ! [V_n,V_a,T_a] :
% 168.17/168.30 ( class_Rings_Olinordered__idom(T_a)
% 168.17/168.30 => 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) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__one__right,axiom,
% 168.17/168.30 ! [V_a,T_a] :
% 168.17/168.30 ( class_Groups_Omonoid__mult(T_a)
% 168.17/168.30 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zero__le__power,axiom,
% 168.17/168.30 ! [V_n,V_a,T_a] :
% 168.17/168.30 ( class_Rings_Olinordered__semidom(T_a)
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 168.17/168.30 => 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))) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__mono,axiom,
% 168.17/168.30 ! [V_n,V_b,V_a,T_a] :
% 168.17/168.30 ( class_Rings_Olinordered__semidom(T_a)
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 168.17/168.30 => 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))) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zero__less__power,axiom,
% 168.17/168.30 ! [V_n,V_a,T_a] :
% 168.17/168.30 ( class_Rings_Olinordered__semidom(T_a)
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 168.17/168.30 => 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))) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__eq__0__iff,axiom,
% 168.17/168.30 ! [V_n_2,V_a_2,T_b] :
% 168.17/168.30 ( ( class_Power_Opower(T_b)
% 168.17/168.30 & class_Rings_Omult__zero(T_b)
% 168.17/168.30 & class_Rings_Ono__zero__divisors(T_b)
% 168.17/168.30 & class_Rings_Ozero__neq__one(T_b) )
% 168.17/168.30 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_b)
% 168.17/168.30 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
% 168.17/168.30 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_one__le__power,axiom,
% 168.17/168.30 ! [V_n,V_a,T_a] :
% 168.17/168.30 ( class_Rings_Olinordered__semidom(T_a)
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 168.17/168.30 => 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))) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__0__Suc,axiom,
% 168.17/168.30 ! [V_n,T_a] :
% 168.17/168.30 ( ( class_Power_Opower(T_a)
% 168.17/168.30 & class_Rings_Osemiring__0(T_a) )
% 168.17/168.30 => 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) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__inject__exp,axiom,
% 168.17/168.30 ! [V_n_2,V_m_2,V_a_2,T_b] :
% 168.17/168.30 ( class_Rings_Olinordered__semidom(T_b)
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2))
% 168.17/168.30 => ( 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)
% 168.17/168.30 <=> V_m_2 = V_n_2 ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__Suc,axiom,
% 168.17/168.30 ! [V_n,V_a,T_a] :
% 168.17/168.30 ( class_Power_Opower(T_a)
% 168.17/168.30 => 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)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__Suc2,axiom,
% 168.17/168.30 ! [V_n,V_a,T_a] :
% 168.17/168.30 ( class_Groups_Omonoid__mult(T_a)
% 168.17/168.30 => 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) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_nat__one__le__power,axiom,
% 168.17/168.30 ! [V_n,V_i] :
% 168.17/168.30 ( 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))
% 168.17/168.30 => 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))) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__0,axiom,
% 168.17/168.30 ! [V_a,T_a] :
% 168.17/168.30 ( class_Power_Opower(T_a)
% 168.17/168.30 => 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) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__add,axiom,
% 168.17/168.30 ! [V_n,V_m,V_a,T_a] :
% 168.17/168.30 ( class_Groups_Omonoid__mult(T_a)
% 168.17/168.30 => 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)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_nonzero__power__divide,axiom,
% 168.17/168.30 ! [V_n,V_a,V_b,T_a] :
% 168.17/168.30 ( class_Fields_Ofield(T_a)
% 168.17/168.30 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.30 => 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)) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__one__over,axiom,
% 168.17/168.30 ! [V_n,V_a,T_a] :
% 168.17/168.30 ( class_Fields_Ofield__inverse__zero(T_a)
% 168.17/168.30 => 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) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_abs__power__minus,axiom,
% 168.17/168.30 ! [V_n,V_a,T_a] :
% 168.17/168.30 ( class_Rings_Olinordered__idom(T_a)
% 168.17/168.30 => 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)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__less__imp__less__base,axiom,
% 168.17/168.30 ! [V_b,V_n,V_a,T_a] :
% 168.17/168.30 ( class_Rings_Olinordered__semidom(T_a)
% 168.17/168.30 => ( 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)))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 168.17/168.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__le__imp__le__base,axiom,
% 168.17/168.30 ! [V_b,V_n,V_a,T_a] :
% 168.17/168.30 ( class_Rings_Olinordered__semidom(T_a)
% 168.17/168.30 => ( 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))))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 168.17/168.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__inject__base,axiom,
% 168.17/168.30 ! [V_b,V_n,V_a,T_a] :
% 168.17/168.30 ( class_Rings_Olinordered__semidom(T_a)
% 168.17/168.30 => ( 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))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 168.17/168.30 => V_a = V_b ) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__less__power__Suc,axiom,
% 168.17/168.30 ! [V_n,V_a,T_a] :
% 168.17/168.30 ( class_Rings_Olinordered__semidom(T_a)
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 168.17/168.30 => 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)))) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__gt1__lemma,axiom,
% 168.17/168.30 ! [V_n,V_a,T_a] :
% 168.17/168.30 ( class_Rings_Olinordered__semidom(T_a)
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 168.17/168.30 => 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)))) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__0__left,axiom,
% 168.17/168.30 ! [V_n,T_a] :
% 168.17/168.30 ( ( class_Power_Opower(T_a)
% 168.17/168.30 & class_Rings_Osemiring__0(T_a) )
% 168.17/168.30 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.30 => 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) )
% 168.17/168.30 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.30 => 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) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__gt1,axiom,
% 168.17/168.30 ! [V_n,V_a,T_a] :
% 168.17/168.30 ( class_Rings_Olinordered__semidom(T_a)
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 168.17/168.30 => 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)))) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__strict__increasing,axiom,
% 168.17/168.30 ! [V_a,V_N,V_n,T_a] :
% 168.17/168.30 ( class_Rings_Olinordered__semidom(T_a)
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 168.17/168.30 => 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))) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__less__imp__less__exp,axiom,
% 168.17/168.30 ! [V_n,V_m,V_a,T_a] :
% 168.17/168.30 ( class_Rings_Olinordered__semidom(T_a)
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 168.17/168.30 => ( 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)))
% 168.17/168.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__strict__increasing__iff,axiom,
% 168.17/168.30 ! [V_y_2,V_x_2,V_b_2,T_b] :
% 168.17/168.30 ( class_Rings_Olinordered__semidom(T_b)
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2)))
% 168.17/168.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zero__le__power__abs,axiom,
% 168.17/168.30 ! [V_n,V_a,T_a] :
% 168.17/168.30 ( class_Rings_Olinordered__idom(T_a)
% 168.17/168.30 => 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))) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__increasing,axiom,
% 168.17/168.30 ! [V_a,V_N,V_n,T_a] :
% 168.17/168.30 ( class_Rings_Olinordered__semidom(T_a)
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 168.17/168.30 => 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))) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__minus,axiom,
% 168.17/168.30 ! [V_n,V_a,T_a] :
% 168.17/168.30 ( class_Rings_Oring__1(T_a)
% 168.17/168.30 => 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)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__Suc__less,axiom,
% 168.17/168.30 ! [V_n,V_a,T_a] :
% 168.17/168.30 ( class_Rings_Olinordered__semidom(T_a)
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 168.17/168.30 => 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))) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__eq__imp__eq__base,axiom,
% 168.17/168.30 ! [V_b,V_n,V_a,T_a] :
% 168.17/168.30 ( class_Rings_Olinordered__semidom(T_a)
% 168.17/168.30 => ( 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)
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 168.17/168.30 => V_a = V_b ) ) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__Suc__less__one,axiom,
% 168.17/168.30 ! [V_n,V_a,T_a] :
% 168.17/168.30 ( class_Rings_Olinordered__semidom(T_a)
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 168.17/168.30 => 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))) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__strict__decreasing,axiom,
% 168.17/168.30 ! [V_a,V_N,V_n,T_a] :
% 168.17/168.30 ( class_Rings_Olinordered__semidom(T_a)
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 168.17/168.30 => 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))) ) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__decreasing,axiom,
% 168.17/168.30 ! [V_a,V_N,V_n,T_a] :
% 168.17/168.30 ( class_Rings_Olinordered__semidom(T_a)
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 168.17/168.30 => 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))) ) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__le__imp__le__exp,axiom,
% 168.17/168.30 ! [V_n,V_m,V_a,T_a] :
% 168.17/168.30 ( class_Rings_Olinordered__semidom(T_a)
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 168.17/168.30 => ( 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)))
% 168.17/168.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_nat__aux__def,axiom,
% 168.17/168.30 ! [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) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_transfer__morphism__nat__int,axiom,
% 168.17/168.30 c_Nat__Transfer_Otransfer__morphism(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_card__Pow,axiom,
% 168.17/168.30 ! [V_A_2,T_b] :
% 168.17/168.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.30 => 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)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__power__power,axiom,
% 168.17/168.30 ! [T_b] :
% 168.17/168.30 ( class_Power_Opower(T_b)
% 168.17/168.30 => 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)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__m1__odd,axiom,
% 168.17/168.30 ! [V_n,T_a] :
% 168.17/168.30 ( class_Int_Onumber__ring(T_a)
% 168.17/168.30 => 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) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_PowI,axiom,
% 168.17/168.30 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.17/168.30 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_rel__simps_I24_J,axiom,
% 168.17/168.30 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_rel__simps_I7_J,axiom,
% 168.17/168.30 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_rel__simps_I40_J,axiom,
% 168.17/168.30 c_Int_OMin != c_Int_OPls ).
% 168.17/168.30
% 168.17/168.30 fof(fact_rel__simps_I37_J,axiom,
% 168.17/168.30 c_Int_OPls != c_Int_OMin ).
% 168.17/168.30
% 168.17/168.30 fof(fact_Bit1__Min,axiom,
% 168.17/168.30 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ).
% 168.17/168.30
% 168.17/168.30 fof(fact_rel__simps_I43_J,axiom,
% 168.17/168.30 ! [V_l_2] :
% 168.17/168.30 ( c_Int_OMin = c_Int_OBit1(V_l_2)
% 168.17/168.30 <=> c_Int_OMin = V_l_2 ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_rel__simps_I47_J,axiom,
% 168.17/168.30 ! [V_k_2] :
% 168.17/168.30 ( c_Int_OBit1(V_k_2) = c_Int_OMin
% 168.17/168.30 <=> V_k_2 = c_Int_OMin ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_rel__simps_I45_J,axiom,
% 168.17/168.30 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ).
% 168.17/168.30
% 168.17/168.30 fof(fact_rel__simps_I42_J,axiom,
% 168.17/168.30 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_Pow__top,axiom,
% 168.17/168.30 ! [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))) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_Union__Pow__eq,axiom,
% 168.17/168.30 ! [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 ).
% 168.17/168.30
% 168.17/168.30 fof(fact_Pow__not__empty,axiom,
% 168.17/168.30 ! [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)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_bin__less__0__simps_I2_J,axiom,
% 168.17/168.30 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_rel__simps_I20_J,axiom,
% 168.17/168.30 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_rel__simps_I23_J,axiom,
% 168.17/168.30 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_rel__simps_I30_J,axiom,
% 168.17/168.30 ! [V_k_2] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 168.17/168.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_rel__simps_I26_J,axiom,
% 168.17/168.30 ! [V_k_2] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 168.17/168.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_rel__simps_I3_J,axiom,
% 168.17/168.30 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_rel__simps_I6_J,axiom,
% 168.17/168.30 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_rel__simps_I13_J,axiom,
% 168.17/168.30 ! [V_k_2] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 168.17/168.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_rel__simps_I9_J,axiom,
% 168.17/168.30 ! [V_k_2] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 168.17/168.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_rel__simps_I28_J,axiom,
% 168.17/168.30 ! [V_k_2] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 168.17/168.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_rel__simps_I8_J,axiom,
% 168.17/168.30 ! [V_k_2] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 168.17/168.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_eq__number__of__Pls__Min,axiom,
% 168.17/168.30 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) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_Int_OMin__def,axiom,
% 168.17/168.30 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_mult__Min,axiom,
% 168.17/168.30 ! [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) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_neg__number__of__Min,axiom,
% 168.17/168.30 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_pred__Pls,axiom,
% 168.17/168.30 c_Int_Opred(c_Int_OPls) = c_Int_OMin ).
% 168.17/168.30
% 168.17/168.30 fof(fact_add__Min,axiom,
% 168.17/168.30 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_add__Min__right,axiom,
% 168.17/168.30 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_pred__Min,axiom,
% 168.17/168.30 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_nonzero__number__of__Min,axiom,
% 168.17/168.30 ! [T_a] :
% 168.17/168.30 ( class_Int_Onumber__ring(T_a)
% 168.17/168.30 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_succ__Min,axiom,
% 168.17/168.30 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ).
% 168.17/168.30
% 168.17/168.30 fof(fact_diff__bin__simps_I2_J,axiom,
% 168.17/168.30 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_Pow__bottom,axiom,
% 168.17/168.30 ! [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))) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_PowD,axiom,
% 168.17/168.30 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
% 168.17/168.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_Pow__iff,axiom,
% 168.17/168.30 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
% 168.17/168.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_Pow__mono,axiom,
% 168.17/168.30 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.17/168.30 => 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))) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_finite__Pow__iff,axiom,
% 168.17/168.30 ! [V_A_2,T_b] :
% 168.17/168.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)))
% 168.17/168.30 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_mult__minus1,axiom,
% 168.17/168.30 ! [V_z,T_a] :
% 168.17/168.30 ( class_Int_Onumber__ring(T_a)
% 168.17/168.30 => 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) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_mult__minus1__right,axiom,
% 168.17/168.30 ! [V_z,T_a] :
% 168.17/168.30 ( class_Int_Onumber__ring(T_a)
% 168.17/168.30 => 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) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_subset__Pow__Union,axiom,
% 168.17/168.30 ! [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)))) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_number__of__Min,axiom,
% 168.17/168.30 ! [T_a] :
% 168.17/168.30 ( class_Int_Onumber__ring(T_a)
% 168.17/168.30 => 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)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_arith__simps_I31_J,axiom,
% 168.17/168.30 ! [T_a] :
% 168.17/168.30 ( class_Int_Onumber__ring(T_a)
% 168.17/168.30 => 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) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_abs__minus__one,axiom,
% 168.17/168.30 ! [T_a] :
% 168.17/168.30 ( ( class_Int_Onumber__ring(T_a)
% 168.17/168.30 & class_Rings_Olinordered__idom(T_a) )
% 168.17/168.30 => 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) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_divide__minus1,axiom,
% 168.17/168.30 ! [V_x,T_a] :
% 168.17/168.30 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 168.17/168.30 & class_Int_Onumber__ring(T_a) )
% 168.17/168.30 => 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) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_rel__simps_I25_J,axiom,
% 168.17/168.30 ! [V_k_2] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 168.17/168.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_rel__simps_I11_J,axiom,
% 168.17/168.30 ! [V_k_2] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 168.17/168.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zmod__minus1__right,axiom,
% 168.17/168.30 ! [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) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_diff__bin__simps_I4_J,axiom,
% 168.17/168.30 ! [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)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_minus__Min,axiom,
% 168.17/168.30 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_pos__zmult__eq__1__iff__lemma,axiom,
% 168.17/168.30 ! [V_n,V_m] :
% 168.17/168.30 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 168.17/168.30 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 168.17/168.30 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zmult__eq__1__iff,axiom,
% 168.17/168.30 ! [V_n_2,V_m_2] :
% 168.17/168.30 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 168.17/168.30 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 168.17/168.30 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 168.17/168.30 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
% 168.17/168.30 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_diff__bin__simps_I6_J,axiom,
% 168.17/168.30 ! [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)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_diff__bin__simps_I5_J,axiom,
% 168.17/168.30 ! [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)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power_Opower_Opower__0,axiom,
% 168.17/168.30 ! [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 ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power_Opower_Opower__Suc,axiom,
% 168.17/168.30 ! [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)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zdiv__minus1__right,axiom,
% 168.17/168.30 ! [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) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_Pow__Int__eq,axiom,
% 168.17/168.30 ! [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)) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_minus1__divide,axiom,
% 168.17/168.30 ! [V_x,T_a] :
% 168.17/168.30 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 168.17/168.30 & class_Int_Onumber__ring(T_a) )
% 168.17/168.30 => 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)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_abs__power__minus__one,axiom,
% 168.17/168.30 ! [V_n,T_a] :
% 168.17/168.30 ( ( class_Int_Onumber__ring(T_a)
% 168.17/168.30 & class_Rings_Olinordered__idom(T_a) )
% 168.17/168.30 => 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) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_div__eq__minus1,axiom,
% 168.17/168.30 ! [V_b] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 168.17/168.30 => 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) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_Pow__empty,axiom,
% 168.17/168.30 ! [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))) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_Un__Pow__subset,axiom,
% 168.17/168.30 ! [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)))) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_div__pos__neg__trivial,axiom,
% 168.17/168.30 ! [V_b,V_a] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 168.17/168.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.30 => 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) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_zmod__minus1,axiom,
% 168.17/168.30 ! [V_b] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 168.17/168.30 => 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)) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_power__m1__even,axiom,
% 168.17/168.30 ! [V_n,T_a] :
% 168.17/168.30 ( class_Int_Onumber__ring(T_a)
% 168.17/168.30 => 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) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_code__numeral_Osize_I1_J,axiom,
% 168.17/168.30 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) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_of__int__of__nat,axiom,
% 168.17/168.30 ! [V_k,T_a] :
% 168.17/168.30 ( class_Rings_Oring__1(T_a)
% 168.17/168.30 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.30 => 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)))) )
% 168.17/168.30 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.30 => 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)) ) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_Nitpick_Oint__lcm__def,axiom,
% 168.17/168.30 ! [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)))) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_negD,axiom,
% 168.17/168.30 ! [V_x] :
% 168.17/168.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.30 => ? [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))) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_code__numeral_Osize_I3_J,axiom,
% 168.17/168.30 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) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_of__int__eq__iff,axiom,
% 168.17/168.30 ! [V_z_2,V_w_2,T_b] :
% 168.17/168.30 ( class_Int_Oring__char__0(T_b)
% 168.17/168.30 => ( 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)
% 168.17/168.30 <=> V_w_2 = V_z_2 ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_number__of__eq,axiom,
% 168.17/168.30 ! [V_k,T_a] :
% 168.17/168.30 ( class_Int_Onumber__ring(T_a)
% 168.17/168.30 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_int__number__of__def,axiom,
% 168.17/168.30 ! [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) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_of__int__int__eq,axiom,
% 168.17/168.30 ! [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) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_of__int__eq__0__iff,axiom,
% 168.17/168.30 ! [V_z_2,T_b] :
% 168.17/168.30 ( class_Int_Oring__char__0(T_b)
% 168.17/168.30 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) = c_Groups_Ozero__class_Ozero(T_b)
% 168.17/168.30 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 168.17/168.30
% 168.17/168.30 fof(fact_of__int__0__eq__iff,axiom,
% 168.17/168.30 ! [V_z_2,T_b] :
% 168.17/168.31 ( class_Int_Oring__char__0(T_b)
% 168.17/168.31 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)
% 168.17/168.31 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_of__int__0,axiom,
% 168.17/168.31 ! [T_a] :
% 168.17/168.31 ( class_Rings_Oring__1(T_a)
% 168.17/168.31 => 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) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_of__int__le__iff,axiom,
% 168.17/168.31 ! [V_z_2,V_w_2,T_b] :
% 168.17/168.31 ( class_Rings_Olinordered__idom(T_b)
% 168.17/168.31 => ( 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)))
% 168.17/168.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_of__int__less__iff,axiom,
% 168.17/168.31 ! [V_z_2,V_w_2,T_b] :
% 168.17/168.31 ( class_Rings_Olinordered__idom(T_b)
% 168.17/168.31 => ( 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)))
% 168.17/168.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_of__int__add,axiom,
% 168.17/168.31 ! [V_z,V_w,T_a] :
% 168.17/168.31 ( class_Rings_Oring__1(T_a)
% 168.17/168.31 => 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)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_of__int__number__of__eq,axiom,
% 168.17/168.31 ! [V_v,T_a] :
% 168.17/168.31 ( class_Int_Onumber__ring(T_a)
% 168.17/168.31 => 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) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_of__int__mult,axiom,
% 168.17/168.31 ! [V_z,V_w,T_a] :
% 168.17/168.31 ( class_Rings_Oring__1(T_a)
% 168.17/168.31 => 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)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_of__int__1,axiom,
% 168.17/168.31 ! [T_a] :
% 168.17/168.31 ( class_Rings_Oring__1(T_a)
% 168.17/168.31 => 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) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_of__int__diff,axiom,
% 168.17/168.31 ! [V_z,V_w,T_a] :
% 168.17/168.31 ( class_Rings_Oring__1(T_a)
% 168.17/168.31 => 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)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_of__int__of__nat__eq,axiom,
% 168.17/168.31 ! [V_n,T_a] :
% 168.17/168.31 ( class_Rings_Oring__1(T_a)
% 168.17/168.31 => 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) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_of__int__minus,axiom,
% 168.17/168.31 ! [V_z,T_a] :
% 168.17/168.31 ( class_Rings_Oring__1(T_a)
% 168.17/168.31 => 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)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Ints__of__int,axiom,
% 168.17/168.31 ! [V_z_2,T_b] :
% 168.17/168.31 ( class_Rings_Oring__1(T_b)
% 168.17/168.31 => 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))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_of__int__power,axiom,
% 168.17/168.31 ! [V_n,V_z,T_a] :
% 168.17/168.31 ( class_Rings_Oring__1(T_a)
% 168.17/168.31 => 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) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_of__int__m1,axiom,
% 168.17/168.31 ! [T_a] :
% 168.17/168.31 ( class_Int_Onumber__ring(T_a)
% 168.17/168.31 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_of__int__0__le__iff,axiom,
% 168.17/168.31 ! [V_z_2,T_b] :
% 168.17/168.31 ( class_Rings_Olinordered__idom(T_b)
% 168.17/168.31 => ( 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)))
% 168.17/168.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_of__int__le__0__iff,axiom,
% 168.17/168.31 ! [V_z_2,T_b] :
% 168.17/168.31 ( class_Rings_Olinordered__idom(T_b)
% 168.17/168.31 => ( 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)))
% 168.17/168.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_of__int__0__less__iff,axiom,
% 168.17/168.31 ! [V_z_2,T_b] :
% 168.17/168.31 ( class_Rings_Olinordered__idom(T_b)
% 168.17/168.31 => ( 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)))
% 168.17/168.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_of__int__less__0__iff,axiom,
% 168.17/168.31 ! [V_z_2,T_b] :
% 168.17/168.31 ( class_Rings_Olinordered__idom(T_b)
% 168.17/168.31 => ( 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)))
% 168.17/168.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_of__nat__nat,axiom,
% 168.17/168.31 ! [V_z,T_a] :
% 168.17/168.31 ( class_Rings_Oring__1(T_a)
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 168.17/168.31 => 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) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Nitpick_Onat__lcm__def,axiom,
% 168.17/168.31 ! [V_y,V_x] : c_Nitpick_Onat__lcm(V_x,V_y) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x),V_y)),c_Nitpick_Onat__gcd(V_x,V_y)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_code__numeral_Osize_I4_J,axiom,
% 168.17/168.31 ! [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))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_code__numeral_Osize_I2_J,axiom,
% 168.17/168.31 ! [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))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_sgn__neg,axiom,
% 168.17/168.31 ! [V_a,T_a] :
% 168.17/168.31 ( class_Rings_Olinordered__idom(T_a)
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 168.17/168.31 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_sgn__1__neg,axiom,
% 168.17/168.31 ! [V_a_2,T_b] :
% 168.17/168.31 ( class_Rings_Olinordered__idom(T_b)
% 168.17/168.31 => ( 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))
% 168.17/168.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_sgn__sgn,axiom,
% 168.17/168.31 ! [V_a,T_a] :
% 168.17/168.31 ( class_Rings_Olinordered__idom(T_a)
% 168.17/168.31 => 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) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_code__numeral_Oinject,axiom,
% 168.17/168.31 ! [V_code__numeral_H_2,V_code__numeral_2] :
% 168.17/168.31 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2)
% 168.17/168.31 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_sgn__0__0,axiom,
% 168.17/168.31 ! [V_a_2,T_b] :
% 168.17/168.31 ( class_Rings_Olinordered__idom(T_b)
% 168.17/168.31 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 168.17/168.31 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_sgn0,axiom,
% 168.17/168.31 ! [T_a] :
% 168.17/168.31 ( class_Groups_Osgn__if(T_a)
% 168.17/168.31 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_sgn__times,axiom,
% 168.17/168.31 ! [V_b,V_a,T_a] :
% 168.17/168.31 ( class_Rings_Olinordered__idom(T_a)
% 168.17/168.31 => 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)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_code__numeral_Osimps_I2_J,axiom,
% 168.17/168.31 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_code__numeral_Osimps_I3_J,axiom,
% 168.17/168.31 ! [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) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_sgn__less,axiom,
% 168.17/168.31 ! [V_a_2,T_b] :
% 168.17/168.31 ( class_Rings_Olinordered__idom(T_b)
% 168.17/168.31 => ( 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)))
% 168.17/168.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_sgn__greater,axiom,
% 168.17/168.31 ! [V_a_2,T_b] :
% 168.17/168.31 ( class_Rings_Olinordered__idom(T_b)
% 168.17/168.31 => ( 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)))
% 168.17/168.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_abs__sgn,axiom,
% 168.17/168.31 ! [V_k,T_a] :
% 168.17/168.31 ( class_Rings_Olinordered__idom(T_a)
% 168.17/168.31 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_mult__sgn__abs,axiom,
% 168.17/168.31 ! [V_x,T_a] :
% 168.17/168.31 ( class_Rings_Olinordered__idom(T_a)
% 168.17/168.31 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_x)) = V_x ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Suc__code__numeral__minus__one,axiom,
% 168.17/168.31 ! [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 ).
% 168.17/168.31
% 168.17/168.31 fof(fact_sgn__pos,axiom,
% 168.17/168.31 ! [V_a,T_a] :
% 168.17/168.31 ( class_Rings_Olinordered__idom(T_a)
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 168.17/168.31 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_sgn__1__pos,axiom,
% 168.17/168.31 ! [V_a_2,T_b] :
% 168.17/168.31 ( class_Rings_Olinordered__idom(T_b)
% 168.17/168.31 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Oone__class_Oone(T_b)
% 168.17/168.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_nat__gcd_Osimps,axiom,
% 168.17/168.31 ! [V_x,V_y] :
% 168.17/168.31 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.31 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x )
% 168.17/168.31 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.31 => 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)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_zsgn__def,axiom,
% 168.17/168.31 ! [V_i] :
% 168.17/168.31 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.31 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 168.17/168.31 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.31 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 168.17/168.31 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 168.17/168.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 168.17/168.31 => 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)) ) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_sgn__if,axiom,
% 168.17/168.31 ! [V_x,T_a] :
% 168.17/168.31 ( class_Groups_Osgn__if(T_a)
% 168.17/168.31 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.31 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) )
% 168.17/168.31 & ( V_x != c_Groups_Ozero__class_Ozero(T_a)
% 168.17/168.31 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 168.17/168.31 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) )
% 168.17/168.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 168.17/168.31 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Nitpick_Oint__gcd__def,axiom,
% 168.17/168.31 ! [V_y,V_x] : hAPP(hAPP(c_Nitpick_Oint__gcd,V_x),V_y) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__gcd(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_y)))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_code__numeral_Osimps_I5_J,axiom,
% 168.17/168.31 ! [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) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_compl__unique,axiom,
% 168.17/168.31 ! [V_y,V_x,T_a] :
% 168.17/168.31 ( class_Lattices_Oboolean__algebra(T_a)
% 168.17/168.31 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a)
% 168.17/168.31 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a)
% 168.17/168.31 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_int__val__lemma,axiom,
% 168.17/168.31 ! [V_k_2,V_f_2,V_n_2] :
% 168.17/168.31 ( ! [B_i] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 168.17/168.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2))
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 168.17/168.31 => ? [B_i] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 168.17/168.31 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_nat0__intermed__int__val,axiom,
% 168.17/168.31 ! [V_k_2,V_f_2,V_n_2] :
% 168.17/168.31 ( ! [B_i] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 168.17/168.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2))
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 168.17/168.31 => ? [B_i] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 168.17/168.31 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_UNIV__I,axiom,
% 168.17/168.31 ! [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)))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Pow__UNIV,axiom,
% 168.17/168.31 ! [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)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_finite__fun__UNIVD2,axiom,
% 168.17/168.31 ! [T_c,T_b] :
% 168.17/168.31 ( 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))))
% 168.17/168.31 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_UNIV__not__empty,axiom,
% 168.17/168.31 ! [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)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_finite__UNIV,axiom,
% 168.17/168.31 ! [T_b] :
% 168.17/168.31 ( class_Finite__Set_Ofinite(T_b)
% 168.17/168.31 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Sup__UNIV,axiom,
% 168.17/168.31 ! [T_b] :
% 168.17/168.31 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 168.17/168.31 => 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) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Union__UNIV,axiom,
% 168.17/168.31 ! [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)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_UNIV__Plus__UNIV,axiom,
% 168.17/168.31 ! [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)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_top__apply,axiom,
% 168.17/168.31 ! [V_x_2,T_c,T_b] :
% 168.17/168.31 ( class_Orderings_Otop(T_b)
% 168.17/168.31 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Otop__class_Otop(T_b) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_finite__option__UNIV,axiom,
% 168.17/168.31 ! [T_b] :
% 168.17/168.31 ( 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))))
% 168.17/168.31 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_finite__Prod__UNIV,axiom,
% 168.17/168.31 ! [T_c,T_b] :
% 168.17/168.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 168.17/168.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
% 168.17/168.31 => 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)))) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Int__UNIV__right,axiom,
% 168.17/168.31 ! [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 ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Int__UNIV__left,axiom,
% 168.17/168.31 ! [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 ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Un__UNIV__right,axiom,
% 168.17/168.31 ! [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)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Un__UNIV__left,axiom,
% 168.17/168.31 ! [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)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_subset__UNIV,axiom,
% 168.17/168.31 ! [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)))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_card__UNIV__unit,axiom,
% 168.17/168.31 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) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_finite__Plus__UNIV__iff,axiom,
% 168.17/168.31 ! [T_c,T_b] :
% 168.17/168.31 ( 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))))
% 168.17/168.31 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 168.17/168.31 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_top__greatest,axiom,
% 168.17/168.31 ! [V_x,T_a] :
% 168.17/168.31 ( class_Orderings_Otop(T_a)
% 168.17/168.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_sup__top__right,axiom,
% 168.17/168.31 ! [V_x,T_a] :
% 168.17/168.31 ( class_Lattices_Obounded__lattice__top(T_a)
% 168.17/168.31 => 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) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_sup__top__left,axiom,
% 168.17/168.31 ! [V_x,T_a] :
% 168.17/168.31 ( class_Lattices_Obounded__lattice__top(T_a)
% 168.17/168.31 => 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) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_inf__top__left,axiom,
% 168.17/168.31 ! [V_x,T_a] :
% 168.17/168.31 ( class_Lattices_Obounded__lattice__top(T_a)
% 168.17/168.31 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_inf__top__right,axiom,
% 168.17/168.31 ! [V_x,T_a] :
% 168.17/168.31 ( class_Lattices_Obounded__lattice__top(T_a)
% 168.17/168.31 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_inf__eq__top__iff,axiom,
% 168.17/168.31 ! [V_y_2,V_x_2,T_b] :
% 168.17/168.31 ( class_Lattices_Obounded__lattice__top(T_b)
% 168.17/168.31 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_b)
% 168.17/168.31 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_b)
% 168.17/168.31 & V_y_2 = c_Orderings_Otop__class_Otop(T_b) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Diff__UNIV,axiom,
% 168.17/168.31 ! [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)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
% 168.17/168.31 ! [V_A_2,T_b] :
% 168.17/168.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 168.17/168.31 => ( 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)))
% 168.17/168.31 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Compl__empty__eq,axiom,
% 168.17/168.31 ! [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)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Compl__UNIV__eq,axiom,
% 168.17/168.31 ! [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)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_finite__compl,axiom,
% 168.17/168.31 ! [V_A_2,T_b] :
% 168.17/168.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 168.17/168.31 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Compl__partition2,axiom,
% 168.17/168.31 ! [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)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Compl__partition,axiom,
% 168.17/168.31 ! [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)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Compl__eq__Diff__UNIV,axiom,
% 168.17/168.31 ! [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) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_compl__bot__eq,axiom,
% 168.17/168.31 ! [T_a] :
% 168.17/168.31 ( class_Lattices_Oboolean__algebra(T_a)
% 168.17/168.31 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_compl__top__eq,axiom,
% 168.17/168.31 ! [T_a] :
% 168.17/168.31 ( class_Lattices_Oboolean__algebra(T_a)
% 168.17/168.31 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_sup__compl__top,axiom,
% 168.17/168.31 ! [V_x,T_a] :
% 168.17/168.31 ( class_Lattices_Oboolean__algebra(T_a)
% 168.17/168.31 => 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) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_compl__sup__top,axiom,
% 168.17/168.31 ! [V_x,T_a] :
% 168.17/168.31 ( class_Lattices_Oboolean__algebra(T_a)
% 168.17/168.31 => 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) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_finite__UNIV__card__ge__0,axiom,
% 168.17/168.31 ! [T_b] :
% 168.17/168.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 168.17/168.31 => 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))))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_card__UNIV__bool,axiom,
% 168.17/168.31 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))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_code__numeral_Osimps_I4_J,axiom,
% 168.17/168.31 ! [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 ).
% 168.17/168.31
% 168.17/168.31 fof(fact_finite__fun__UNIVD1,axiom,
% 168.17/168.31 ! [T_c,T_b] :
% 168.17/168.31 ( 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))))
% 168.17/168.31 => ( 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))
% 168.17/168.31 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Inf__fold__inf,axiom,
% 168.17/168.31 ! [V_A_2,T_b] :
% 168.17/168.31 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 168.17/168.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.31 => 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) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom,
% 168.17/168.31 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_nat__mod__eq__lemma,axiom,
% 168.17/168.31 ! [V_y,V_n,V_x] :
% 168.17/168.31 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n)
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x))
% 168.17/168.31 => ? [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)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_mod__induct__0,axiom,
% 168.17/168.31 ! [V_i_2,V_P_2,V_p_2] :
% 168.17/168.31 ( ! [B_i] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2))
% 168.17/168.31 => ( hBOOL(hAPP(V_P_2,B_i))
% 168.17/168.31 => hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) )
% 168.17/168.31 => ( hBOOL(hAPP(V_P_2,V_i_2))
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2))
% 168.17/168.31 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_finite__Inter,axiom,
% 168.17/168.31 ! [V_M_2,T_b] :
% 168.17/168.31 ( ? [B_x] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_M_2))
% 168.17/168.31 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) )
% 168.17/168.31 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_M_2))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_top1I,axiom,
% 168.17/168.31 ! [V_x_2,T_b] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_x_2)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_InterE,axiom,
% 168.17/168.31 ! [V_X_2,V_C_2,V_A_2,T_b] :
% 168.17/168.31 ( 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)))
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 168.17/168.31 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_InterD,axiom,
% 168.17/168.31 ! [V_X_2,V_C_2,V_A_2,T_b] :
% 168.17/168.31 ( 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)))
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 168.17/168.31 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Inter__UNIV,axiom,
% 168.17/168.31 ! [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)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom,
% 168.17/168.31 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Inter__empty,axiom,
% 168.17/168.31 ! [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)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom,
% 168.17/168.31 ! [V_y,V_x] :
% 168.17/168.31 ( c_Nat__Transfer_Ois__nat(V_x)
% 168.17/168.31 => ( c_Nat__Transfer_Ois__nat(V_y)
% 168.17/168.31 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom,
% 168.17/168.31 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom,
% 168.17/168.31 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom,
% 168.17/168.31 ! [V_y,V_x] :
% 168.17/168.31 ( c_Nat__Transfer_Ois__nat(V_x)
% 168.17/168.31 => ( c_Nat__Transfer_Ois__nat(V_y)
% 168.17/168.31 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_le__Inf__iff,axiom,
% 168.17/168.31 ! [V_A_2,V_b_2,T_b] :
% 168.17/168.31 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)))
% 168.17/168.31 <=> ! [B_x] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.17/168.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Inf__less__iff,axiom,
% 168.17/168.31 ! [V_a_2,V_S_2,T_b] :
% 168.17/168.31 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 168.17/168.31 & class_Orderings_Olinorder(T_b) )
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_S_2)),V_a_2))
% 168.17/168.31 <=> ? [B_x] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 168.17/168.31 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_a_2)) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom,
% 168.17/168.31 ! [V_y,V_x] :
% 168.17/168.31 ( c_Nat__Transfer_Ois__nat(V_x)
% 168.17/168.31 => ( c_Nat__Transfer_Ois__nat(V_y)
% 168.17/168.31 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom,
% 168.17/168.31 ! [V_y,V_x] :
% 168.17/168.31 ( c_Nat__Transfer_Ois__nat(V_x)
% 168.17/168.31 => ( c_Nat__Transfer_Ois__nat(V_y)
% 168.17/168.31 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Inf__UNIV,axiom,
% 168.17/168.31 ! [T_b] :
% 168.17/168.31 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 168.17/168.31 => 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) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom,
% 168.17/168.31 ! [V_n,V_x] :
% 168.17/168.31 ( c_Nat__Transfer_Ois__nat(V_x)
% 168.17/168.31 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom,
% 168.17/168.31 ! [V_y,V_x] :
% 168.17/168.31 ( c_Nat__Transfer_Ois__nat(V_x)
% 168.17/168.31 => ( c_Nat__Transfer_Ois__nat(V_y)
% 168.17/168.31 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Inter__lower,axiom,
% 168.17/168.31 ! [V_A_2,V_B_2,T_b] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 168.17/168.31 => 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)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Inter__anti__mono,axiom,
% 168.17/168.31 ! [V_A_2,V_B_2,T_b] :
% 168.17/168.31 ( 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))
% 168.17/168.31 => 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))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Inter__insert,axiom,
% 168.17/168.31 ! [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)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_is__nat__def,axiom,
% 168.17/168.31 ! [V_x_2] :
% 168.17/168.31 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 168.17/168.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Inf__lower,axiom,
% 168.17/168.31 ! [V_A_2,V_x_2,T_b] :
% 168.17/168.31 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.31 => 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)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Inter__Un__distrib,axiom,
% 168.17/168.31 ! [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)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Inf__singleton,axiom,
% 168.17/168.31 ! [V_a_2,T_b] :
% 168.17/168.31 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 168.17/168.31 => 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 ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Inf__empty,axiom,
% 168.17/168.31 ! [T_b] :
% 168.17/168.31 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 168.17/168.31 => 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) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Inf__insert,axiom,
% 168.17/168.31 ! [V_A_2,V_a_2,T_b] :
% 168.17/168.31 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 168.17/168.31 => 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)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Int__eq__Inter,axiom,
% 168.17/168.31 ! [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))))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom,
% 168.17/168.31 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Inter__Un__subset,axiom,
% 168.17/168.31 ! [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)))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Inf__binary,axiom,
% 168.17/168.31 ! [V_b_2,V_a_2,T_b] :
% 168.17/168.31 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 168.17/168.31 => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),V_b_2) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_inf__Inf__fold__inf,axiom,
% 168.17/168.31 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.31 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 168.17/168.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.31 => 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) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Inf__fin__Inf,axiom,
% 168.17/168.31 ! [V_A_2,T_b] :
% 168.17/168.31 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 168.17/168.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.31 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.31 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_iso__tuple__UNIV__I,axiom,
% 168.17/168.31 ! [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)))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_nat__intermed__int__val,axiom,
% 168.17/168.31 ! [V_k_2,V_f_2,V_n_2,V_m_2] :
% 168.17/168.31 ( ! [B_i] :
% 168.17/168.31 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 168.17/168.31 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) )
% 168.17/168.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2))
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 168.17/168.31 => ? [B_i] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 168.17/168.31 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 168.17/168.31 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_log_Osimps,axiom,
% 168.17/168.31 ! [V_i,V_b] :
% 168.17/168.31 ( ( ( 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)))
% 168.17/168.31 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 168.17/168.31 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 168.17/168.31 & ( ~ ( 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)))
% 168.17/168.31 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 168.17/168.31 => 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))) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_mod__div__decomp,axiom,
% 168.17/168.31 ! [V_b,V_a,T_a] :
% 168.17/168.31 ( class_Divides_Osemiring__div(T_a)
% 168.17/168.31 => 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)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_field__le__epsilon,axiom,
% 168.17/168.31 ! [V_y,V_x,T_a] :
% 168.17/168.31 ( class_Fields_Olinordered__field(T_a)
% 168.17/168.31 => ( ! [B_e] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_e))
% 168.17/168.31 => 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))) )
% 168.17/168.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_minus__shift__def,axiom,
% 168.17/168.31 ! [V_r,V_l,V_k] :
% 168.17/168.31 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 168.17/168.31 => 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) )
% 168.17/168.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 168.17/168.31 => 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) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_inc__shift__def,axiom,
% 168.17/168.31 ! [V_k,V_v] :
% 168.17/168.31 ( ( V_v = V_k
% 168.17/168.31 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 168.17/168.31 & ( V_v != V_k
% 168.17/168.31 => 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)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Inter__subset,axiom,
% 168.17/168.31 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.31 ( ! [B_X] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2))
% 168.17/168.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_B_2)) )
% 168.17/168.31 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 168.17/168.31 => 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)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_InterI,axiom,
% 168.17/168.31 ! [V_A_2,V_C_2,T_b] :
% 168.17/168.31 ( ! [B_X] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2))
% 168.17/168.31 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) )
% 168.17/168.31 => 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))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_subtract__code__numeral__def,axiom,
% 168.17/168.31 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_minus__code__numeral__code,axiom,
% 168.17/168.31 ! [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) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_pair__box_Osize_I1_J,axiom,
% 168.17/168.31 ! [V_b_2,V_a_2,V_fb_2,V_fa_2,T_c,T_b] : c_Nitpick_Opair__box_Opair__box__size(T_b,T_c,V_fa_2,V_fb_2,c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(V_fb_2,V_b_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_negDivAlg__eqn__1__number__of,axiom,
% 168.17/168.31 ! [V_w] :
% 168.17/168.31 ( 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)))
% 168.17/168.31 => ( ( 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))))
% 168.17/168.31 => 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))) )
% 168.17/168.31 & ( ~ 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))))
% 168.17/168.31 => 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)))) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_pair__box_Oinject,axiom,
% 168.17/168.31 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 168.17/168.31 ( c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2) = c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_H_2,V_b_H_2)
% 168.17/168.31 <=> ( V_a_2 = V_a_H_2
% 168.17/168.31 & V_b_2 = V_b_H_2 ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_negDivAlg__div__mod,axiom,
% 168.17/168.31 ! [V_l,V_k] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 168.17/168.31 => 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)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_negDivAlg__minus1,axiom,
% 168.17/168.31 ! [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))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_negDivAlg_Osimps,axiom,
% 168.17/168.31 ! [V_b,V_a] :
% 168.17/168.31 ( ( ( 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)))
% 168.17/168.31 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 168.17/168.31 => 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)) )
% 168.17/168.31 & ( ~ ( 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)))
% 168.17/168.31 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 168.17/168.31 => 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))) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_negDivAlg__eqn__number__of,axiom,
% 168.17/168.31 ! [V_w,V_v] :
% 168.17/168.31 ( 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)))
% 168.17/168.31 => ( ( 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))))
% 168.17/168.31 => 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))) )
% 168.17/168.31 & ( ~ 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))))
% 168.17/168.31 => 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)))) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_negDivAlg__eqn,axiom,
% 168.17/168.31 ! [V_a,V_b] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 168.17/168.31 => ( ( 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)))
% 168.17/168.31 => 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)) )
% 168.17/168.31 & ( ~ 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)))
% 168.17/168.31 => 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))) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_posDivAlg__eqn__1__number__of,axiom,
% 168.17/168.31 ! [V_w] :
% 168.17/168.31 ( 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)))
% 168.17/168.31 => ( ( 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)))
% 168.17/168.31 => 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)) )
% 168.17/168.31 & ( ~ 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)))
% 168.17/168.31 => 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)))) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_posDivAlg_Osimps,axiom,
% 168.17/168.31 ! [V_b,V_a] :
% 168.17/168.31 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 168.17/168.31 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 168.17/168.31 => 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) )
% 168.17/168.31 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 168.17/168.31 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 168.17/168.31 => 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))) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_in__rel__def,axiom,
% 168.17/168.31 ! [V_y_2,V_x_2,V_R_2,T_c,T_b] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_b,T_c,V_R_2),V_x_2),V_y_2))
% 168.17/168.31 <=> 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)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_posDivAlg__eqn,axiom,
% 168.17/168.31 ! [V_a,V_b] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 168.17/168.31 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 168.17/168.31 => 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) )
% 168.17/168.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 168.17/168.31 => 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))) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_posDivAlg__0,axiom,
% 168.17/168.31 ! [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)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_posDivAlg__div__mod,axiom,
% 168.17/168.31 ! [V_l,V_k] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 168.17/168.31 => 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)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_posDivAlg__eqn__number__of,axiom,
% 168.17/168.31 ! [V_w,V_v] :
% 168.17/168.31 ( 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)))
% 168.17/168.31 => ( ( 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)))
% 168.17/168.31 => 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)) )
% 168.17/168.31 & ( ~ 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)))
% 168.17/168.31 => 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)))) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_div__mod__code__numeral__def,axiom,
% 168.17/168.31 ! [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)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Nitpick_Orefl_H__def,axiom,
% 168.17/168.31 ! [V_r_2,T_b] :
% 168.17/168.31 ( c_Nitpick_Orefl_H(T_b,V_r_2)
% 168.17/168.31 <=> ! [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)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_divmod__nat__step,axiom,
% 168.17/168.31 ! [V_m,V_n] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 168.17/168.31 => 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)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_pair__box_Osize_I2_J,axiom,
% 168.17/168.31 ! [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) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_divmod__nat__zero,axiom,
% 168.17/168.31 ! [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) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_divmod__nat__base,axiom,
% 168.17/168.31 ! [V_n,V_m] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 168.17/168.31 => 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) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_divmod__nat__div__mod,axiom,
% 168.17/168.31 ! [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)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_divmod__nat__rel__mult2__eq,axiom,
% 168.17/168.31 ! [V_c,V_r,V_q,V_b,V_a] :
% 168.17/168.31 ( 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)))
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b))
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 168.17/168.31 => 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)))) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_divmod__nat__rel__mult1__eq,axiom,
% 168.17/168.31 ! [V_a,V_r,V_q,V_c,V_b] :
% 168.17/168.31 ( 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)))
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 168.17/168.31 => 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)))) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_pair__box_Orecs,axiom,
% 168.17/168.31 ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Nitpick_Opair__box_Opair__box__rec(T_c,T_d,T_b,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_pair__box_Osimps_I2_J,axiom,
% 168.17/168.31 ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Nitpick_Opair__box_Opair__box__case(T_c,T_d,T_b,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_divmod__nat__rel__unique,axiom,
% 168.17/168.31 ! [V_qr_H,V_qr,V_n,V_m] :
% 168.17/168.31 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 168.17/168.31 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H))
% 168.17/168.31 => V_qr = V_qr_H ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_divmod__nat__eq,axiom,
% 168.17/168.31 ! [V_qr,V_n,V_m] :
% 168.17/168.31 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 168.17/168.31 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_divmod__nat__rel__divmod__nat,axiom,
% 168.17/168.31 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_mod__eq,axiom,
% 168.17/168.31 ! [V_r,V_q,V_n,V_m] :
% 168.17/168.31 ( 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)))
% 168.17/168.31 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_div__eq,axiom,
% 168.17/168.31 ! [V_r,V_q,V_n,V_m] :
% 168.17/168.31 ( 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)))
% 168.17/168.31 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_divmod__nat__rel,axiom,
% 168.17/168.31 ! [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)))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_divmod__nat__rel__add1__eq,axiom,
% 168.17/168.31 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 168.17/168.31 ( 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)))
% 168.17/168.31 => ( 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)))
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 168.17/168.31 => 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)))) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_negDivAlg_Opsimps,axiom,
% 168.17/168.31 ! [V_b_2,V_a_2] :
% 168.17/168.31 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2)))
% 168.17/168.31 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2)))
% 168.17/168.31 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 168.17/168.31 => c_Divides_OnegDivAlg(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2)) )
% 168.17/168.31 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2)))
% 168.17/168.31 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 168.17/168.31 => c_Divides_OnegDivAlg(V_a_2,V_b_2) = hAPP(c_Divides_Oadjust(V_b_2),c_Divides_OnegDivAlg(V_a_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b_2))) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_pdivmod__posDivAlg,axiom,
% 168.17/168.31 ! [V_k,V_l] :
% 168.17/168.31 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.31 => 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)) )
% 168.17/168.31 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.31 => 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)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_pdivmod__def,axiom,
% 168.17/168.31 ! [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))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_zmult2__lemma,axiom,
% 168.17/168.31 ! [V_c,V_r,V_q,V_b,V_a] :
% 168.17/168.31 ( 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)))
% 168.17/168.31 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 168.17/168.31 => 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)))) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_unique__remainder,axiom,
% 168.17/168.31 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 168.17/168.31 ( 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)))
% 168.17/168.31 => ( 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)))
% 168.17/168.31 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.31 => V_r = V_r_H ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_unique__quotient,axiom,
% 168.17/168.31 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 168.17/168.31 ( 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)))
% 168.17/168.31 => ( 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)))
% 168.17/168.31 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.31 => V_q = V_q_H ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_self__remainder,axiom,
% 168.17/168.31 ! [V_r,V_q,V_a] :
% 168.17/168.31 ( 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)))
% 168.17/168.31 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.31 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_divmod__int__rel__0,axiom,
% 168.17/168.31 ! [V_b] :
% 168.17/168.31 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.31 => 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)))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_self__quotient,axiom,
% 168.17/168.31 ! [V_r,V_q,V_a] :
% 168.17/168.31 ( 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)))
% 168.17/168.31 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.31 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_divmod__int__rel__mod,axiom,
% 168.17/168.31 ! [V_r,V_q,V_b,V_a] :
% 168.17/168.31 ( 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)))
% 168.17/168.31 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.31 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_divmod__int__rel__div,axiom,
% 168.17/168.31 ! [V_r,V_q,V_b,V_a] :
% 168.17/168.31 ( 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)))
% 168.17/168.31 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.31 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_negDivAlg__correct,axiom,
% 168.17/168.31 ! [V_b,V_a] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 168.17/168.31 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_divmod__int__rel__div__mod,axiom,
% 168.17/168.31 ! [V_a,V_b] :
% 168.17/168.31 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.31 => 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)))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_posDivAlg__correct,axiom,
% 168.17/168.31 ! [V_b,V_a] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 168.17/168.31 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_zadd1__lemma,axiom,
% 168.17/168.31 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 168.17/168.31 ( 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)))
% 168.17/168.31 => ( 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)))
% 168.17/168.31 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.31 => 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)))) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_zminus1__lemma,axiom,
% 168.17/168.31 ! [V_r_2,V_q_2,V_b_2,V_a_2] :
% 168.17/168.31 ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a_2,V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_2),V_r_2)))
% 168.17/168.31 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,V_r_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_q_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_q_2)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,V_r_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b_2),V_r_2))))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_divmod__int__relI,axiom,
% 168.17/168.31 ! [V_r,V_q,V_b,V_a] :
% 168.17/168.31 ( 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)
% 168.17/168.31 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 168.17/168.31 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) )
% 168.17/168.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 168.17/168.31 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 168.17/168.31 => 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))) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_zmult1__lemma,axiom,
% 168.17/168.31 ! [V_a,V_r,V_q,V_c,V_b] :
% 168.17/168.31 ( 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)))
% 168.17/168.31 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.31 => 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)))) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_posDivAlg_Opsimps,axiom,
% 168.17/168.31 ! [V_b_2,V_a_2] :
% 168.17/168.31 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2)))
% 168.17/168.31 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 168.17/168.31 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 168.17/168.31 => c_Divides_OposDivAlg(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2) )
% 168.17/168.31 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 168.17/168.31 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 168.17/168.31 => c_Divides_OposDivAlg(V_a_2,V_b_2) = hAPP(c_Divides_Oadjust(V_b_2),c_Divides_OposDivAlg(V_a_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b_2))) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_negDivAlg_Opinduct,axiom,
% 168.17/168.31 ! [V_P_2,V_a1_2,V_a0_2] :
% 168.17/168.31 ( 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)))
% 168.17/168.31 => ( ! [B_a,B_b] :
% 168.17/168.31 ( 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)))
% 168.17/168.31 => ( ( ~ ( 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)))
% 168.17/168.31 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 168.17/168.31 => hBOOL(hAPP(hAPP(V_P_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b))) )
% 168.17/168.31 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 168.17/168.31 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_posDivAlg_Opinduct,axiom,
% 168.17/168.31 ! [V_P_2,V_a1_2,V_a0_2] :
% 168.17/168.31 ( 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)))
% 168.17/168.31 => ( ! [B_a,B_b] :
% 168.17/168.31 ( 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)))
% 168.17/168.31 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b))
% 168.17/168.31 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 168.17/168.31 => hBOOL(hAPP(hAPP(V_P_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b))) )
% 168.17/168.31 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 168.17/168.31 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_accp__subset,axiom,
% 168.17/168.31 ! [V_R2_2,V_R1_2,T_b] :
% 168.17/168.31 ( 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))
% 168.17/168.31 => 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))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_rev__predicate2D,axiom,
% 168.17/168.31 ! [V_Q_2,T_c,T_b,V_y_2,V_x_2,V_P_2] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_P_2),V_Q_2))
% 168.17/168.31 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_predicate2D,axiom,
% 168.17/168.31 ! [V_y_2,V_x_2,V_Q_2,V_P_2,T_c,T_b] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_P_2),V_Q_2))
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 168.17/168.31 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_accp_Osimps,axiom,
% 168.17/168.31 ! [V_a_2,V_r_2,T_b] :
% 168.17/168.31 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
% 168.17/168.31 <=> ! [B_x] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 168.17/168.31 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_accp_Oequations,axiom,
% 168.17/168.31 ! [V_a_2,V_r_2,T_b] :
% 168.17/168.31 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
% 168.17/168.31 <=> ! [B_x] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 168.17/168.31 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_accp__downward,axiom,
% 168.17/168.31 ! [V_a_2,V_b_2,V_r_2,T_b] :
% 168.17/168.31 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_b_2))
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 168.17/168.31 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_nat__gcd_Opsimps,axiom,
% 168.17/168.31 ! [V_y_2,V_x_2] :
% 168.17/168.31 ( 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)))
% 168.17/168.31 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.31 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 )
% 168.17/168.31 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.31 => 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)) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_nat_Osize_I2_J,axiom,
% 168.17/168.31 ! [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))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_in__measure,axiom,
% 168.17/168.31 ! [V_f_2,V_y_2,V_x_2,T_b] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)))
% 168.17/168.31 <=> 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))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_mlex__leq,axiom,
% 168.17/168.31 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
% 168.17/168.31 ( 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)))
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_R_2))
% 168.17/168.31 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2))) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_nat_Osize_I1_J,axiom,
% 168.17/168.31 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_mlex__less,axiom,
% 168.17/168.31 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
% 168.17/168.31 ( 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)))
% 168.17/168.31 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_nat__gcd_Opinduct,axiom,
% 168.17/168.31 ! [V_P_2,V_a1_2,V_a0_2] :
% 168.17/168.31 ( 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)))
% 168.17/168.31 => ( ! [B_x,B_y] :
% 168.17/168.31 ( 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)))
% 168.17/168.31 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.31 => hBOOL(hAPP(hAPP(V_P_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) )
% 168.17/168.31 => hBOOL(hAPP(hAPP(V_P_2,B_x),B_y)) ) )
% 168.17/168.31 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_nat_Osize_I4_J,axiom,
% 168.17/168.31 ! [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))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_divmod__int__def,axiom,
% 168.17/168.31 ! [V_b,V_a] :
% 168.17/168.31 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 168.17/168.31 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 168.17/168.31 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) )
% 168.17/168.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 168.17/168.31 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.31 => 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)) )
% 168.17/168.31 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.31 => 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))) ) ) ) ) )
% 168.17/168.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 168.17/168.31 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 168.17/168.31 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) )
% 168.17/168.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 168.17/168.31 => 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))) ) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_mod__pos__pos__1__number__of,axiom,
% 168.17/168.31 ! [V_w] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 168.17/168.31 => 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))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_mod__int__def,axiom,
% 168.17/168.31 ! [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)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_nat__size,axiom,
% 168.17/168.31 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ).
% 168.17/168.31
% 168.17/168.31 fof(fact_nat_Osize_I3_J,axiom,
% 168.17/168.31 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) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_mod__pos__neg,axiom,
% 168.17/168.31 ! [V_b,V_a] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.31 => 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)))) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_negateSnd__eq,axiom,
% 168.17/168.31 ! [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)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_mod__neg__neg,axiom,
% 168.17/168.31 ! [V_b,V_a] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.31 => 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)))) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_divmod__int__rel__neg,axiom,
% 168.17/168.31 ! [V_qr,V_b,V_a] :
% 168.17/168.31 ( 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))
% 168.17/168.31 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_mod__neg__pos,axiom,
% 168.17/168.31 ! [V_b,V_a] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 168.17/168.31 => 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)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_divmod__int__correct,axiom,
% 168.17/168.31 ! [V_a,V_b] :
% 168.17/168.31 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.31 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_mod__pos__neg__1__number__of,axiom,
% 168.17/168.31 ! [V_w] :
% 168.17/168.31 ( 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)))
% 168.17/168.31 => 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))))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_mod__pos__pos,axiom,
% 168.17/168.31 ! [V_b,V_a] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 168.17/168.31 => 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)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_divmod__int__mod__div,axiom,
% 168.17/168.31 ! [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)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_div__pos__neg__1__number__of,axiom,
% 168.17/168.31 ! [V_w] :
% 168.17/168.31 ( 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)))
% 168.17/168.31 => 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))))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_div__neg__neg,axiom,
% 168.17/168.31 ! [V_b,V_a] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.31 => 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)))) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_snd__eqD,axiom,
% 168.17/168.31 ! [V_a,V_y,V_x,T_a,T_b] :
% 168.17/168.31 ( 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
% 168.17/168.31 => V_y = V_a ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_snd__conv,axiom,
% 168.17/168.31 ! [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 ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Pair__fst__snd__eq,axiom,
% 168.17/168.31 ! [T_c,T_b,V_t_2,V_s_2] :
% 168.17/168.31 ( V_s_2 = V_t_2
% 168.17/168.31 <=> ( hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2)
% 168.17/168.31 & hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_prod__eqI,axiom,
% 168.17/168.31 ! [V_q,V_p,T_b,T_a] :
% 168.17/168.31 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q)
% 168.17/168.31 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q)
% 168.17/168.31 => V_p = V_q ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_fst__conv,axiom,
% 168.17/168.31 ! [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 ).
% 168.17/168.31
% 168.17/168.31 fof(fact_fst__eqD,axiom,
% 168.17/168.31 ! [V_a,V_y,V_x,T_b,T_a] :
% 168.17/168.31 ( 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
% 168.17/168.31 => V_x = V_a ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_surjective__pairing,axiom,
% 168.17/168.31 ! [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)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_pair__collapse,axiom,
% 168.17/168.31 ! [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 ).
% 168.17/168.31
% 168.17/168.31 fof(fact_div__int__def,axiom,
% 168.17/168.31 ! [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)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_mod__nat__def,axiom,
% 168.17/168.31 ! [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)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Pair__inject,axiom,
% 168.17/168.31 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] :
% 168.17/168.31 ( 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)
% 168.17/168.31 => ~ ( V_a = V_a_H
% 168.17/168.31 => V_b != V_b_H ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Pair__eq,axiom,
% 168.17/168.31 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 168.17/168.31 ( hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2)
% 168.17/168.31 <=> ( V_a_2 = V_a_H_2
% 168.17/168.31 & V_b_2 = V_b_H_2 ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_split__paired__All,axiom,
% 168.17/168.31 ! [T_c,T_b,V_P_2] :
% 168.17/168.31 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 168.17/168.31 <=> ! [B_a,B_b] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_div__neg__pos,axiom,
% 168.17/168.31 ! [V_b,V_a] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 168.17/168.31 => 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)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_div__pos__pos,axiom,
% 168.17/168.31 ! [V_b,V_a] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 168.17/168.31 => 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)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_div__pos__pos__1__number__of,axiom,
% 168.17/168.31 ! [V_w] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
% 168.17/168.31 => 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))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_div__pos__neg,axiom,
% 168.17/168.31 ! [V_b,V_a] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.31 => 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)))) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_prod__size__simp,axiom,
% 168.17/168.31 ! [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))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_conjI__realizer,axiom,
% 168.17/168.31 ! [T_c,T_b,V_q_2,V_Q_2,V_p_2,V_P_2] :
% 168.17/168.31 ( hBOOL(hAPP(V_P_2,V_p_2))
% 168.17/168.31 => ( hBOOL(hAPP(V_Q_2,V_q_2))
% 168.17/168.31 => ( hBOOL(hAPP(V_P_2,hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2))))
% 168.17/168.31 & 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)))) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_exI__realizer,axiom,
% 168.17/168.31 ! [T_b,T_c,V_x_2,V_y_2,V_P_2] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(V_P_2,V_y_2),V_x_2))
% 168.17/168.31 => hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2))),hAPP(c_Product__Type_Ofst(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_prod_Orecs,axiom,
% 168.17/168.31 ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Product__Type_Oprod_Oprod__rec(T_c,T_d,T_b,V_f1_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_div__nat__def,axiom,
% 168.17/168.31 ! [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)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_divmod__nat__rel__def,axiom,
% 168.17/168.31 ! [V_qr_2,V_n_2,V_m_2] :
% 168.17/168.31 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2))
% 168.17/168.31 <=> ( 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))
% 168.17/168.31 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.31 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 168.17/168.31 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.31 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 168.17/168.31 => ( 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)))
% 168.17/168.31 & 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)) ) )
% 168.17/168.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 168.17/168.31 => ( 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)))
% 168.17/168.31 & 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))) ) ) ) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_range,axiom,
% 168.17/168.31 ! [V_s,V_k] :
% 168.17/168.31 ( 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))
% 168.17/168.31 => 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)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_in__lex__prod,axiom,
% 168.17/168.31 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2))),c_Wellfounded_Olex__prod(T_b,T_c,V_r_2,V_s_2)))
% 168.17/168.31 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_H_2)),V_r_2))
% 168.17/168.31 | ( V_a_2 = V_a_H_2
% 168.17/168.31 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_b_2),V_b_H_2)),V_s_2)) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_in__finite__psubset,axiom,
% 168.17/168.31 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.31 ( 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)))
% 168.17/168.31 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.17/168.31 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_pair__lessI2,axiom,
% 168.17/168.31 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2))
% 168.17/168.31 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__less)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_pair__lessI1,axiom,
% 168.17/168.31 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 168.17/168.31 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__less)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_same__fstI,axiom,
% 168.17/168.31 ! [T_b,V_R_2,V_y_2,V_y_H_2,T_c,V_x_2,V_P_2] :
% 168.17/168.31 ( hBOOL(hAPP(V_P_2,V_x_2))
% 168.17/168.31 => ( 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)))
% 168.17/168.31 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_H_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2))),c_Recdef_Osame__fst(T_b,T_c,V_P_2,V_R_2))) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_pair__leqI2,axiom,
% 168.17/168.31 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2))
% 168.17/168.31 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__leq)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_smax__insertI,axiom,
% 168.17/168.31 ! [V_X_2,V_x_2,V_Y_2,V_y_2] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2))
% 168.17/168.31 => ( 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))
% 168.17/168.31 => ( 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))
% 168.17/168.31 => 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)) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_smin__insertI,axiom,
% 168.17/168.31 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 168.17/168.31 => ( 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))
% 168.17/168.31 => ( 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))
% 168.17/168.31 => 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)) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_smin__emptyI,axiom,
% 168.17/168.31 ! [V_X_2] :
% 168.17/168.31 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 168.17/168.31 => 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)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_smax__emptyI,axiom,
% 168.17/168.31 ! [V_Y_2] :
% 168.17/168.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2))
% 168.17/168.31 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 168.17/168.31 => 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)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_pair__leqI1,axiom,
% 168.17/168.31 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 168.17/168.31 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__leq)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_wmin__insertI,axiom,
% 168.17/168.31 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 168.17/168.31 => ( 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))
% 168.17/168.31 => ( 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))
% 168.17/168.31 => 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)) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_wmax__insertI,axiom,
% 168.17/168.31 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))
% 168.17/168.31 => ( 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))
% 168.17/168.31 => ( 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))
% 168.17/168.31 => 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)) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_wmin__emptyI,axiom,
% 168.17/168.31 ! [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)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_wmax__emptyI,axiom,
% 168.17/168.31 ! [V_X_2] :
% 168.17/168.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2))
% 168.17/168.31 => 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)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_less__by__empty,axiom,
% 168.17/168.31 ! [V_B_2,T_b,V_A_2] :
% 168.17/168.31 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 168.17/168.31 => 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)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_min__weak__def,axiom,
% 168.17/168.31 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)))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_max__weak__def,axiom,
% 168.17/168.31 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)))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_max__rpair__set,axiom,
% 168.17/168.31 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)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_min__rpair__set,axiom,
% 168.17/168.31 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)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_max__strict__def,axiom,
% 168.17/168.31 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_max__ext__additive,axiom,
% 168.17/168.31 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_b] :
% 168.17/168.31 ( 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)))
% 168.17/168.31 => ( 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)))
% 168.17/168.31 => 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))) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_min__strict__def,axiom,
% 168.17/168.31 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_less__than__iff,axiom,
% 168.17/168.31 ! [V_y_2,V_x_2] :
% 168.17/168.31 ( 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))
% 168.17/168.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_intrel__iff,axiom,
% 168.17/168.31 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 168.17/168.31 ( 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))
% 168.17/168.31 <=> 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) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_rp__inv__image__rp,axiom,
% 168.17/168.31 ! [V_f_2,T_c,V_P_2,T_b] :
% 168.17/168.31 ( c_FunDef_Oreduction__pair(T_b,V_P_2)
% 168.17/168.31 => c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_P_2),V_f_2)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_max__ext_Ointros,axiom,
% 168.17/168.31 ! [V_R_2,V_Y_2,V_X_2,T_b] :
% 168.17/168.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2))
% 168.17/168.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2))
% 168.17/168.31 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.31 => ( ! [B_x] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2))
% 168.17/168.31 => ? [B_xa] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2))
% 168.17/168.31 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_R_2)) ) )
% 168.17/168.31 => 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))) ) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_pair__less__def,axiom,
% 168.17/168.31 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_equiv__intrel__iff,axiom,
% 168.17/168.31 ! [V_y_2,V_x_2] :
% 168.17/168.31 ( 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))))
% 168.17/168.31 <=> 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)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Nitpick_Ozero__frac__def,axiom,
% 168.17/168.31 ! [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))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_measure__def,axiom,
% 168.17/168.31 ! [T_b] : c_Wellfounded_Omeasure(T_b) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_b),c_Wellfounded_Oless__than) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_adjust__eq,axiom,
% 168.17/168.31 ! [V_r_2,V_q_2,V_b_2] : hAPP(c_Divides_Oadjust(V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_2),V_r_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_r_2),V_b_2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_q_2)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_q_2)),V_r_2))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_setsum__abs,axiom,
% 168.17/168.31 ! [V_A_2,V_f_2,T_c,T_b] :
% 168.17/168.31 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 168.17/168.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_setsum__abs__ge__zero,axiom,
% 168.17/168.31 ! [V_A_2,V_f_2,T_c,T_b] :
% 168.17/168.31 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 168.17/168.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_sup__Un__eq2,axiom,
% 168.17/168.31 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
% 168.17/168.31 ( 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))
% 168.17/168.31 <=> 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))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_setprod_Odistrib,axiom,
% 168.17/168.31 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 168.17/168.31 ( class_Groups_Ocomm__monoid__mult(T_c)
% 168.17/168.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.31 => 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)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_setsum_Odistrib,axiom,
% 168.17/168.31 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 168.17/168.31 ( class_Groups_Ocomm__monoid__add(T_c)
% 168.17/168.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.31 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Oplus__class_Oplus(T_c)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_h_2),V_A_2)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_nat__number__of__Bit0,axiom,
% 168.17/168.31 ! [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))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_setsum__addf,axiom,
% 168.17/168.31 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 168.17/168.31 ( class_Groups_Ocomm__monoid__add(T_b)
% 168.17/168.31 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Oplus__class_Oplus(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),V_A_2)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Powp__def,axiom,
% 168.17/168.31 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.31 ( hBOOL(hAPP(c_Predicate_OPowp(T_b,V_A_2),V_B_2))
% 168.17/168.31 <=> ! [B_x] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 168.17/168.31 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_int__setprod,axiom,
% 168.17/168.31 ! [V_A_2,V_f_2,T_b] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__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) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_setsum__subtractf,axiom,
% 168.17/168.31 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 168.17/168.31 ( class_Groups_Oab__group__add(T_b)
% 168.17/168.31 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),V_A_2)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_fun__diff__def,axiom,
% 168.17/168.31 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 168.17/168.31 ( class_Groups_Ominus(T_b)
% 168.17/168.31 => 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)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_setsum__0,axiom,
% 168.17/168.31 ! [V_A_2,T_c,T_b] :
% 168.17/168.31 ( class_Groups_Ocomm__monoid__add(T_b)
% 168.17/168.31 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Ozero__class_Ozero(T_b))),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_setsum__divide__distrib,axiom,
% 168.17/168.31 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
% 168.17/168.31 ( class_Fields_Ofield(T_b)
% 168.17/168.31 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Rings_Oinverse__class_Odivide(T_b)),V_f_2)),V_r_2)),V_A_2) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_abs__setsum__abs,axiom,
% 168.17/168.31 ! [V_A_2,V_f_2,T_c,T_b] :
% 168.17/168.31 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 168.17/168.31 => hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_abs__setprod,axiom,
% 168.17/168.31 ! [V_A_2,V_f_2,T_c,T_b] :
% 168.17/168.31 ( class_Fields_Olinordered__field(T_b)
% 168.17/168.31 => 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) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_int__setsum,axiom,
% 168.17/168.31 ! [V_A_2,V_f_2,T_b] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_setsum__commute,axiom,
% 168.17/168.31 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 168.17/168.31 ( class_Groups_Ocomm__monoid__add(T_b)
% 168.17/168.31 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_b),T_d),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))),V_A_2)),V_B_2) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom,
% 168.17/168.31 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 168.17/168.31 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 168.17/168.31 => 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)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom,
% 168.17/168.31 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 168.17/168.31 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 168.17/168.31 => 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)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_setprod__1,axiom,
% 168.17/168.31 ! [V_A_2,T_c,T_b] :
% 168.17/168.31 ( class_Groups_Ocomm__monoid__mult(T_b)
% 168.17/168.31 => 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) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_setprod__timesf,axiom,
% 168.17/168.31 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 168.17/168.31 ( class_Groups_Ocomm__monoid__mult(T_b)
% 168.17/168.31 => 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)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_inf__fun__def,axiom,
% 168.17/168.31 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 168.17/168.31 ( class_Lattices_Olattice(T_b)
% 168.17/168.31 => 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)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_setsum__right__distrib,axiom,
% 168.17/168.31 ! [V_A_2,V_f_2,T_c,V_r_2,T_b] :
% 168.17/168.31 ( class_Rings_Osemiring__0(T_b)
% 168.17/168.31 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_r_2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_r_2)),V_f_2)),V_A_2) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_setsum__left__distrib,axiom,
% 168.17/168.31 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
% 168.17/168.31 ( class_Rings_Osemiring__0(T_b)
% 168.17/168.31 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_r_2)),V_A_2) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_setsum__product,axiom,
% 168.17/168.31 ! [V_B_2,V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 168.17/168.31 ( class_Rings_Osemiring__0(T_b)
% 168.17/168.31 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,T_b),tc_fun(T_d,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_b),tc_fun(tc_fun(T_d,T_b),tc_fun(T_d,T_b)),T_c),c_COMBB(T_b,T_b,T_d)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2))),V_g_2))),V_B_2)),V_A_2) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_fold__image__def,axiom,
% 168.17/168.31 ! [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)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_setsum__negf,axiom,
% 168.17/168.31 ! [V_A_2,V_f_2,T_c,T_b] :
% 168.17/168.31 ( class_Groups_Oab__group__add(T_b)
% 168.17/168.31 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Ouminus__class_Ouminus(T_b)),V_f_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_fun__Compl__def,axiom,
% 168.17/168.31 ! [V_x_2,V_A_2,T_c,T_b] :
% 168.17/168.31 ( class_Groups_Ouminus(T_b)
% 168.17/168.31 => 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)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_of__int__setsum,axiom,
% 168.17/168.31 ! [V_A_2,V_f_2,T_c,T_b] :
% 168.17/168.31 ( class_Rings_Oring__1(T_b)
% 168.17/168.31 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,T_c),c_Int_Oring__1__class_Oof__int(T_b)),V_f_2)),V_A_2) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_of__int__setprod,axiom,
% 168.17/168.31 ! [V_A_2,V_f_2,T_c,T_b] :
% 168.17/168.31 ( ( class_Groups_Ocomm__monoid__mult(T_b)
% 168.17/168.31 & class_Rings_Oring__1(T_b) )
% 168.17/168.31 => 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) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_inf__Int__eq,axiom,
% 168.17/168.31 ! [V_x_2,V_S_2,V_R_2,T_b] :
% 168.17/168.31 ( 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))
% 168.17/168.31 <=> 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))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_pred__equals__eq,axiom,
% 168.17/168.31 ! [V_S_2,V_R_2,T_b] :
% 168.17/168.31 ( 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)
% 168.17/168.31 <=> V_R_2 = V_S_2 ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_setprod__dividef,axiom,
% 168.17/168.31 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
% 168.17/168.31 ( class_Fields_Ofield__inverse__zero(T_c)
% 168.17/168.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.31 => 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)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_pred__subset__eq,axiom,
% 168.17/168.31 ! [V_S_2,V_R_2,T_b] :
% 168.17/168.31 ( 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)))
% 168.17/168.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_sup__Un__eq,axiom,
% 168.17/168.31 ! [V_x_2,V_S_2,V_R_2,T_b] :
% 168.17/168.31 ( 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))
% 168.17/168.31 <=> 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))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_inf__Int__eq2,axiom,
% 168.17/168.31 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
% 168.17/168.31 ( 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))
% 168.17/168.31 <=> 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))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_pred__equals__eq2,axiom,
% 168.17/168.31 ! [V_S_2,V_R_2,T_c,T_b] :
% 168.17/168.31 ( 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)
% 168.17/168.31 <=> V_R_2 = V_S_2 ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_less__eq__Suc__le__raw,axiom,
% 168.17/168.31 ! [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)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_sup__fun__def,axiom,
% 168.17/168.31 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 168.17/168.31 ( class_Lattices_Olattice(T_b)
% 168.17/168.31 => 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)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_bot__fun__def,axiom,
% 168.17/168.31 ! [V_x_2,T_c,T_b] :
% 168.17/168.31 ( class_Orderings_Obot(T_b)
% 168.17/168.31 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_bot__empty__eq2,axiom,
% 168.17/168.31 ! [V_y_2,V_x_2,T_c,T_b] :
% 168.17/168.31 ( 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))
% 168.17/168.31 <=> 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)))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_bot__empty__eq,axiom,
% 168.17/168.31 ! [V_x_2,T_b] :
% 168.17/168.31 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_x_2))
% 168.17/168.31 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_of__nat__setsum,axiom,
% 168.17/168.31 ! [V_A_2,V_f_2,T_c,T_b] :
% 168.17/168.31 ( class_Rings_Osemiring__1(T_b)
% 168.17/168.31 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,T_c),c_Nat_Osemiring__1__class_Oof__nat(T_b)),V_f_2)),V_A_2) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom,
% 168.17/168.31 ! [V_A_2,V_f_2,T_b] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_card__eq__setsum,axiom,
% 168.17/168.31 ! [V_A_2,T_b] : hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_A_2) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_of__nat__setprod,axiom,
% 168.17/168.31 ! [V_A_2,V_f_2,T_c,T_b] :
% 168.17/168.31 ( ( class_Groups_Ocomm__monoid__mult(T_b)
% 168.17/168.31 & class_Rings_Osemiring__1(T_b) )
% 168.17/168.31 => 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) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom,
% 168.17/168.31 ! [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)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_setsum__delta_H,axiom,
% 168.17/168.31 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 168.17/168.31 ( class_Groups_Ocomm__monoid__add(T_c)
% 168.17/168.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 168.17/168.31 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 168.17/168.31 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) )
% 168.17/168.31 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 168.17/168.31 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_setsum__delta,axiom,
% 168.17/168.31 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 168.17/168.31 ( class_Groups_Ocomm__monoid__add(T_c)
% 168.17/168.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 168.17/168.31 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 168.17/168.31 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) )
% 168.17/168.31 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 168.17/168.31 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_setprod__delta_H,axiom,
% 168.17/168.31 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 168.17/168.31 ( class_Groups_Ocomm__monoid__mult(T_c)
% 168.17/168.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 168.17/168.31 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 168.17/168.31 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) )
% 168.17/168.31 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 168.17/168.31 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_setprod__delta,axiom,
% 168.17/168.31 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 168.17/168.31 ( class_Groups_Ocomm__monoid__mult(T_c)
% 168.17/168.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 168.17/168.31 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 168.17/168.31 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) )
% 168.17/168.31 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 168.17/168.31 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_setsum__constant,axiom,
% 168.17/168.31 ! [V_A_2,V_y_2,T_c,T_b] :
% 168.17/168.31 ( class_Rings_Osemiring__1(T_b)
% 168.17/168.31 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_y_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(c_Finite__Set_Ocard(T_c),V_A_2))),V_y_2) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_power__number__of__even,axiom,
% 168.17/168.31 ! [V_w_2,V_z_2,T_b] :
% 168.17/168.31 ( class_Int_Onumber__ring(T_b)
% 168.17/168.31 => 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))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_fold__image__distrib,axiom,
% 168.17/168.31 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 168.17/168.31 ( class_Groups_Ocomm__monoid__mult(T_c)
% 168.17/168.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.31 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Otimes__class_Otimes(T_c)),V_g_2)),V_h_2)),c_Groups_Oone__class_Oone(T_c)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_h_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_setprod__constant,axiom,
% 168.17/168.31 ! [V_y_2,V_A_2,T_b,T_c] :
% 168.17/168.31 ( class_Groups_Ocomm__monoid__mult(T_c)
% 168.17/168.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.31 => 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)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_zpower__number__of__even,axiom,
% 168.17/168.31 ! [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))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_pred__subset__eq2,axiom,
% 168.17/168.31 ! [V_S_2,V_R_2,T_c,T_b] :
% 168.17/168.31 ( 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)))
% 168.17/168.31 <=> 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)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Powp__Pow__eq,axiom,
% 168.17/168.31 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.31 ( hBOOL(hAPP(c_Predicate_OPowp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),V_x_2))
% 168.17/168.31 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_b),V_A_2))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_setsum__restrict__set,axiom,
% 168.17/168.31 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
% 168.17/168.31 ( class_Groups_Ocomm__monoid__add(T_c)
% 168.17/168.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.31 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_c))),V_A_2) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_power__number__of__even__number__of,axiom,
% 168.17/168.31 ! [V_w_2,V_v_2,T_b] :
% 168.17/168.31 ( class_Int_Onumber__ring(T_b)
% 168.17/168.31 => 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))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_card_Oeq__fold__g,axiom,
% 168.17/168.31 ! [V_A_2,T_b] :
% 168.17/168.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.31 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_b,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_card__def,axiom,
% 168.17/168.31 ! [V_A_2,T_b] :
% 168.17/168.31 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.31 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_b,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) )
% 168.17/168.31 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.31 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_fun__left__comm__idem__remove,axiom,
% 168.17/168.31 ! [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))))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_diff__nat__eq__if,axiom,
% 168.17/168.31 ! [V_z_2,V_z_H_2] :
% 168.17/168.31 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 168.17/168.31 => 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) )
% 168.17/168.31 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 168.17/168.31 => 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)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_minus__fold__remove,axiom,
% 168.17/168.31 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.31 => 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) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_eq__number__of__Suc,axiom,
% 168.17/168.31 ! [V_n_2,V_v_2] :
% 168.17/168.31 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2)
% 168.17/168.31 <=> 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))))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Suc__eq__number__of,axiom,
% 168.17/168.31 ! [V_v_2,V_n_2] :
% 168.17/168.31 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 168.17/168.31 <=> 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))))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_nat__number__of__Bit1,axiom,
% 168.17/168.31 ! [V_w_2] :
% 168.17/168.31 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 168.17/168.31 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 168.17/168.31 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 168.17/168.31 => 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)))) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_less__Suc__number__of,axiom,
% 168.17/168.31 ! [V_v_2,V_n_2] :
% 168.17/168.31 ( 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)))
% 168.17/168.31 <=> 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))))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_less__number__of__Suc,axiom,
% 168.17/168.31 ! [V_n_2,V_v_2] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)))
% 168.17/168.31 <=> 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)))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_le__number__of__Suc,axiom,
% 168.17/168.31 ! [V_n_2,V_v_2] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Nat_OSuc,V_n_2)))
% 168.17/168.31 <=> 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)))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_le__Suc__number__of,axiom,
% 168.17/168.31 ! [V_v_2,V_n_2] :
% 168.17/168.31 ( 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)))
% 168.17/168.31 <=> 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))))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_power__number__of__odd,axiom,
% 168.17/168.31 ! [V_z_2,V_w_2,T_b] :
% 168.17/168.31 ( class_Int_Onumber__ring(T_b)
% 168.17/168.31 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 168.17/168.31 => 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))) )
% 168.17/168.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 168.17/168.31 => 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) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_setprod__gen__delta,axiom,
% 168.17/168.31 ! [V_c_2,V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 168.17/168.31 ( class_Groups_Ocomm__monoid__mult(T_c)
% 168.17/168.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 168.17/168.31 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 168.17/168.31 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_c_2)),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_b_2,V_a_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
% 168.17/168.31 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 168.17/168.31 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_c_2)),V_S_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_c_2),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)) ) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_zpower__number__of__odd,axiom,
% 168.17/168.31 ! [V_z_2,V_w_2] :
% 168.17/168.31 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 168.17/168.31 => 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))) )
% 168.17/168.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 168.17/168.31 => 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) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_min__number__of__Suc,axiom,
% 168.17/168.31 ! [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)))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_min__Suc__number__of,axiom,
% 168.17/168.31 ! [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)))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_power__number__of__odd__number__of,axiom,
% 168.17/168.31 ! [V_v_2,V_w_2,T_b] :
% 168.17/168.31 ( class_Int_Onumber__ring(T_b)
% 168.17/168.31 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 168.17/168.31 => 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))) )
% 168.17/168.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 168.17/168.31 => 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) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_diff__nat__number__of,axiom,
% 168.17/168.31 ! [V_v_2,V_v_H_2] :
% 168.17/168.31 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 168.17/168.31 => 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) )
% 168.17/168.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 168.17/168.31 => 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)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Nitpick_Oone__frac__def,axiom,
% 168.17/168.31 ! [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))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Nitpick_Onumber__of__frac__def,axiom,
% 168.17/168.31 ! [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))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Image__singleton__iff,axiom,
% 168.17/168.31 ! [V_a_2,V_r_2,T_c,V_b_2,T_b] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
% 168.17/168.31 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2),V_b_2)),V_r_2)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_norm__frac_Osimps,axiom,
% 168.17/168.31 ! [V_a_2,V_b_2] :
% 168.17/168.31 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.31 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b_2)) )
% 168.17/168.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.31 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.31 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 168.17/168.31 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
% 168.17/168.31 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.31 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 168.17/168.31 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,V_a_2),V_b_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b_2))) ) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_sup2CI,axiom,
% 168.17/168.31 ! [T_c,T_b,V_A_2,V_y_2,V_x_2,V_B_2] :
% 168.17/168.31 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 168.17/168.31 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) )
% 168.17/168.31 => 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)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_sup2E,axiom,
% 168.17/168.31 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 168.17/168.31 ( 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))
% 168.17/168.31 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 168.17/168.31 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_inf2I,axiom,
% 168.17/168.31 ! [T_c,T_b,V_B_2,V_y_2,V_x_2,V_A_2] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 168.17/168.31 => 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)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_inf2E,axiom,
% 168.17/168.31 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 168.17/168.31 ( 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))
% 168.17/168.31 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 168.17/168.31 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_bot2E,axiom,
% 168.17/168.31 ! [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)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_sup2I2,axiom,
% 168.17/168.31 ! [V_A_2,T_c,T_b,V_y_2,V_x_2,V_B_2] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 168.17/168.31 => 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)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_sup2I1,axiom,
% 168.17/168.31 ! [V_B_2,T_c,T_b,V_y_2,V_x_2,V_A_2] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 168.17/168.31 => 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)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_inf2D1,axiom,
% 168.17/168.31 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 168.17/168.31 ( 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))
% 168.17/168.31 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_inf2D2,axiom,
% 168.17/168.31 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 168.17/168.31 ( 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))
% 168.17/168.31 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Image__empty,axiom,
% 168.17/168.31 ! [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)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Image__Un,axiom,
% 168.17/168.31 ! [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)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Image__Int__subset,axiom,
% 168.17/168.31 ! [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)))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Image__mono,axiom,
% 168.17/168.31 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_c,T_b] :
% 168.17/168.31 ( 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))
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_H_2),V_A_2))
% 168.17/168.31 => 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))) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Un__Image,axiom,
% 168.17/168.31 ! [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)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_in__inv__image,axiom,
% 168.17/168.31 ! [V_f_2,V_r_2,T_c,V_y_2,V_x_2,T_b] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_r_2),V_f_2)))
% 168.17/168.31 <=> 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)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_rev__ImageI,axiom,
% 168.17/168.31 ! [V_r_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.17/168.31 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
% 168.17/168.31 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Image__iff,axiom,
% 168.17/168.31 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
% 168.17/168.31 <=> ? [B_x] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 168.17/168.31 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_norm__frac_Opsimps,axiom,
% 168.17/168.31 ! [V_b_2,V_a_2] :
% 168.17/168.31 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2)))
% 168.17/168.31 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.31 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b_2)) )
% 168.17/168.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.31 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.31 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 168.17/168.31 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
% 168.17/168.31 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.31 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 168.17/168.31 => c_Nitpick_Onorm__frac(V_a_2,V_b_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,V_a_2),V_b_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b_2))) ) ) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_of__int__num,axiom,
% 168.17/168.31 ! [V_k_2,T_b] :
% 168.17/168.31 ( class_Rings_Oring__1(T_b)
% 168.17/168.31 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.31 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = c_Groups_Ozero__class_Ozero(T_b) )
% 168.17/168.31 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.31 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.31 => 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))) )
% 168.17/168.31 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.31 => 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))))) ) ) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_max__extp__max__ext__eq,axiom,
% 168.17/168.31 ! [V_xa_2,V_x_2,V_R_2,T_b] :
% 168.17/168.31 ( 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)
% 168.17/168.31 <=> 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))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_nat__case__add__eq__if,axiom,
% 168.17/168.31 ! [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)))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_split__weak__cong,axiom,
% 168.17/168.31 ! [V_c_2,T_d,T_c,T_b,V_q_2,V_p_2] :
% 168.17/168.31 ( V_p_2 = V_q_2
% 168.17/168.31 => hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_c_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_c_2),V_q_2) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_prod_Osimps_I2_J,axiom,
% 168.17/168.31 ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_split__conv,axiom,
% 168.17/168.31 ! [V_b_2,V_a_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f_2,V_a_2),V_b_2) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_split__twice,axiom,
% 168.17/168.31 ! [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) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_split__eta,axiom,
% 168.17/168.31 ! [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 ).
% 168.17/168.31
% 168.17/168.31 fof(fact_fst__def,axiom,
% 168.17/168.31 ! [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) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_snd__def,axiom,
% 168.17/168.31 ! [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) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_nat__case__0,axiom,
% 168.17/168.31 ! [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 ).
% 168.17/168.31
% 168.17/168.31 fof(fact_nat__case__Suc,axiom,
% 168.17/168.31 ! [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) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_prod__case__beta,axiom,
% 168.17/168.31 ! [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)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_split__comp__eq,axiom,
% 168.17/168.31 ! [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)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_split__beta,axiom,
% 168.17/168.31 ! [V_z_2,V_P_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_P_2),V_z_2) = hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_z_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_z_2)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_split__def,axiom,
% 168.17/168.31 ! [V_p_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_c_2),V_p_2) = hAPP(hAPP(V_c_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_less__eq__nat_Osimps_I2_J,axiom,
% 168.17/168.31 ! [V_n_2,V_m_2] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 168.17/168.31 <=> 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)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_diff__Suc,axiom,
% 168.17/168.31 ! [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)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_min__Suc2,axiom,
% 168.17/168.31 ! [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) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_min__Suc1,axiom,
% 168.17/168.31 ! [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) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_divmod__int__rel__def,axiom,
% 168.17/168.31 ! [V_b_2,V_a_2] : c_Divides_Odivmod__int__rel(V_a_2,V_b_2) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fequal,V_a_2))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_2)))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(c_fNot,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_mlex__prod__def,axiom,
% 168.17/168.31 ! [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))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_nat__case__number__of,axiom,
% 168.17/168.31 ! [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))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_adjust__def,axiom,
% 168.17/168.31 ! [V_b_2] : c_Divides_Oadjust(V_b_2) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Nitpick_OFrac__def,axiom,
% 168.17/168.31 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)))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_divmod__int__pdivmod,axiom,
% 168.17/168.31 ! [V_l_2,V_k_2] :
% 168.17/168.31 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.31 => 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)) )
% 168.17/168.31 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.31 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.31 => 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) )
% 168.17/168.31 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.31 => 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)))) ) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_divmod__int__code,axiom,
% 168.17/168.31 ! [V_l_2,V_k_2] :
% 168.17/168.31 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.31 => 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)) )
% 168.17/168.31 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.31 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.31 => 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) )
% 168.17/168.31 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 168.17/168.31 => 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)))) ) ) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_of__int,axiom,
% 168.17/168.31 ! [V_j_2,V_i_2,T_b] :
% 168.17/168.31 ( class_Rings_Oring__1(T_b)
% 168.17/168.31 => 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)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_mem__splitI,axiom,
% 168.17/168.31 ! [T_d,T_c,V_b_2,V_a_2,V_c_2,V_z_2,T_b] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,V_a_2),V_b_2)))
% 168.17/168.31 => hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_prod__caseI,axiom,
% 168.17/168.31 ! [T_c,T_b,V_b_2,V_a_2,V_f1_2] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2))
% 168.17/168.31 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_splitI,axiom,
% 168.17/168.31 ! [T_c,T_b,V_b_2,V_a_2,V_f_2] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2))
% 168.17/168.31 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_splitD_H,axiom,
% 168.17/168.31 ! [V_c_2,V_b_2,V_a_2,V_R_2,T_d,T_c,T_b] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_R_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_c_2))
% 168.17/168.31 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_c_2)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_splitD,axiom,
% 168.17/168.31 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 168.17/168.31 ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))
% 168.17/168.31 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_apsnd__conv,axiom,
% 168.17/168.31 ! [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)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_fst__apsnd,axiom,
% 168.17/168.31 ! [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) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_snd__apsnd,axiom,
% 168.17/168.31 ! [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)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_apsnd__eq__conv,axiom,
% 168.17/168.31 ! [V_g_2,V_x_2,V_f_2,T_b,T_c,T_d] :
% 168.17/168.31 ( 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)
% 168.17/168.31 <=> 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)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_negateSnd__def,axiom,
% 168.17/168.31 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_rp__inv__image__def,axiom,
% 168.17/168.31 ! [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))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_divmod__nat__if,axiom,
% 168.17/168.31 ! [V_m_2,V_n_2] :
% 168.17/168.31 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.31 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 168.17/168.31 => 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) )
% 168.17/168.31 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.17/168.31 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 168.17/168.31 => 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)) ) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_minus,axiom,
% 168.17/168.31 ! [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))))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_Zero__int__def,axiom,
% 168.17/168.31 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))))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_int__def,axiom,
% 168.17/168.31 ! [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))))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_add,axiom,
% 168.17/168.31 ! [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))))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_nat,axiom,
% 168.17/168.31 ! [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) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_less,axiom,
% 168.17/168.31 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 168.17/168.31 ( 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)))))))
% 168.17/168.31 <=> 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))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_le,axiom,
% 168.17/168.31 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 168.17/168.31 ( 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)))))))
% 168.17/168.31 <=> 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))) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_mult,axiom,
% 168.17/168.31 ! [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))))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_One__int__def,axiom,
% 168.17/168.31 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))))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_nat__rec__add__eq__if,axiom,
% 168.17/168.31 ! [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))))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_semiring__1__class_Oof__nat__code,axiom,
% 168.17/168.31 ! [V_n_2,T_b] :
% 168.17/168.31 ( class_Rings_Osemiring__1(T_b)
% 168.17/168.31 => 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)) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_nat__rec__number__of,axiom,
% 168.17/168.31 ! [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)))) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_dual__max,axiom,
% 168.17/168.31 ! [T_b] :
% 168.17/168.31 ( class_Orderings_Olinorder(T_b)
% 168.17/168.31 => 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) ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_nat__rec__0,axiom,
% 168.17/168.31 ! [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 ).
% 168.17/168.31
% 168.17/168.31 fof(fact_nat__rec__Suc,axiom,
% 168.17/168.31 ! [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)) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_of__nat__aux_Osimps_I1_J,axiom,
% 168.17/168.31 ! [V_i_2,V_inc_2,T_b] :
% 168.17/168.31 ( class_Rings_Osemiring__1(T_b)
% 168.17/168.31 => 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 ) ).
% 168.17/168.31
% 168.17/168.31 fof(fact_of__nat__aux_Osimps_I2_J,axiom,
% 168.17/168.31 ! [V_i_2,V_n_2,V_inc_2,T_b] :
% 168.17/168.31 ( class_Rings_Osemiring__1(T_b)
% 168.17/168.32 => 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)) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom,
% 168.17/168.32 ! [V_f_2,V_A_2,T_b] :
% 168.17/168.32 ( ! [B_x] :
% 168.17/168.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.17/168.32 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 168.17/168.32 => 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)) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_irrefl__def,axiom,
% 168.17/168.32 ! [V_r_2,T_b] :
% 168.17/168.32 ( c_Relation_Oirrefl(T_b,V_r_2)
% 168.17/168.32 <=> ! [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)) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom,
% 168.17/168.32 ! [V_f_2,V_A_2,T_b] :
% 168.17/168.32 ( ! [B_x] :
% 168.17/168.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.17/168.32 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 168.17/168.32 => 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)) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_norm__frac_Opinduct,axiom,
% 168.17/168.32 ! [V_P_2,V_a1_2,V_a0_2] :
% 168.17/168.32 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
% 168.17/168.32 => ( ! [B_a,B_b] :
% 168.17/168.32 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b)))
% 168.17/168.32 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 168.17/168.32 => hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_b))) )
% 168.17/168.32 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 168.17/168.32 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_Nitpick_Ofrac__def,axiom,
% 168.17/168.32 ! [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)) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_eq__Abs__Integ,axiom,
% 168.17/168.32 ! [V_z_2] :
% 168.17/168.32 ~ ! [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))))) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_arith__series__int,axiom,
% 168.17/168.32 ! [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)))) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_Field__insert,axiom,
% 168.17/168.32 ! [V_r_2,V_b_2,V_a_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OField(T_b),V_r_2)) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_finite__lessThan,axiom,
% 168.17/168.32 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_lessThan__0,axiom,
% 168.17/168.32 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)) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_lessThan__eq__iff,axiom,
% 168.17/168.32 ! [V_y_2,V_x_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2)
% 168.17/168.32 <=> V_x_2 = V_y_2 ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_card__lessThan,axiom,
% 168.17/168.32 ! [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 ).
% 168.17/168.32
% 168.17/168.32 fof(fact_lessThan__Suc,axiom,
% 168.17/168.32 ! [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)) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_lessThan__iff,axiom,
% 168.17/168.32 ! [V_k_2,V_i_2,T_b] :
% 168.17/168.32 ( class_Orderings_Oord(T_b)
% 168.17/168.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)))
% 168.17/168.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_i_2),V_k_2)) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_lessThan__subset__iff,axiom,
% 168.17/168.32 ! [V_y_2,V_x_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( 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)))
% 168.17/168.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_setsum__lessThan__Suc,axiom,
% 168.17/168.32 ! [V_n_2,V_f_2,T_b] :
% 168.17/168.32 ( class_Groups_Ocomm__monoid__add(T_b)
% 168.17/168.32 => 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)) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_lessThan__strict__subset__iff,axiom,
% 168.17/168.32 ! [V_n_2,V_m_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( 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)))
% 168.17/168.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_n_2)) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_single__Diff__lessThan,axiom,
% 168.17/168.32 ! [V_k_2,T_b] :
% 168.17/168.32 ( class_Orderings_Oorder(T_b)
% 168.17/168.32 => 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))) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_finite__nat__set__iff__bounded,axiom,
% 168.17/168.32 ! [V_N_2] :
% 168.17/168.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 168.17/168.32 <=> ? [B_m] :
% 168.17/168.32 ! [B_x] :
% 168.17/168.32 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 168.17/168.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_Field__empty,axiom,
% 168.17/168.32 ! [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)) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_mono__Field,axiom,
% 168.17/168.32 ! [V_s_2,V_r_2,T_b] :
% 168.17/168.32 ( 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))
% 168.17/168.32 => 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))) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_finite__nat__set__iff__bounded__le,axiom,
% 168.17/168.32 ! [V_N_2] :
% 168.17/168.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 168.17/168.32 <=> ? [B_m] :
% 168.17/168.32 ! [B_x] :
% 168.17/168.32 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 168.17/168.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_Field__Un,axiom,
% 168.17/168.32 ! [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)) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_finite__Field,axiom,
% 168.17/168.32 ! [V_r_2,T_b] :
% 168.17/168.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 168.17/168.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_OField(T_b),V_r_2))) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_arith__series__general,axiom,
% 168.17/168.32 ! [V_n_2,V_d_2,V_a_2,T_b] :
% 168.17/168.32 ( class_Rings_Ocomm__semiring__1(T_b)
% 168.17/168.32 => 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)))) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_arith__series__nat,axiom,
% 168.17/168.32 ! [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)))) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_ord_OatMost__iff,axiom,
% 168.17/168.32 ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
% 168.17/168.32 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatMost(T_b,V_less__eq_2,V_k_2)))
% 168.17/168.32 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_ord_OatLeast__iff,axiom,
% 168.17/168.32 ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
% 168.17/168.32 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeast(T_b,V_less__eq_2,V_k_2)))
% 168.17/168.32 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_ord_OlessThan__iff,axiom,
% 168.17/168.32 ! [V_k_2,V_less_2,V_i_2,T_b] :
% 168.17/168.32 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OlessThan(T_b,V_less_2,V_k_2)))
% 168.17/168.32 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_ord_OgreaterThan__iff,axiom,
% 168.17/168.32 ! [V_k_2,V_less_2,V_i_2,T_b] :
% 168.17/168.32 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThan(T_b,V_less_2,V_k_2)))
% 168.17/168.32 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_infinite__UNIV__nat,axiom,
% 168.17/168.32 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_ord_OgreaterThanAtMost__iff,axiom,
% 168.17/168.32 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
% 168.17/168.32 ( 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)))
% 168.17/168.32 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 168.17/168.32 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_ord_OatLeastLessThan__iff,axiom,
% 168.17/168.32 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
% 168.17/168.32 ( 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)))
% 168.17/168.32 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 168.17/168.32 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_ord_OgreaterThanLessThan__iff,axiom,
% 168.17/168.32 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_b] :
% 168.17/168.32 ( 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)))
% 168.17/168.32 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 168.17/168.32 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_ord_OatLeastAtMost__iff,axiom,
% 168.17/168.32 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_b] :
% 168.17/168.32 ( 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)))
% 168.17/168.32 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 168.17/168.32 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_setsum__nonneg__leq__bound,axiom,
% 168.17/168.32 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_b,T_c] :
% 168.17/168.32 ( class_Groups_Oordered__ab__group__add(T_c)
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 168.17/168.32 => ( ! [B_i] :
% 168.17/168.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
% 168.17/168.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
% 168.17/168.32 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = V_B_2
% 168.17/168.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
% 168.17/168.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_setsum__nonneg__0,axiom,
% 168.17/168.32 ! [V_i_2,V_f_2,V_s_2,T_b,T_c] :
% 168.17/168.32 ( class_Groups_Oordered__ab__group__add(T_c)
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 168.17/168.32 => ( ! [B_i] :
% 168.17/168.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
% 168.17/168.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
% 168.17/168.32 => ( 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)
% 168.17/168.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
% 168.17/168.32 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_max__number__of__Suc,axiom,
% 168.17/168.32 ! [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)))) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_max__Suc__number__of,axiom,
% 168.17/168.32 ! [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)))) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_le__max__iff__disj,axiom,
% 168.17/168.32 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( 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)))
% 168.17/168.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_x_2))
% 168.17/168.32 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_y_2)) ) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_Ole__supE,axiom,
% 168.17/168.32 ! [V_x,V_b,V_a,T_a] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_a)
% 168.17/168.32 => ( 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))
% 168.17/168.32 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 168.17/168.32 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_Osup__mono,axiom,
% 168.17/168.32 ! [V_d,V_b,V_c,V_a,T_a] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_a)
% 168.17/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 168.17/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 168.17/168.32 => 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))) ) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_Osup__least,axiom,
% 168.17/168.32 ! [V_z,V_x,V_y,T_a] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_a)
% 168.17/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 168.17/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 168.17/168.32 => 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)) ) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_Ole__supI,axiom,
% 168.17/168.32 ! [V_b,V_x,V_a,T_a] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_a)
% 168.17/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 168.17/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 168.17/168.32 => 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)) ) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_Osup__absorb1,axiom,
% 168.17/168.32 ! [V_x,V_y,T_a] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_a)
% 168.17/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 168.17/168.32 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_Osup__absorb2,axiom,
% 168.17/168.32 ! [V_y,V_x,T_a] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_a)
% 168.17/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 168.17/168.32 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_Ole__supI2,axiom,
% 168.17/168.32 ! [V_a,V_b,V_x,T_a] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_a)
% 168.17/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 168.17/168.32 => 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))) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_Ole__supI1,axiom,
% 168.17/168.32 ! [V_b,V_a,V_x,T_a] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_a)
% 168.17/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 168.17/168.32 => 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))) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_Ole__sup__iff,axiom,
% 168.17/168.32 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( 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))
% 168.17/168.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 168.17/168.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_Ole__iff__sup,axiom,
% 168.17/168.32 ! [V_y_2,V_x_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 168.17/168.32 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2) = V_y_2 ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_le__maxI2,axiom,
% 168.17/168.32 ! [V_x,V_y,T_a] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_a)
% 168.17/168.32 => 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))) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_le__maxI1,axiom,
% 168.17/168.32 ! [V_y,V_x,T_a] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_a)
% 168.17/168.32 => 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))) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_Osup_Oidem,axiom,
% 168.17/168.32 ! [V_a,T_a] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_a)
% 168.17/168.32 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_Osup_Ocommute,axiom,
% 168.17/168.32 ! [V_b,V_a,T_a] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_a)
% 168.17/168.32 => 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) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_Osup__commute,axiom,
% 168.17/168.32 ! [V_y,V_x,T_a] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_a)
% 168.17/168.32 => 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) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_Osup_Oleft__idem,axiom,
% 168.17/168.32 ! [V_b,V_a,T_a] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_a)
% 168.17/168.32 => 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) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_Osup__left__idem,axiom,
% 168.17/168.32 ! [V_y,V_x,T_a] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_a)
% 168.17/168.32 => 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) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_Osup_Oleft__commute,axiom,
% 168.17/168.32 ! [V_c,V_a,V_b,T_a] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_a)
% 168.17/168.32 => 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)) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_Osup__left__commute,axiom,
% 168.17/168.32 ! [V_z,V_y,V_x,T_a] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_a)
% 168.17/168.32 => 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)) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_Osup_Oassoc,axiom,
% 168.17/168.32 ! [V_c,V_b,V_a,T_a] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_a)
% 168.17/168.32 => 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)) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_Osup__assoc,axiom,
% 168.17/168.32 ! [V_z,V_y,V_x,T_a] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_a)
% 168.17/168.32 => 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)) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_Max_Oidem,axiom,
% 168.17/168.32 ! [V_x,T_a] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_a)
% 168.17/168.32 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_Oinf__sup__distrib2,axiom,
% 168.17/168.32 ! [V_x,V_z,V_y,T_a] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_a)
% 168.17/168.32 => 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)) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_Osup__inf__distrib2,axiom,
% 168.17/168.32 ! [V_x,V_z,V_y,T_a] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_a)
% 168.17/168.32 => 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)) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_Oinf__sup__distrib1,axiom,
% 168.17/168.32 ! [V_z,V_y,V_x,T_a] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_a)
% 168.17/168.32 => 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)) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_Osup__inf__distrib1,axiom,
% 168.17/168.32 ! [V_z,V_y,V_x,T_a] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_a)
% 168.17/168.32 => 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)) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_Oinf__sup__absorb,axiom,
% 168.17/168.32 ! [V_y,V_x,T_a] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_a)
% 168.17/168.32 => 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 ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_Osup__inf__absorb,axiom,
% 168.17/168.32 ! [V_y,V_x,T_a] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_a)
% 168.17/168.32 => 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 ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_max__Suc__Suc,axiom,
% 168.17/168.32 ! [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)) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_max__0L,axiom,
% 168.17/168.32 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 168.17/168.32
% 168.17/168.32 fof(fact_max__0R,axiom,
% 168.17/168.32 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ).
% 168.17/168.32
% 168.17/168.32 fof(fact_max__diff__distrib__left,axiom,
% 168.17/168.32 ! [V_z,V_y,V_x,T_a] :
% 168.17/168.32 ( class_Groups_Oordered__ab__group__add(T_a)
% 168.17/168.32 => 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)) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_max__add__distrib__left,axiom,
% 168.17/168.32 ! [V_z,V_y,V_x,T_a] :
% 168.17/168.32 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 168.17/168.32 => 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)) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_Oless__supI1,axiom,
% 168.17/168.32 ! [V_b,V_a,V_x,T_a] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_a)
% 168.17/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 168.17/168.32 => 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))) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_Oless__supI2,axiom,
% 168.17/168.32 ! [V_a,V_b,V_x,T_a] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_a)
% 168.17/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 168.17/168.32 => 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))) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_less__max__iff__disj,axiom,
% 168.17/168.32 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( 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)))
% 168.17/168.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
% 168.17/168.32 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_max__less__iff__conj,axiom,
% 168.17/168.32 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( 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))
% 168.17/168.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
% 168.17/168.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom,
% 168.17/168.32 ! [T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_sup__nat__def,axiom,
% 168.17/168.32 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_sup__max,axiom,
% 168.17/168.32 ! [T_b] :
% 168.17/168.32 ( ( class_Lattices_Osemilattice__sup(T_b)
% 168.17/168.32 & class_Orderings_Olinorder(T_b) )
% 168.17/168.32 => c_Lattices_Osemilattice__sup__class_Osup(T_b) = c_Orderings_Oord__class_Omax(T_b) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_max__number__of,axiom,
% 168.17/168.32 ! [V_v,V_u,T_b] :
% 168.17/168.32 ( ( class_Int_Onumber(T_b)
% 168.17/168.32 & class_Orderings_Oord(T_b) )
% 168.17/168.32 => ( ( 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)))
% 168.17/168.32 => 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) )
% 168.17/168.32 & ( ~ 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)))
% 168.17/168.32 => 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) ) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_Odistrib__inf__le,axiom,
% 168.17/168.32 ! [V_z,V_y,V_x,T_a] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_a)
% 168.17/168.32 => 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)))) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_Odistrib__sup__le,axiom,
% 168.17/168.32 ! [V_z,V_y,V_x,T_a] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_a)
% 168.17/168.32 => 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)))) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_minus__max__eq__min,axiom,
% 168.17/168.32 ! [V_y,V_x,T_a] :
% 168.17/168.32 ( class_Groups_Olinordered__ab__group__add(T_a)
% 168.17/168.32 => 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)) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_minus__min__eq__max,axiom,
% 168.17/168.32 ! [V_y,V_x,T_a] :
% 168.17/168.32 ( class_Groups_Olinordered__ab__group__add(T_a)
% 168.17/168.32 => 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)) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_nat__minus__add__max,axiom,
% 168.17/168.32 ! [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) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_max__Suc2,axiom,
% 168.17/168.32 ! [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) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_max__Suc1,axiom,
% 168.17/168.32 ! [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) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_max__ord__max,axiom,
% 168.17/168.32 ! [T_b] :
% 168.17/168.32 ( class_Orderings_Oord(T_b)
% 168.17/168.32 => c_Orderings_Oord__class_Omax(T_b) = c_Orderings_Oord_Omax(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_Ofold__sup__insert,axiom,
% 168.17/168.32 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.32 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),V_A_2)) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_dual__min,axiom,
% 168.17/168.32 ! [T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => 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) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_Osup__le__fold__sup,axiom,
% 168.17/168.32 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.17/168.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),V_A_2))) ) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_Osup__Inf__absorb,axiom,
% 168.17/168.32 ! [V_a_2,V_A_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.17/168.32 => 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 ) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_Max_Oremove,axiom,
% 168.17/168.32 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.32 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 168.17/168.32 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 )
% 168.17/168.32 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 168.17/168.32 => 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)))))) ) ) ) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_OInf__le__Sup,axiom,
% 168.17/168.32 ! [V_A_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.32 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.32 => 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))) ) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_OSup__fin_Oremove,axiom,
% 168.17/168.32 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.32 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 168.17/168.32 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = V_x_2 )
% 168.17/168.32 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 168.17/168.32 => 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)))))) ) ) ) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_sum__diff__distrib,axiom,
% 168.17/168.32 ! [V_n_2,V_P_2,V_Q_2] :
% 168.17/168.32 ( ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_Q_2,B_x)),hAPP(V_P_2,B_x)))
% 168.17/168.32 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_P_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_Q_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_P_2)),V_Q_2)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_Max_Osingleton,axiom,
% 168.17/168.32 ! [V_x_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => 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 ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_OSup__fin_Oin__idem,axiom,
% 168.17/168.32 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.32 => 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) ) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_Max__ge,axiom,
% 168.17/168.32 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.32 => 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))) ) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_OSup__fin_Osingleton,axiom,
% 168.17/168.32 ! [V_x_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => 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 ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_Max__in,axiom,
% 168.17/168.32 ! [V_A_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.32 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.32 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_Max_Oin__idem,axiom,
% 168.17/168.32 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.32 => 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) ) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_OSup__fin_OF__eq,axiom,
% 168.17/168.32 ! [V_A_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.32 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omax(T_b)),V_A_2) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_Max_OF__eq,axiom,
% 168.17/168.32 ! [V_A_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.32 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omax(T_b)),V_A_2) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom,
% 168.17/168.32 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.32 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.32 => 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)) ) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_OSup__fin_Osubset__idem,axiom,
% 168.17/168.32 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.32 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 168.17/168.32 => 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) ) ) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_Oinf__Sup__absorb,axiom,
% 168.17/168.32 ! [V_a_2,V_A_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.17/168.32 => 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 ) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_OSup__fin_Ounion__idem,axiom,
% 168.17/168.32 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.32 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.32 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.32 => 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)) ) ) ) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_Max__mono,axiom,
% 168.17/168.32 ! [V_N_2,V_M_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
% 168.17/168.32 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 168.17/168.32 => 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))) ) ) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom,
% 168.17/168.32 ! [V_a_2,V_A_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.32 => 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) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_Max__insert,axiom,
% 168.17/168.32 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.32 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.32 => 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)) ) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_Max_Osubset__idem,axiom,
% 168.17/168.32 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.32 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 168.17/168.32 => 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) ) ) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_Max__Un,axiom,
% 168.17/168.32 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.32 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.32 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.32 => 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)) ) ) ) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_Max_Oeq__fold__idem_H,axiom,
% 168.17/168.32 ! [V_a_2,V_A_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.32 => 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) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_OSup__fin_Oinsert,axiom,
% 168.17/168.32 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.32 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.32 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.32 => 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)) ) ) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom,
% 168.17/168.32 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.32 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 168.17/168.32 => 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 )
% 168.17/168.32 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 168.17/168.32 => 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)))))) ) ) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom,
% 168.17/168.32 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.32 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.32 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.32 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.32 => 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)) ) ) ) ) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_OSup__fin_Ounion__inter,axiom,
% 168.17/168.32 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.32 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.32 => 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)) ) ) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom,
% 168.17/168.32 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.32 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.32 => 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) ) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_Max_Oinsert,axiom,
% 168.17/168.32 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.32 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.32 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.32 => 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)) ) ) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_Max_Oinsert__remove,axiom,
% 168.17/168.32 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.32 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 168.17/168.32 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 168.17/168.32 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 168.17/168.32 => 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)))))) ) ) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_Max_Ounion__disjoint,axiom,
% 168.17/168.32 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.32 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.32 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.32 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.32 => 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)) ) ) ) ) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_Max_Ounion__inter,axiom,
% 168.17/168.32 ! [V_B_2,V_A_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.17/168.32 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.32 => 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)) ) ) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_Max_Oeq__fold_H,axiom,
% 168.17/168.32 ! [V_x_2,V_A_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.32 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.17/168.32 => 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) ) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_min__max_OSup__fin_Oclosed,axiom,
% 168.17/168.32 ! [V_A_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.32 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.32 => ( ! [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))))))
% 168.17/168.32 => 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)) ) ) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_Max_Oclosed,axiom,
% 168.17/168.32 ! [V_A_2,T_b] :
% 168.17/168.32 ( class_Orderings_Olinorder(T_b)
% 168.17/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.17/168.32 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.17/168.32 => ( ! [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))))))
% 168.17/168.32 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_apfst__apsnd,axiom,
% 168.17/168.32 ! [V_x_2,V_g_2,T_e,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(c_Product__Type_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))) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_apsnd__apfst,axiom,
% 168.17/168.32 ! [V_x_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_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))) ).
% 168.17/168.32
% 168.17/168.32 fof(fact_apfst__conv,axiom,
% 168.50/168.32 ! [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) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_apfst__eq__conv,axiom,
% 168.50/168.32 ! [V_g_2,V_x_2,V_f_2,T_c,T_b,T_d] :
% 168.50/168.32 ( 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)
% 168.50/168.32 <=> 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)) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_fst__apfst,axiom,
% 168.50/168.32 ! [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)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_snd__apfst,axiom,
% 168.50/168.32 ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_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) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_apsnd__apfst__commute,axiom,
% 168.50/168.32 ! [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)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_setsum__natinterval__difff,axiom,
% 168.50/168.32 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 168.50/168.32 ( class_Groups_Oab__group__add(T_b)
% 168.50/168.32 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 168.50/168.32 => 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)))) )
% 168.50/168.32 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 168.50/168.32 => 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) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_gauss__sum,axiom,
% 168.50/168.32 ! [V_n_2,T_b] :
% 168.50/168.32 ( class_Rings_Ocomm__semiring__1(T_b)
% 168.50/168.32 => 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))) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INFI__fold__inf,axiom,
% 168.50/168.32 ! [V_f_2,V_A_2,T_b,T_c] :
% 168.50/168.32 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 168.50/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.32 => 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) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_SUPR__fold__sup,axiom,
% 168.50/168.32 ! [V_f_2,V_A_2,T_b,T_c] :
% 168.50/168.32 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 168.50/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.32 => 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) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INF1__E,axiom,
% 168.50/168.32 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
% 168.50/168.32 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 168.50/168.32 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INF1__D,axiom,
% 168.50/168.32 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.50/168.32 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INT__D,axiom,
% 168.50/168.32 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
% 168.50/168.32 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INT__E,axiom,
% 168.50/168.32 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 168.50/168.32 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
% 168.50/168.32 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UN__I,axiom,
% 168.50/168.32 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
% 168.50/168.32 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_SUP1__I,axiom,
% 168.50/168.32 ! [T_c,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 168.50/168.32 => hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_SUP2__I,axiom,
% 168.50/168.32 ! [T_d,T_c,V_c_2,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
% 168.50/168.32 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INF2__D,axiom,
% 168.50/168.32 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.50/168.32 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INF2__E,axiom,
% 168.50/168.32 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
% 168.50/168.32 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
% 168.50/168.32 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_finite__INT,axiom,
% 168.50/168.32 ! [V_A_2,T_c,V_I_2,T_b] :
% 168.50/168.32 ( ? [B_x] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 168.50/168.32 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) )
% 168.50/168.32 => 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))) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_finite__atLeastAtMost,axiom,
% 168.50/168.32 ! [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))) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INT__extend__simps_I5_J,axiom,
% 168.50/168.32 ! [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)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INT__simps_I5_J,axiom,
% 168.50/168.32 ! [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)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_finite__UN,axiom,
% 168.50/168.32 ! [V_B_2,T_c,V_A_2,T_b] :
% 168.50/168.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.32 => ( 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)))
% 168.50/168.32 <=> ! [B_x] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.50/168.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INT__extend__simps_I4_J,axiom,
% 168.50/168.32 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 168.50/168.32 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.32 => 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 )
% 168.50/168.32 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.32 => 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)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UNION__empty__conv_I2_J,axiom,
% 168.50/168.32 ! [V_B_2,V_A_2,T_b,T_c] :
% 168.50/168.32 ( 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))
% 168.50/168.32 <=> ! [B_x] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 168.50/168.32 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UN__constant,axiom,
% 168.50/168.32 ! [V_c_2,T_c,T_b,V_A_2] :
% 168.50/168.32 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.32 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 168.50/168.32 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.32 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = V_c_2 ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UN__empty2,axiom,
% 168.50/168.32 ! [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)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UNION__empty__conv_I1_J,axiom,
% 168.50/168.32 ! [V_B_2,V_A_2,T_c,T_b] :
% 168.50/168.32 ( 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)
% 168.50/168.32 <=> ! [B_x] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 168.50/168.32 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_Image__UN,axiom,
% 168.50/168.32 ! [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)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UN__simps_I7_J,axiom,
% 168.50/168.32 ! [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)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UN__extend__simps_I7_J,axiom,
% 168.50/168.32 ! [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)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_SUPR__apply,axiom,
% 168.50/168.32 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
% 168.50/168.32 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 168.50/168.32 => 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)) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INFI__apply,axiom,
% 168.50/168.32 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
% 168.50/168.32 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 168.50/168.32 => 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)) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_SUP__commute,axiom,
% 168.50/168.32 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
% 168.50/168.32 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 168.50/168.32 => 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))) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INF__commute,axiom,
% 168.50/168.32 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
% 168.50/168.32 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 168.50/168.32 => 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))) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UN__simps_I8_J,axiom,
% 168.50/168.32 ! [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)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INT__simps_I8_J,axiom,
% 168.50/168.32 ! [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)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UN__extend__simps_I8_J,axiom,
% 168.50/168.32 ! [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) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INT__extend__simps_I8_J,axiom,
% 168.50/168.32 ! [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) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_Compl__INT,axiom,
% 168.50/168.32 ! [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)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_Compl__UN,axiom,
% 168.50/168.32 ! [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)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_Pow__INT__eq,axiom,
% 168.50/168.32 ! [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)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UN__iff,axiom,
% 168.50/168.32 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 168.50/168.32 <=> ? [B_x] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 168.50/168.32 & hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INT__iff,axiom,
% 168.50/168.32 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 168.50/168.32 <=> ! [B_x] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 168.50/168.32 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UN__Pow__subset,axiom,
% 168.50/168.32 ! [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)))) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INT__subset__iff,axiom,
% 168.50/168.32 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] :
% 168.50/168.32 ( 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)))
% 168.50/168.32 <=> ! [B_x] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
% 168.50/168.32 => 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))) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UN__subset__iff,axiom,
% 168.50/168.32 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),V_B_2))
% 168.50/168.32 <=> ! [B_x] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
% 168.50/168.32 => 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)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UN__simps_I6_J,axiom,
% 168.50/168.32 ! [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) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UN__extend__simps_I6_J,axiom,
% 168.50/168.32 ! [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)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_Int__UN__distrib2,axiom,
% 168.50/168.32 ! [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))) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UN__extend__simps_I4_J,axiom,
% 168.50/168.32 ! [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)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_Int__UN__distrib,axiom,
% 168.50/168.32 ! [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)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UN__extend__simps_I5_J,axiom,
% 168.50/168.32 ! [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)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INT__Int__distrib,axiom,
% 168.50/168.32 ! [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)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UN__simps_I4_J,axiom,
% 168.50/168.32 ! [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) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UN__simps_I5_J,axiom,
% 168.50/168.32 ! [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)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_Union__def,axiom,
% 168.50/168.32 ! [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))) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INTER__UNIV__conv_I1_J,axiom,
% 168.50/168.32 ! [V_B_2,V_A_2,T_c,T_b] :
% 168.50/168.32 ( 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)
% 168.50/168.32 <=> ! [B_x] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 168.50/168.32 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INTER__UNIV__conv_I2_J,axiom,
% 168.50/168.32 ! [V_B_2,V_A_2,T_b,T_c] :
% 168.50/168.32 ( 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))
% 168.50/168.32 <=> ! [B_x] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 168.50/168.32 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INT__simps_I4_J,axiom,
% 168.50/168.32 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 168.50/168.32 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.32 => 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)) )
% 168.50/168.32 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.32 => 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)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_Inter__def,axiom,
% 168.50/168.32 ! [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))) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_Un__INT__distrib2,axiom,
% 168.50/168.32 ! [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))) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INT__extend__simps_I6_J,axiom,
% 168.50/168.32 ! [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)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UN__Un,axiom,
% 168.50/168.32 ! [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)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_Un__INT__distrib,axiom,
% 168.50/168.32 ! [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)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INT__extend__simps_I7_J,axiom,
% 168.50/168.32 ! [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)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UN__Un__distrib,axiom,
% 168.50/168.32 ! [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)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INT__simps_I6_J,axiom,
% 168.50/168.32 ! [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) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INT__simps_I7_J,axiom,
% 168.50/168.32 ! [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)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INF__INT__eq2,axiom,
% 168.50/168.32 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
% 168.50/168.32 ( 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))
% 168.50/168.32 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_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))) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_SUP__UN__eq2,axiom,
% 168.50/168.32 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),T_b),hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d))))),V_r_2)),V_x_2),V_y_2))
% 168.50/168.32 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INFI__bool__eq,axiom,
% 168.50/168.32 ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_HOL_Obool) = c_Set_OBall(T_b) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_le__INF__iff,axiom,
% 168.50/168.32 ! [V_M_2,V_A_2,T_c,V_u_2,T_b] :
% 168.50/168.32 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 168.50/168.32 => ( 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)))
% 168.50/168.32 <=> ! [B_x] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 168.50/168.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_SUP__le__iff,axiom,
% 168.50/168.32 ! [V_u_2,V_M_2,V_A_2,T_c,T_b] :
% 168.50/168.32 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 168.50/168.32 => ( 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))
% 168.50/168.32 <=> ! [B_x] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 168.50/168.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_less__SUP__iff,axiom,
% 168.50/168.32 ! [V_f_2,V_A_2,T_c,V_a_2,T_b] :
% 168.50/168.32 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 168.50/168.32 & class_Orderings_Olinorder(T_b) )
% 168.50/168.32 => ( 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)))
% 168.50/168.32 <=> ? [B_x] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 168.50/168.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INF__less__iff,axiom,
% 168.50/168.32 ! [V_a_2,V_f_2,V_A_2,T_c,T_b] :
% 168.50/168.32 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 168.50/168.32 & class_Orderings_Olinorder(T_b) )
% 168.50/168.32 => ( 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))
% 168.50/168.32 <=> ? [B_x] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 168.50/168.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INT__insert__distrib,axiom,
% 168.50/168.32 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
% 168.50/168.32 => 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)) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INT__lower,axiom,
% 168.50/168.32 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.50/168.32 => 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))) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INF__INT__eq,axiom,
% 168.50/168.32 ! [V_x_2,V_r_2,T_c,T_b] :
% 168.50/168.32 ( 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))
% 168.50/168.32 <=> 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))) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INT__absorb,axiom,
% 168.50/168.32 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
% 168.50/168.32 => 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) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_SUP__const,axiom,
% 168.50/168.32 ! [V_M_2,T_b,V_A_2,T_c] :
% 168.50/168.32 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 168.50/168.32 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.32 => 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 ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INF__const,axiom,
% 168.50/168.32 ! [V_M_2,T_b,V_A_2,T_c] :
% 168.50/168.32 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 168.50/168.32 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.32 => 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 ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UN__insert__distrib,axiom,
% 168.50/168.32 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
% 168.50/168.32 => 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)) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INT__constant,axiom,
% 168.50/168.32 ! [V_c_2,T_c,T_b,V_A_2] :
% 168.50/168.32 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.32 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 168.50/168.32 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.32 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = V_c_2 ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INT__empty,axiom,
% 168.50/168.32 ! [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)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UN__upper,axiom,
% 168.50/168.32 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.50/168.32 => 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))) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INT__extend__simps_I2_J,axiom,
% 168.50/168.32 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 168.50/168.32 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.32 => 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 )
% 168.50/168.32 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.32 => 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)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INT__extend__simps_I1_J,axiom,
% 168.50/168.32 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 168.50/168.32 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.32 => 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 )
% 168.50/168.32 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.32 => 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)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_SUP__UN__eq,axiom,
% 168.50/168.32 ! [V_x_2,V_r_2,T_c,T_b] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c))),V_r_2)),V_x_2))
% 168.50/168.32 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UN__absorb,axiom,
% 168.50/168.32 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
% 168.50/168.32 => 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) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INT__insert,axiom,
% 168.50/168.32 ! [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)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UN__simps_I1_J,axiom,
% 168.50/168.32 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
% 168.50/168.32 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.32 => 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)) )
% 168.50/168.32 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.32 => 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)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UN__singleton,axiom,
% 168.50/168.32 ! [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 ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UN__extend__simps_I1_J,axiom,
% 168.50/168.32 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
% 168.50/168.32 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.32 => 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))) )
% 168.50/168.32 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.32 => 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)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INT__Un,axiom,
% 168.50/168.32 ! [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)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UN__extend__simps_I2_J,axiom,
% 168.50/168.32 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 168.50/168.32 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.32 => 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 )
% 168.50/168.32 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.32 => 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)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UN__extend__simps_I3_J,axiom,
% 168.50/168.32 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 168.50/168.32 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.32 => 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 )
% 168.50/168.32 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.32 => 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)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UN__simps_I2_J,axiom,
% 168.50/168.32 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 168.50/168.32 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.32 => 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)) )
% 168.50/168.32 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.32 => 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) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UN__simps_I3_J,axiom,
% 168.50/168.32 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 168.50/168.32 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.32 => 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)) )
% 168.50/168.32 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.32 => 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)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UN__insert,axiom,
% 168.50/168.32 ! [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)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_Image__INT__subset,axiom,
% 168.50/168.32 ! [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)))) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_Int__Union,axiom,
% 168.50/168.32 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),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)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_Int__Union2,axiom,
% 168.50/168.32 ! [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)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_Un__Inter,axiom,
% 168.50/168.32 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),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)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_atLeastatMost__empty__iff2,axiom,
% 168.50/168.32 ! [V_b_2,V_a_2,T_b] :
% 168.50/168.32 ( class_Orderings_Oorder(T_b)
% 168.50/168.32 => ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)
% 168.50/168.32 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_atLeastatMost__empty__iff,axiom,
% 168.50/168.32 ! [V_b_2,V_a_2,T_b] :
% 168.50/168.32 ( class_Orderings_Oorder(T_b)
% 168.50/168.32 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.32 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_atLeastatMost__empty,axiom,
% 168.50/168.32 ! [V_a_2,V_b_2,T_b] :
% 168.50/168.32 ( class_Orderings_Oorder(T_b)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
% 168.50/168.32 => c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_atLeastatMost__subset__iff,axiom,
% 168.50/168.32 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 168.50/168.32 ( class_Orderings_Oorder(T_b)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)))
% 168.50/168.32 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 168.50/168.32 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2))
% 168.50/168.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_atLeastAtMost__singleton_H,axiom,
% 168.50/168.32 ! [V_b_2,V_a_2,T_b] :
% 168.50/168.32 ( class_Orderings_Oorder(T_b)
% 168.50/168.32 => ( V_a_2 = V_b_2
% 168.50/168.32 => c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_atLeastAtMost__singleton__iff,axiom,
% 168.50/168.32 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 168.50/168.32 ( class_Orderings_Oorder(T_b)
% 168.50/168.32 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
% 168.50/168.32 <=> ( V_a_2 = V_b_2
% 168.50/168.32 & V_b_2 = V_c_2 ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_atLeastAtMost__singleton,axiom,
% 168.50/168.32 ! [V_a_2,T_b] :
% 168.50/168.32 ( class_Orderings_Oorder(T_b)
% 168.50/168.32 => 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))) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom,
% 168.50/168.32 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 168.50/168.32 ( class_Groups_Ocomm__monoid__add(T_b)
% 168.50/168.32 => 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)) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom,
% 168.50/168.32 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
% 168.50/168.32 ( class_Groups_Ocomm__monoid__add(T_b)
% 168.50/168.32 => 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)) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UN__lessThan__UNIV,axiom,
% 168.50/168.32 hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INF__subset,axiom,
% 168.50/168.32 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 168.50/168.32 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.50/168.32 => 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))) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_SUP__subset,axiom,
% 168.50/168.32 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 168.50/168.32 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.50/168.32 => 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))) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INT__simps_I2_J,axiom,
% 168.50/168.32 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 168.50/168.32 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.32 => 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)) )
% 168.50/168.32 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.32 => 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)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INT__simps_I1_J,axiom,
% 168.50/168.32 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 168.50/168.32 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.32 => 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)) )
% 168.50/168.32 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.32 => 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) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INT__simps_I3_J,axiom,
% 168.50/168.32 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 168.50/168.32 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.32 => 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)) )
% 168.50/168.32 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.32 => 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) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INT__extend__simps_I3_J,axiom,
% 168.50/168.32 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 168.50/168.32 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.32 => 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) )
% 168.50/168.32 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.32 => 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)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_Image__eq__UN,axiom,
% 168.50/168.32 ! [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))))) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_card__atLeastAtMost,axiom,
% 168.50/168.32 ! [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) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_atLeastAtMostSuc__conv,axiom,
% 168.50/168.32 ! [V_n_2,V_m_2] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 168.50/168.32 => 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)) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_le__SUPI,axiom,
% 168.50/168.32 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
% 168.50/168.32 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 168.50/168.32 => 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))) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INF__leI,axiom,
% 168.50/168.32 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
% 168.50/168.32 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 168.50/168.32 => 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))) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_setsum__shift__lb__Suc0__0,axiom,
% 168.50/168.32 ! [V_k_2,V_f_2] :
% 168.50/168.32 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.50/168.32 => 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)) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_Int__atLeastAtMost,axiom,
% 168.50/168.32 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 168.50/168.32 ( class_Orderings_Olinorder(T_b)
% 168.50/168.32 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_atLeastatMost__psubset__iff,axiom,
% 168.50/168.32 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 168.50/168.32 ( class_Orderings_Oorder(T_b)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)))
% 168.50/168.32 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 168.50/168.32 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2))
% 168.50/168.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
% 168.50/168.32 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_a_2))
% 168.50/168.32 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_d_2)) ) ) )
% 168.50/168.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2)) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_ivl__disj__int_I4_J,axiom,
% 168.50/168.32 ! [V_u_2,V_l_2,T_b] :
% 168.50/168.32 ( class_Orderings_Oorder(T_b)
% 168.50/168.32 => 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)) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_setsum__head__Suc,axiom,
% 168.50/168.32 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 168.50/168.32 ( class_Groups_Ocomm__monoid__add(T_b)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 168.50/168.32 => 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))) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_setsum__cl__ivl__Suc,axiom,
% 168.50/168.32 ! [V_f_2,V_m_2,V_n_2,T_b] :
% 168.50/168.32 ( class_Groups_Ocomm__monoid__add(T_b)
% 168.50/168.32 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 168.50/168.32 => 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) )
% 168.50/168.32 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 168.50/168.32 => 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))) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_sup__SUPR__fold__sup,axiom,
% 168.50/168.32 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 168.50/168.32 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 168.50/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.32 => 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) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_inf__INFI__fold__inf,axiom,
% 168.50/168.32 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 168.50/168.32 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 168.50/168.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.32 => 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) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_setsum__ub__add__nat,axiom,
% 168.50/168.32 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_b] :
% 168.50/168.32 ( class_Groups_Ocomm__monoid__add(T_b)
% 168.50/168.32 => ( 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))))
% 168.50/168.32 => 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)))) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_minus__int__def,axiom,
% 168.50/168.32 ! [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))))))) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_ex__nat__less,axiom,
% 168.50/168.32 ! [V_P_2,V_n_2] :
% 168.50/168.32 ( ? [B_m] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 168.50/168.32 & hBOOL(hAPP(V_P_2,B_m)) )
% 168.50/168.32 <=> ? [B_x] :
% 168.50/168.32 ( 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)))
% 168.50/168.32 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_all__nat__less,axiom,
% 168.50/168.32 ! [V_P_2,V_n_2] :
% 168.50/168.32 ( ! [B_m] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 168.50/168.32 => hBOOL(hAPP(V_P_2,B_m)) )
% 168.50/168.32 <=> ! [B_x] :
% 168.50/168.32 ( 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)))
% 168.50/168.32 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_nat__def,axiom,
% 168.50/168.32 ! [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)))))) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_SUP2__iff,axiom,
% 168.50/168.32 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
% 168.50/168.32 <=> ? [B_x] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.50/168.32 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INF2__iff,axiom,
% 168.50/168.32 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
% 168.50/168.32 <=> ! [B_x] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.50/168.32 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_SUP1__iff,axiom,
% 168.50/168.32 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
% 168.50/168.32 <=> ? [B_x] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.50/168.32 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INF1__iff,axiom,
% 168.50/168.32 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
% 168.50/168.32 <=> ! [B_x] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.50/168.32 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UN__UN__flatten,axiom,
% 168.50/168.32 ! [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)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UN__simps_I9_J,axiom,
% 168.50/168.32 ! [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)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INT__simps_I9_J,axiom,
% 168.50/168.32 ! [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)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UN__extend__simps_I9_J,axiom,
% 168.50/168.32 ! [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) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_INT__extend__simps_I9_J,axiom,
% 168.50/168.32 ! [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) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_ball__UN,axiom,
% 168.50/168.32 ! [V_P_2,V_B_2,V_A_2,T_c,T_b] :
% 168.50/168.32 ( ! [B_x] :
% 168.50/168.32 ( 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)))
% 168.50/168.32 => hBOOL(hAPP(V_P_2,B_x)) )
% 168.50/168.32 <=> ! [B_x] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 168.50/168.32 => ! [B_xa] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x)))
% 168.50/168.32 => hBOOL(hAPP(V_P_2,B_xa)) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_Rep__Integ__inject,axiom,
% 168.50/168.32 ! [V_y_2,V_x_2] :
% 168.50/168.32 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2)
% 168.50/168.32 <=> V_x_2 = V_y_2 ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_Rep__Integ__inverse,axiom,
% 168.50/168.32 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ).
% 168.50/168.32
% 168.50/168.32 fof(fact_simp__from__to,axiom,
% 168.50/168.32 ! [V_i_2,V_j_2] :
% 168.50/168.32 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 168.50/168.32 => 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)) )
% 168.50/168.32 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 168.50/168.32 => 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)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_card__atLeastAtMost__int,axiom,
% 168.50/168.32 ! [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))) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_aset_I6_J,axiom,
% 168.50/168.32 ! [V_A_2,V_t_2,V_D_2] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 168.50/168.32 => ( 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))
% 168.50/168.32 => ! [B_x] :
% 168.50/168.32 ( ! [B_xa] :
% 168.50/168.32 ( 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)))
% 168.50/168.32 => ! [B_xb] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 168.50/168.32 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 168.50/168.32 => 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)) ) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_bset_I8_J,axiom,
% 168.50/168.32 ! [V_B_2,V_t_2,V_D_2] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 168.50/168.32 => ( 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))
% 168.50/168.32 => ! [B_x] :
% 168.50/168.32 ( ! [B_xa] :
% 168.50/168.32 ( 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)))
% 168.50/168.32 => ! [B_xb] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 168.50/168.32 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 168.50/168.32 => 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))) ) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_aset_I8_J,axiom,
% 168.50/168.32 ! [V_t_2,V_A_2,V_D_2] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 168.50/168.32 => ! [B_x] :
% 168.50/168.32 ( ! [B_xa] :
% 168.50/168.32 ( 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)))
% 168.50/168.32 => ! [B_xb] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 168.50/168.32 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 168.50/168.32 => 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))) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_bset_I6_J,axiom,
% 168.50/168.32 ! [V_t_2,V_B_2,V_D_2] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 168.50/168.32 => ! [B_x] :
% 168.50/168.32 ( ! [B_xa] :
% 168.50/168.32 ( 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)))
% 168.50/168.32 => ! [B_xb] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 168.50/168.32 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 168.50/168.32 => 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)) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_finite__atLeastAtMost__int,axiom,
% 168.50/168.32 ! [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))) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_aset_I4_J,axiom,
% 168.50/168.32 ! [V_A_2,V_t_2,V_D_2] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 168.50/168.32 => ! [B_x] :
% 168.50/168.32 ( ! [B_xa] :
% 168.50/168.32 ( 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)))
% 168.50/168.32 => ! [B_xb] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 168.50/168.32 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 168.50/168.32 => ( B_x != V_t_2
% 168.50/168.32 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_bset_I4_J,axiom,
% 168.50/168.32 ! [V_B_2,V_t_2,V_D_2] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 168.50/168.32 => ! [B_x] :
% 168.50/168.32 ( ! [B_xa] :
% 168.50/168.32 ( 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)))
% 168.50/168.32 => ! [B_xb] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 168.50/168.32 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 168.50/168.32 => ( B_x != V_t_2
% 168.50/168.32 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_bset_I7_J,axiom,
% 168.50/168.32 ! [V_B_2,V_t_2,V_D_2] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 168.50/168.32 => ! [B_x] :
% 168.50/168.32 ( ! [B_xa] :
% 168.50/168.32 ( 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)))
% 168.50/168.32 => ! [B_xb] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 168.50/168.32 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 168.50/168.32 => 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))) ) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_infinite__UNIV__int,axiom,
% 168.50/168.32 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_bset_I3_J,axiom,
% 168.50/168.32 ! [V_B_2,V_t_2,V_D_2] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 168.50/168.32 => ( 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))
% 168.50/168.32 => ( ! [B_x] :
% 168.50/168.32 ( 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)))
% 168.50/168.32 => ! [B_xa] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2))
% 168.50/168.32 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) )
% 168.50/168.32 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_aset_I3_J,axiom,
% 168.50/168.32 ! [V_A_2,V_t_2,V_D_2] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 168.50/168.32 => ( 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))
% 168.50/168.32 => ( ! [B_x] :
% 168.50/168.32 ( 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)))
% 168.50/168.32 => ! [B_xa] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2))
% 168.50/168.32 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) )
% 168.50/168.32 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_aset_I5_J,axiom,
% 168.50/168.32 ! [V_A_2,V_t_2,V_D_2] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 168.50/168.32 => ! [B_x] :
% 168.50/168.32 ( ! [B_xa] :
% 168.50/168.32 ( 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)))
% 168.50/168.32 => ! [B_xb] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 168.50/168.32 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 168.50/168.32 => 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)) ) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_periodic__finite__ex,axiom,
% 168.50/168.32 ! [V_P_2,V_d_2] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 168.50/168.32 => ( ! [B_x,B_k] :
% 168.50/168.32 ( hBOOL(hAPP(V_P_2,B_x))
% 168.50/168.32 <=> hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B_k),V_d_2)))) )
% 168.50/168.32 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 168.50/168.32 <=> ? [B_x] :
% 168.50/168.32 ( 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)))
% 168.50/168.32 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_bset_I5_J,axiom,
% 168.50/168.32 ! [V_t_2,V_B_2,V_D_2] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 168.50/168.32 => ! [B_x] :
% 168.50/168.32 ( ! [B_xa] :
% 168.50/168.32 ( 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)))
% 168.50/168.32 => ! [B_xb] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 168.50/168.32 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 168.50/168.32 => 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)) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_aset_I7_J,axiom,
% 168.50/168.32 ! [V_t_2,V_A_2,V_D_2] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 168.50/168.32 => ! [B_x] :
% 168.50/168.32 ( ! [B_xa] :
% 168.50/168.32 ( 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)))
% 168.50/168.32 => ! [B_xb] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 168.50/168.32 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 168.50/168.32 => 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))) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_card__greaterThanLessThan__int,axiom,
% 168.50/168.32 ! [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)))) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_Id__on__def,axiom,
% 168.50/168.32 ! [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)))) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UN__le__eq__Un0,axiom,
% 168.50/168.32 ! [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))) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_finite__atMost,axiom,
% 168.50/168.32 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_finite__greaterThanLessThan__int,axiom,
% 168.50/168.32 ! [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))) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_atMost__eq__iff,axiom,
% 168.50/168.32 ! [V_y_2,V_x_2,T_b] :
% 168.50/168.32 ( class_Orderings_Olinorder(T_b)
% 168.50/168.32 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2)
% 168.50/168.32 <=> V_x_2 = V_y_2 ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_ivl__disj__int_I1_J,axiom,
% 168.50/168.32 ! [V_u_2,V_l_2,T_b] :
% 168.50/168.32 ( class_Orderings_Oorder(T_b)
% 168.50/168.32 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_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)) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_ivl__disj__un_I7_J,axiom,
% 168.50/168.32 ! [V_u_2,V_l_2,T_b] :
% 168.50/168.32 ( class_Orderings_Olinorder(T_b)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 168.50/168.32 => 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) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_Id__on__def_H,axiom,
% 168.50/168.32 ! [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)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_atLeast0AtMost,axiom,
% 168.50/168.32 ! [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) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_greaterThanLessThan__empty,axiom,
% 168.50/168.32 ! [V_k_2,V_l_2,T_b] :
% 168.50/168.32 ( class_Orderings_Oorder(T_b)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
% 168.50/168.32 => 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)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_lessThan__Suc__atMost,axiom,
% 168.50/168.32 ! [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) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_card__atMost,axiom,
% 168.50/168.32 ! [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) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_atMost__Suc,axiom,
% 168.50/168.32 ! [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)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_atMost__iff,axiom,
% 168.50/168.32 ! [V_k_2,V_i_2,T_b] :
% 168.50/168.32 ( class_Orderings_Oord(T_b)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)))
% 168.50/168.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_k_2)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_atMost__subset__iff,axiom,
% 168.50/168.32 ! [V_y_2,V_x_2,T_b] :
% 168.50/168.32 ( class_Orderings_Oorder(T_b)
% 168.50/168.32 => ( 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)))
% 168.50/168.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_Id__on__empty,axiom,
% 168.50/168.32 ! [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)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_Image__Id__on,axiom,
% 168.50/168.32 ! [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) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UN__atMost__UNIV,axiom,
% 168.50/168.32 hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatMost(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_setsum__atMost__Suc,axiom,
% 168.50/168.32 ! [V_n_2,V_f_2,T_b] :
% 168.50/168.32 ( class_Groups_Ocomm__monoid__add(T_b)
% 168.50/168.32 => 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))) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_ivl__disj__int_I13_J,axiom,
% 168.50/168.32 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 168.50/168.32 ( class_Orderings_Oorder(T_b)
% 168.50/168.32 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_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)) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_ivl__disj__int_I12_J,axiom,
% 168.50/168.32 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 168.50/168.32 ( class_Orderings_Oorder(T_b)
% 168.50/168.32 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_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)) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_atMost__0,axiom,
% 168.50/168.32 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))) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_Int__greaterThanLessThan,axiom,
% 168.50/168.32 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 168.50/168.32 ( class_Orderings_Olinorder(T_b)
% 168.50/168.32 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_Id__on__eqI,axiom,
% 168.50/168.32 ! [V_A_2,T_b,V_b_2,V_a_2] :
% 168.50/168.32 ( V_a_2 = V_b_2
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.50/168.32 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Relation_OId__on(T_b,V_A_2))) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_Id__on__iff,axiom,
% 168.50/168.32 ! [V_A_2,V_y_2,V_x_2,T_b] :
% 168.50/168.32 ( hBOOL(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)))
% 168.50/168.32 <=> ( V_x_2 = V_y_2
% 168.50/168.32 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_Int__atLeastAtMostR1,axiom,
% 168.50/168.32 ! [V_d_2,V_c_2,V_b_2,T_b] :
% 168.50/168.32 ( class_Orderings_Olinorder(T_b)
% 168.50/168.32 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_Int__atLeastAtMostL1,axiom,
% 168.50/168.32 ! [V_d_2,V_b_2,V_a_2,T_b] :
% 168.50/168.32 ( class_Orderings_Olinorder(T_b)
% 168.50/168.32 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UN__le__add__shift,axiom,
% 168.50/168.32 ! [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) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_ivl__disj__un_I2_J,axiom,
% 168.50/168.32 ! [V_u_2,T_b] :
% 168.50/168.32 ( class_Orderings_Olinorder(T_b)
% 168.50/168.32 => 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) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_ivl__disj__un_I10_J,axiom,
% 168.50/168.32 ! [V_u_2,V_l_2,T_b] :
% 168.50/168.32 ( class_Orderings_Olinorder(T_b)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 168.50/168.32 => 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) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_ivl__disj__un_I19_J,axiom,
% 168.50/168.32 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 168.50/168.32 ( class_Orderings_Olinorder(T_b)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 168.50/168.32 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_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) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_ivl__disj__un_I4_J,axiom,
% 168.50/168.32 ! [V_u_2,V_l_2,T_b] :
% 168.50/168.32 ( class_Orderings_Olinorder(T_b)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 168.50/168.32 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(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) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_quotient__def,axiom,
% 168.50/168.32 ! [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)))) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_finite__greaterThanAtMost,axiom,
% 168.50/168.32 ! [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))) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_finite__greaterThanLessThan,axiom,
% 168.50/168.32 ! [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))) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_finite__greaterThanAtMost__int,axiom,
% 168.50/168.32 ! [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))) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_quotient__is__empty,axiom,
% 168.50/168.32 ! [V_r_2,V_A_2,T_b] :
% 168.50/168.32 ( 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))
% 168.50/168.32 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_quotient__is__empty2,axiom,
% 168.50/168.32 ! [V_r_2,V_A_2,T_b] :
% 168.50/168.32 ( 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)
% 168.50/168.32 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_quotient__empty,axiom,
% 168.50/168.32 ! [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)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_greaterThanAtMost__empty,axiom,
% 168.50/168.32 ! [V_k_2,V_l_2,T_b] :
% 168.50/168.32 ( class_Orderings_Oorder(T_b)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
% 168.50/168.32 => 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)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_greaterThanAtMost__empty__iff2,axiom,
% 168.50/168.32 ! [V_l_2,V_k_2,T_b] :
% 168.50/168.32 ( class_Orderings_Oorder(T_b)
% 168.50/168.32 => ( 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)
% 168.50/168.32 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_greaterThanAtMost__empty__iff,axiom,
% 168.50/168.32 ! [V_l_2,V_k_2,T_b] :
% 168.50/168.32 ( class_Orderings_Oorder(T_b)
% 168.50/168.32 => ( 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))
% 168.50/168.32 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_ivl__disj__un_I20_J,axiom,
% 168.50/168.32 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 168.50/168.32 ( class_Orderings_Olinorder(T_b)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 168.50/168.32 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_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) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_ivl__disj__int_I14_J,axiom,
% 168.50/168.32 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 168.50/168.32 ( class_Orderings_Oorder(T_b)
% 168.50/168.32 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_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)) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom,
% 168.50/168.32 ! [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) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_card__greaterThanAtMost,axiom,
% 168.50/168.32 ! [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) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_ivl__disj__un_I22_J,axiom,
% 168.50/168.32 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 168.50/168.32 ( class_Orderings_Olinorder(T_b)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 168.50/168.32 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_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) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 168.50/168.32 ! [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) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_ivl__disj__int_I16_J,axiom,
% 168.50/168.32 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 168.50/168.32 ( class_Orderings_Oorder(T_b)
% 168.50/168.32 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_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)) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_Int__greaterThanAtMost,axiom,
% 168.50/168.32 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 168.50/168.32 ( class_Orderings_Olinorder(T_b)
% 168.50/168.32 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_ivl__disj__un_I9_J,axiom,
% 168.50/168.32 ! [V_u_2,V_l_2,T_b] :
% 168.50/168.32 ( class_Orderings_Olinorder(T_b)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 168.50/168.32 => 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) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_quotientI,axiom,
% 168.50/168.32 ! [V_r_2,V_A_2,V_x_2,T_b] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.50/168.32 => 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))) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_ivl__disj__int_I3_J,axiom,
% 168.50/168.32 ! [V_u_2,V_l_2,T_b] :
% 168.50/168.32 ( class_Orderings_Oorder(T_b)
% 168.50/168.32 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_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)) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_ivl__disj__int_I10_J,axiom,
% 168.50/168.32 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 168.50/168.32 ( class_Orderings_Oorder(T_b)
% 168.50/168.32 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_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)) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_card__greaterThanLessThan,axiom,
% 168.50/168.32 ! [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)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_card__greaterThanAtMost__int,axiom,
% 168.50/168.32 ! [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)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_singleton__quotient,axiom,
% 168.50/168.32 ! [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))) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_ivl__disj__un_I16_J,axiom,
% 168.50/168.32 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 168.50/168.32 ( class_Orderings_Olinorder(T_b)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
% 168.50/168.32 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_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) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_setsum__head,axiom,
% 168.50/168.32 ! [V_P_2,V_n_2,V_m_2,T_b] :
% 168.50/168.32 ( class_Groups_Ocomm__monoid__add(T_b)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 168.50/168.32 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_P_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_P_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_P_2),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_m_2,V_n_2))) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_ivl__disj__un_I5_J,axiom,
% 168.50/168.32 ! [V_u_2,V_l_2,T_b] :
% 168.50/168.32 ( class_Orderings_Olinorder(T_b)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 168.50/168.32 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),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) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_equiv__class__nondisjoint,axiom,
% 168.50/168.32 ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_b] :
% 168.50/168.32 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))))
% 168.50/168.32 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_subset__equiv__class,axiom,
% 168.50/168.32 ! [V_a_2,V_b_2,V_r_2,V_A_2,T_b] :
% 168.50/168.32 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 168.50/168.32 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_quotientE,axiom,
% 168.50/168.32 ! [V_r_2,V_A_2,V_X_2,T_b] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 168.50/168.32 => ~ ! [B_x] :
% 168.50/168.32 ( 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))))
% 168.50/168.32 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_equiv__intrel,axiom,
% 168.50/168.32 c_Equiv__Relations_Oequiv(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Int_Ointrel) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_Union__quotient,axiom,
% 168.50/168.32 ! [V_r_2,V_A_2,T_b] :
% 168.50/168.32 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 168.50/168.32 => 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 ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_equiv__class__self,axiom,
% 168.50/168.32 ! [V_a_2,V_r_2,V_A_2,T_b] :
% 168.50/168.32 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.50/168.32 => 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)))))) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_quotient__disj,axiom,
% 168.50/168.32 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 168.50/168.32 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 168.50/168.32 => ( 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)))
% 168.50/168.32 => ( V_X_2 = V_Y_2
% 168.50/168.32 | 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)) ) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_equiv__class__eq,axiom,
% 168.50/168.32 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
% 168.50/168.32 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 168.50/168.32 => hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_quotient__eq__iff,axiom,
% 168.50/168.32 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 168.50/168.32 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 168.50/168.32 => ( 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)))
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
% 168.50/168.32 => ( V_X_2 = V_Y_2
% 168.50/168.32 <=> hBOOL(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)) ) ) ) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_quotient__eqI,axiom,
% 168.50/168.32 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 168.50/168.32 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 168.50/168.32 => ( 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)))
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
% 168.50/168.32 => ( hBOOL(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))
% 168.50/168.32 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_eq__equiv__class,axiom,
% 168.50/168.32 ! [V_A_2,V_b_2,V_a_2,V_r_2,T_b] :
% 168.50/168.32 ( hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 168.50/168.32 => ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 168.50/168.32 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_eq__equiv__class__iff,axiom,
% 168.50/168.32 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 168.50/168.32 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 168.50/168.32 => ( 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))))
% 168.50/168.32 <=> hBOOL(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)) ) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_equiv__class__eq__iff,axiom,
% 168.50/168.32 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 168.50/168.32 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 168.50/168.32 => ( hBOOL(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))
% 168.50/168.32 <=> ( 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))))
% 168.50/168.32 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.50/168.32 & hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_equiv__class__subset,axiom,
% 168.50/168.32 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
% 168.50/168.32 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 168.50/168.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_eq__equiv__class__iff2,axiom,
% 168.50/168.32 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 168.50/168.32 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 168.50/168.32 => ( 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)
% 168.50/168.32 <=> hBOOL(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)) ) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UN__equiv__class,axiom,
% 168.50/168.32 ! [V_a_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 168.50/168.32 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 168.50/168.32 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.50/168.32 => 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) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UN__equiv__class2,axiom,
% 168.50/168.32 ! [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] :
% 168.50/168.32 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 168.50/168.32 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 168.50/168.32 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a1_2),V_A1_2))
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a2_2),V_A2_2))
% 168.50/168.32 => 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) ) ) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_equivp__equiv,axiom,
% 168.50/168.32 ! [V_A_2,T_b] :
% 168.50/168.32 ( c_Equiv__Relations_Oequiv(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_A_2)
% 168.50/168.32 <=> c_Equiv__Relations_Oequivp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_A_2)) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_identity__equivp,axiom,
% 168.50/168.32 ! [T_b] : c_Equiv__Relations_Oequivp(T_b,c_fequal) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_equivp__def,axiom,
% 168.50/168.32 ! [V_R_2,T_b] :
% 168.50/168.32 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 168.50/168.32 <=> ! [B_x,B_y] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
% 168.50/168.32 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_equivp__reflp,axiom,
% 168.50/168.32 ! [V_x_2,V_R_2,T_b] :
% 168.50/168.32 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 168.50/168.32 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_equivp__symp,axiom,
% 168.50/168.32 ! [V_y_2,V_x_2,V_R_2,T_b] :
% 168.50/168.32 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 168.50/168.32 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_equivp__transp,axiom,
% 168.50/168.32 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] :
% 168.50/168.32 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
% 168.50/168.32 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_congruent2__implies__congruent,axiom,
% 168.50/168.32 ! [V_a_2,V_f_2,V_r2_2,T_d,T_c,V_r1_2,V_A_2,T_b] :
% 168.50/168.32 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r1_2)
% 168.50/168.32 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.50/168.32 => c_Equiv__Relations_Ocongruent(T_c,T_d,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_congruent__def,axiom,
% 168.50/168.32 ! [V_f_2,V_r_2,T_c,T_b] :
% 168.50/168.32 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
% 168.50/168.32 <=> ! [B_x] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
% 168.50/168.32 => 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)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_congruent2D,axiom,
% 168.50/168.32 ! [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] :
% 168.50/168.32 ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
% 168.50/168.32 => ( 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))
% 168.50/168.32 => ( 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))
% 168.50/168.32 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_congruentD,axiom,
% 168.50/168.32 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_c,T_b] :
% 168.50/168.32 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
% 168.50/168.32 => ( 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))
% 168.50/168.32 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_congruent2__implies__congruent__UN,axiom,
% 168.50/168.32 ! [V_a_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
% 168.50/168.32 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 168.50/168.32 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 168.50/168.32 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A2_2))
% 168.50/168.32 => 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)) ) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UN__equiv__class__inject,axiom,
% 168.50/168.32 ! [V_Y_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 168.50/168.32 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 168.50/168.32 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 168.50/168.32 => ( 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)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 168.50/168.32 => ( 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)))
% 168.50/168.32 => ( ! [B_x] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.50/168.32 => ! [B_y] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 168.50/168.32 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 168.50/168.32 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2)) ) ) )
% 168.50/168.32 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UN__equiv__class__type2,axiom,
% 168.50/168.32 ! [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] :
% 168.50/168.32 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 168.50/168.32 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 168.50/168.32 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 168.50/168.32 => ( 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)))
% 168.50/168.32 => ( 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)))
% 168.50/168.32 => ( ! [B_x1] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x1),V_A1_2))
% 168.50/168.32 => ! [B_x2] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x2),V_A2_2))
% 168.50/168.32 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) )
% 168.50/168.32 => 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)) ) ) ) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_UN__equiv__class__type,axiom,
% 168.50/168.32 ! [V_B_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 168.50/168.32 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 168.50/168.32 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 168.50/168.32 => ( ! [B_x] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.50/168.32 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) )
% 168.50/168.32 => 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)) ) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_Integ__def,axiom,
% 168.50/168.32 c_Int_OInteg = hAPP(hAPP(c_Equiv__Relations_Oquotient(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Int_Ointrel) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_refl__on__def_H,axiom,
% 168.50/168.32 ! [V_r_2,V_A_2,T_b] :
% 168.50/168.32 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 168.50/168.32 <=> ( ! [B_x] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
% 168.50/168.32 => 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)) )
% 168.50/168.32 & ! [B_x] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.50/168.32 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_card__quotient__disjoint,axiom,
% 168.50/168.32 ! [V_r_2,V_A_2,T_b] :
% 168.50/168.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.32 => ( 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)
% 168.50/168.32 => 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) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_refl__on__Id__on,axiom,
% 168.50/168.32 ! [V_A_2,T_b] : c_Relation_Orefl__on(T_b,V_A_2,c_Relation_OId__on(T_b,V_A_2)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_refl__on__empty,axiom,
% 168.50/168.32 ! [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))) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_refl__on__Un,axiom,
% 168.50/168.32 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
% 168.50/168.32 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 168.50/168.32 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
% 168.50/168.32 => 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)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_refl__on__Int,axiom,
% 168.50/168.32 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
% 168.50/168.32 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 168.50/168.32 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
% 168.50/168.32 => 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)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_Rep__Integ,axiom,
% 168.50/168.32 ! [V_x_2] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_x_2)),c_Int_OInteg)) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_refl__onD2,axiom,
% 168.50/168.32 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 168.50/168.32 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 168.50/168.32 => ( hBOOL(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))
% 168.50/168.32 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_refl__onD1,axiom,
% 168.50/168.32 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 168.50/168.32 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 168.50/168.32 => ( hBOOL(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))
% 168.50/168.32 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_refl__onD,axiom,
% 168.50/168.32 ! [V_a_2,V_r_2,V_A_2,T_b] :
% 168.50/168.32 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.50/168.32 => 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)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_quotient__diff1,axiom,
% 168.50/168.32 ! [V_a_2,V_A_2,V_r_2,T_b] :
% 168.50/168.32 ( 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)
% 168.50/168.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.50/168.32 => 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)) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_inj__uminus,axiom,
% 168.50/168.32 ! [V_A_2,T_b] :
% 168.50/168.32 ( class_Groups_Oordered__ab__group__add(T_b)
% 168.50/168.32 => c_Fun_Oinj__on(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b),V_A_2) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_inj__on__empty,axiom,
% 168.50/168.32 ! [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))) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_inj__singleton,axiom,
% 168.50/168.32 ! [T_b] : c_Fun_Oinj__on(T_b,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_inj__Suc,axiom,
% 168.50/168.32 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_inj__on__add__nat,axiom,
% 168.50/168.32 ! [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) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_inj__of__nat,axiom,
% 168.50/168.32 ! [T_b] :
% 168.50/168.32 ( class_Nat_Osemiring__char__0(T_b)
% 168.50/168.32 => c_Fun_Oinj__on(tc_Nat_Onat,T_b,c_Nat_Osemiring__1__class_Oof__nat(T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_inj__int,axiom,
% 168.50/168.32 c_Fun_Oinj__on(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_swap__inj__on,axiom,
% 168.50/168.32 ! [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) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_inj__on__def,axiom,
% 168.50/168.32 ! [V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.32 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 168.50/168.32 <=> ! [B_x] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.50/168.32 => ! [B_xa] :
% 168.50/168.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 168.50/168.32 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa)
% 168.50/168.32 => B_x = B_xa ) ) ) ) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_inj__on__id2,axiom,
% 168.50/168.32 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_COMBI(T_b),V_A_2) ).
% 168.50/168.32
% 168.50/168.32 fof(fact_inj__on__contraD,axiom,
% 168.50/168.32 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.32 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 168.50/168.32 => ( V_x_2 != V_y_2
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 168.50/168.33 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_inj__on__iff,axiom,
% 168.50/168.33 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 168.50/168.33 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 168.50/168.33 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_inj__onD,axiom,
% 168.50/168.33 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 168.50/168.33 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 168.50/168.33 => V_x_2 = V_y_2 ) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_subset__inj__on,axiom,
% 168.50/168.33 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.50/168.33 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_injD,axiom,
% 168.50/168.33 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 168.50/168.33 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 168.50/168.33 => V_x_2 = V_y_2 ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_inj__eq,axiom,
% 168.50/168.33 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 168.50/168.33 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 168.50/168.33 <=> V_x_2 = V_y_2 ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_inj__on__Int,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 168.50/168.33 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 168.50/168.33 => 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)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_inj__on__diff,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 168.50/168.33 => 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)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_inj__fun,axiom,
% 168.50/168.33 ! [T_d,V_f_2,T_c,T_b] :
% 168.50/168.33 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 168.50/168.33 => 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))) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Id__onE,axiom,
% 168.50/168.33 ! [V_A_2,V_c_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_c_2),c_Relation_OId__on(T_b,V_A_2)))
% 168.50/168.33 => ~ ! [B_x] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.50/168.33 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_type__definition__Integ,axiom,
% 168.50/168.33 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) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_ImageE,axiom,
% 168.50/168.33 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
% 168.50/168.33 => ~ ! [B_x] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2))
% 168.50/168.33 => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_type__definition_OAbs__inject,axiom,
% 168.50/168.33 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 168.50/168.33 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
% 168.50/168.33 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2)
% 168.50/168.33 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_type__definition_OAbs__inverse,axiom,
% 168.50/168.33 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 168.50/168.33 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
% 168.50/168.33 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_type__definition_ORep,axiom,
% 168.50/168.33 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 168.50/168.33 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 168.50/168.33 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_type__definition_ORep__inverse,axiom,
% 168.50/168.33 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 168.50/168.33 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 168.50/168.33 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_type__definition_ORep__inject,axiom,
% 168.50/168.33 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 168.50/168.33 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 168.50/168.33 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2)
% 168.50/168.33 <=> V_x_2 = V_y_2 ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_geometric__sum,axiom,
% 168.50/168.33 ! [V_n_2,V_x_2,T_b] :
% 168.50/168.33 ( class_Fields_Ofield(T_b)
% 168.50/168.33 => ( V_x_2 != c_Groups_Oone__class_Oone(T_b)
% 168.50/168.33 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(c_Power_Opower__class_Opower(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),V_n_2)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_x_2),c_Groups_Oone__class_Oone(T_b))) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_ivl__disj__un_I18_J,axiom,
% 168.50/168.33 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 168.50/168.33 ( class_Orderings_Olinorder(T_b)
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
% 168.50/168.33 => 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) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_atMost__Int__atLeast,axiom,
% 168.50/168.33 ! [V_n_2,T_b] :
% 168.50/168.33 ( class_Orderings_Oorder(T_b)
% 168.50/168.33 => 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))) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_finite__atLeastLessThan__int,axiom,
% 168.50/168.33 ! [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))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_finite__atLeastLessThan,axiom,
% 168.50/168.33 ! [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))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_ivl__disj__int_I8_J,axiom,
% 168.50/168.33 ! [V_u_2,V_l_2,T_b] :
% 168.50/168.33 ( class_Orderings_Oorder(T_b)
% 168.50/168.33 => 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)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_ivl__disj__un_I14_J,axiom,
% 168.50/168.33 ! [V_u_2,V_l_2,T_b] :
% 168.50/168.33 ( class_Orderings_Olinorder(T_b)
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 168.50/168.33 => 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) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_atLeastLessThan__inj_I2_J,axiom,
% 168.50/168.33 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 168.50/168.33 ( class_Orderings_Olinorder(T_b)
% 168.50/168.33 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
% 168.50/168.33 => V_b_2 = V_d_2 ) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_atLeastLessThan__inj_I1_J,axiom,
% 168.50/168.33 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 168.50/168.33 ( class_Orderings_Olinorder(T_b)
% 168.50/168.33 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
% 168.50/168.33 => V_a_2 = V_c_2 ) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_atLeastLessThan__eq__iff,axiom,
% 168.50/168.33 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 168.50/168.33 ( class_Orderings_Olinorder(T_b)
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
% 168.50/168.33 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
% 168.50/168.33 <=> ( V_a_2 = V_c_2
% 168.50/168.33 & V_b_2 = V_d_2 ) ) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_atLeast__eq__iff,axiom,
% 168.50/168.33 ! [V_y_2,V_x_2,T_b] :
% 168.50/168.33 ( class_Orderings_Olinorder(T_b)
% 168.50/168.33 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2)
% 168.50/168.33 <=> V_x_2 = V_y_2 ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_all__nat__less__eq,axiom,
% 168.50/168.33 ! [V_P_2,V_n_2] :
% 168.50/168.33 ( ! [B_m] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 168.50/168.33 => hBOOL(hAPP(V_P_2,B_m)) )
% 168.50/168.33 <=> ! [B_x] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)))
% 168.50/168.33 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_ex__nat__less__eq,axiom,
% 168.50/168.33 ! [V_P_2,V_n_2] :
% 168.50/168.33 ( ? [B_m] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 168.50/168.33 & hBOOL(hAPP(V_P_2,B_m)) )
% 168.50/168.33 <=> ? [B_x] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)))
% 168.50/168.33 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_atLeastLessThan__add__Un,axiom,
% 168.50/168.33 ! [V_k_2,V_j_2,V_i_2] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 168.50/168.33 => 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))) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom,
% 168.50/168.33 ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),hAPP(c_Nat_OSuc,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_atLeastLessThan0,axiom,
% 168.50/168.33 ! [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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_atLeast0LessThan,axiom,
% 168.50/168.33 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_subset__card__intvl__is__intvl,axiom,
% 168.50/168.33 ! [V_k_2,V_A_2] :
% 168.50/168.33 ( 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)))))
% 168.50/168.33 => 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))) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_card__atLeastLessThan,axiom,
% 168.50/168.33 ! [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) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_atLeastLessThan__empty,axiom,
% 168.50/168.33 ! [V_a_2,V_b_2,T_b] :
% 168.50/168.33 ( class_Orderings_Oorder(T_b)
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
% 168.50/168.33 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_atLeastLessThan__empty__iff2,axiom,
% 168.50/168.33 ! [V_b_2,V_a_2,T_b] :
% 168.50/168.33 ( class_Orderings_Oorder(T_b)
% 168.50/168.33 => ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)
% 168.50/168.33 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_atLeastLessThan__empty__iff,axiom,
% 168.50/168.33 ! [V_b_2,V_a_2,T_b] :
% 168.50/168.33 ( class_Orderings_Oorder(T_b)
% 168.50/168.33 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.33 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_atLeastLessThan__subset__iff,axiom,
% 168.50/168.33 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 168.50/168.33 ( class_Orderings_Olinorder(T_b)
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)))
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
% 168.50/168.33 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2))
% 168.50/168.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_setsum__shift__bounds__Suc__ivl,axiom,
% 168.50/168.33 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 168.50/168.33 ( class_Groups_Ocomm__monoid__add(T_b)
% 168.50/168.33 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_ivl__disj__un_I17_J,axiom,
% 168.50/168.33 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 168.50/168.33 ( class_Orderings_Olinorder(T_b)
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 168.50/168.33 => 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) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_setsum__shift__bounds__nat__ivl,axiom,
% 168.50/168.33 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
% 168.50/168.33 ( class_Groups_Ocomm__monoid__add(T_b)
% 168.50/168.33 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n_2),V_k_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_ivl__diff,axiom,
% 168.50/168.33 ! [V_m_2,V_n_2,V_i_2,T_b] :
% 168.50/168.33 ( class_Orderings_Olinorder(T_b)
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_n_2))
% 168.50/168.33 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_i_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_i_2),V_n_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_n_2),V_m_2) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_ivl__disj__int_I11_J,axiom,
% 168.50/168.33 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 168.50/168.33 ( class_Orderings_Oorder(T_b)
% 168.50/168.33 => 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)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom,
% 168.50/168.33 ! [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) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_finite__atLeastZeroLessThan__int,axiom,
% 168.50/168.33 ! [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))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_atLeast__iff,axiom,
% 168.50/168.33 ! [V_k_2,V_i_2,T_b] :
% 168.50/168.33 ( class_Orderings_Oord(T_b)
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)))
% 168.50/168.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_k_2),V_i_2)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_atLeast__subset__iff,axiom,
% 168.50/168.33 ! [V_y_2,V_x_2,T_b] :
% 168.50/168.33 ( class_Orderings_Oorder(T_b)
% 168.50/168.33 => ( 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)))
% 168.50/168.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_setsum__add__nat__ivl,axiom,
% 168.50/168.33 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
% 168.50/168.33 ( class_Groups_Ocomm__monoid__add(T_b)
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 168.50/168.33 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2),V_p_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2)) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_setsum__diff__nat__ivl,axiom,
% 168.50/168.33 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
% 168.50/168.33 ( class_Groups_Oab__group__add(T_b)
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 168.50/168.33 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2),V_p_2)) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_atLeast__0,axiom,
% 168.50/168.33 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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_atLeastLessThan__singleton,axiom,
% 168.50/168.33 ! [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))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Compl__atLeast,axiom,
% 168.50/168.33 ! [V_k_2,T_b] :
% 168.50/168.33 ( class_Orderings_Olinorder(T_b)
% 168.50/168.33 => 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) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Compl__lessThan,axiom,
% 168.50/168.33 ! [V_k_2,T_b] :
% 168.50/168.33 ( class_Orderings_Olinorder(T_b)
% 168.50/168.33 => 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) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_UN__UN__finite__eq,axiom,
% 168.50/168.33 ! [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) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 168.50/168.33 ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_u_2),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_l_2,V_u_2) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_ivl__disj__un_I21_J,axiom,
% 168.50/168.33 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 168.50/168.33 ( class_Orderings_Olinorder(T_b)
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 168.50/168.33 => 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) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_ivl__disj__int_I15_J,axiom,
% 168.50/168.33 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 168.50/168.33 ( class_Orderings_Oorder(T_b)
% 168.50/168.33 => 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)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Int__atLeastLessThan,axiom,
% 168.50/168.33 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 168.50/168.33 ( class_Orderings_Olinorder(T_b)
% 168.50/168.33 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_ivl__disj__un_I8_J,axiom,
% 168.50/168.33 ! [V_u_2,V_l_2,T_b] :
% 168.50/168.33 ( class_Orderings_Olinorder(T_b)
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 168.50/168.33 => 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) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_ivl__disj__int_I2_J,axiom,
% 168.50/168.33 ! [V_u_2,V_l_2,T_b] :
% 168.50/168.33 ( class_Orderings_Oorder(T_b)
% 168.50/168.33 => 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)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_ivl__disj__int_I9_J,axiom,
% 168.50/168.33 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 168.50/168.33 ( class_Orderings_Oorder(T_b)
% 168.50/168.33 => 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)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom,
% 168.50/168.33 ! [V_k_2,V_f_2,T_b] :
% 168.50/168.33 ( class_Groups_Ocomm__monoid__add(T_b)
% 168.50/168.33 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_b)
% 168.50/168.33 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_setsum__head__upt__Suc,axiom,
% 168.50/168.33 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 168.50/168.33 ( class_Groups_Ocomm__monoid__add(T_b)
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 168.50/168.33 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_n_2))) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_card__atLeastZeroLessThan__int,axiom,
% 168.50/168.33 ! [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) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_card__atLeastLessThan__int,axiom,
% 168.50/168.33 ! [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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 168.50/168.33 ! [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) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_atLeastLessThanSuc,axiom,
% 168.50/168.33 ! [V_n_2,V_m_2] :
% 168.50/168.33 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 168.50/168.33 => 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)) )
% 168.50/168.33 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 168.50/168.33 => 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)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Int__atLeastAtMostL2,axiom,
% 168.50/168.33 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 168.50/168.33 ( class_Orderings_Olinorder(T_b)
% 168.50/168.33 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_c_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),V_b_2) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Int__atLeastAtMostR2,axiom,
% 168.50/168.33 ! [V_d_2,V_c_2,V_a_2,T_b] :
% 168.50/168.33 ( class_Orderings_Olinorder(T_b)
% 168.50/168.33 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_a_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),V_d_2) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_UN__atLeast__UNIV,axiom,
% 168.50/168.33 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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_ivl__disj__int_I6_J,axiom,
% 168.50/168.33 ! [V_u_2,V_l_2,T_b] :
% 168.50/168.33 ( class_Orderings_Oorder(T_b)
% 168.50/168.33 => 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)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_atLeast__Suc,axiom,
% 168.50/168.33 ! [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)))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_setsum__op__ivl__Suc,axiom,
% 168.50/168.33 ! [V_f_2,V_m_2,V_n_2,T_b] :
% 168.50/168.33 ( class_Groups_Ocomm__monoid__add(T_b)
% 168.50/168.33 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 168.50/168.33 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = c_Groups_Ozero__class_Ozero(T_b) )
% 168.50/168.33 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 168.50/168.33 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2))),hAPP(V_f_2,V_n_2)) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_ivl__disj__un_I15_J,axiom,
% 168.50/168.33 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 168.50/168.33 ( class_Orderings_Olinorder(T_b)
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 168.50/168.33 => 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) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_ivl__disj__un_I6_J,axiom,
% 168.50/168.33 ! [V_u_2,V_l_2,T_b] :
% 168.50/168.33 ( class_Orderings_Olinorder(T_b)
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 168.50/168.33 => 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) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_ivl__disj__un_I3_J,axiom,
% 168.50/168.33 ! [V_u_2,V_l_2,T_b] :
% 168.50/168.33 ( class_Orderings_Olinorder(T_b)
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 168.50/168.33 => 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) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_UN__finite2__subset,axiom,
% 168.50/168.33 ! [V_B_2,V_k_2,V_A_2,T_b] :
% 168.50/168.33 ( ! [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)))
% 168.50/168.33 => 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))) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_UN__finite2__eq,axiom,
% 168.50/168.33 ! [V_B_2,V_k_2,V_A_2,T_b] :
% 168.50/168.33 ( ! [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)
% 168.50/168.33 => 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) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_UN__finite__subset,axiom,
% 168.50/168.33 ! [V_C_2,V_A_2,T_b] :
% 168.50/168.33 ( ! [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))
% 168.50/168.33 => 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)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_greaterThan__Suc,axiom,
% 168.50/168.33 ! [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)))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_ivl__disj__un_I12_J,axiom,
% 168.50/168.33 ! [V_u_2,V_l_2,T_b] :
% 168.50/168.33 ( class_Orderings_Olinorder(T_b)
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 168.50/168.33 => 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) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_ivl__disj__un_I13_J,axiom,
% 168.50/168.33 ! [V_u_2,V_l_2,T_b] :
% 168.50/168.33 ( class_Orderings_Olinorder(T_b)
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 168.50/168.33 => 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) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_greaterThan__eq__iff,axiom,
% 168.50/168.33 ! [V_y_2,V_x_2,T_b] :
% 168.50/168.33 ( class_Orderings_Olinorder(T_b)
% 168.50/168.33 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)
% 168.50/168.33 <=> V_x_2 = V_y_2 ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_greaterThan__iff,axiom,
% 168.50/168.33 ! [V_k_2,V_i_2,T_b] :
% 168.50/168.33 ( class_Orderings_Oord(T_b)
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)))
% 168.50/168.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_greaterThan__subset__iff,axiom,
% 168.50/168.33 ! [V_y_2,V_x_2,T_b] :
% 168.50/168.33 ( class_Orderings_Olinorder(T_b)
% 168.50/168.33 => ( 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)))
% 168.50/168.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Compl__greaterThan,axiom,
% 168.50/168.33 ! [V_k_2,T_b] :
% 168.50/168.33 ( class_Orderings_Olinorder(T_b)
% 168.50/168.33 => 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) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Compl__atMost,axiom,
% 168.50/168.33 ! [V_k_2,T_b] :
% 168.50/168.33 ( class_Orderings_Olinorder(T_b)
% 168.50/168.33 => 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) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_atLeast__Suc__greaterThan,axiom,
% 168.50/168.33 ! [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) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_INT__greaterThan__UNIV,axiom,
% 168.50/168.33 hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_ivl__disj__int_I7_J,axiom,
% 168.50/168.33 ! [V_u_2,V_l_2,T_b] :
% 168.50/168.33 ( class_Orderings_Oorder(T_b)
% 168.50/168.33 => 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)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_ivl__disj__un_I11_J,axiom,
% 168.50/168.33 ! [V_u_2,V_l_2,T_b] :
% 168.50/168.33 ( class_Orderings_Olinorder(T_b)
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 168.50/168.33 => 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) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_ivl__disj__int_I5_J,axiom,
% 168.50/168.33 ! [V_u_2,V_l_2,T_b] :
% 168.50/168.33 ( class_Orderings_Oorder(T_b)
% 168.50/168.33 => 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)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_ivl__disj__un_I1_J,axiom,
% 168.50/168.33 ! [V_l_2,T_b] :
% 168.50/168.33 ( class_Orderings_Olinorder(T_b)
% 168.50/168.33 => 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) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_image__minus__const__atLeastLessThan__nat,axiom,
% 168.50/168.33 ! [V_x_2,V_y_2,V_c_2] :
% 168.50/168.33 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2))
% 168.50/168.33 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_c_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_y_2),V_c_2)) )
% 168.50/168.33 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2))
% 168.50/168.33 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 168.50/168.33 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) )
% 168.50/168.33 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 168.50/168.33 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_image__atLeastZeroLessThan__int,axiom,
% 168.50/168.33 ! [V_u_2] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2))
% 168.50/168.33 => 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))) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_accp__acc__eq,axiom,
% 168.50/168.33 ! [V_x_2,V_r_2,T_b] :
% 168.50/168.33 ( 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))
% 168.50/168.33 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_image__eqI,axiom,
% 168.50/168.33 ! [T_b,V_A_2,T_c,V_x_2,V_f_2,V_b_2] :
% 168.50/168.33 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 168.50/168.33 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_finite__imageI,axiom,
% 168.50/168.33 ! [V_h_2,T_c,V_F_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 168.50/168.33 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2))) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_range__composition,axiom,
% 168.50/168.33 ! [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)))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_INT__simps_I10_J,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),V_B_2),V_f_2)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_INT__extend__simps_I10_J,axiom,
% 168.50/168.33 ! [V_f_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_B_2) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_image__image,axiom,
% 168.50/168.33 ! [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) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_transfer__nat__int__set__relations_I4_J,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.50/168.33 <=> 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))) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_transfer__nat__int__set__relations_I3_J,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2] :
% 168.50/168.33 ( V_A_2 = V_B_2
% 168.50/168.33 <=> 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) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_image__Pow__surj,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
% 168.50/168.33 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_B_2
% 168.50/168.33 => 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) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_image__is__empty,axiom,
% 168.50/168.33 ! [V_A_2,V_f_2,T_b,T_c] :
% 168.50/168.33 ( 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))
% 168.50/168.33 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_image__empty,axiom,
% 168.50/168.33 ! [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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_empty__is__image,axiom,
% 168.50/168.33 ! [V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( 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)
% 168.50/168.33 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_image__insert,axiom,
% 168.50/168.33 ! [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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_UN__extend__simps_I10_J,axiom,
% 168.50/168.33 ! [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) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_image__UN,axiom,
% 168.50/168.33 ! [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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_UN__simps_I10_J,axiom,
% 168.50/168.33 ! [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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_rev__image__eqI,axiom,
% 168.50/168.33 ! [T_c,V_f_2,V_b_2,V_A_2,V_x_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.50/168.33 => ( V_b_2 = hAPP(V_f_2,V_x_2)
% 168.50/168.33 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_imageI,axiom,
% 168.50/168.33 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.50/168.33 => 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))) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_image__iff,axiom,
% 168.50/168.33 ! [V_A_2,V_f_2,T_c,V_z_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 168.50/168.33 <=> ? [B_x] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 168.50/168.33 & V_z_2 = hAPP(V_f_2,B_x) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_image__ident,axiom,
% 168.50/168.33 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ).
% 168.50/168.33
% 168.50/168.33 fof(fact_image__Pow__mono,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( 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))
% 168.50/168.33 => 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))) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_image__Un,axiom,
% 168.50/168.33 ! [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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_subset__image__iff,axiom,
% 168.50/168.33 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
% 168.50/168.33 ( 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)))
% 168.50/168.33 <=> ? [B_AA] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2))
% 168.50/168.33 & V_B_2 = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_image__mono,axiom,
% 168.50/168.33 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.50/168.33 => 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))) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_insert__image,axiom,
% 168.50/168.33 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.50/168.33 => 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) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_rangeI,axiom,
% 168.50/168.33 ! [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))))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_range__eqI,axiom,
% 168.50/168.33 ! [T_c,T_b,V_x_2,V_f_2,V_b_2] :
% 168.50/168.33 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 168.50/168.33 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_finite__surj,axiom,
% 168.50/168.33 ! [V_f_2,V_B_2,T_c,V_A_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.33 => ( 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)))
% 168.50/168.33 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_image__Int__subset,axiom,
% 168.50/168.33 ! [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)))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_finite__imageD,axiom,
% 168.50/168.33 ! [V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 168.50/168.33 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2)
% 168.50/168.33 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_image__diff__subset,axiom,
% 168.50/168.33 ! [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)))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_inj__image__eq__iff,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 168.50/168.33 => ( 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)
% 168.50/168.33 <=> V_A_2 = V_B_2 ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_inj__on__Un__image__eq__iff,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( 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))
% 168.50/168.33 => ( 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)
% 168.50/168.33 <=> V_A_2 = V_B_2 ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_image__uminus__atLeastAtMost,axiom,
% 168.50/168.33 ! [V_y_2,V_x_2,T_b] :
% 168.50/168.33 ( class_Groups_Oordered__ab__group__add(T_b)
% 168.50/168.33 => 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)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_card__image,axiom,
% 168.50/168.33 ! [V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 168.50/168.33 => 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) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_image__Suc__atLeastLessThan,axiom,
% 168.50/168.33 ! [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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_type__definition_ORep__range,axiom,
% 168.50/168.33 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 168.50/168.33 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 168.50/168.33 => 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 ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_type__definition_OAbs__image,axiom,
% 168.50/168.33 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 168.50/168.33 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 168.50/168.33 => 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)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_image__Suc__atLeastAtMost,axiom,
% 168.50/168.33 ! [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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_image__uminus__greaterThanLessThan,axiom,
% 168.50/168.33 ! [V_y_2,V_x_2,T_b] :
% 168.50/168.33 ( class_Groups_Oordered__ab__group__add(T_b)
% 168.50/168.33 => 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)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_inj__on__strict__subset,axiom,
% 168.50/168.33 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.50/168.33 => 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))) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_image__constant__conv,axiom,
% 168.50/168.33 ! [V_c_2,T_c,T_b,V_A_2] :
% 168.50/168.33 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.33 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 168.50/168.33 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.33 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_finite__range__imageI,axiom,
% 168.50/168.33 ! [V_f_2,T_d,V_g_2,T_c,T_b] :
% 168.50/168.33 ( 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)))))
% 168.50/168.33 => 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))))) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_transfer__nat__int__set__relations_I2_J,axiom,
% 168.50/168.33 ! [V_A_2,V_x_2] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2))
% 168.50/168.33 <=> 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))) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom,
% 168.50/168.33 ! [V_A_2,V_f_2,T_b] :
% 168.50/168.33 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 168.50/168.33 & class_Groups_Ocomm__monoid__mult(T_b) )
% 168.50/168.33 => 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)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_image__add__atLeastLessThan,axiom,
% 168.50/168.33 ! [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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_image__add__atLeastAtMost,axiom,
% 168.50/168.33 ! [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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_transfer__nat__int__set__relations_I5_J,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.50/168.33 <=> 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))) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_image__Union,axiom,
% 168.50/168.33 ! [V_S_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Set_Oimage(T_c,T_b,V_f_2)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_inj__image__mem__iff,axiom,
% 168.50/168.33 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 168.50/168.33 => ( 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)))
% 168.50/168.33 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_range__ex1__eq,axiom,
% 168.50/168.33 ! [V_b_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))
% 168.50/168.33 <=> ? [B_x] :
% 168.50/168.33 ( V_b_2 = hAPP(V_f_2,B_x)
% 168.50/168.33 & ! [B_y] :
% 168.50/168.33 ( V_b_2 = hAPP(V_f_2,B_y)
% 168.50/168.33 => B_y = B_x ) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_inj__on__iff__surj,axiom,
% 168.50/168.33 ! [V_A_H_2,T_c,T_b,V_A_2] :
% 168.50/168.33 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.33 => ( ? [B_f] :
% 168.50/168.33 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2)
% 168.50/168.33 & 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)) )
% 168.50/168.33 <=> ? [B_g] : hAPP(c_Set_Oimage(T_c,T_b,B_g),V_A_H_2) = V_A_2 ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_finite__surj__inj,axiom,
% 168.50/168.33 ! [V_f_2,V_A_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.33 => ( 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)))
% 168.50/168.33 => c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_endo__inj__surj,axiom,
% 168.50/168.33 ! [V_f_2,V_A_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.33 => ( 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))
% 168.50/168.33 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2)
% 168.50/168.33 => hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2) = V_A_2 ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_finite__UNIV__inj__surj,axiom,
% 168.50/168.33 ! [V_f_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 168.50/168.33 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 168.50/168.33 => 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)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_finite__UNIV__surj__inj,axiom,
% 168.50/168.33 ! [V_f_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 168.50/168.33 => ( 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))
% 168.50/168.33 => c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_card__image__le,axiom,
% 168.50/168.33 ! [V_f_2,T_c,V_A_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.33 => 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))) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_inj__image__subset__iff,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 168.50/168.33 => ( 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)))
% 168.50/168.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_inj__on__image__Int,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 168.50/168.33 => 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)) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_image__Int,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 168.50/168.33 => 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)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_inj__on__iff__eq__card,axiom,
% 168.50/168.33 ! [V_f_2,T_c,V_A_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.33 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 168.50/168.33 <=> 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) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_eq__card__imp__inj__on,axiom,
% 168.50/168.33 ! [V_f_2,T_c,V_A_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.33 => ( 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)
% 168.50/168.33 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_acc__subset,axiom,
% 168.50/168.33 ! [V_R2_2,V_R1_2,T_b] :
% 168.50/168.33 ( 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))
% 168.50/168.33 => 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))) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_inj__on__image__set__diff,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 168.50/168.33 => 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)) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_image__set__diff,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 168.50/168.33 => 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)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_pigeonhole,axiom,
% 168.50/168.33 ! [V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( 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)))
% 168.50/168.33 => ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_surj__Compl__image__subset,axiom,
% 168.50/168.33 ! [V_A_2,V_f_2,T_b,T_c] :
% 168.50/168.33 ( 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))
% 168.50/168.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),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)))) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_image__uminus__atLeastLessThan,axiom,
% 168.50/168.33 ! [V_y_2,V_x_2,T_b] :
% 168.50/168.33 ( class_Groups_Oordered__ab__group__add(T_b)
% 168.50/168.33 => 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)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_image__uminus__greaterThanAtMost,axiom,
% 168.50/168.33 ! [V_y_2,V_x_2,T_b] :
% 168.50/168.33 ( class_Groups_Oordered__ab__group__add(T_b)
% 168.50/168.33 => 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)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_image__constant,axiom,
% 168.50/168.33 ! [V_c_2,T_c,V_A_2,V_x_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.50/168.33 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_image__eq__UN,axiom,
% 168.50/168.33 ! [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)))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_image__uminus__greaterThan,axiom,
% 168.50/168.33 ! [V_x_2,T_b] :
% 168.50/168.33 ( class_Groups_Oordered__ab__group__add(T_b)
% 168.50/168.33 => 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)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_image__uminus__lessThan,axiom,
% 168.50/168.33 ! [V_x_2,T_b] :
% 168.50/168.33 ( class_Groups_Oordered__ab__group__add(T_b)
% 168.50/168.33 => 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)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_image__uminus__atMost,axiom,
% 168.50/168.33 ! [V_x_2,T_b] :
% 168.50/168.33 ( class_Groups_Oordered__ab__group__add(T_b)
% 168.50/168.33 => 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)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_image__uminus__atLeast,axiom,
% 168.50/168.33 ! [V_x_2,T_b] :
% 168.50/168.33 ( class_Groups_Oordered__ab__group__add(T_b)
% 168.50/168.33 => 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)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom,
% 168.50/168.33 ! [V_A_2,V_f_2,T_b] :
% 168.50/168.33 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 168.50/168.33 & class_Groups_Ocomm__monoid__mult(T_b) )
% 168.50/168.33 => 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)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_transfer__nat__int__set__relations_I1_J,axiom,
% 168.50/168.33 ! [V_A_2] :
% 168.50/168.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2))
% 168.50/168.33 <=> 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))) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom,
% 168.50/168.33 ! [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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom,
% 168.50/168.33 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))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_card__bij__eq,axiom,
% 168.50/168.33 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 168.50/168.33 => ( 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))
% 168.50/168.33 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
% 168.50/168.33 => ( 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))
% 168.50/168.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 168.50/168.33 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_inj__image__Compl__subset,axiom,
% 168.50/168.33 ! [V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 168.50/168.33 => 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)))) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_acc_Osimps,axiom,
% 168.50/168.33 ! [V_r_2,V_a_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 168.50/168.33 <=> ! [B_x] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_a_2)),V_r_2))
% 168.50/168.33 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_acc__downward,axiom,
% 168.50/168.33 ! [V_a_2,V_r_2,V_b_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 168.50/168.33 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_image__eq__fold__image,axiom,
% 168.50/168.33 ! [V_f_2,T_c,V_A_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.33 => 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) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_lessThan__Suc__eq__insert__0,axiom,
% 168.50/168.33 ! [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))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_greaterThan__0,axiom,
% 168.50/168.33 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))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_inj__on__insert,axiom,
% 168.50/168.33 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))
% 168.50/168.33 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 168.50/168.33 & ~ 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))))))) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_inj__on__Un,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( 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))
% 168.50/168.33 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 168.50/168.33 & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 168.50/168.33 & 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)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_inj__on__iff__card__le,axiom,
% 168.50/168.33 ! [V_B_2,T_c,V_A_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 168.50/168.33 => ( ? [B_f] :
% 168.50/168.33 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2)
% 168.50/168.33 & 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)) )
% 168.50/168.33 <=> 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))) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_card__inj__on__le,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 168.50/168.33 => ( 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))
% 168.50/168.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 168.50/168.33 => 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))) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_minus__Max__eq__Min,axiom,
% 168.50/168.33 ! [V_S_2,T_b] :
% 168.50/168.33 ( class_Groups_Olinordered__ab__group__add(T_b)
% 168.50/168.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 168.50/168.33 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.33 => 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)) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_minus__Min__eq__Max,axiom,
% 168.50/168.33 ! [V_S_2,T_b] :
% 168.50/168.33 ( class_Groups_Olinordered__ab__group__add(T_b)
% 168.50/168.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 168.50/168.33 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.33 => 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)) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom,
% 168.50/168.33 ! [V_n_2,V_m_2] :
% 168.50/168.33 ( c_Nat__Transfer_Ois__nat(V_m_2)
% 168.50/168.33 => ( c_Nat__Transfer_Ois__nat(V_n_2)
% 168.50/168.33 => 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))) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_image__INT,axiom,
% 168.50/168.33 ! [V_j_2,V_B_2,V_A_2,T_d,V_C_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 168.50/168.33 => ( ! [B_x] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2))
% 168.50/168.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,B_x)),V_C_2)) )
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_j_2),V_A_2))
% 168.50/168.33 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),c_Set_Oimage(T_b,T_c,V_f_2)),V_B_2)) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_fun__upd__image,axiom,
% 168.50/168.33 ! [V_y_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 168.50/168.33 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.50/168.33 => hAPP(c_Set_Oimage(T_b,T_c,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)))))) )
% 168.50/168.33 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.50/168.33 => hAPP(c_Set_Oimage(T_b,T_c,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) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_the__inv__into__into,axiom,
% 168.50/168.33 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.50/168.33 => 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)) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_fun__upd__triv,axiom,
% 168.50/168.33 ! [V_x_2,V_f_2,T_c,T_b] : c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,hAPP(V_f_2,V_x_2)) = V_f_2 ).
% 168.50/168.33
% 168.50/168.33 fof(fact_pair__imageI,axiom,
% 168.50/168.33 ! [V_f_2,T_d,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_A_2))
% 168.50/168.33 => hBOOL(hAPP(hAPP(c_member(T_d),hAPP(hAPP(V_f_2,V_a_2),V_b_2)),hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),V_A_2))) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Cantors__paradox,axiom,
% 168.50/168.33 ! [V_A_2,T_b] :
% 168.50/168.33 ~ ? [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) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_fun__upd__def,axiom,
% 168.50/168.33 ! [V_b_2,V_f_2,T_c,T_b,V_a_2,V_x_2] :
% 168.50/168.33 ( ( V_x_2 = V_a_2
% 168.50/168.33 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_a_2,V_b_2),V_x_2) = V_b_2 )
% 168.50/168.33 & ( V_x_2 != V_a_2
% 168.50/168.33 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_a_2,V_b_2),V_x_2) = hAPP(V_f_2,V_x_2) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_fun__upd__idem__iff,axiom,
% 168.50/168.33 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2) = V_f_2
% 168.50/168.33 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_fun__upd__upd,axiom,
% 168.50/168.33 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] : c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_x_2,V_z_2) = c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_z_2) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_fun__upd__same,axiom,
% 168.50/168.33 ! [V_y_2,V_x_2,V_f_2,T_b,T_c] : hAPP(c_Fun_Ofun__upd(T_c,T_b,V_f_2,V_x_2,V_y_2),V_x_2) = V_y_2 ).
% 168.50/168.33
% 168.50/168.33 fof(fact_fun__upd__apply,axiom,
% 168.50/168.33 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
% 168.50/168.33 ( ( V_z_2 = V_x_2
% 168.50/168.33 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_z_2) = V_y_2 )
% 168.50/168.33 & ( V_z_2 != V_x_2
% 168.50/168.33 => 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) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_fun__upd__twist,axiom,
% 168.50/168.33 ! [V_d_2,V_b_2,V_m_2,T_c,T_b,V_c_2,V_a_2] :
% 168.50/168.33 ( V_a_2 != V_c_2
% 168.50/168.33 => c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_m_2,V_a_2,V_b_2),V_c_2,V_d_2) = c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_m_2,V_c_2,V_d_2),V_a_2,V_b_2) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_fun__upd__other,axiom,
% 168.50/168.33 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
% 168.50/168.33 ( V_z_2 != V_x_2
% 168.50/168.33 => 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) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_fun__upd__idem,axiom,
% 168.50/168.33 ! [T_b,T_c,V_y_2,V_x_2,V_f_2] :
% 168.50/168.33 ( hAPP(V_f_2,V_x_2) = V_y_2
% 168.50/168.33 => c_Fun_Ofun__upd(T_c,T_b,V_f_2,V_x_2,V_y_2) = V_f_2 ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Field__Union,axiom,
% 168.50/168.33 ! [V_R_2,T_b] : hAPP(c_Relation_OField(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),V_R_2)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Relation_OField(T_b)),V_R_2)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_UNION__eq__Union__image,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Union__image__eq,axiom,
% 168.50/168.33 ! [V_A_2,V_B_2,T_c,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Inter__image__eq,axiom,
% 168.50/168.33 ! [V_A_2,V_B_2,T_c,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_INTER__eq__Inter__image,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_transfer__int__nat__set__return__embed,axiom,
% 168.50/168.33 ! [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 ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom,
% 168.50/168.33 ! [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))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Un__Union__image,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_C_2))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Int__Inter__image,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_C_2))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_the__inv__into__f__eq,axiom,
% 168.50/168.33 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 168.50/168.33 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.50/168.33 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_the__inv__into__f__f,axiom,
% 168.50/168.33 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.50/168.33 => 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 ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_the__inv__f__f,axiom,
% 168.50/168.33 ! [V_x_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 168.50/168.33 => 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 ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_inj__on__the__inv__into,axiom,
% 168.50/168.33 ! [V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 168.50/168.33 => 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)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_the__inv__into__onto,axiom,
% 168.50/168.33 ! [V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 168.50/168.33 => 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 ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Pow__insert,axiom,
% 168.50/168.33 ! [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))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom,
% 168.50/168.33 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))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_inj__on__fun__updI,axiom,
% 168.50/168.33 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 168.50/168.33 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 168.50/168.33 => c_Fun_Oinj__on(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_A_2) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom,
% 168.50/168.33 ! [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))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_image__add__int__atLeastLessThan,axiom,
% 168.50/168.33 ! [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) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom,
% 168.50/168.33 ! [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))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_f__the__inv__into__f,axiom,
% 168.50/168.33 ! [V_y_2,V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 168.50/168.33 => 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 ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom,
% 168.50/168.33 ! [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))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom,
% 168.50/168.33 ! [V_f_2,V_A_2,T_b] :
% 168.50/168.33 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 168.50/168.33 & class_Groups_Ocomm__monoid__mult(T_b) )
% 168.50/168.33 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 168.50/168.33 => 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)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2] :
% 168.50/168.33 ( c_Nat__Transfer_Onat__set(V_A_2)
% 168.50/168.33 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 168.50/168.33 => 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))) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_min__max_OSup__fin_Ohom__commute,axiom,
% 168.50/168.33 ! [V_N_2,V_h_2,T_b] :
% 168.50/168.33 ( class_Orderings_Olinorder(T_b)
% 168.50/168.33 => ( ! [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))
% 168.50/168.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 168.50/168.33 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.33 => 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)) ) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_transfer__int__nat__set__relations_I3_J,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2] :
% 168.50/168.33 ( c_Nat__Transfer_Onat__set(V_A_2)
% 168.50/168.33 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 168.50/168.33 => ( V_A_2 = V_B_2
% 168.50/168.33 <=> 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) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2] :
% 168.50/168.33 ( c_Nat__Transfer_Onat__set(V_A_2)
% 168.50/168.33 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 168.50/168.33 => 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)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2] :
% 168.50/168.33 ( c_Nat__Transfer_Onat__set(V_A_2)
% 168.50/168.33 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 168.50/168.33 => 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)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom,
% 168.50/168.33 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_nat__set__def,axiom,
% 168.50/168.33 ! [V_S_2] :
% 168.50/168.33 ( c_Nat__Transfer_Onat__set(V_S_2)
% 168.50/168.33 <=> ! [B_x] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2))
% 168.50/168.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom,
% 168.50/168.33 ! [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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom,
% 168.50/168.33 ! [V_y_2,V_x_2] :
% 168.50/168.33 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 168.50/168.33 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom,
% 168.50/168.33 ! [V_x_2,V_A_2] :
% 168.50/168.33 ( c_Nat__Transfer_Onat__set(V_A_2)
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 168.50/168.33 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom,
% 168.50/168.33 ! [V_y_2,V_x_2] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 168.50/168.33 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_transfer__nat__int__set__return__embed,axiom,
% 168.50/168.33 ! [V_A_2] :
% 168.50/168.33 ( c_Nat__Transfer_Onat__set(V_A_2)
% 168.50/168.33 => 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 ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2] :
% 168.50/168.33 ( c_Nat__Transfer_Onat__set(V_A_2)
% 168.50/168.33 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 168.50/168.33 => 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))) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom,
% 168.50/168.33 ! [V_x_2,V_A_2] :
% 168.50/168.33 ( c_Nat__Transfer_Onat__set(V_A_2)
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 168.50/168.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_transfer__int__nat__set__relations_I1_J,axiom,
% 168.50/168.33 ! [V_A_2] :
% 168.50/168.33 ( c_Nat__Transfer_Onat__set(V_A_2)
% 168.50/168.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2))
% 168.50/168.33 <=> 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))) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom,
% 168.50/168.33 ! [V_A_2] :
% 168.50/168.33 ( c_Nat__Transfer_Onat__set(V_A_2)
% 168.50/168.33 => 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)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_transfer__int__nat__set__relations_I2_J,axiom,
% 168.50/168.33 ! [V_A_2,V_x_2] :
% 168.50/168.33 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 168.50/168.33 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 168.50/168.33 <=> 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))) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_transfer__int__nat__set__relations_I5_J,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2] :
% 168.50/168.33 ( c_Nat__Transfer_Onat__set(V_A_2)
% 168.50/168.33 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.50/168.33 <=> 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))) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_transfer__int__nat__set__relations_I4_J,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2] :
% 168.50/168.33 ( c_Nat__Transfer_Onat__set(V_A_2)
% 168.50/168.33 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.50/168.33 <=> 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))) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom,
% 168.50/168.33 ! [V_f_2,V_A_2,T_b] :
% 168.50/168.33 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 168.50/168.33 & class_Groups_Ocomm__monoid__mult(T_b) )
% 168.50/168.33 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 168.50/168.33 => 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)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_min__max_OInf__fin_Ohom__commute,axiom,
% 168.50/168.33 ! [V_N_2,V_h_2,T_b] :
% 168.50/168.33 ( class_Orderings_Olinorder(T_b)
% 168.50/168.33 => ( ! [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))
% 168.50/168.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 168.50/168.33 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.33 => 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)) ) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Max_Ohom__commute,axiom,
% 168.50/168.33 ! [V_N_2,V_h_2,T_b] :
% 168.50/168.33 ( class_Orderings_Olinorder(T_b)
% 168.50/168.33 => ( ! [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))
% 168.50/168.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 168.50/168.33 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.33 => 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)) ) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Min_Ohom__commute,axiom,
% 168.50/168.33 ! [V_N_2,V_h_2,T_b] :
% 168.50/168.33 ( class_Orderings_Olinorder(T_b)
% 168.50/168.33 => ( ! [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))
% 168.50/168.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 168.50/168.33 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.33 => 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)) ) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Inf__fin_Ohom__commute,axiom,
% 168.50/168.33 ! [V_N_2,V_h_2,T_b] :
% 168.50/168.33 ( class_Lattices_Olattice(T_b)
% 168.50/168.33 => ( ! [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))
% 168.50/168.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 168.50/168.33 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.33 => 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)) ) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Sup__fin_Ohom__commute,axiom,
% 168.50/168.33 ! [V_N_2,V_h_2,T_b] :
% 168.50/168.33 ( class_Lattices_Olattice(T_b)
% 168.50/168.33 => ( ! [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))
% 168.50/168.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 168.50/168.33 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.33 => 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)) ) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_hom__fold1__commute,axiom,
% 168.50/168.33 ! [V_N_2,V_h_2,T_b] :
% 168.50/168.33 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 168.50/168.33 => ( ! [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))
% 168.50/168.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 168.50/168.33 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.33 => 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)) ) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom,
% 168.50/168.33 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
% 168.50/168.33 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 168.50/168.33 & class_Groups_Ocomm__monoid__mult(T_b) )
% 168.50/168.33 => ( V_A_2 = V_B_2
% 168.50/168.33 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 168.50/168.33 => ( ! [B_x] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 168.50/168.33 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 168.50/168.33 => 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) ) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom,
% 168.50/168.33 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
% 168.50/168.33 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 168.50/168.33 & class_Groups_Ocomm__monoid__mult(T_b) )
% 168.50/168.33 => ( V_A_2 = V_B_2
% 168.50/168.33 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 168.50/168.33 => ( ! [B_x] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 168.50/168.33 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 168.50/168.33 => 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) ) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_max__extp_Oequations,axiom,
% 168.50/168.33 ! [V_a2_2,V_a1_2,V_R_2,T_b] :
% 168.50/168.33 ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2)
% 168.50/168.33 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 168.50/168.33 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 168.50/168.33 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.33 & ! [B_x] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 168.50/168.33 => ? [B_xa] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 168.50/168.33 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_inj__on__Inter,axiom,
% 168.50/168.33 ! [V_f_2,T_c,T_b,V_S_2] :
% 168.50/168.33 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 168.50/168.33 => ( ! [B_A] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_A),V_S_2))
% 168.50/168.33 => c_Fun_Oinj__on(T_b,T_c,V_f_2,B_A) )
% 168.50/168.33 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_S_2)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_the__elem__def,axiom,
% 168.50/168.33 ! [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))))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_folding__one__idem_Ohom__commute,axiom,
% 168.50/168.33 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_b] :
% 168.50/168.33 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 168.50/168.33 => ( ! [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))
% 168.50/168.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 168.50/168.33 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.33 => 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)) ) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_The__split__eq,axiom,
% 168.50/168.33 ! [V_y_2,V_x_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_split__paired__The,axiom,
% 168.50/168.33 ! [V_P_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),V_P_2) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_P_2)),c_Product__Type_OPair(T_b,T_c)))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_the__inv__into__def,axiom,
% 168.50/168.33 ! [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))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_fold__def,axiom,
% 168.50/168.33 ! [V_A_2,V_z_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_b,V_f_2),V_z_2),V_A_2) = c_HOL_OThe(T_b,c_Finite__Set_Ofold__graph(T_c,T_b,V_f_2,V_z_2,V_A_2)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_divmod__nat__def,axiom,
% 168.50/168.33 ! [V_n_2,V_m_2] : c_Divides_Odivmod__nat(V_m_2,V_n_2) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(V_m_2,V_n_2)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_fold1__def,axiom,
% 168.50/168.33 ! [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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_The__split,axiom,
% 168.50/168.33 ! [V_P_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2)) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_P_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_flat__lub__def,axiom,
% 168.50/168.33 ! [V_b_2,V_A_2,T_b] :
% 168.50/168.33 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
% 168.50/168.33 => c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = V_b_2 )
% 168.50/168.33 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
% 168.50/168.33 => c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_inj__vimage__singleton,axiom,
% 168.50/168.33 ! [V_a_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 168.50/168.33 => 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))))) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Rep__Integ__induct,axiom,
% 168.50/168.33 ! [V_P_2,V_y_2] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 168.50/168.33 => ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Int_ORep__Integ,B_x)))
% 168.50/168.33 => hBOOL(hAPP(V_P_2,V_y_2)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_vimageI,axiom,
% 168.50/168.33 ! [T_c,V_B_2,T_b,V_b_2,V_a_2,V_f_2] :
% 168.50/168.33 ( hAPP(V_f_2,V_a_2) = V_b_2
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_B_2))
% 168.50/168.33 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_vimage__Int,axiom,
% 168.50/168.33 ! [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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_vimage__Un,axiom,
% 168.50/168.33 ! [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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_vimage__INT,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Ovimage(T_b,T_c,V_f_2)),V_B_2)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_vimage__Diff,axiom,
% 168.50/168.33 ! [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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_vimage__ident,axiom,
% 168.50/168.33 ! [V_Y_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ).
% 168.50/168.33
% 168.50/168.33 fof(fact_vimage__UN,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_vimage__empty,axiom,
% 168.50/168.33 ! [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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_vimage__code,axiom,
% 168.50/168.33 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2),V_x_2))
% 168.50/168.33 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_vimage__Compl,axiom,
% 168.50/168.33 ! [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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_vimage__UNIV,axiom,
% 168.50/168.33 ! [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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_vimageI2,axiom,
% 168.50/168.33 ! [T_c,V_A_2,V_a_2,V_f_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2))
% 168.50/168.33 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_vimageD,axiom,
% 168.50/168.33 ! [V_A_2,V_f_2,T_c,V_a_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)))
% 168.50/168.33 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_A_2)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_vimage__eq,axiom,
% 168.50/168.33 ! [V_B_2,V_f_2,T_c,V_a_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)))
% 168.50/168.33 <=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_vimage__mono,axiom,
% 168.50/168.33 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.50/168.33 => 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))) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_image__vimage__subset,axiom,
% 168.50/168.33 ! [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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_surj__image__vimage__eq,axiom,
% 168.50/168.33 ! [V_A_2,V_f_2,T_b,T_c] :
% 168.50/168.33 ( 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))
% 168.50/168.33 => 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 ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_vimage__Union,axiom,
% 168.50/168.33 ! [V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Set_Ovimage(T_b,T_c,V_f_2)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_vimage__singleton__eq,axiom,
% 168.50/168.33 ! [V_b_2,V_f_2,T_c,V_a_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
% 168.50/168.33 <=> hAPP(V_f_2,V_a_2) = V_b_2 ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_vimage__insert,axiom,
% 168.50/168.33 ! [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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_finite__vimageD,axiom,
% 168.50/168.33 ! [V_F_2,V_h_2,T_c,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2)))
% 168.50/168.33 => ( 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))
% 168.50/168.33 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_vimage__subsetD,axiom,
% 168.50/168.33 ! [V_A_2,V_B_2,V_f_2,T_b,T_c] :
% 168.50/168.33 ( 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))
% 168.50/168.33 => ( 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))
% 168.50/168.33 => 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))) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_image__vimage__eq,axiom,
% 168.50/168.33 ! [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)))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_finite__vimageI,axiom,
% 168.50/168.33 ! [V_h_2,T_c,V_F_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 168.50/168.33 => ( c_Fun_Oinj__on(T_c,T_b,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 168.50/168.33 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Ovimage(T_c,T_b,V_h_2),V_F_2))) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_inj__vimage__image__eq,axiom,
% 168.50/168.33 ! [V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 168.50/168.33 => 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 ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_vimage__const,axiom,
% 168.50/168.33 ! [T_c,V_A_2,V_c_2,T_b] :
% 168.50/168.33 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 168.50/168.33 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 168.50/168.33 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 168.50/168.33 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_vimage__eq__UN,axiom,
% 168.50/168.33 ! [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))))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_vimage__subsetI,axiom,
% 168.50/168.33 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 168.50/168.33 => ( 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)))
% 168.50/168.33 => 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)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_vimage__if,axiom,
% 168.50/168.33 ! [V_B_2,T_c,V_d_2,V_A_2,V_c_2,T_b] :
% 168.50/168.33 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 168.50/168.33 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 168.50/168.33 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 168.50/168.33 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 168.50/168.33 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = V_B_2 ) ) )
% 168.50/168.33 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 168.50/168.33 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 168.50/168.33 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_B_2) )
% 168.50/168.33 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 168.50/168.33 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_image__split__eq__Sigma,axiom,
% 168.50/168.33 ! [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))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Rep__Integ__cases,axiom,
% 168.50/168.33 ! [V_y_2] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 168.50/168.33 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_inj__on__INTER,axiom,
% 168.50/168.33 ! [V_A_2,V_f_2,T_d,T_c,T_b,V_I_2] :
% 168.50/168.33 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.33 => ( ! [B_i] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_I_2))
% 168.50/168.33 => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(V_A_2,B_i)) )
% 168.50/168.33 => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_SigmaI,axiom,
% 168.50/168.33 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
% 168.50/168.33 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Sigma__empty1,axiom,
% 168.50/168.33 ! [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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Times__eq__cancel2,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
% 168.50/168.33 => ( 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))
% 168.50/168.33 <=> V_A_2 = V_B_2 ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Sigma__Diff__distrib2,axiom,
% 168.50/168.33 ! [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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Times__Diff__distrib1,axiom,
% 168.50/168.33 ! [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))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Sigma__Diff__distrib1,axiom,
% 168.50/168.33 ! [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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Sigma__Union,axiom,
% 168.50/168.33 ! [V_B_2,V_X_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_X_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Product__Type_OSigma(T_b,T_c)),V_B_2)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_card__cartesian__product,axiom,
% 168.50/168.33 ! [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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_setsum__cartesian__product,axiom,
% 168.50/168.33 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 168.50/168.33 ( class_Groups_Ocomm__monoid__add(T_b)
% 168.50/168.33 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(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))) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Times__empty,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2,T_c,T_b] :
% 168.50/168.33 ( 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))
% 168.50/168.33 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.33 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Sigma__empty2,axiom,
% 168.50/168.33 ! [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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Compl__Times__UNIV1,axiom,
% 168.50/168.33 ! [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))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Compl__Times__UNIV2,axiom,
% 168.50/168.33 ! [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)))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_setprod__cartesian__product,axiom,
% 168.50/168.33 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 168.50/168.33 ( class_Groups_Ocomm__monoid__mult(T_b)
% 168.50/168.33 => 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))) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Sigma__Un__distrib1,axiom,
% 168.50/168.33 ! [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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Times__Un__distrib1,axiom,
% 168.50/168.33 ! [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))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Sigma__Un__distrib2,axiom,
% 168.50/168.33 ! [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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_swap__product,axiom,
% 168.50/168.33 ! [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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_finite__cartesian__product,axiom,
% 168.50/168.33 ! [V_B_2,T_c,V_A_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 168.50/168.33 => 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)))) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_equiv__type,axiom,
% 168.50/168.33 ! [V_r_2,V_A_2,T_b] :
% 168.50/168.33 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 168.50/168.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Sigma__Int__distrib2,axiom,
% 168.50/168.33 ! [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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Times__Int__distrib1,axiom,
% 168.50/168.33 ! [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))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Sigma__Int__distrib1,axiom,
% 168.50/168.33 ! [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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Id__on__subset__Times,axiom,
% 168.50/168.33 ! [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)))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_UNIV__Times__UNIV,axiom,
% 168.50/168.33 ! [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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_SigmaE2,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
% 168.50/168.33 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.50/168.33 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_SigmaD2,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
% 168.50/168.33 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_SigmaD1,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
% 168.50/168.33 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_mem__Sigma__iff,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
% 168.50/168.33 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.50/168.33 & hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_card__cartesian__product__singleton,axiom,
% 168.50/168.33 ! [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) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Times__subset__cancel2,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
% 168.50/168.33 => ( 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))))
% 168.50/168.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Image__subset,axiom,
% 168.50/168.33 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 168.50/168.33 ( 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))))
% 168.50/168.33 => 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)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_finite__cartesian__productD2,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2,T_c,T_b] :
% 168.50/168.33 ( 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))))
% 168.50/168.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.33 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_finite__cartesian__productD1,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2,T_c,T_b] :
% 168.50/168.33 ( 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))))
% 168.50/168.33 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
% 168.50/168.33 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_fst__image__times,axiom,
% 168.50/168.33 ! [V_A_2,T_c,T_b,V_B_2] :
% 168.50/168.33 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.33 => 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)) )
% 168.50/168.33 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.33 => 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 ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_snd__image__times,axiom,
% 168.50/168.33 ! [V_B_2,T_c,T_b,V_A_2] :
% 168.50/168.33 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.33 => 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)) )
% 168.50/168.33 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.33 => 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 ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_refl__on__def,axiom,
% 168.50/168.33 ! [V_r_2,V_A_2,T_b] :
% 168.50/168.33 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 168.50/168.33 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 168.50/168.33 & ! [B_x] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.50/168.33 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_insert__times__insert,axiom,
% 168.50/168.33 ! [V_B_2,V_b_2,V_A_2,V_a_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2)))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_finite__equiv__class,axiom,
% 168.50/168.33 ! [V_X_2,V_r_2,V_A_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 168.50/168.33 => ( 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)))
% 168.50/168.33 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_UN__Times__distrib,axiom,
% 168.50/168.33 ! [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))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Sigma__def,axiom,
% 168.50/168.33 ! [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))))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_finite__quotient,axiom,
% 168.50/168.33 ! [V_r_2,V_A_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 168.50/168.33 => 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))) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Ex__inj__on__UNION__Sigma,axiom,
% 168.50/168.33 ! [V_A_2,V_I_2,T_c,T_b] :
% 168.50/168.33 ? [B_f] :
% 168.50/168.33 ( 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))
% 168.50/168.33 & 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))) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_refl__onI,axiom,
% 168.50/168.33 ! [V_A_2,V_r_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 168.50/168.33 => ( ! [B_x] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.50/168.33 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) )
% 168.50/168.33 => c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_fold__image__Sigma,axiom,
% 168.50/168.33 ! [V_g_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 168.50/168.33 ( class_Groups_Ocomm__monoid__mult(T_d)
% 168.50/168.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.33 => ( ! [B_x] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.50/168.33 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 168.50/168.33 => 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)) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_setprod__Sigma,axiom,
% 168.50/168.33 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 168.50/168.33 ( class_Groups_Ocomm__monoid__mult(T_d)
% 168.50/168.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.33 => ( ! [B_x] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.50/168.33 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 168.50/168.33 => 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)) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_setsum__Sigma,axiom,
% 168.50/168.33 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 168.50/168.33 ( class_Groups_Ocomm__monoid__add(T_d)
% 168.50/168.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.33 => ( ! [B_x] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.50/168.33 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 168.50/168.33 => 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)) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_card__SigmaI,axiom,
% 168.50/168.33 ! [V_B_2,T_c,V_A_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.33 => ( ! [B_x] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.50/168.33 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 168.50/168.33 => 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) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_finite__SigmaI,axiom,
% 168.50/168.33 ! [V_B_2,T_c,V_A_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.33 => ( ! [B_a] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 168.50/168.33 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
% 168.50/168.33 => 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))) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_SigmaE,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2,V_c_2,T_c,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_c_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
% 168.50/168.33 => ~ ! [B_x] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.50/168.33 => ! [B_y] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(V_B_2,B_x)))
% 168.50/168.33 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_map__pair__surj,axiom,
% 168.50/168.33 ! [V_g_2,T_d,T_e,V_f_2,T_b,T_c] :
% 168.50/168.33 ( 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))
% 168.50/168.33 => ( 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))
% 168.50/168.33 => 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)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_map__pair__imageI,axiom,
% 168.50/168.33 ! [V_g_2,V_f_2,T_e,T_d,V_R_2,V_b_2,V_a_2,T_c,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_R_2))
% 168.50/168.33 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2))),hAPP(c_Set_Oimage(tc_prod(T_b,T_c),tc_prod(T_d,T_e),c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2)),V_R_2))) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_map__pair__simp,axiom,
% 168.50/168.33 ! [V_b_2,V_a_2,V_g_2,V_f_2,T_c,T_e,T_b,T_d] : hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),V_a_2),V_b_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_map__pair__ident,axiom,
% 168.50/168.33 ! [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 ).
% 168.50/168.33
% 168.50/168.33 fof(fact_snd__prod__fun,axiom,
% 168.50/168.33 ! [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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_fst__map__pair,axiom,
% 168.50/168.33 ! [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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_map__pair__def,axiom,
% 168.50/168.33 ! [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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_map__pair__surj__on,axiom,
% 168.50/168.33 ! [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] :
% 168.50/168.33 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2
% 168.50/168.33 => ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),V_B_2) = V_B_H_2
% 168.50/168.33 => 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)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_map__pair__inj__on,axiom,
% 168.50/168.33 ! [V_B_2,V_g_2,T_e,T_d,V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.33 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 168.50/168.33 => ( c_Fun_Oinj__on(T_d,T_e,V_g_2,V_B_2)
% 168.50/168.33 => 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))) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_prod__fun__imageE,axiom,
% 168.50/168.33 ! [V_R_2,V_g_2,V_f_2,T_e,T_d,V_c_2,T_c,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_c_2),hAPP(c_Set_Oimage(tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2)),V_R_2)))
% 168.50/168.33 => ~ ! [B_x,B_y] :
% 168.50/168.33 ( V_c_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_y))
% 168.50/168.33 => ~ 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)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_card__less__Suc2,axiom,
% 168.50/168.33 ! [V_i_2,V_M_2] :
% 168.50/168.33 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 168.50/168.33 => 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))))) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_card__less,axiom,
% 168.50/168.33 ! [V_i_2,V_M_2] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 168.50/168.33 => 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) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_CollectI,axiom,
% 168.50/168.33 ! [T_b,V_a_2,V_P_2] :
% 168.50/168.33 ( hBOOL(hAPP(V_P_2,V_a_2))
% 168.50/168.33 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2))) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_finite__Collect__conjI,axiom,
% 168.50/168.33 ! [V_Q_2,V_P_2,T_b] :
% 168.50/168.33 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 168.50/168.33 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2))) )
% 168.50/168.33 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2)),V_Q_2)))) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_finite__Collect__less__nat,axiom,
% 168.50/168.33 ! [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)))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_finite__Collect__le__nat,axiom,
% 168.50/168.33 ! [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)))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Collect__split,axiom,
% 168.50/168.33 ! [V_Q_2,V_P_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_OCollect(T_c),V_Q_2))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_SetCompr__Sigma__eq,axiom,
% 168.50/168.33 ! [V_Q_2,V_P_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),V_Q_2)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Collect__neg__eq,axiom,
% 168.50/168.33 ! [V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_vimage__Collect__eq,axiom,
% 168.50/168.33 ! [V_P_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Set_OCollect(T_c),V_P_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),V_P_2),V_f_2)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_CollectE,axiom,
% 168.50/168.33 ! [V_P_2,V_a_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 168.50/168.33 => hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_CollectD,axiom,
% 168.50/168.33 ! [V_P_2,V_a_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 168.50/168.33 => hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_mem__Collect__eq,axiom,
% 168.50/168.33 ! [V_P_2,V_a_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 168.50/168.33 <=> hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Collect__mem__eq,axiom,
% 168.50/168.33 ! [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 ).
% 168.50/168.33
% 168.50/168.33 fof(fact_UNIV__def,axiom,
% 168.50/168.33 ! [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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_finite__Collect__disjI,axiom,
% 168.50/168.33 ! [V_Q_2,V_P_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_P_2)),V_Q_2))))
% 168.50/168.33 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 168.50/168.33 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2))) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Collect__def,axiom,
% 168.50/168.33 ! [V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),V_P_2) = V_P_2 ).
% 168.50/168.33
% 168.50/168.33 fof(fact_empty__def,axiom,
% 168.50/168.33 ! [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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Collect__empty__eq,axiom,
% 168.50/168.33 ! [V_P_2,T_b] :
% 168.50/168.33 ( hAPP(c_Set_OCollect(T_b),V_P_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.33 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_empty__Collect__eq,axiom,
% 168.50/168.33 ! [V_P_2,T_b] :
% 168.50/168.33 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_P_2)
% 168.50/168.33 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_insert__Collect,axiom,
% 168.50/168.33 ! [V_P_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)))),V_P_2)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Collect__disj__eq,axiom,
% 168.50/168.33 ! [V_Q_2,V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(c_Set_OCollect(T_b),V_Q_2)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Collect__conj__eq,axiom,
% 168.50/168.33 ! [V_Q_2,V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(c_Set_OCollect(T_b),V_Q_2)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_insert__compr,axiom,
% 168.50/168.33 ! [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))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_insert__compr__raw,axiom,
% 168.50/168.33 ! [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))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Un__def,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = 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))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Int__def,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = 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))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Int__Collect,axiom,
% 168.50/168.33 ! [V_P_2,V_A_2,V_x_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2))))
% 168.50/168.33 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.50/168.33 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Collect__conv__if,axiom,
% 168.50/168.33 ! [T_b,V_a_2,V_P_2] :
% 168.50/168.33 ( ( hBOOL(hAPP(V_P_2,V_a_2))
% 168.50/168.33 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) )
% 168.50/168.33 & ( ~ hBOOL(hAPP(V_P_2,V_a_2))
% 168.50/168.33 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Collect__conv__if2,axiom,
% 168.50/168.33 ! [T_b,V_a_2,V_P_2] :
% 168.50/168.33 ( ( hBOOL(hAPP(V_P_2,V_a_2))
% 168.50/168.33 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) )
% 168.50/168.33 & ( ~ hBOOL(hAPP(V_P_2,V_a_2))
% 168.50/168.33 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_singleton__conv,axiom,
% 168.50/168.33 ! [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))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_singleton__conv2,axiom,
% 168.50/168.33 ! [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))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_set__diff__eq,axiom,
% 168.50/168.33 ! [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)))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_finite__Collect__not,axiom,
% 168.50/168.33 ! [V_P_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 168.50/168.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2))))
% 168.50/168.33 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_insert__def,axiom,
% 168.50/168.33 ! [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) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Compl__eq,axiom,
% 168.50/168.33 ! [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))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_vimage__def,axiom,
% 168.50/168.33 ! [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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Collect__ball__eq,axiom,
% 168.50/168.33 ! [V_P_2,V_A_2,T_c,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fimplies),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),V_P_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_OCollect(T_b)),hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_P_2))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Collect__imp__eq,axiom,
% 168.50/168.33 ! [V_Q_2,V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2))),hAPP(c_Set_OCollect(T_b),V_Q_2)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Inter__eq,axiom,
% 168.50/168.33 ! [V_A_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_b,tc_HOL_Obool))),V_A_2)))),c_member(T_b)))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_finite__M__bounded__by__nat,axiom,
% 168.50/168.33 ! [V_i_2,V_P_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),V_P_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2))))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_setsum__setsum__restrict,axiom,
% 168.50/168.33 ! [V_R_2,V_f_2,V_T_2,T_c,V_S_2,T_b,T_d] :
% 168.50/168.33 ( class_Groups_Ocomm__monoid__add(T_d)
% 168.50/168.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 168.50/168.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
% 168.50/168.33 => 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) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_INTER__def,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fimplies),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_member(T_b))),V_B_2)))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_if__image__distrib,axiom,
% 168.50/168.33 ! [V_S_2,V_g_2,V_f_2,V_P_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),V_P_2)),V_f_2)),V_g_2)),V_S_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),V_P_2)))),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),V_P_2))))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_nat__seg__image__imp__finite,axiom,
% 168.50/168.33 ! [V_n_2,V_f_2,T_b,V_A_2] :
% 168.50/168.33 ( 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)))
% 168.50/168.33 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_setsum__restrict__set_H,axiom,
% 168.50/168.33 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
% 168.50/168.33 ( class_Groups_Ocomm__monoid__add(T_c)
% 168.50/168.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.33 => 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) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_setsum__image__gen,axiom,
% 168.50/168.33 ! [V_f_2,T_d,V_g_2,V_S_2,T_b,T_c] :
% 168.50/168.33 ( class_Groups_Ocomm__monoid__add(T_c)
% 168.50/168.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 168.50/168.33 => 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)) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Inf__Sup,axiom,
% 168.50/168.33 ! [V_A_2,T_b] :
% 168.50/168.33 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 168.50/168.33 => c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),c_Orderings_Oord__class_Oless__eq(T_b))))) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Sup__Inf,axiom,
% 168.50/168.33 ! [V_A_2,T_b] :
% 168.50/168.33 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 168.50/168.33 => c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b)))))) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Image__singleton,axiom,
% 168.50/168.33 ! [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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_setsum__cases,axiom,
% 168.50/168.33 ! [V_g_2,V_f_2,V_P_2,V_A_2,T_b,T_c] :
% 168.50/168.33 ( class_Groups_Ocomm__monoid__add(T_c)
% 168.50/168.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.33 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),V_P_2)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2))))) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_card__less__Suc,axiom,
% 168.50/168.33 ! [V_i_2,V_M_2] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 168.50/168.33 => 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))))) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_setsum__multicount,axiom,
% 168.50/168.33 ! [V_k_2,V_R_2,V_T_2,T_c,V_S_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 168.50/168.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
% 168.50/168.33 => ( ! [B_x] :
% 168.50/168.33 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_T_2))
% 168.50/168.33 => 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 )
% 168.50/168.33 => 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)) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_min__max_Oinf__Sup1__distrib,axiom,
% 168.50/168.33 ! [V_x_2,V_A_2,T_b] :
% 168.50/168.33 ( class_Orderings_Olinorder(T_b)
% 168.50/168.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.33 => 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))))) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_min__max_Oinf__Sup2__distrib,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2,T_b] :
% 168.50/168.33 ( class_Orderings_Olinorder(T_b)
% 168.50/168.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.50/168.33 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.33 => 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))))))) ) ) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_finite__Collect__subsets,axiom,
% 168.50/168.33 ! [V_A_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.33 => 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)))) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Pow__Compl,axiom,
% 168.50/168.33 ! [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))))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Pow__def,axiom,
% 168.50/168.33 ! [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)) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_finite__Collect__bounded__ex,axiom,
% 168.50/168.33 ! [V_Q_2,T_c,V_P_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 168.50/168.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),V_Q_2)))))
% 168.50/168.33 <=> ! [B_y] :
% 168.50/168.33 ( hBOOL(hAPP(V_P_2,B_y))
% 168.50/168.33 => 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)))) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_finite__image__set,axiom,
% 168.50/168.33 ! [V_f_2,T_c,V_P_2,T_b] :
% 168.50/168.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 168.50/168.33 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_b)),c_fequal)),V_f_2)))),V_P_2))))) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_inj__graph,axiom,
% 168.50/168.33 ! [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))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom,
% 168.50/168.33 ! [V_P_2] : c_Nat__Transfer_Onat__set(hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_finite__psubset__def,axiom,
% 168.50/168.33 ! [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)))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_inv__image__def,axiom,
% 168.50/168.33 ! [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))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
% 168.50/168.33 ! [V_P_2] : hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Nat_Onat),V_P_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom,
% 168.50/168.33 ! [V_P_2] : hAPP(c_Set_OCollect(tc_Nat_Onat),V_P_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),V_P_2),c_Int_Onat)))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_add__Min__commute,axiom,
% 168.50/168.33 ! [V_k_2,V_N_2,T_b] :
% 168.50/168.33 ( class_Groups_Olinordered__ab__semigroup__add(T_b)
% 168.50/168.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 168.50/168.33 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.33 => 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))))) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_add__Max__commute,axiom,
% 168.50/168.33 ! [V_k_2,V_N_2,T_b] :
% 168.50/168.33 ( class_Groups_Olinordered__ab__semigroup__add(T_b)
% 168.50/168.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 168.50/168.33 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.33 => 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))))) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_sup__Inf2__distrib,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2,T_b] :
% 168.50/168.33 ( class_Lattices_Odistrib__lattice(T_b)
% 168.50/168.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.50/168.33 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.33 => 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))))))) ) ) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_sup__Inf1__distrib,axiom,
% 168.50/168.33 ! [V_x_2,V_A_2,T_b] :
% 168.50/168.33 ( class_Lattices_Odistrib__lattice(T_b)
% 168.50/168.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.33 => 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))))) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_inf__Sup2__distrib,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2,T_b] :
% 168.50/168.33 ( class_Lattices_Odistrib__lattice(T_b)
% 168.50/168.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.50/168.33 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.33 => 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))))))) ) ) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_inf__Sup1__distrib,axiom,
% 168.50/168.33 ! [V_x_2,V_A_2,T_b] :
% 168.50/168.33 ( class_Lattices_Odistrib__lattice(T_b)
% 168.50/168.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.33 => 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))))) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_min__max_Osup__Inf2__distrib,axiom,
% 168.50/168.33 ! [V_B_2,V_A_2,T_b] :
% 168.50/168.33 ( class_Orderings_Olinorder(T_b)
% 168.50/168.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.50/168.33 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.33 => 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))))))) ) ) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_min__max_Osup__Inf1__distrib,axiom,
% 168.50/168.33 ! [V_x_2,V_A_2,T_b] :
% 168.50/168.33 ( class_Orderings_Olinorder(T_b)
% 168.50/168.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.33 => 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))))) ) ) ) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_Nitpick_Oprod__def,axiom,
% 168.50/168.33 ! [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)))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_int__ge__less__than__def,axiom,
% 168.50/168.33 ! [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)))) ).
% 168.50/168.33
% 168.50/168.33 fof(fact_int__ge__less__than2__def,axiom,
% 168.50/168.34 ! [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)))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_reflp__def,axiom,
% 168.50/168.34 ! [V_r_2,T_b] :
% 168.50/168.34 ( c_Predicate_Oreflp(T_b,V_r_2)
% 168.50/168.34 <=> 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))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_setsum__mult__setsum__if__inj,axiom,
% 168.50/168.34 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] :
% 168.50/168.34 ( class_Rings_Osemiring__0(T_d)
% 168.50/168.34 => ( 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)))
% 168.50/168.34 => 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))))))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_setsum__multicount__gen,axiom,
% 168.50/168.34 ! [V_k_2,V_R_2,V_t_2,T_c,V_s_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 168.50/168.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_t_2))
% 168.50/168.34 => ( ! [B_x] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_t_2))
% 168.50/168.34 => 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) )
% 168.50/168.34 => 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) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_inj__on__id,axiom,
% 168.50/168.34 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_Fun_Oid(T_b),V_A_2) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_id__def,axiom,
% 168.50/168.34 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ).
% 168.50/168.34
% 168.50/168.34 fof(fact_id__apply,axiom,
% 168.50/168.34 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ).
% 168.50/168.34
% 168.50/168.34 fof(fact_apsnd__id,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_reflpE,axiom,
% 168.50/168.34 ! [V_x_2,V_r_2,T_b] :
% 168.50/168.34 ( c_Predicate_Oreflp(T_b,V_r_2)
% 168.50/168.34 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_apfst__id,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_vimage__id,axiom,
% 168.50/168.34 ! [V_A_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_Fun_Oid(T_b)),V_A_2) = V_A_2 ).
% 168.50/168.34
% 168.50/168.34 fof(fact_map__pair_Oidentity,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_map__pair_Oid,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_image__id,axiom,
% 168.50/168.34 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),V_Y_2) = V_Y_2 ).
% 168.50/168.34
% 168.50/168.34 fof(fact_of__int__eq__id,axiom,
% 168.50/168.34 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_surj__id,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_apsnd__def,axiom,
% 168.50/168.34 ! [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) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_apfst__def,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_split__Pair,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_setsum__reindex__id,axiom,
% 168.50/168.34 ! [V_B_2,V_f_2,T_b,T_c] :
% 168.50/168.34 ( class_Groups_Ocomm__monoid__add(T_c)
% 168.50/168.34 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 168.50/168.34 => 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)) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_setprod__reindex__id,axiom,
% 168.50/168.34 ! [V_B_2,V_f_2,T_b,T_c] :
% 168.50/168.34 ( class_Groups_Ocomm__monoid__mult(T_c)
% 168.50/168.34 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 168.50/168.34 => 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)) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_finite__conv__nat__seg__image,axiom,
% 168.50/168.34 ! [V_A_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.34 <=> ? [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))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rel__comp__def,axiom,
% 168.50/168.34 ! [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))))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Range__Collect__split,axiom,
% 168.50/168.34 ! [V_P_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(c_Set_OCollect(tc_prod(T_c,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_P_2))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rel__compI,axiom,
% 168.50/168.34 ! [V_s_2,V_c_2,T_d,V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_b_2),V_c_2)),V_s_2))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_a_2),V_c_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_RangeI,axiom,
% 168.50/168.34 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rel__comp__UNION__distrib,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rel__comp__UNION__distrib2,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rel__comp__mono,axiom,
% 168.50/168.34 ! [V_s_2,V_s_H_2,T_d,V_r_2,V_r_H_2,T_c,T_b] :
% 168.50/168.34 ( 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))
% 168.50/168.34 => ( 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))
% 168.50/168.34 => 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))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Range__Id__on,axiom,
% 168.50/168.34 ! [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 ).
% 168.50/168.34
% 168.50/168.34 fof(fact_O__assoc,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rel__comp__empty2,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rel__comp__empty1,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rel__comp__distrib,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rel__comp__distrib2,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_union__comp__emptyR,axiom,
% 168.50/168.34 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 168.50/168.34 ( 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))
% 168.50/168.34 => ( 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))
% 168.50/168.34 => 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)) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_union__comp__emptyL,axiom,
% 168.50/168.34 ! [V_B_2,V_C_2,V_A_2,T_b] :
% 168.50/168.34 ( 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))
% 168.50/168.34 => ( 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))
% 168.50/168.34 => 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)) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Range__Union,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Range__empty,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Range__empty__iff,axiom,
% 168.50/168.34 ! [V_r_2,T_b,T_c] :
% 168.50/168.34 ( hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.34 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rel__comp__subset__Sigma,axiom,
% 168.50/168.34 ! [V_C_2,V_s_2,T_d,V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 168.50/168.34 ( 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))))
% 168.50/168.34 => ( 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))))
% 168.50/168.34 => 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)))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Range__Un__eq,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_finite__Range,axiom,
% 168.50/168.34 ! [V_r_2,T_c,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
% 168.50/168.34 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_snd__eq__Range,axiom,
% 168.50/168.34 ! [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) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Range__iff,axiom,
% 168.50/168.34 ! [V_r_2,T_c,V_a_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
% 168.50/168.34 <=> ? [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)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Range__insert,axiom,
% 168.50/168.34 ! [V_r_2,V_b_2,V_a_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Range__Int__subset,axiom,
% 168.50/168.34 ! [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)))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Range__Diff__subset,axiom,
% 168.50/168.34 ! [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)))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_max__ext__compat,axiom,
% 168.50/168.34 ! [V_S_2,V_R_2,T_b] :
% 168.50/168.34 ( 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))
% 168.50/168.34 => 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))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_min__ext__compat,axiom,
% 168.50/168.34 ! [V_S_2,V_R_2,T_b] :
% 168.50/168.34 ( 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))
% 168.50/168.34 => 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))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_RangeP__Range__eq,axiom,
% 168.50/168.34 ! [V_x_2,V_r_2,T_c,T_b] :
% 168.50/168.34 ( 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))
% 168.50/168.34 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_RangeE,axiom,
% 168.50/168.34 ! [V_r_2,T_c,V_b_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
% 168.50/168.34 => ~ ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_pred__comp__rel__comp__eq,axiom,
% 168.50/168.34 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_d,T_c,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d)))),V_s_2)),V_x_2),V_y_2))
% 168.50/168.34 <=> 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))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_pred__comp_Ointros,axiom,
% 168.50/168.34 ! [T_d,T_c,T_b,V_c_2,V_s_2,V_b_2,V_a_2,V_r_2] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_c_2))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2),V_a_2),V_c_2)) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_RangeP_Ointros,axiom,
% 168.50/168.34 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 168.50/168.34 => hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_b_2)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_pred__comp_Oequations,axiom,
% 168.50/168.34 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_d,T_c,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2),V_a1_2),V_a3_2))
% 168.50/168.34 <=> ? [B_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b))
% 168.50/168.34 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_RangeP_Oequations,axiom,
% 168.50/168.34 ! [V_a2_2,V_r_2,T_c,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_a2_2))
% 168.50/168.34 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_reduction__pairI,axiom,
% 168.50/168.34 ! [V_S_2,V_R_2,T_b] :
% 168.50/168.34 ( c_Wellfounded_Owf(T_b,V_R_2)
% 168.50/168.34 => ( 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))
% 168.50/168.34 => 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)) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Domain__Collect__split,axiom,
% 168.50/168.34 ! [V_P_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),V_P_2)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_the__eq__trivial,axiom,
% 168.50/168.34 ! [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 ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf__less__than,axiom,
% 168.50/168.34 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf__empty,axiom,
% 168.50/168.34 ! [T_b] : c_Wellfounded_Owf(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf__inv__image,axiom,
% 168.50/168.34 ! [V_f_2,T_c,V_r_2,T_b] :
% 168.50/168.34 ( c_Wellfounded_Owf(T_b,V_r_2)
% 168.50/168.34 => c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf__lex__prod,axiom,
% 168.50/168.34 ! [V_rb_2,T_c,V_ra_2,T_b] :
% 168.50/168.34 ( c_Wellfounded_Owf(T_b,V_ra_2)
% 168.50/168.34 => ( c_Wellfounded_Owf(T_c,V_rb_2)
% 168.50/168.34 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_ra_2,V_rb_2)) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf__measure,axiom,
% 168.50/168.34 ! [V_f_2,T_b] : c_Wellfounded_Owf(T_b,hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_DomainI,axiom,
% 168.50/168.34 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf__comp__self,axiom,
% 168.50/168.34 ! [V_R_2,T_b] :
% 168.50/168.34 ( c_Wellfounded_Owf(T_b,V_R_2)
% 168.50/168.34 <=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_min__ext__wf,axiom,
% 168.50/168.34 ! [V_r_2,T_b] :
% 168.50/168.34 ( c_Wellfounded_Owf(T_b,V_r_2)
% 168.50/168.34 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_b,V_r_2)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf__subset,axiom,
% 168.50/168.34 ! [V_p_2,V_r_2,T_b] :
% 168.50/168.34 ( c_Wellfounded_Owf(T_b,V_r_2)
% 168.50/168.34 => ( 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))
% 168.50/168.34 => c_Wellfounded_Owf(T_b,V_p_2) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf__irrefl,axiom,
% 168.50/168.34 ! [V_a_2,V_r_2,T_b] :
% 168.50/168.34 ( c_Wellfounded_Owf(T_b,V_r_2)
% 168.50/168.34 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf__asym,axiom,
% 168.50/168.34 ! [V_x_2,V_a_2,V_r_2,T_b] :
% 168.50/168.34 ( c_Wellfounded_Owf(T_b,V_r_2)
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_x_2)),V_r_2))
% 168.50/168.34 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_a_2)),V_r_2)) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf__not__sym,axiom,
% 168.50/168.34 ! [V_x_2,V_a_2,V_r_2,T_b] :
% 168.50/168.34 ( c_Wellfounded_Owf(T_b,V_r_2)
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_x_2)),V_r_2))
% 168.50/168.34 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_a_2)),V_r_2)) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf__not__refl,axiom,
% 168.50/168.34 ! [V_a_2,V_r_2,T_b] :
% 168.50/168.34 ( c_Wellfounded_Owf(T_b,V_r_2)
% 168.50/168.34 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf__finite__psubset,axiom,
% 168.50/168.34 ! [T_b] : c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf__mlex,axiom,
% 168.50/168.34 ! [V_f_2,V_R_2,T_b] :
% 168.50/168.34 ( c_Wellfounded_Owf(T_b,V_R_2)
% 168.50/168.34 => c_Wellfounded_Owf(T_b,c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Domain__Id__on,axiom,
% 168.50/168.34 ! [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 ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf__pair__less,axiom,
% 168.50/168.34 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_max__ext__wf,axiom,
% 168.50/168.34 ! [V_r_2,T_b] :
% 168.50/168.34 ( c_Wellfounded_Owf(T_b,V_r_2)
% 168.50/168.34 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_b,V_r_2)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf__Int2,axiom,
% 168.50/168.34 ! [V_r_H_2,V_r_2,T_b] :
% 168.50/168.34 ( c_Wellfounded_Owf(T_b,V_r_2)
% 168.50/168.34 => 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)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf__Int1,axiom,
% 168.50/168.34 ! [V_r_H_2,V_r_2,T_b] :
% 168.50/168.34 ( c_Wellfounded_Owf(T_b,V_r_2)
% 168.50/168.34 => 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)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf__less,axiom,
% 168.50/168.34 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)))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf__int__ge__less__than2,axiom,
% 168.50/168.34 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf__int__ge__less__than,axiom,
% 168.50/168.34 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf__Un,axiom,
% 168.50/168.34 ! [V_s_2,V_r_2,T_b] :
% 168.50/168.34 ( c_Wellfounded_Owf(T_b,V_r_2)
% 168.50/168.34 => ( c_Wellfounded_Owf(T_b,V_s_2)
% 168.50/168.34 => ( 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))
% 168.50/168.34 => 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)) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf__acc__iff,axiom,
% 168.50/168.34 ! [V_r_2,T_b] :
% 168.50/168.34 ( c_Wellfounded_Owf(T_b,V_r_2)
% 168.50/168.34 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_acc__wfD,axiom,
% 168.50/168.34 ! [V_x_2,V_r_2,T_b] :
% 168.50/168.34 ( c_Wellfounded_Owf(T_b,V_r_2)
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf__no__loop,axiom,
% 168.50/168.34 ! [V_R_2,T_b] :
% 168.50/168.34 ( 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))
% 168.50/168.34 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf__union__merge,axiom,
% 168.50/168.34 ! [V_S_2,V_R_2,T_b] :
% 168.50/168.34 ( 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))
% 168.50/168.34 <=> 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)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Domain__empty,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Domain__empty__iff,axiom,
% 168.50/168.34 ! [V_r_2,T_c,T_b] :
% 168.50/168.34 ( hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.34 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Domain__mono,axiom,
% 168.50/168.34 ! [V_s_2,V_r_2,T_c,T_b] :
% 168.50/168.34 ( 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))
% 168.50/168.34 => 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))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Domain__Un__eq,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_finite__Domain,axiom,
% 168.50/168.34 ! [V_r_2,T_c,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
% 168.50/168.34 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_fst__eq__Domain,axiom,
% 168.50/168.34 ! [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) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf__iff__no__infinite__down__chain,axiom,
% 168.50/168.34 ! [V_r_2,T_b] :
% 168.50/168.34 ( c_Wellfounded_Owf(T_b,V_r_2)
% 168.50/168.34 <=> ~ ? [B_f] :
% 168.50/168.34 ! [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)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wfE__pf,axiom,
% 168.50/168.34 ! [V_A_2,V_R_2,T_b] :
% 168.50/168.34 ( c_Wellfounded_Owf(T_b,V_R_2)
% 168.50/168.34 => ( 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)))
% 168.50/168.34 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf__union__compatible,axiom,
% 168.50/168.34 ! [V_S_2,V_R_2,T_b] :
% 168.50/168.34 ( c_Wellfounded_Owf(T_b,V_R_2)
% 168.50/168.34 => ( c_Wellfounded_Owf(T_b,V_S_2)
% 168.50/168.34 => ( 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))
% 168.50/168.34 => 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)) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Domain__iff,axiom,
% 168.50/168.34 ! [V_r_2,T_c,V_a_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
% 168.50/168.34 <=> ? [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)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf,axiom,
% 168.50/168.34 ! [T_b] :
% 168.50/168.34 ( class_Orderings_Owellorder(T_b)
% 168.50/168.34 => 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)))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Domain__insert,axiom,
% 168.50/168.34 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_reduction__pair__def,axiom,
% 168.50/168.34 ! [V_P_2,T_b] :
% 168.50/168.34 ( c_FunDef_Oreduction__pair(T_b,V_P_2)
% 168.50/168.34 <=> ( c_Wellfounded_Owf(T_b,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2))
% 168.50/168.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_reduction__pair__lemma,axiom,
% 168.50/168.34 ! [V_S_2,V_R_2,V_P_2,T_b] :
% 168.50/168.34 ( c_FunDef_Oreduction__pair(T_b,V_P_2)
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)))
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_S_2),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)))
% 168.50/168.34 => ( c_Wellfounded_Owf(T_b,V_S_2)
% 168.50/168.34 => 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)) ) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Domain__Int__subset,axiom,
% 168.50/168.34 ! [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)))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Domain__Diff__subset,axiom,
% 168.50/168.34 ! [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)))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Field__def,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf__map__pair__image,axiom,
% 168.50/168.34 ! [V_f_2,T_c,V_r_2,T_b] :
% 168.50/168.34 ( c_Wellfounded_Owf(T_b,V_r_2)
% 168.50/168.34 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 168.50/168.34 => 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)) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Domain__Union,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_the__sym__eq__trivial,axiom,
% 168.50/168.34 ! [V_x_2,T_b] : c_HOL_OThe(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 168.50/168.34
% 168.50/168.34 fof(fact_DomainP__Domain__eq,axiom,
% 168.50/168.34 ! [V_x_2,V_r_2,T_c,T_b] :
% 168.50/168.34 ( 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))
% 168.50/168.34 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf__lenlex,axiom,
% 168.50/168.34 ! [V_r_2,T_b] :
% 168.50/168.34 ( c_Wellfounded_Owf(T_b,V_r_2)
% 168.50/168.34 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olenlex(T_b,V_r_2)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_DomainE,axiom,
% 168.50/168.34 ! [V_r_2,T_c,V_a_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
% 168.50/168.34 => ~ ! [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)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_DomainP_Ointros,axiom,
% 168.50/168.34 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 168.50/168.34 => hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a_2)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_DomainP_Oequations,axiom,
% 168.50/168.34 ! [V_a1_2,V_r_2,T_c,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a1_2))
% 168.50/168.34 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_pred__nat__def,axiom,
% 168.50/168.34 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))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf__lex,axiom,
% 168.50/168.34 ! [V_r_2,T_b] :
% 168.50/168.34 ( c_Wellfounded_Owf(T_b,V_r_2)
% 168.50/168.34 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olex(T_b,V_r_2)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf__lexn,axiom,
% 168.50/168.34 ! [V_n_2,V_r_2,T_b] :
% 168.50/168.34 ( c_Wellfounded_Owf(T_b,V_r_2)
% 168.50/168.34 => c_Wellfounded_Owf(tc_List_Olist(T_b),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_lex__def,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_lexn_Osimps_I1_J,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf__pred__nat,axiom,
% 168.50/168.34 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf__same__fst,axiom,
% 168.50/168.34 ! [T_b,V_R_2,T_c,V_P_2] :
% 168.50/168.34 ( ! [B_x] :
% 168.50/168.34 ( hBOOL(hAPP(V_P_2,B_x))
% 168.50/168.34 => c_Wellfounded_Owf(T_c,hAPP(V_R_2,B_x)) )
% 168.50/168.34 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Recdef_Osame__fst(T_b,T_c,V_P_2,V_R_2)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf__if__measure,axiom,
% 168.50/168.34 ! [T_b,V_g_2,V_f_2,V_P_2] :
% 168.50/168.34 ( ! [B_x] :
% 168.50/168.34 ( hBOOL(hAPP(V_P_2,B_x))
% 168.50/168.34 => 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))) )
% 168.50/168.34 => c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),V_g_2))))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wfP__def,axiom,
% 168.50/168.34 ! [V_r_2,T_b] :
% 168.50/168.34 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 168.50/168.34 <=> 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))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wfP__empty,axiom,
% 168.50/168.34 ! [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))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_accp__wfPD,axiom,
% 168.50/168.34 ! [V_x_2,V_r_2,T_b] :
% 168.50/168.34 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 168.50/168.34 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_x_2)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wfP__accp__iff,axiom,
% 168.50/168.34 ! [V_r_2,T_b] :
% 168.50/168.34 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 168.50/168.34 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x1)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wfP__subset,axiom,
% 168.50/168.34 ! [V_p_2,V_r_2,T_b] :
% 168.50/168.34 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 168.50/168.34 => ( 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))
% 168.50/168.34 => c_Wellfounded_OwfP(T_b,V_p_2) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf__in__rel,axiom,
% 168.50/168.34 ! [V_R_2,T_b] :
% 168.50/168.34 ( c_Wellfounded_Owf(T_b,V_R_2)
% 168.50/168.34 => c_Wellfounded_OwfP(T_b,c_FunDef_Oin__rel(T_b,T_b,V_R_2)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wfP__wf__eq,axiom,
% 168.50/168.34 ! [V_r_2,T_b] :
% 168.50/168.34 ( 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))
% 168.50/168.34 <=> c_Wellfounded_Owf(T_b,V_r_2) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wfP__acyclicP,axiom,
% 168.50/168.34 ! [V_r_2,T_b] :
% 168.50/168.34 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 168.50/168.34 => 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))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_pigeonhole__infinite,axiom,
% 168.50/168.34 ! [V_f_2,T_c,V_A_2,T_b] :
% 168.50/168.34 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 168.50/168.34 => ? [B_x] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.50/168.34 & ~ 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)))))) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Abs__Integ__induct,axiom,
% 168.50/168.34 ! [V_x_2,V_P_2] :
% 168.50/168.34 ( ! [B_y] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg))
% 168.50/168.34 => hBOOL(hAPP(V_P_2,hAPP(c_Int_OAbs__Integ,B_y))) )
% 168.50/168.34 => hBOOL(hAPP(V_P_2,V_x_2)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf__acyclic,axiom,
% 168.50/168.34 ! [V_r_2,T_b] :
% 168.50/168.34 ( c_Wellfounded_Owf(T_b,V_r_2)
% 168.50/168.34 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_acyclic__subset,axiom,
% 168.50/168.34 ! [V_r_2,V_s_2,T_b] :
% 168.50/168.34 ( c_Wellfounded_Oacyclic(T_b,V_s_2)
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 168.50/168.34 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf__iff__acyclic__if__finite,axiom,
% 168.50/168.34 ! [V_r_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 168.50/168.34 => ( c_Wellfounded_Owf(T_b,V_r_2)
% 168.50/168.34 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_finite__acyclic__wf,axiom,
% 168.50/168.34 ! [V_r_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 168.50/168.34 => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 168.50/168.34 => c_Wellfounded_Owf(T_b,V_r_2) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Nitpick_Owf_H__def,axiom,
% 168.50/168.34 ! [V_r_2,T_b] :
% 168.50/168.34 ( c_Nitpick_Owf_H(T_b,V_r_2)
% 168.50/168.34 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 168.50/168.34 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 168.50/168.34 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Abs__Integ__cases,axiom,
% 168.50/168.34 ! [V_x_2] :
% 168.50/168.34 ~ ! [B_y] :
% 168.50/168.34 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y)
% 168.50/168.34 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_finite__UN__I,axiom,
% 168.50/168.34 ! [V_B_2,T_c,V_A_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.34 => ( ! [B_a] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 168.50/168.34 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
% 168.50/168.34 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_inj__on__diff__nat,axiom,
% 168.50/168.34 ! [V_k_2,V_N_2] :
% 168.50/168.34 ( ! [B_x] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) )
% 168.50/168.34 => 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) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wfP__SUP,axiom,
% 168.50/168.34 ! [T_b,V_r_2,T_c] :
% 168.50/168.34 ( ! [B_i] : c_Wellfounded_OwfP(T_c,hAPP(V_r_2,B_i))
% 168.50/168.34 => ( ! [B_i,B_j] :
% 168.50/168.34 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j)
% 168.50/168.34 => 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)) )
% 168.50/168.34 => 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)) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_mem__splitE,axiom,
% 168.50/168.34 ! [V_p_2,V_c_2,T_d,T_c,V_z_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_c_2),V_p_2)))
% 168.50/168.34 => ~ ! [B_x,B_y] :
% 168.50/168.34 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y)
% 168.50/168.34 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,B_x),B_y))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_mem__splitI2,axiom,
% 168.50/168.34 ! [V_c_2,V_z_2,T_d,T_c,T_b,V_p_2] :
% 168.50/168.34 ( ! [B_a,B_b] :
% 168.50/168.34 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(V_c_2,B_a),B_b))) )
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_c_2),V_p_2))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_vimage__Times,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Eps__split,axiom,
% 168.50/168.34 ! [V_P_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2)) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_P_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_id__o,axiom,
% 168.50/168.34 ! [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 ).
% 168.50/168.34
% 168.50/168.34 fof(fact_o__id,axiom,
% 168.50/168.34 ! [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 ).
% 168.50/168.34
% 168.50/168.34 fof(fact_o__eq__id__dest,axiom,
% 168.50/168.34 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] :
% 168.50/168.34 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_c,T_c,T_b,c_Fun_Oid(T_c)),V_c_2)
% 168.50/168.34 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_exE__some,axiom,
% 168.50/168.34 ! [T_b,V_c_2,V_P_2] :
% 168.50/168.34 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 168.50/168.34 => ( V_c_2 = c_Hilbert__Choice_OEps(T_b,V_P_2)
% 168.50/168.34 => hBOOL(hAPP(V_P_2,V_c_2)) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_o__def,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_o__assoc,axiom,
% 168.50/168.34 ! [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) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_o__apply,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_o__eq__dest,axiom,
% 168.50/168.34 ! [V_v_2,V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
% 168.50/168.34 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_c_2),V_d_2)
% 168.50/168.34 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,hAPP(V_d_2,V_v_2)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_o__eq__elim,axiom,
% 168.50/168.34 ! [V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
% 168.50/168.34 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_c_2),V_d_2)
% 168.50/168.34 => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_c_2,hAPP(V_d_2,B_v)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_apsnd__compose,axiom,
% 168.50/168.34 ! [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) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_tfl__some,axiom,
% 168.50/168.34 ! [T_b,B_P] :
% 168.50/168.34 ( ? [B_x] : hBOOL(hAPP(B_P,B_x))
% 168.50/168.34 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_b,B_P))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_someI,axiom,
% 168.50/168.34 ! [T_b,V_x_2,V_P_2] :
% 168.50/168.34 ( hBOOL(hAPP(V_P_2,V_x_2))
% 168.50/168.34 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_comp__cong,axiom,
% 168.50/168.34 ! [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] :
% 168.50/168.34 ( 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))
% 168.50/168.34 => 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) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_fun__left__comm_Ofun__comp__comm,axiom,
% 168.50/168.34 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 168.50/168.34 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 168.50/168.34 => 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)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_o__eq__dest__lhs,axiom,
% 168.50/168.34 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] :
% 168.50/168.34 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = V_c_2
% 168.50/168.34 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom,
% 168.50/168.34 ! [V_x_2,V_f_2,T_c,T_b] :
% 168.50/168.34 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 168.50/168.34 => 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) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_some__sym__eq__trivial,axiom,
% 168.50/168.34 ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 168.50/168.34
% 168.50/168.34 fof(fact_some__eq__trivial,axiom,
% 168.50/168.34 ! [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 ).
% 168.50/168.34
% 168.50/168.34 fof(fact_some__eq__ex,axiom,
% 168.50/168.34 ! [T_b,V_P_2] :
% 168.50/168.34 ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2)))
% 168.50/168.34 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_someI__ex,axiom,
% 168.50/168.34 ! [T_b,V_P_2] :
% 168.50/168.34 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 168.50/168.34 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_K__record__comp,axiom,
% 168.50/168.34 ! [V_x_2,V_f_2,V_c_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_f_2),V_x_2) = V_c_2 ).
% 168.50/168.34
% 168.50/168.34 fof(fact_apfst__compose,axiom,
% 168.50/168.34 ! [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) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_fun__upd__comp,axiom,
% 168.50/168.34 ! [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),c_Fun_Ofun__upd(T_b,T_d,V_g_2,V_x_2,V_y_2)) = 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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_vimage__compose,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_map__pair_Ocompositionality,axiom,
% 168.50/168.34 ! [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) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_map__pair__compose,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_map__pair_Ocomp,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_image__compose,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_comp__surj,axiom,
% 168.50/168.34 ! [V_g_2,T_d,V_f_2,T_b,T_c] :
% 168.50/168.34 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.34 => ( 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))
% 168.50/168.34 => 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)) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_inj__comp,axiom,
% 168.50/168.34 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 168.50/168.34 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 168.50/168.34 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))
% 168.50/168.34 => 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))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_inj__on__imageI2,axiom,
% 168.50/168.34 ! [V_A_2,V_f_2,V_f_H_2,T_d,T_c,T_b] :
% 168.50/168.34 ( 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)
% 168.50/168.34 => c_Fun_Oinj__on(T_b,T_d,V_f_2,V_A_2) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_comp__inj__on__iff,axiom,
% 168.50/168.34 ! [V_f_H_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.34 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 168.50/168.34 => ( 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))
% 168.50/168.34 <=> 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) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_comp__inj__on,axiom,
% 168.50/168.34 ! [V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.34 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 168.50/168.34 => ( 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))
% 168.50/168.34 => 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) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_inj__on__imageI,axiom,
% 168.50/168.34 ! [V_A_2,V_f_2,V_g_2,T_d,T_c,T_b] :
% 168.50/168.34 ( 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)
% 168.50/168.34 => 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)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_setsum__reindex,axiom,
% 168.50/168.34 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
% 168.50/168.34 ( class_Groups_Ocomm__monoid__add(T_d)
% 168.50/168.34 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 168.50/168.34 => 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) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_setprod__reindex,axiom,
% 168.50/168.34 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
% 168.50/168.34 ( class_Groups_Ocomm__monoid__mult(T_d)
% 168.50/168.34 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 168.50/168.34 => 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) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_setprod__reindex__cong,axiom,
% 168.50/168.34 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 168.50/168.34 ( class_Groups_Ocomm__monoid__mult(T_d)
% 168.50/168.34 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 168.50/168.34 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 168.50/168.34 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)
% 168.50/168.34 => 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) ) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_split__paired__Eps,axiom,
% 168.50/168.34 ! [V_P_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),V_P_2) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_P_2)),c_Product__Type_OPair(T_b,T_c)))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Eps__split__eq,axiom,
% 168.50/168.34 ! [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) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_setsum_Oreindex,axiom,
% 168.50/168.34 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
% 168.50/168.34 ( class_Groups_Ocomm__monoid__add(T_c)
% 168.50/168.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.34 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 168.50/168.34 => 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) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_setprod_Oreindex,axiom,
% 168.50/168.34 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
% 168.50/168.34 ( class_Groups_Ocomm__monoid__mult(T_c)
% 168.50/168.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.34 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 168.50/168.34 => 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) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_the__inv__into__comp,axiom,
% 168.50/168.34 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
% 168.50/168.34 ( 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))
% 168.50/168.34 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
% 168.50/168.34 => ( 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))))
% 168.50/168.34 => 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) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_fold__image__reindex,axiom,
% 168.50/168.34 ! [V_z_2,V_g_2,V_h_2,T_c,V_A_2,T_b,T_d] :
% 168.50/168.34 ( class_Groups_Oab__semigroup__mult(T_d)
% 168.50/168.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.34 => ( c_Fun_Oinj__on(T_b,T_c,V_h_2,V_A_2)
% 168.50/168.34 => 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) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_folding_Oremove,axiom,
% 168.50/168.34 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 168.50/168.34 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 168.50/168.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.50/168.34 => 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)) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_folding__image_Oreindex,axiom,
% 168.50/168.34 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 168.50/168.34 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 168.50/168.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 168.50/168.34 => ( c_Fun_Oinj__on(T_c,T_c,V_h_2,V_A_2)
% 168.50/168.34 => 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) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_folding_Ounion,axiom,
% 168.50/168.34 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 168.50/168.34 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 168.50/168.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.50/168.34 => ( 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))
% 168.50/168.34 => 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)) ) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_folding_Ocommute__comps_I1_J,axiom,
% 168.50/168.34 ! [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] :
% 168.50/168.34 ( c_Finite__Set_Ofolding(T_b,T_c,V_fa_2,V_F_2)
% 168.50/168.34 => 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) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_folding_Ocommute__comp,axiom,
% 168.50/168.34 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_c,T_b] :
% 168.50/168.34 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 168.50/168.34 => 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)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_folding_Ocommute__left__comp,axiom,
% 168.50/168.34 ! [V_g_2,V_x_2,V_y_2,T_d,V_F_2,V_f_2,T_c,T_b] :
% 168.50/168.34 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 168.50/168.34 => 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)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_UN__o,axiom,
% 168.50/168.34 ! [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) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_fst__comp__map__pair,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_snd__comp__map__pair,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_folding__image_Odistrib,axiom,
% 168.50/168.34 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 168.50/168.34 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 168.50/168.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 168.50/168.34 => 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)) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_split__comp,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_folding_Ocommute__comp_H,axiom,
% 168.50/168.34 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 168.50/168.34 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 168.50/168.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.34 => 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)) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_folding_Ocommute__left__comp_H,axiom,
% 168.50/168.34 ! [V_g_2,V_x_2,T_d,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 168.50/168.34 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 168.50/168.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.34 => 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)) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_folding_Ocommute__comp_H_H,axiom,
% 168.50/168.34 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 168.50/168.34 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 168.50/168.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.50/168.34 => 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)) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_folding_Ocommute__left__comp_H_H,axiom,
% 168.50/168.34 ! [V_g_2,T_d,V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 168.50/168.34 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 168.50/168.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.50/168.34 => 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)) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_folding_Oempty,axiom,
% 168.50/168.34 ! [V_F_2,V_f_2,T_c,T_b] :
% 168.50/168.34 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 168.50/168.34 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Fun_Oid(T_c) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_folding_Oeq__fold,axiom,
% 168.50/168.34 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 168.50/168.34 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 168.50/168.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.34 => 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) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_folding__image_Oeq__fold,axiom,
% 168.50/168.34 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 168.50/168.34 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 168.50/168.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 168.50/168.34 => 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) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_folding_Oinsert,axiom,
% 168.50/168.34 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 168.50/168.34 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 168.50/168.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.34 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.50/168.34 => 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)) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_folding_Ounion__inter,axiom,
% 168.50/168.34 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 168.50/168.34 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 168.50/168.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.50/168.34 => 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)) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_folding_Oinsert__remove,axiom,
% 168.50/168.34 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 168.50/168.34 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 168.50/168.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.34 => 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)) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_setsum__reindex__nonzero,axiom,
% 168.50/168.34 ! [T_c,V_h_2,V_f_2,V_S_2,T_b,T_d] :
% 168.50/168.34 ( class_Groups_Ocomm__monoid__add(T_d)
% 168.50/168.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 168.50/168.34 => ( ! [B_x] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 168.50/168.34 => ! [B_y] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_S_2))
% 168.50/168.34 => ( B_x != B_y
% 168.50/168.34 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 168.50/168.34 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) )
% 168.50/168.34 => 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) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_folding__idem_Ounion__idem,axiom,
% 168.50/168.34 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 168.50/168.34 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 168.50/168.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.50/168.34 => 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)) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_folding__idem_Osubset__comp__idem,axiom,
% 168.50/168.34 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 168.50/168.34 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 168.50/168.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 168.50/168.34 => 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) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_folding__idem_Oidem__comp,axiom,
% 168.50/168.34 ! [V_x_2,V_F_2,V_f_2,T_c,T_b] :
% 168.50/168.34 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 168.50/168.34 => 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) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_folding__idem_Oidem__left__comp,axiom,
% 168.50/168.34 ! [V_g_2,V_x_2,T_d,V_F_2,V_f_2,T_c,T_b] :
% 168.50/168.34 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 168.50/168.34 => 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) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_folding__idem_Oin__comp__idem,axiom,
% 168.50/168.34 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 168.50/168.34 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 168.50/168.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.50/168.34 => 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) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_folding__idem_Oinsert__idem,axiom,
% 168.50/168.34 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 168.50/168.34 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 168.50/168.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.34 => 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)) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_strong__setprod__reindex__cong,axiom,
% 168.50/168.34 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 168.50/168.34 ( class_Groups_Ocomm__monoid__mult(T_d)
% 168.50/168.34 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 168.50/168.34 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 168.50/168.34 => ( ! [B_x] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.50/168.34 => 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) )
% 168.50/168.34 => 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) ) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wfI__pf,axiom,
% 168.50/168.34 ! [V_R_2,T_b] :
% 168.50/168.34 ( ! [B_A] :
% 168.50/168.34 ( 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)))
% 168.50/168.34 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
% 168.50/168.34 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Sigma__mono,axiom,
% 168.50/168.34 ! [V_D_2,V_B_2,T_c,V_C_2,V_A_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 168.50/168.34 => ( ! [B_x] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.50/168.34 => 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))) )
% 168.50/168.34 => 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))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_not__acc__down,axiom,
% 168.50/168.34 ! [V_R_2,V_x_2,T_b] :
% 168.50/168.34 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_R_2)))
% 168.50/168.34 => ~ ! [B_z] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_x_2)),V_R_2))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(T_b),B_z),c_Wellfounded_Oacc(T_b,V_R_2))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_acc_OaccI,axiom,
% 168.50/168.34 ! [V_r_2,V_x_2,T_b] :
% 168.50/168.34 ( ! [B_y] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_x_2)),V_r_2))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(T_b),B_y),c_Wellfounded_Oacc(T_b,V_r_2))) )
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_max__ext_Osimps,axiom,
% 168.50/168.34 ! [V_R_2,V_a2_2,V_a1_2,T_b] :
% 168.50/168.34 ( 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)))
% 168.50/168.34 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 168.50/168.34 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 168.50/168.34 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.34 & ! [B_x] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 168.50/168.34 => ? [B_xa] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 168.50/168.34 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_R_2)) ) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_min__max_Ofold__sup__le__sup,axiom,
% 168.50/168.34 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 168.50/168.34 ( class_Orderings_Olinorder(T_b)
% 168.50/168.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.34 => ( ! [B_x] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_c_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_b_2),V_c_2))) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Max__eqI,axiom,
% 168.50/168.34 ! [V_x_2,V_A_2,T_b] :
% 168.50/168.34 ( class_Orderings_Olinorder(T_b)
% 168.50/168.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.34 => ( ! [B_y] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_y),V_x_2)) )
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.50/168.34 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf__no__infinite__down__chainE,axiom,
% 168.50/168.34 ! [V_f_2,V_r_2,T_b] :
% 168.50/168.34 ( c_Wellfounded_Owf(T_b,V_r_2)
% 168.50/168.34 => ~ ! [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)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_iterate_Osimps,axiom,
% 168.50/168.34 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
% 168.50/168.34 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 168.50/168.34 => 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) )
% 168.50/168.34 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 168.50/168.34 => 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)) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_setsum__reindex__cong,axiom,
% 168.50/168.34 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 168.50/168.34 ( class_Groups_Ocomm__monoid__add(T_d)
% 168.50/168.34 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 168.50/168.34 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 168.50/168.34 => ( ! [B_a] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 168.50/168.34 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) )
% 168.50/168.34 => 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) ) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_scomp__unfold,axiom,
% 168.50/168.34 ! [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))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Pair__scomp,axiom,
% 168.50/168.34 ! [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) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_scomp__Pair,axiom,
% 168.50/168.34 ! [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 ).
% 168.50/168.34
% 168.50/168.34 fof(fact_scomp__scomp,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_scomp__apply,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_scomp__def,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_setsum__ivl__cong,axiom,
% 168.50/168.34 ! [V_g_2,V_f_2,V_d_2,V_b_2,V_c_2,V_a_2,T_b,T_c] :
% 168.50/168.34 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 168.50/168.34 & class_Orderings_Oord(T_b) )
% 168.50/168.34 => ( V_a_2 = V_c_2
% 168.50/168.34 => ( V_b_2 = V_d_2
% 168.50/168.34 => ( ! [B_x] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),B_x))
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_d_2))
% 168.50/168.34 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) )
% 168.50/168.34 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)) ) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_less__eq,axiom,
% 168.50/168.34 ! [V_n_2,V_m_2] :
% 168.50/168.34 ( 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)))
% 168.50/168.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf__eq__minimal,axiom,
% 168.50/168.34 ! [V_r_2,T_b] :
% 168.50/168.34 ( c_Wellfounded_Owf(T_b,V_r_2)
% 168.50/168.34 <=> ! [B_Q] :
% 168.50/168.34 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
% 168.50/168.34 => ? [B_x] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
% 168.50/168.34 & ! [B_y] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2))
% 168.50/168.34 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),B_Q)) ) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf__trancl,axiom,
% 168.50/168.34 ! [V_r_2,T_b] :
% 168.50/168.34 ( c_Wellfounded_Owf(T_b,V_r_2)
% 168.50/168.34 => c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_less__than__def,axiom,
% 168.50/168.34 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_acyclic__def,axiom,
% 168.50/168.34 ! [V_r_2,T_b] :
% 168.50/168.34 ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 168.50/168.34 <=> ! [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))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_trancl_Or__into__trancl,axiom,
% 168.50/168.34 ! [V_r_2,V_b_2,V_a_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_trancl__subset__Field2,axiom,
% 168.50/168.34 ! [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))))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_trancl__Int__subset,axiom,
% 168.50/168.34 ! [V_s_2,V_r_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 168.50/168.34 => ( 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))
% 168.50/168.34 => 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)) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_r__into__trancl_H,axiom,
% 168.50/168.34 ! [V_r_2,V_p_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_trancl__empty,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_trancl__domain,axiom,
% 168.50/168.34 ! [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) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_trancl__range,axiom,
% 168.50/168.34 ! [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) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_finite__trancl,axiom,
% 168.50/168.34 ! [V_r_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 168.50/168.34 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_r__r__into__trancl,axiom,
% 168.50/168.34 ! [V_c_2,V_R_2,V_b_2,V_a_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_R_2))
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_R_2))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_trancl__into__trancl2,axiom,
% 168.50/168.34 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom,
% 168.50/168.34 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_trancl__trans,axiom,
% 168.50/168.34 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_trancl__mono,axiom,
% 168.50/168.34 ! [V_s_2,V_r_2,V_p_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_s_2))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_trancl__unfold,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_trancl__subset__Sigma,axiom,
% 168.50/168.34 ! [V_A_2,V_r_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 168.50/168.34 => 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)))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_trancl__insert,axiom,
% 168.50/168.34 ! [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)))))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_reflcl__set__eq,axiom,
% 168.50/168.34 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 168.50/168.34 ( 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))
% 168.50/168.34 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),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)))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_acyclicI,axiom,
% 168.50/168.34 ! [V_r_2,T_b] :
% 168.50/168.34 ( ! [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)))
% 168.50/168.34 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_r__into__rtrancl,axiom,
% 168.50/168.34 ! [V_r_2,V_p_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rtrancl_Ortrancl__refl,axiom,
% 168.50/168.34 ! [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))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_IdI,axiom,
% 168.50/168.34 ! [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))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_trancl__into__rtrancl,axiom,
% 168.50/168.34 ! [V_r_2,V_b_2,V_a_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_trancl__unfold__left,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_trancl__unfold__right,axiom,
% 168.50/168.34 ! [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) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_reflcl__trancl,axiom,
% 168.50/168.34 ! [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) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_trancl__reflcl,axiom,
% 168.50/168.34 ! [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) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rtrancl__trancl__absorb,axiom,
% 168.50/168.34 ! [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) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_trancl__rtrancl__absorb,axiom,
% 168.50/168.34 ! [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) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Domain__rtrancl,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Range__rtrancl,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rtrancl__idemp,axiom,
% 168.50/168.34 ! [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) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_refl__rtrancl,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_converse__rtrancl__into__rtrancl,axiom,
% 168.50/168.34 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
% 168.50/168.34 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rtrancl__trans,axiom,
% 168.50/168.34 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rtrancl__r__diff__Id,axiom,
% 168.50/168.34 ! [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) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Image__closed__trancl,axiom,
% 168.50/168.34 ! [V_X_2,V_r_2,T_b] :
% 168.50/168.34 ( 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))
% 168.50/168.34 => hAPP(c_Relation_OImage(T_b,T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_X_2) = V_X_2 ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rtrancl__subset__rtrancl,axiom,
% 168.50/168.34 ! [V_s_2,V_r_2,T_b] :
% 168.50/168.34 ( 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)))
% 168.50/168.34 => 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))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rtrancl__subset,axiom,
% 168.50/168.34 ! [V_S_2,V_R_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2))
% 168.50/168.34 => ( 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)))
% 168.50/168.34 => c_Transitive__Closure_Ortrancl(T_b,V_S_2) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rtrancl__mono,axiom,
% 168.50/168.34 ! [V_s_2,V_r_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 168.50/168.34 => 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))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rtrancl__reflcl,axiom,
% 168.50/168.34 ! [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) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rtrancl__Un__rtrancl,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rtrancl__reflcl__absorb,axiom,
% 168.50/168.34 ! [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) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_in__rtrancl__UnI,axiom,
% 168.50/168.34 ! [V_S_2,V_R_2,V_x_2,T_b] :
% 168.50/168.34 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 168.50/168.34 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) )
% 168.50/168.34 => 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)))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rtrancl__Un__subset,axiom,
% 168.50/168.34 ! [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)))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rtrancl__Int__subset,axiom,
% 168.50/168.34 ! [V_r_2,V_s_2,T_b] :
% 168.50/168.34 ( 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))
% 168.50/168.34 => ( 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))
% 168.50/168.34 => 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)) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rtrancl__unfold,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rtrancl__idemp__self__comp,axiom,
% 168.50/168.34 ! [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) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_r__comp__rtrancl__eq,axiom,
% 168.50/168.34 ! [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) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rtrancl__empty,axiom,
% 168.50/168.34 ! [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) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_R__O__Id,axiom,
% 168.50/168.34 ! [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 ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Id__O__R,axiom,
% 168.50/168.34 ! [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 ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Image__Id,axiom,
% 168.50/168.34 ! [V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId(T_b)),V_A_2) = V_A_2 ).
% 168.50/168.34
% 168.50/168.34 fof(fact_pair__in__Id__conv,axiom,
% 168.50/168.34 ! [V_b_2,V_a_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Relation_OId(T_b)))
% 168.50/168.34 <=> V_a_2 = V_b_2 ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rtrancl__eq__or__trancl,axiom,
% 168.50/168.34 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 168.50/168.34 <=> ( V_x_2 = V_y_2
% 168.50/168.34 | ( V_x_2 != V_y_2
% 168.50/168.34 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rtrancl__into__trancl2,axiom,
% 168.50/168.34 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rtranclD,axiom,
% 168.50/168.34 ! [V_R_2,V_b_2,V_a_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 168.50/168.34 => ( V_a_2 = V_b_2
% 168.50/168.34 | ( V_a_2 != V_b_2
% 168.50/168.34 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rtrancl__into__trancl1,axiom,
% 168.50/168.34 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_trancl__rtrancl__trancl,axiom,
% 168.50/168.34 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rtrancl__trancl__trancl,axiom,
% 168.50/168.34 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Domain__Id,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Range__Id,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_refl__Id,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_pair__leq__def,axiom,
% 168.50/168.34 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))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Not__Domain__rtrancl,axiom,
% 168.50/168.34 ! [V_y_2,V_R_2,V_x_2,T_b] :
% 168.50/168.34 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_b),V_R_2)))
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 168.50/168.34 <=> V_x_2 = V_y_2 ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_acc__downwards,axiom,
% 168.50/168.34 ! [V_b_2,V_r_2,V_a_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_acc__downwards__aux,axiom,
% 168.50/168.34 ! [V_r_2,V_a_2,V_b_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf__insert,axiom,
% 168.50/168.34 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 168.50/168.34 ( 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))
% 168.50/168.34 <=> ( c_Wellfounded_Owf(T_b,V_r_2)
% 168.50/168.34 & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_acyclic__insert,axiom,
% 168.50/168.34 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 168.50/168.34 ( 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))
% 168.50/168.34 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 168.50/168.34 & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_refl__reflcl,axiom,
% 168.50/168.34 ! [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))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Id__def,axiom,
% 168.50/168.34 ! [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))))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_irrefl__diff__Id,axiom,
% 168.50/168.34 ! [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))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_pred__nat__trancl__eq__le,axiom,
% 168.50/168.34 ! [V_n_2,V_m_2] :
% 168.50/168.34 ( 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)))
% 168.50/168.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_trancl__subset__Sigma__aux,axiom,
% 168.50/168.34 ! [V_A_2,V_r_2,V_b_2,V_a_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 168.50/168.34 => ( V_a_2 = V_b_2
% 168.50/168.34 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_irrefl__tranclI,axiom,
% 168.50/168.34 ! [V_x_2,V_r_2,T_b] :
% 168.50/168.34 ( 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))
% 168.50/168.34 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_x_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_sequence__trans,axiom,
% 168.50/168.34 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_b] :
% 168.50/168.34 ( ! [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)))
% 168.50/168.34 => 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))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_total__on__diff__Id,axiom,
% 168.50/168.34 ! [V_r_2,V_A_2,T_b] :
% 168.50/168.34 ( 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)))
% 168.50/168.34 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rtrancl__converse,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_converse__Id,axiom,
% 168.50/168.34 ! [T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId(T_b)) = c_Relation_OId(T_b) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_acyclic__converse,axiom,
% 168.50/168.34 ! [V_r_2,T_b] :
% 168.50/168.34 ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 168.50/168.34 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_converseD,axiom,
% 168.50/168.34 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),V_r_2)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_converseI,axiom,
% 168.50/168.34 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_converse__iff,axiom,
% 168.50/168.34 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
% 168.50/168.34 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),V_r_2)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_converse__INTER,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_converse__Int,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_converse__Id__on,axiom,
% 168.50/168.34 ! [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) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_converse__inv__image,axiom,
% 168.50/168.34 ! [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) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Field__converse,axiom,
% 168.50/168.34 ! [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) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_converse__converse,axiom,
% 168.50/168.34 ! [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 ).
% 168.50/168.34
% 168.50/168.34 fof(fact_total__on__converse,axiom,
% 168.50/168.34 ! [V_r_2,V_A_2,T_b] :
% 168.50/168.34 ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 168.50/168.34 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_finite__converse,axiom,
% 168.50/168.34 ! [V_r_2,T_c,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
% 168.50/168.34 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_b)),V_r_2)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_refl__on__converse,axiom,
% 168.50/168.34 ! [V_r_2,V_A_2,T_b] :
% 168.50/168.34 ( c_Relation_Orefl__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 168.50/168.34 <=> c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_converse__Un,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_converse__rel__comp,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_converse__UNION,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_trancl__converse,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf__converse__trancl,axiom,
% 168.50/168.34 ! [V_r_2,T_b] :
% 168.50/168.34 ( c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 168.50/168.34 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_equiv__comp__eq,axiom,
% 168.50/168.34 ! [V_r_2,V_A_2,T_b] :
% 168.50/168.34 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 168.50/168.34 => 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 ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Range__def,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Domain__converse,axiom,
% 168.50/168.34 ! [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) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Range__converse,axiom,
% 168.50/168.34 ! [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) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_total__on__empty,axiom,
% 168.50/168.34 ! [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) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rtrancl__converseD,axiom,
% 168.50/168.34 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rtrancl__converseI,axiom,
% 168.50/168.34 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_trancl__converseD,axiom,
% 168.50/168.34 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_trancl__converseI,axiom,
% 168.50/168.34 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Image__subset__eq,axiom,
% 168.50/168.34 ! [V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 168.50/168.34 ( 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))
% 168.50/168.34 <=> 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))))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_refl__on__comp__subset,axiom,
% 168.50/168.34 ! [V_r_2,V_A_2,T_b] :
% 168.50/168.34 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_comp__equivI,axiom,
% 168.50/168.34 ! [V_A_2,V_r_2,T_b] :
% 168.50/168.34 ( 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
% 168.50/168.34 => ( hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) = V_A_2
% 168.50/168.34 => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_finite__acyclic__wf__converse,axiom,
% 168.50/168.34 ! [V_r_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 168.50/168.34 => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 168.50/168.34 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_total__on__def,axiom,
% 168.50/168.34 ! [V_r_2,V_A_2,T_b] :
% 168.50/168.34 ( c_Relation_Ototal__on(T_b,V_A_2,V_r_2)
% 168.50/168.34 <=> ! [B_x] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.50/168.34 => ! [B_xa] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 168.50/168.34 => ( B_x != B_xa
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_r_2))
% 168.50/168.34 | 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)) ) ) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_converse__def,axiom,
% 168.50/168.34 ! [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))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Image__INT__eq,axiom,
% 168.50/168.34 ! [V_B_2,T_d,V_A_2,V_r_2,T_c,T_b] :
% 168.50/168.34 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))
% 168.50/168.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
% 168.50/168.34 => 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)) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rtrancl__imp__UN__rel__pow,axiom,
% 168.50/168.34 ! [V_R_2,V_p_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 168.50/168.34 => 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)))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_single__valued__Id,axiom,
% 168.50/168.34 ! [T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId(T_b)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rel__pow__1,axiom,
% 168.50/168.34 ! [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 ).
% 168.50/168.34
% 168.50/168.34 fof(fact_single__valued__rel__pow,axiom,
% 168.50/168.34 ! [V_n_2,V_R_2,T_b] :
% 168.50/168.34 ( c_Relation_Osingle__valued(T_b,T_b,V_R_2)
% 168.50/168.34 => 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)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rel__pow__commute,axiom,
% 168.50/168.34 ! [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) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_comp__funpow,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_wf__exp,axiom,
% 168.50/168.34 ! [V_R_2,V_n_2,T_b] :
% 168.50/168.34 ( 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))
% 168.50/168.34 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_single__valued__subset,axiom,
% 168.50/168.34 ! [V_s_2,V_r_2,T_c,T_b] :
% 168.50/168.34 ( 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))
% 168.50/168.34 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2)
% 168.50/168.34 => c_Relation_Osingle__valued(T_b,T_c,V_r_2) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_funpow__mult,axiom,
% 168.50/168.34 ! [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) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_funpow__swap1,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_single__valued__rel__comp,axiom,
% 168.50/168.34 ! [V_s_2,T_d,V_r_2,T_c,T_b] :
% 168.50/168.34 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 168.50/168.34 => ( c_Relation_Osingle__valued(T_c,T_d,V_s_2)
% 168.50/168.34 => 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)) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rel__pow__imp__rtrancl,axiom,
% 168.50/168.34 ! [V_R_2,V_n_2,V_p_2,T_b] :
% 168.50/168.34 ( 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)))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rtrancl__power,axiom,
% 168.50/168.34 ! [V_R_2,V_p_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 168.50/168.34 <=> ? [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))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_single__valued__Id__on,axiom,
% 168.50/168.34 ! [V_A_2,T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_relpow_Osimps_I2_J,axiom,
% 168.50/168.34 ! [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) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rel__pow__add,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_relpow_Osimps_I1_J,axiom,
% 168.50/168.34 ! [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) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rel__pow__0__E,axiom,
% 168.50/168.34 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),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)))
% 168.50/168.34 => V_x_2 = V_y_2 ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rel__pow__0__I,axiom,
% 168.50/168.34 ! [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))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rel__pow__Suc__I,axiom,
% 168.50/168.34 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),V_R_2))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rel__pow__Suc__I2,axiom,
% 168.50/168.34 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_R_2))
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_funpow_Osimps_I2_J,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_funpow__add,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_single__valuedD,axiom,
% 168.50/168.34 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_c,T_b] :
% 168.50/168.34 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),V_r_2))
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_z_2)),V_r_2))
% 168.50/168.34 => V_y_2 = V_z_2 ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_single__valued__def,axiom,
% 168.50/168.34 ! [V_r_2,T_c,T_b] :
% 168.50/168.34 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 168.50/168.34 <=> ! [B_x,B_y] :
% 168.50/168.34 ( 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))
% 168.50/168.34 => ! [B_z] :
% 168.50/168.34 ( 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))
% 168.50/168.34 => B_y = B_z ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_funpow_Osimps_I1_J,axiom,
% 168.50/168.34 ! [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) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_trancl__power,axiom,
% 168.50/168.34 ! [V_R_2,V_p_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
% 168.50/168.34 <=> ? [B_n] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 168.50/168.34 & 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))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rtrancl__is__UN__rel__pow,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_single__valued__confluent,axiom,
% 168.50/168.34 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
% 168.50/168.34 ( c_Relation_Osingle__valued(T_b,T_b,V_r_2)
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 168.50/168.34 | 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))) ) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Image__Int__eq,axiom,
% 168.50/168.34 ! [V_B_2,V_A_2,V_R_2,T_c,T_b] :
% 168.50/168.34 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_R_2))
% 168.50/168.34 => 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)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_funpow__code__def,axiom,
% 168.50/168.34 ! [T_b] : c_Nat_Ofunpow(T_b) = c_Nat_Ocompow(T_b,T_b) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rel__pow__E,axiom,
% 168.50/168.34 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
% 168.50/168.34 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.50/168.34 => V_x_2 != V_z_2 )
% 168.50/168.34 => ~ ! [B_y,B_m] :
% 168.50/168.34 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_m),V_R_2)))
% 168.50/168.34 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),V_R_2)) ) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rel__pow__E2,axiom,
% 168.50/168.34 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
% 168.50/168.34 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.50/168.34 => V_x_2 != V_z_2 )
% 168.50/168.34 => ~ ! [B_y,B_m] :
% 168.50/168.34 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2))
% 168.50/168.34 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_m),V_R_2))) ) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rtrancl__Un__separatorE,axiom,
% 168.50/168.34 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2),V_Q_2))))
% 168.50/168.34 => ( ! [B_x] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),B_x)),c_Transitive__Closure_Ortrancl(T_b,V_P_2)))
% 168.50/168.34 => ! [B_y] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_Q_2))
% 168.50/168.34 => B_x = B_y ) )
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_P_2))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rtrancl__Un__separator__converseE,axiom,
% 168.50/168.34 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2),V_Q_2))))
% 168.50/168.34 => ( ! [B_x] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_P_2)))
% 168.50/168.34 => ! [B_y] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_Q_2))
% 168.50/168.34 => B_y = B_x ) )
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_P_2))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rel__pow__Suc__E,axiom,
% 168.50/168.34 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
% 168.50/168.34 => ~ ! [B_y] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
% 168.50/168.34 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),V_R_2)) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rel__pow__Suc__D2,axiom,
% 168.50/168.34 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
% 168.50/168.34 => ? [B_y] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2))
% 168.50/168.34 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rel__pow__Suc__E2,axiom,
% 168.50/168.34 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
% 168.50/168.34 => ~ ! [B_y] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2))
% 168.50/168.34 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_tranclD2,axiom,
% 168.50/168.34 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
% 168.50/168.34 => ? [B_z] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_z)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 168.50/168.34 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_y_2)),V_R_2)) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_tranclD,axiom,
% 168.50/168.34 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
% 168.50/168.34 => ? [B_z] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_z)),V_R_2))
% 168.50/168.34 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_IdE,axiom,
% 168.50/168.34 ! [V_p_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Relation_OId(T_b)))
% 168.50/168.34 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_transfer__nat__int__set__cong,axiom,
% 168.50/168.34 ! [V_P_H_2,V_P_2] :
% 168.50/168.34 ( ! [B_x] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 168.50/168.34 => ( hBOOL(hAPP(V_P_2,B_x))
% 168.50/168.34 <=> hBOOL(hAPP(V_P_H_2,B_x)) ) )
% 168.50/168.34 => hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_H_2)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Int__Collect__mono,axiom,
% 168.50/168.34 ! [V_Q_2,V_P_2,V_B_2,V_A_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.50/168.34 => ( ! [B_x] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.50/168.34 => ( hBOOL(hAPP(V_P_2,B_x))
% 168.50/168.34 => hBOOL(hAPP(V_Q_2,B_x)) ) )
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_OCollect(T_b),V_Q_2)))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rel__compE,axiom,
% 168.50/168.34 ! [V_s_2,V_r_2,T_d,V_xz_2,T_c,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_xz_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_r_2),V_s_2)))
% 168.50/168.34 => ~ ! [B_x,B_y,B_z] :
% 168.50/168.34 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),B_x),B_y)),V_r_2))
% 168.50/168.34 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),B_y),B_z)),V_s_2)) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_converseE,axiom,
% 168.50/168.34 ! [V_r_2,V_yx_2,T_c,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_yx_2),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
% 168.50/168.34 => ~ ! [B_x,B_y] :
% 168.50/168.34 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_y),B_x)
% 168.50/168.34 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),B_y)),V_r_2)) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Nitpick_Oplus__frac__def,axiom,
% 168.50/168.34 ! [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))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Nitpick_Otimes__frac__def,axiom,
% 168.50/168.34 ! [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))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Nitpick_Oof__frac__def,axiom,
% 168.50/168.34 ! [V_q,T_a,T_b] :
% 168.50/168.34 ( ( class_Rings_Oinverse(T_b)
% 168.50/168.34 & class_Rings_Oring__1(T_b) )
% 168.50/168.34 => 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))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Nitpick_Oinverse__frac__def,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Nitpick_Ouminus__frac__def,axiom,
% 168.50/168.34 ! [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))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Nitpick_Oless__frac__def,axiom,
% 168.50/168.34 ! [V_r_2,V_q_2,T_b] :
% 168.50/168.34 ( c_Nitpick_Oless__frac(T_b,V_q_2,V_r_2)
% 168.50/168.34 <=> 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))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Nitpick_Oless__eq__frac__def,axiom,
% 168.50/168.34 ! [V_r_2,V_q_2,T_b] :
% 168.50/168.34 ( c_Nitpick_Oless__eq__frac(T_b,V_q_2,V_r_2)
% 168.50/168.34 <=> 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))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Nitpick_Odenom__def,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Nitpick_Onum__def,axiom,
% 168.50/168.34 ! [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)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_internal__split__def,axiom,
% 168.50/168.34 ! [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) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_bool_Osize_I2_J,axiom,
% 168.50/168.34 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_internal__split__conv,axiom,
% 168.50/168.34 ! [V_b_2,V_a_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ointernal__split(T_c,T_d,T_b),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_c_2,V_a_2),V_b_2) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_bool_Osize_I1_J,axiom,
% 168.50/168.34 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_finite__less__ub,axiom,
% 168.50/168.34 ! [V_u_2,V_f_2] :
% 168.50/168.34 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_n),hAPP(V_f_2,B_n)))
% 168.50/168.34 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),V_f_2)),V_u_2)))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_lenlex__def,axiom,
% 168.50/168.34 ! [V_r_2,T_b] : c_List_Olenlex(T_b,V_r_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(T_b)),tc_List_Olist(T_b)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(T_b),c_Wellfounded_Oless__than,c_List_Olex(T_b,V_r_2))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_prod(tc_Nat_Onat,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(T_b),tc_prod(tc_Nat_Onat,tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(T_b))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_COMBI(tc_List_Olist(T_b)))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_neq__if__length__neq,axiom,
% 168.50/168.34 ! [V_ys,V_xs,T_a] :
% 168.50/168.34 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)
% 168.50/168.34 => V_xs != V_ys ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_lexn__length,axiom,
% 168.50/168.34 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)))
% 168.50/168.34 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = V_n_2
% 168.50/168.34 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_lenlex__conv,axiom,
% 168.50/168.34 ! [V_r_2,T_b] : c_List_Olenlex(T_b,V_r_2) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBC(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))))),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b))))),c_List_Olex(T_b,V_r_2)))))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_length__sublist,axiom,
% 168.50/168.34 ! [V_I_2,V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Osublist(T_b,V_xs_2,V_I_2)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_I_2)))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_lexn_Osimps_I2_J,axiom,
% 168.50/168.34 ! [V_n_2,V_r_2,T_b] : hAPP(c_List_Olexn(T_b,V_r_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(T_b,tc_List_Olist(T_b)),tc_prod(T_b,tc_List_Olist(T_b))),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_Product__Type_Omap__pair(tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)))),c_Wellfounded_Olex__prod(T_b,tc_List_Olist(T_b),V_r_2,hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,V_n_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,V_n_2)))))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_impossible__Cons,axiom,
% 168.50/168.34 ! [V_x,V_ys,V_xs,T_a] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)))
% 168.50/168.34 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_not__Cons__self,axiom,
% 168.50/168.34 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_not__Cons__self2,axiom,
% 168.50/168.34 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ).
% 168.50/168.34
% 168.50/168.34 fof(fact_list_Oinject,axiom,
% 168.50/168.34 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_b] :
% 168.50/168.34 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_list_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_H_2),V_list_H_2)
% 168.50/168.34 <=> ( V_a_2 = V_a_H_2
% 168.50/168.34 & V_list_2 = V_list_H_2 ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_list_Osize_I4_J,axiom,
% 168.50/168.34 ! [V_list,V_a,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a),V_list)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_list)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Cons__in__lex,axiom,
% 168.50/168.34 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olex(T_b,V_r_2)))
% 168.50/168.34 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 168.50/168.34 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) )
% 168.50/168.34 | ( V_x_2 = V_y_2
% 168.50/168.34 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olex(T_b,V_r_2))) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_set__Cons__def,axiom,
% 168.50/168.34 ! [V_XS_2,V_A_2,T_b] : c_List_Oset__Cons(T_b,V_A_2,V_XS_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(T_b)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),c_COMBS(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),T_b),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_List_Olist(T_b),tc_HOL_Obool,tc_List_Olist(T_b))),c_fequal))),c_List_Olist_OCons(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_b))),V_XS_2)))))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_pick_Osimps,axiom,
% 168.50/168.34 ! [V_xs,V_x,T_a,V_i] :
% 168.50/168.34 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x)))
% 168.50/168.34 => hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),V_x),V_xs)),V_i) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_a),V_x) )
% 168.50/168.34 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x)))
% 168.50/168.34 => hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),V_x),V_xs)),V_i) = hAPP(c_Random_Opick(T_a,V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_select__weight__cons__zero,axiom,
% 168.50/168.34 ! [V_xs_2,V_x_2,T_b] : c_Random_Oselect__weight(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_x_2)),V_xs_2)) = c_Random_Oselect__weight(T_b,V_xs_2) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_lexord__cons__cons,axiom,
% 168.50/168.34 ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_x_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_y_2))),c_List_Olexord(T_b,V_r_2)))
% 168.50/168.34 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 168.50/168.34 | ( V_a_2 = V_b_2
% 168.50/168.34 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_lexord__lex,axiom,
% 168.50/168.34 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olex(T_b,V_r_2)))
% 168.50/168.34 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
% 168.50/168.34 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rtrancl__listrel1__ConsI2,axiom,
% 168.50/168.34 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_list_Osize_I2_J,axiom,
% 168.50/168.34 ! [V_list_2,V_a_2,V_fa_2,T_b] : c_List_Olist_Olist__size(T_b,V_fa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_list_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),c_List_Olist_Olist__size(T_b,V_fa_2,V_list_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Cons__acc__listrel1I,axiom,
% 168.50/168.34 ! [V_xs_2,V_r_2,V_x_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom,
% 168.50/168.34 ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_listrel1__converse,axiom,
% 168.50/168.34 ! [V_r_2,T_b] : c_List_Olistrel1(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olistrel1(T_b,V_r_2)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_listrel1__mono,axiom,
% 168.50/168.34 ! [V_s_2,V_r_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,V_r_2)),c_List_Olistrel1(T_b,V_s_2))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_listrel1I2,axiom,
% 168.50/168.34 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_ys_2))),c_List_Olistrel1(T_b,V_r_2))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rtrancl__listrel1__ConsI1,axiom,
% 168.50/168.34 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_listrel1__eq__len,axiom,
% 168.50/168.34 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 168.50/168.34 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rtrancl__listrel1__eq__len,axiom,
% 168.50/168.34 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
% 168.50/168.34 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_in__listrel1__converse,axiom,
% 168.50/168.34 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olistrel1(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
% 168.50/168.34 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olistrel1(T_b,V_r_2)))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_listrel1I1,axiom,
% 168.50/168.34 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_xs_2))),c_List_Olistrel1(T_b,V_r_2))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Cons__listrel1__Cons,axiom,
% 168.50/168.34 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel1(T_b,V_r_2)))
% 168.50/168.34 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 168.50/168.34 & V_xs_2 = V_ys_2 )
% 168.50/168.34 | ( V_x_2 = V_y_2
% 168.50/168.34 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_listrel__Cons,axiom,
% 168.50/168.34 ! [V_xs_2,V_x_2,V_r_2,T_b] : hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = c_List_Oset__Cons(T_b,hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),V_xs_2),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_lexord__irreflexive,axiom,
% 168.50/168.34 ! [V_y_2,V_r_2,T_b] :
% 168.50/168.34 ( ! [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))
% 168.50/168.34 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_listrel__rtrancl__refl,axiom,
% 168.50/168.34 ! [V_r_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_xs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_listrel__mono,axiom,
% 168.50/168.34 ! [V_s_2,V_r_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),c_List_Olistrel(T_b,V_s_2))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_listrel__subset__rtrancl__listrel1,axiom,
% 168.50/168.34 ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_listrel__eq__len,axiom,
% 168.50/168.34 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
% 168.50/168.34 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_listrel__rtrancl__trans,axiom,
% 168.50/168.34 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))))
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_ys_2),V_zs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_zs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
% 168.50/168.34 ! [V_r_2,T_b] : c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_listrel__reflcl__if__listrel1,axiom,
% 168.50/168.34 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_listrel1__subset__listrel,axiom,
% 168.50/168.34 ! [V_r_H_2,V_r_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_r_H_2))
% 168.50/168.34 => ( c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_r_H_2)
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,V_r_2)),c_List_Olistrel(T_b,V_r_H_2))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_rtrancl__listrel1__if__listrel,axiom,
% 168.50/168.34 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_listrel_OCons,axiom,
% 168.50/168.34 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel(T_b,V_r_2))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_listrelp__listrel__eq,axiom,
% 168.50/168.34 ! [V_xa_2,V_x_2,V_r_2,T_b] :
% 168.50/168.34 ( c_List_Olistrelp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2),V_x_2,V_xa_2)
% 168.50/168.34 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_xa_2)),c_List_Olistrel(T_b,V_r_2))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_listrel__Cons2,axiom,
% 168.50/168.34 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel(T_b,V_r_2)))
% 168.50/168.34 => ~ ! [B_x,B_xs] :
% 168.50/168.34 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs)
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_y_2)),V_r_2))
% 168.50/168.34 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),B_xs),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_listrelp_OCons,axiom,
% 168.50/168.34 ! [V_ys_2,V_xs_2,T_b,V_y_2,V_x_2,V_r_2] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 168.50/168.34 => ( c_List_Olistrelp(T_b,V_r_2,V_xs_2,V_ys_2)
% 168.50/168.34 => c_List_Olistrelp(T_b,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_listrelp_Oequations_I2_J,axiom,
% 168.50/168.34 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_b] :
% 168.50/168.34 ( c_List_Olistrelp(T_b,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a3_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a4_2))
% 168.50/168.34 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2))
% 168.50/168.34 & c_List_Olistrelp(T_b,V_r_2,V_a3_2,V_a4_2) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_listrel__Cons1,axiom,
% 168.50/168.34 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)),V_xs_2)),c_List_Olistrel(T_b,V_r_2)))
% 168.50/168.34 => ~ ! [B_y,B_ys] :
% 168.50/168.34 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_ys)
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),B_y)),V_r_2))
% 168.50/168.34 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_ys_2),B_ys)),c_List_Olistrel(T_b,V_r_2))) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_listrel__subset,axiom,
% 168.50/168.34 ! [V_A_2,V_r_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olists(T_b,V_A_2)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_List_Olist(T_b)),c_List_Olists(T_b,V_A_2))))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_lists__UNIV,axiom,
% 168.50/168.34 ! [T_b] : c_List_Olists(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_lists__mono,axiom,
% 168.50/168.34 ! [V_B_2,V_A_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),c_List_Olists(T_b,V_A_2)),c_List_Olists(T_b,V_B_2))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_equiv__listrel,axiom,
% 168.50/168.34 ! [V_r_2,V_A_2,T_b] :
% 168.50/168.34 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 168.50/168.34 => c_Equiv__Relations_Oequiv(tc_List_Olist(T_b),c_List_Olists(T_b,V_A_2),c_List_Olistrel(T_b,V_r_2)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_listrel__refl__on,axiom,
% 168.50/168.34 ! [V_r_2,V_A_2,T_b] :
% 168.50/168.34 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 168.50/168.34 => c_Relation_Orefl__on(tc_List_Olist(T_b),c_List_Olists(T_b,V_A_2),c_List_Olistrel(T_b,V_r_2)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_Cons__in__lists__iff,axiom,
% 168.50/168.34 ! [V_A_2,V_xs_2,V_x_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_List_Olists(T_b,V_A_2)))
% 168.50/168.34 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.50/168.34 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_lists__accI,axiom,
% 168.50/168.34 ! [V_r_2,V_xs_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,c_Wellfounded_Oacc(T_b,V_r_2)))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_lists__accD,axiom,
% 168.50/168.34 ! [V_r_2,V_xs_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,c_Wellfounded_Oacc(T_b,V_r_2))))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_listrel__iff__nth,axiom,
% 168.50/168.34 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
% 168.50/168.34 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 168.50/168.34 & ! [B_n] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_n))),V_r_2)) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_lexord__linear,axiom,
% 168.50/168.34 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 168.50/168.34 ( ! [B_a,B_b] :
% 168.50/168.34 ( 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))
% 168.50/168.34 | B_a = B_b
% 168.50/168.34 | 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)) )
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
% 168.50/168.34 | V_x_2 = V_y_2
% 168.50/168.34 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_x_2)),c_List_Olexord(T_b,V_r_2))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_infinite__UNIV__listI,axiom,
% 168.50/168.34 ! [T_b] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_list__eq__iff__nth__eq,axiom,
% 168.50/168.34 ! [T_b,V_ys_2,V_xs_2] :
% 168.50/168.34 ( V_xs_2 = V_ys_2
% 168.50/168.34 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 168.50/168.34 & ! [B_i] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 168.50/168.34 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_nth__Cons__Suc,axiom,
% 168.50/168.34 ! [V_n,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_nth__Cons__0,axiom,
% 168.50/168.34 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_x ).
% 168.50/168.34
% 168.50/168.34 fof(fact_nth_Osimps,axiom,
% 168.50/168.34 ! [V_n_2,V_xs_2,V_x_2,T_b] : hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_n_2) = c_Nat_Onat_Onat__case(T_b,V_x_2,hAPP(c_List_Onth(T_b),V_xs_2),V_n_2) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_nth__Cons_H,axiom,
% 168.50/168.34 ! [V_xs,V_x,T_a,V_n] :
% 168.50/168.34 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.50/168.34 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x )
% 168.50/168.34 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.50/168.34 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_nth__Cons__number__of,axiom,
% 168.50/168.34 ! [V_xs,V_x,T_a,V_v] :
% 168.50/168.34 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.50/168.34 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = V_x )
% 168.50/168.34 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.50/168.34 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_lexord__take__index__conv,axiom,
% 168.50/168.34 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
% 168.50/168.34 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2)))
% 168.50/168.34 & hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),V_y_2) = V_x_2 )
% 168.50/168.34 | ? [B_i] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2))))
% 168.50/168.34 & hAPP(hAPP(c_List_Otake(T_b),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_b),B_i),V_y_2)
% 168.50/168.34 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_x_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_y_2),B_i))),V_r_2)) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_set__sublist,axiom,
% 168.50/168.34 ! [V_I_2,V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_b),V_xs_2))))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_I_2))))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_finite__set,axiom,
% 168.50/168.34 ! [V_xs_2,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_set__subset__Cons,axiom,
% 168.50/168.34 ! [V_x_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_take__all,axiom,
% 168.50/168.34 ! [V_n,V_xs,T_a] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n))
% 168.50/168.34 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_set__take__subset__set__take,axiom,
% 168.50/168.34 ! [V_xs_2,T_b,V_n_2,V_m_2] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2)))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_set__take__subset,axiom,
% 168.50/168.34 ! [V_xs_2,V_n_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_set__sublist__subset,axiom,
% 168.50/168.34 ! [V_I_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_nth__take,axiom,
% 168.50/168.34 ! [V_xs,T_a,V_n,V_i] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
% 168.50/168.34 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),V_i) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_take__Suc__Cons,axiom,
% 168.50/168.34 ! [V_xs,V_x,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_notin__set__sublistI,axiom,
% 168.50/168.34 ! [V_I_2,V_xs_2,V_x_2,T_b] :
% 168.50/168.34 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.34 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2)))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_in__set__takeD,axiom,
% 168.50/168.34 ! [V_xs_2,V_n_2,V_x_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2))))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_in__set__sublistD,axiom,
% 168.50/168.34 ! [V_I_2,V_xs_2,V_x_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_set__ConsD,axiom,
% 168.50/168.34 ! [V_xs_2,V_x_2,V_y_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))))
% 168.50/168.34 => ( V_y_2 = V_x_2
% 168.50/168.34 | hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_length__take,axiom,
% 168.50/168.34 ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_take__take,axiom,
% 168.50/168.34 ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Otake(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_n),V_m)),V_xs) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_List_Oset_Osimps_I2_J,axiom,
% 168.50/168.34 ! [V_xs_2,V_x_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_sublist__upt__eq__take,axiom,
% 168.50/168.34 ! [V_n_2,V_l_2,T_b] : c_List_Osublist(T_b,V_l_2,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) = hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_l_2) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_card__length,axiom,
% 168.50/168.34 ! [V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_all__set__conv__all__nth,axiom,
% 168.50/168.34 ! [V_P_2,V_xs_2,T_b] :
% 168.50/168.34 ( ! [B_x] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.34 => hBOOL(hAPP(V_P_2,B_x)) )
% 168.50/168.34 <=> ! [B_i] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 168.50/168.34 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_list__size__estimation,axiom,
% 168.50/168.34 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_list__size__estimation_H,axiom,
% 168.50/168.34 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_in__lists__conv__set,axiom,
% 168.50/168.34 ! [V_A_2,V_xs_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
% 168.50/168.34 <=> ! [B_x] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_length__pos__if__in__set,axiom,
% 168.50/168.34 ! [V_xs_2,V_x_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_nth__mem,axiom,
% 168.50/168.34 ! [V_xs_2,T_b,V_n_2] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2)),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_in__set__conv__nth,axiom,
% 168.50/168.34 ! [V_xs_2,V_x_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.34 <=> ? [B_i] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 168.50/168.34 & hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = V_x_2 ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_lists__eq__set,axiom,
% 168.50/168.34 ! [V_A_2,T_b] : c_List_Olists(T_b,V_A_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_set__conv__nth,axiom,
% 168.50/168.34 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_b),V_xs_2))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_finite__lists__length__eq,axiom,
% 168.50/168.34 ! [V_n_2,V_A_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.34 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2))))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_finite__lists__length__le,axiom,
% 168.50/168.34 ! [V_n_2,V_A_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.34 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2))))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_listrel__iff__zip,axiom,
% 168.50/168.34 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
% 168.50/168.34 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 168.50/168.34 & ! [B_x] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_ys_2))))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),B_x)) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_set__zip,axiom,
% 168.50/168.34 ! [V_ys_2,V_xs_2,T_c,T_b] : hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_b,T_c)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_c),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_b,T_c)),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_prod(T_b,T_c)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_c),tc_fun(tc_Nat_Onat,tc_prod(T_b,T_c)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(T_b,T_c)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_b,T_c)),c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),tc_Nat_Onat),c_Product__Type_OPair(T_b,T_c)),hAPP(c_List_Onth(T_b),V_xs_2))),hAPP(c_List_Onth(T_c),V_ys_2)))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_take__zip,axiom,
% 168.50/168.34 ! [V_ys,V_xs,V_n,T_b,T_a] : hAPP(hAPP(c_List_Otake(tc_prod(T_a,T_b)),V_n),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) = hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Otake(T_b),V_n),V_ys)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_length__zip,axiom,
% 168.50/168.34 ! [V_ys,V_xs,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(T_a,T_b))),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_zip__Cons__Cons,axiom,
% 168.50/168.34 ! [V_ys,V_y,V_xs,V_x,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y),V_ys)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_list__eq__iff__zip__eq,axiom,
% 168.50/168.34 ! [T_b,V_ys_2,V_xs_2] :
% 168.50/168.34 ( V_xs_2 = V_ys_2
% 168.50/168.34 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 168.50/168.34 & ! [B_x] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_ys_2))))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_zip__same,axiom,
% 168.50/168.34 ! [V_xs_2,V_b_2,V_a_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_xs_2))))
% 168.50/168.34 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.34 & V_a_2 = V_b_2 ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_set__zip__leftD,axiom,
% 168.50/168.34 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_set__zip__rightD,axiom,
% 168.50/168.34 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_in__set__zipE,axiom,
% 168.50/168.34 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
% 168.50/168.34 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.34 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_nth__zip,axiom,
% 168.50/168.34 ! [V_ys,T_b,V_xs,T_a,V_i] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)))
% 168.50/168.34 => hAPP(hAPP(c_List_Onth(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Onth(T_b),V_ys),V_i)) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_greaterThanLessThan__upto,axiom,
% 168.50/168.34 ! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_j_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_listsum__setsum__nth,axiom,
% 168.50/168.34 ! [V_xs_2,T_b] :
% 168.50/168.34 ( class_Groups_Ocomm__monoid__add(T_b)
% 168.50/168.34 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(c_List_Onth(T_b),V_xs_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_set__upto,axiom,
% 168.50/168.34 ! [V_j_2,V_i_2] : hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_atLeastAtMost__upto,axiom,
% 168.50/168.34 ! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_listsum__eq__0__nat__iff__nat,axiom,
% 168.50/168.34 ! [V_ns_2] :
% 168.50/168.34 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.50/168.34 <=> ! [B_x] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 168.50/168.34 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_listsum__simps_I2_J,axiom,
% 168.50/168.34 ! [V_xs,V_x,T_a] :
% 168.50/168.34 ( class_Groups_Omonoid__add(T_a)
% 168.50/168.34 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_elem__le__listsum__nat,axiom,
% 168.50/168.34 ! [V_ns,V_k] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),V_ns)))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),V_ns),V_k)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_atLeastLessThan__upto,axiom,
% 168.50/168.34 ! [V_j_2,V_i_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_i_2),V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_j_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_greaterThanAtMost__upto,axiom,
% 168.50/168.34 ! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_nat__list__def,axiom,
% 168.50/168.34 ! [V_l_2] :
% 168.50/168.34 ( c_List_Onat__list(V_l_2)
% 168.50/168.34 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_list__size__pointwise,axiom,
% 168.50/168.34 ! [V_g_2,V_f_2,V_xs_2,T_b] :
% 168.50/168.34 ( ! [B_x] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 168.50/168.34 => 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))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_listsum__update__nat,axiom,
% 168.50/168.34 ! [V_n,V_ns,V_k] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),V_ns)))
% 168.50/168.34 => hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,V_ns),V_k),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns)),V_n)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),V_ns),V_k)) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_butlast__take,axiom,
% 168.50/168.34 ! [V_xs,T_a,V_n] :
% 168.50/168.34 ( 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)))
% 168.50/168.34 => 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) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_list__update__beyond,axiom,
% 168.50/168.34 ! [V_x,V_i,V_xs,T_a] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i))
% 168.50/168.34 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_nth__list__update__neq,axiom,
% 168.50/168.34 ! [V_x,V_xs,T_a,V_j,V_i] :
% 168.50/168.34 ( V_i != V_j
% 168.50/168.34 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_list__update__id,axiom,
% 168.50/168.34 ! [V_i,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)) = V_xs ).
% 168.50/168.34
% 168.50/168.34 fof(fact_butlast__list__update,axiom,
% 168.50/168.34 ! [V_x,V_xs,T_a,V_k] :
% 168.50/168.34 ( ( 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))
% 168.50/168.34 => 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) )
% 168.50/168.34 & ( 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))
% 168.50/168.34 => 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) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_length__list__update,axiom,
% 168.50/168.34 ! [V_x,V_i,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_zip__update,axiom,
% 168.50/168.34 ! [V_y,V_ys,V_x,V_i,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),hAPP(hAPP(c_List_Olist__update(T_b,V_ys),V_i),V_y)) = hAPP(hAPP(c_List_Olist__update(tc_prod(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_update__zip,axiom,
% 168.50/168.34 ! [V_xy,V_i,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Olist__update(tc_prod(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i),V_xy) = hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),hAPP(c_Product__Type_Ofst(T_a,T_b),V_xy))),hAPP(hAPP(c_List_Olist__update(T_b,V_ys),V_i),hAPP(c_Product__Type_Osnd(T_a,T_b),V_xy))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_list__update__overwrite,axiom,
% 168.50/168.34 ! [V_y,V_x,V_i,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i),V_y) = hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_y) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_list__update__swap,axiom,
% 168.50/168.34 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] :
% 168.50/168.34 ( V_i != V_i_H
% 168.50/168.34 => hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i_H),V_x_H) = hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i_H),V_x_H)),V_i),V_x) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_list__update__code_I3_J,axiom,
% 168.50/168.34 ! [V_y,V_i,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Nat_OSuc,V_i)),V_y) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_y)) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_list__update__code_I2_J,axiom,
% 168.50/168.34 ! [V_y,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_y) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_list__update_Osimps_I2_J,axiom,
% 168.50/168.34 ! [V_v_2,V_i_2,V_xs_2,V_x_2,T_b] : hAPP(hAPP(c_List_Olist__update(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_i_2),V_v_2) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_v_2),V_xs_2),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_b),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_b,tc_List_Olist(T_b)),c_List_Olist__update(T_b,V_xs_2)),V_v_2)),V_i_2) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_in__set__butlastD,axiom,
% 168.50/168.34 ! [V_xs_2,V_x_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_set__update__subsetI,axiom,
% 168.50/168.34 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_b] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),V_A_2))
% 168.50/168.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.50/168.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2))),V_A_2)) ) ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_set__update__subset__insert,axiom,
% 168.50/168.34 ! [V_x_2,V_i_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2))),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_nth__list__update__eq,axiom,
% 168.50/168.34 ! [V_x,V_xs,T_a,V_i] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 168.50/168.34 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i) = V_x ) ).
% 168.50/168.34
% 168.50/168.34 fof(fact_list__update__same__conv,axiom,
% 168.50/168.34 ! [V_x_2,V_xs_2,T_b,V_i_2] :
% 168.50/168.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 168.50/168.34 => ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2) = V_xs_2
% 168.50/168.34 <=> hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = V_x_2 ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_nth__list__update,axiom,
% 168.50/168.35 ! [V_x,V_j,V_xs,T_a,V_i] :
% 168.50/168.35 ( 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)))
% 168.50/168.35 => ( ( V_i = V_j
% 168.50/168.35 => 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 )
% 168.50/168.35 & ( V_i != V_j
% 168.50/168.35 => 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) ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_take__butlast,axiom,
% 168.50/168.35 ! [V_xs,T_a,V_n] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 168.50/168.35 => hAPP(hAPP(c_List_Otake(T_a),V_n),c_List_Obutlast(T_a,V_xs)) = hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_length__butlast,axiom,
% 168.50/168.35 ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Obutlast(T_a,V_xs)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_set__update__memI,axiom,
% 168.50/168.35 ! [V_x_2,V_xs_2,T_b,V_n_2] :
% 168.50/168.35 ( 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)))
% 168.50/168.35 => 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)))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_butlast__conv__take,axiom,
% 168.50/168.35 ! [V_xs,T_a] : c_List_Obutlast(T_a,V_xs) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_listrel1__iff__update,axiom,
% 168.50/168.35 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 168.50/168.35 <=> ? [B_y,B_n] :
% 168.50/168.35 ( 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))
% 168.50/168.35 & 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)))
% 168.50/168.35 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),B_n),B_y) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_distinct__list__update,axiom,
% 168.50/168.35 ! [V_i_2,V_a_2,V_xs_2,T_b] :
% 168.50/168.35 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 168.50/168.35 => ( ~ 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))))))
% 168.50/168.35 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_a_2))) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_distinct__upto,axiom,
% 168.50/168.35 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_distinct__take,axiom,
% 168.50/168.35 ! [V_i,V_xs,T_a] :
% 168.50/168.35 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 168.50/168.35 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_distinct__sublistI,axiom,
% 168.50/168.35 ! [V_I_2,V_xs_2,T_b] :
% 168.50/168.35 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 168.50/168.35 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_distinct__zipI1,axiom,
% 168.50/168.35 ! [V_ys,T_b,V_xs,T_a] :
% 168.50/168.35 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 168.50/168.35 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_distinct__zipI2,axiom,
% 168.50/168.35 ! [V_xs,T_b,V_ys,T_a] :
% 168.50/168.35 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys))
% 168.50/168.35 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_distinct_Osimps_I2_J,axiom,
% 168.50/168.35 ! [V_xs_2,V_x_2,T_b] :
% 168.50/168.35 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))
% 168.50/168.35 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.35 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_distinct__card,axiom,
% 168.50/168.35 ! [V_xs_2,T_b] :
% 168.50/168.35 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 168.50/168.35 => 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) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_card__distinct,axiom,
% 168.50/168.35 ! [V_xs_2,T_b] :
% 168.50/168.35 ( 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)
% 168.50/168.35 => hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_nth__eq__iff__index__eq,axiom,
% 168.50/168.35 ! [V_j_2,V_i_2,V_xs_2,T_b] :
% 168.50/168.35 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 168.50/168.35 => ( 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)))
% 168.50/168.35 => ( 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)))
% 168.50/168.35 => ( 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)
% 168.50/168.35 <=> V_i_2 = V_j_2 ) ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_distinct__conv__nth,axiom,
% 168.50/168.35 ! [V_xs_2,T_b] :
% 168.50/168.35 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 168.50/168.35 <=> ! [B_i] :
% 168.50/168.35 ( 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)))
% 168.50/168.35 => ! [B_j] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 168.50/168.35 => ( B_i != B_j
% 168.50/168.35 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j) ) ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_distinct__listsum__conv__Setsum,axiom,
% 168.50/168.35 ! [V_xs_2,T_b] :
% 168.50/168.35 ( class_Groups_Ocomm__monoid__add(T_b)
% 168.50/168.35 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 168.50/168.35 => 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)) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_Nitpick_Ocard_H__def,axiom,
% 168.50/168.35 ! [V_A_2,T_b] :
% 168.50/168.35 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.35 => 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)))) )
% 168.50/168.35 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.35 => c_Nitpick_Ocard_H(T_b,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_nth__take__lemma,axiom,
% 168.50/168.35 ! [V_ys,V_xs,T_a,V_k] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 168.50/168.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)))
% 168.50/168.35 => ( ! [B_i] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k))
% 168.50/168.35 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) )
% 168.50/168.35 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_set__remove1__eq,axiom,
% 168.50/168.35 ! [V_x_2,V_xs_2,T_b] :
% 168.50/168.35 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 168.50/168.35 => 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)))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_take__Cons__number__of,axiom,
% 168.50/168.35 ! [V_xs,V_x,T_a,V_v] :
% 168.50/168.35 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.50/168.35 => 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) )
% 168.50/168.35 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.50/168.35 => 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)) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_lists_ONil,axiom,
% 168.50/168.35 ! [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))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_listrel__Nil1,axiom,
% 168.50/168.35 ! [V_r_2,V_xs_2,T_b] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xs_2)),c_List_Olistrel(T_b,V_r_2)))
% 168.50/168.35 => V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_listrel__Nil2,axiom,
% 168.50/168.35 ! [V_r_2,V_xs_2,T_b] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olistrel(T_b,V_r_2)))
% 168.50/168.35 => V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_distinct__butlast,axiom,
% 168.50/168.35 ! [T_a,V_xs] :
% 168.50/168.35 ( V_xs != c_List_Olist_ONil(T_a)
% 168.50/168.35 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 168.50/168.35 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_distinct__remove1,axiom,
% 168.50/168.35 ! [V_x,V_xs,T_a] :
% 168.50/168.35 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 168.50/168.35 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_distinct_Osimps_I1_J,axiom,
% 168.50/168.35 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_butlast_Osimps_I1_J,axiom,
% 168.50/168.35 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_butlast_Osimps_I2_J,axiom,
% 168.50/168.35 ! [V_x,T_a,V_xs] :
% 168.50/168.35 ( ( V_xs = c_List_Olist_ONil(T_a)
% 168.50/168.35 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) )
% 168.50/168.35 & ( V_xs != c_List_Olist_ONil(T_a)
% 168.50/168.35 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Obutlast(T_a,V_xs)) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_list_Osimps_I2_J,axiom,
% 168.50/168.35 ! [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) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_list_Osimps_I3_J,axiom,
% 168.50/168.35 ! [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) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_remove1_Osimps_I2_J,axiom,
% 168.50/168.35 ! [V_xs,T_a,V_y,V_x] :
% 168.50/168.35 ( ( V_x = V_y
% 168.50/168.35 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs )
% 168.50/168.35 & ( V_x != V_y
% 168.50/168.35 => 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)) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_upto__empty,axiom,
% 168.50/168.35 ! [V_i,V_j] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i))
% 168.50/168.35 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_take__Nil,axiom,
% 168.50/168.35 ! [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) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_take__eq__Nil,axiom,
% 168.50/168.35 ! [V_xs_2,V_n_2,T_b] :
% 168.50/168.35 ( hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 168.50/168.35 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.50/168.35 | V_xs_2 = c_List_Olist_ONil(T_b) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_take__0,axiom,
% 168.50/168.35 ! [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) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sublist__nil,axiom,
% 168.50/168.35 ! [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) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_remove1__commute,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_remove1_Osimps_I1_J,axiom,
% 168.50/168.35 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_listrelp_Oequations_I1_J,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_listrelp_ONil,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_zip__Nil,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_zip_Osimps_I1_J,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_listsum__simps_I1_J,axiom,
% 168.50/168.35 ! [T_a] :
% 168.50/168.35 ( class_Groups_Omonoid__add(T_a)
% 168.50/168.35 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_length__0__conv,axiom,
% 168.50/168.35 ! [V_xs_2,T_b] :
% 168.50/168.35 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.50/168.35 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_list_Osize_I3_J,axiom,
% 168.50/168.35 ! [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) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_set__empty,axiom,
% 168.50/168.35 ! [V_xs_2,T_b] :
% 168.50/168.35 ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.35 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_set__empty2,axiom,
% 168.50/168.35 ! [V_xs_2,T_b] :
% 168.50/168.35 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_List_Oset(T_b),V_xs_2)
% 168.50/168.35 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_List_Oset_Osimps_I1_J,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_list__update__code_I1_J,axiom,
% 168.50/168.35 ! [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) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_list__update_Osimps_I1_J,axiom,
% 168.50/168.35 ! [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) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_list__update__nonempty,axiom,
% 168.50/168.35 ! [V_x_2,V_k_2,V_xs_2,T_b] :
% 168.50/168.35 ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_b)
% 168.50/168.35 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_list_Osize_I1_J,axiom,
% 168.50/168.35 ! [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) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_remove1__idem,axiom,
% 168.50/168.35 ! [V_xs_2,V_x_2,T_b] :
% 168.50/168.35 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.35 => c_List_Oremove1(T_b,V_x_2,V_xs_2) = V_xs_2 ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_notin__set__remove1,axiom,
% 168.50/168.35 ! [V_y_2,V_xs_2,V_x_2,T_b] :
% 168.50/168.35 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.35 => ~ 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)))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_in__set__remove1,axiom,
% 168.50/168.35 ! [V_xs_2,T_b,V_b_2,V_a_2] :
% 168.50/168.35 ( V_a_2 != V_b_2
% 168.50/168.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_b_2,V_xs_2))))
% 168.50/168.35 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sublist__empty,axiom,
% 168.50/168.35 ! [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) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_set__remove1__subset,axiom,
% 168.50/168.35 ! [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))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_length__greater__0__conv,axiom,
% 168.50/168.35 ! [V_xs_2,T_b] :
% 168.50/168.35 ( 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)))
% 168.50/168.35 <=> V_xs_2 != c_List_Olist_ONil(T_b) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_take__1__Cons,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_not__Nil__listrel1,axiom,
% 168.50/168.35 ! [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))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_not__listrel1__Nil,axiom,
% 168.50/168.35 ! [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))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_listrel_ONil,axiom,
% 168.50/168.35 ! [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))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_lexord__Nil__right,axiom,
% 168.50/168.35 ! [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))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_Nil__notin__lex,axiom,
% 168.50/168.35 ! [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))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_Nil2__notin__lex,axiom,
% 168.50/168.35 ! [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))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_take__Cons,axiom,
% 168.50/168.35 ! [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) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_upto_Osimps,axiom,
% 168.50/168.35 ! [V_j,V_i] :
% 168.50/168.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 168.50/168.35 => 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)) )
% 168.50/168.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 168.50/168.35 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sublist__singleton,axiom,
% 168.50/168.35 ! [V_x_2,T_b,V_A_2] :
% 168.50/168.35 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 168.50/168.35 => 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)) )
% 168.50/168.35 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 168.50/168.35 => 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) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_lists__empty,axiom,
% 168.50/168.35 ! [T_b] : c_List_Olists(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_take__Cons_H,axiom,
% 168.50/168.35 ! [V_xs,V_x,T_a,V_n] :
% 168.50/168.35 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.50/168.35 => 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) )
% 168.50/168.35 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.50/168.35 => 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)) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_upto__rec__number__of,axiom,
% 168.50/168.35 ! [V_n,V_m] :
% 168.50/168.35 ( ( 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)))
% 168.50/168.35 => 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))) )
% 168.50/168.35 & ( ~ 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)))
% 168.50/168.35 => 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) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_listrel__Nil,axiom,
% 168.50/168.35 ! [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))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_set__Cons__sing__Nil,axiom,
% 168.50/168.35 ! [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) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_length__remove1,axiom,
% 168.50/168.35 ! [V_xs_2,V_x_2,T_b] :
% 168.50/168.35 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.35 => 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)) )
% 168.50/168.35 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.35 => 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) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_upto_Opsimps,axiom,
% 168.50/168.35 ! [V_j_2,V_i_2] :
% 168.50/168.35 ( 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)))
% 168.50/168.35 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 168.50/168.35 => 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)) )
% 168.50/168.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 168.50/168.35 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_select,axiom,
% 168.50/168.35 ! [V_s_2,T_b,V_xs_2] :
% 168.50/168.35 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 168.50/168.35 => 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))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_listset_Osimps_I1_J,axiom,
% 168.50/168.35 ! [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))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_zip__Cons1,axiom,
% 168.50/168.35 ! [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) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_list_Osimps_I5_J,axiom,
% 168.50/168.35 ! [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) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_list_Osimps_I4_J,axiom,
% 168.50/168.35 ! [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 ).
% 168.50/168.35
% 168.50/168.35 fof(fact_listset_Osimps_I2_J,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_zip__Cons,axiom,
% 168.50/168.35 ! [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) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sorted__list__of__set__remove,axiom,
% 168.50/168.35 ! [V_x_2,V_A_2,T_b] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_b)
% 168.50/168.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.35 => 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)) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_upto_Opinduct,axiom,
% 168.50/168.35 ! [V_P_2,V_a1_2,V_a0_2] :
% 168.50/168.35 ( 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)))
% 168.50/168.35 => ( ! [B_i,B_j] :
% 168.50/168.35 ( 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)))
% 168.50/168.35 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j))
% 168.50/168.35 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint))),B_j)) )
% 168.50/168.35 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) )
% 168.50/168.35 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sorted__list__of__set__empty,axiom,
% 168.50/168.35 ! [T_b] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_b)
% 168.50/168.35 => 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) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_anamorph_Osimps,axiom,
% 168.50/168.35 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
% 168.50/168.35 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 168.50/168.35 => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2),V_k_2),V_x_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),T_c),c_List_Olist_ONil(T_b)),V_x_2) )
% 168.50/168.35 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 168.50/168.35 => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2),V_k_2),V_x_2) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),T_c),c_List_Olist_ONil(T_b)),V_x_2),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(tc_List_Olist(T_b),T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),T_b),c_COMBB(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c),T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),tc_fun(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c)),T_b),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),T_c,tc_prod(tc_List_Olist(T_b),T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),T_b),hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_List_Olist(T_b),T_c))),c_List_Olist_OCons(T_b))))),hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))),hAPP(V_f_2,V_x_2)) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sublist__Cons,axiom,
% 168.50/168.35 ! [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)))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_append__eq__Cons__conv,axiom,
% 168.50/168.35 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_b] :
% 168.50/168.35 ( 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)
% 168.50/168.35 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b)
% 168.50/168.35 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) )
% 168.50/168.35 | ? [B_ys_H] :
% 168.50/168.35 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H)
% 168.50/168.35 & hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_Cons__eq__append__conv,axiom,
% 168.50/168.35 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_b] :
% 168.50/168.35 ( 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)
% 168.50/168.35 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b)
% 168.50/168.35 & hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = V_zs_2 )
% 168.50/168.35 | ? [B_ys_H] :
% 168.50/168.35 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) = V_ys_2
% 168.50/168.35 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_append1__eq__conv,axiom,
% 168.50/168.35 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
% 168.50/168.35 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))) = 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)))
% 168.50/168.35 <=> ( V_xs_2 = V_ys_2
% 168.50/168.35 & V_x_2 = V_y_2 ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_append__Cons,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_Cons__eq__appendI,axiom,
% 168.50/168.35 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] :
% 168.50/168.35 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys
% 168.50/168.35 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs)
% 168.50/168.35 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_append__in__lists__conv,axiom,
% 168.50/168.35 ! [V_A_2,V_ys_2,V_xs_2,T_b] :
% 168.50/168.35 ( 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)))
% 168.50/168.35 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
% 168.50/168.35 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),c_List_Olists(T_b,V_A_2))) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_append__eq__appendI,axiom,
% 168.50/168.35 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] :
% 168.50/168.35 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs
% 168.50/168.35 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us)
% 168.50/168.35 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_append__same__eq,axiom,
% 168.50/168.35 ! [V_zs_2,V_xs_2,V_ys_2,T_b] :
% 168.50/168.35 ( 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)
% 168.50/168.35 <=> V_ys_2 = V_zs_2 ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_same__append__eq,axiom,
% 168.50/168.35 ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
% 168.50/168.35 ( 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)
% 168.50/168.35 <=> V_ys_2 = V_zs_2 ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_append__eq__append__conv2,axiom,
% 168.50/168.35 ! [V_tsa_2,V_zs_2,V_ys_2,V_xs_2,T_b] :
% 168.50/168.35 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_tsa_2)
% 168.50/168.35 <=> ? [B_us] :
% 168.50/168.35 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),B_us)
% 168.50/168.35 & hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ys_2) = V_tsa_2 )
% 168.50/168.35 | ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),B_us) = V_zs_2
% 168.50/168.35 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),V_tsa_2) ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_append__assoc,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_listsum__append,axiom,
% 168.50/168.35 ! [V_ys,V_xs,T_a] :
% 168.50/168.35 ( class_Groups_Omonoid__add(T_a)
% 168.50/168.35 => 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)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_length__append,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_zip__append,axiom,
% 168.50/168.35 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] :
% 168.50/168.35 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_us)
% 168.50/168.35 => ( 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)
% 168.50/168.35 => 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)) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_set__append,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_append__Nil,axiom,
% 168.50/168.35 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ).
% 168.50/168.35
% 168.50/168.35 fof(fact_Nil__is__append__conv,axiom,
% 168.50/168.35 ! [V_ys_2,V_xs_2,T_b] :
% 168.50/168.35 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 168.50/168.35 <=> ( V_xs_2 = c_List_Olist_ONil(T_b)
% 168.50/168.35 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_append__Nil2,axiom,
% 168.50/168.35 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ).
% 168.50/168.35
% 168.50/168.35 fof(fact_self__append__conv,axiom,
% 168.50/168.35 ! [V_ys_2,T_b,V_xs_2] :
% 168.50/168.35 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 168.50/168.35 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_self__append__conv2,axiom,
% 168.50/168.35 ! [V_xs_2,T_b,V_ys_2] :
% 168.50/168.35 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 168.50/168.35 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_append__is__Nil__conv,axiom,
% 168.50/168.35 ! [V_ys_2,V_xs_2,T_b] :
% 168.50/168.35 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_b)
% 168.50/168.35 <=> ( V_xs_2 = c_List_Olist_ONil(T_b)
% 168.50/168.35 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_append__self__conv,axiom,
% 168.50/168.35 ! [V_ys_2,V_xs_2,T_b] :
% 168.50/168.35 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_xs_2
% 168.50/168.35 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_append__self__conv2,axiom,
% 168.50/168.35 ! [V_ys_2,V_xs_2,T_b] :
% 168.50/168.35 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_ys_2
% 168.50/168.35 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_eq__Nil__appendI,axiom,
% 168.50/168.35 ! [T_a,V_ys,V_xs] :
% 168.50/168.35 ( V_xs = V_ys
% 168.50/168.35 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_butlast__append,axiom,
% 168.50/168.35 ! [V_xs,T_a,V_ys] :
% 168.50/168.35 ( ( V_ys = c_List_Olist_ONil(T_a)
% 168.50/168.35 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) )
% 168.50/168.35 & ( V_ys != c_List_Olist_ONil(T_a)
% 168.50/168.35 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Obutlast(T_a,V_ys)) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_nth__append__length,axiom,
% 168.50/168.35 ! [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 ).
% 168.50/168.35
% 168.50/168.35 fof(fact_nth__append__length__plus,axiom,
% 168.50/168.35 ! [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) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_take__append,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_list__update__append1,axiom,
% 168.50/168.35 ! [V_x,V_ys,V_xs,T_a,V_i] :
% 168.50/168.35 ( 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)))
% 168.50/168.35 => 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) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_list__update__length,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_remove1__append,axiom,
% 168.50/168.35 ! [V_ys_2,V_xs_2,V_x_2,T_b] :
% 168.50/168.35 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.35 => 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) )
% 168.50/168.35 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.35 => 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)) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_in__set__butlast__appendI,axiom,
% 168.50/168.35 ! [V_ys_2,V_xs_2,V_x_2,T_b] :
% 168.50/168.35 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
% 168.50/168.35 | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_ys_2)))) )
% 168.50/168.35 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_butlast__snoc,axiom,
% 168.50/168.35 ! [V_x,V_xs,T_a] : c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)))) = V_xs ).
% 168.50/168.35
% 168.50/168.35 fof(fact_append__listrel1I,axiom,
% 168.50/168.35 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 168.50/168.35 ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 168.50/168.35 & V_us_2 = V_vs_2 )
% 168.50/168.35 | ( V_xs_2 = V_ys_2
% 168.50/168.35 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_us_2),V_vs_2)),c_List_Olistrel1(T_b,V_r_2))) ) )
% 168.50/168.35 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),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))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_lexord__append__leftI,axiom,
% 168.50/168.35 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_b] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_u_2),V_v_2)),c_List_Olexord(T_b,V_r_2)))
% 168.50/168.35 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),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))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_distinct__append,axiom,
% 168.50/168.35 ! [V_ys_2,V_xs_2,T_b] :
% 168.50/168.35 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
% 168.50/168.35 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 168.50/168.35 & hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
% 168.50/168.35 & 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)) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_nth__append,axiom,
% 168.50/168.35 ! [V_ys,V_xs,T_a,V_n] :
% 168.50/168.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 168.50/168.35 => 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) )
% 168.50/168.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 168.50/168.35 => 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))) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_list__update__append,axiom,
% 168.50/168.35 ! [V_x,V_ys,V_xs,T_a,V_n] :
% 168.50/168.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 168.50/168.35 => 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) )
% 168.50/168.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 168.50/168.35 => 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)) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sublist__append,axiom,
% 168.50/168.35 ! [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)))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_listrel1I,axiom,
% 168.50/168.35 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 168.50/168.35 => ( 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))
% 168.50/168.35 => ( 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))
% 168.50/168.35 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_lexord__append__left__rightI,axiom,
% 168.50/168.35 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_b] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 168.50/168.35 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_x_2))),hAPP(hAPP(c_List_Oappend(T_b),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_y_2)))),c_List_Olexord(T_b,V_r_2))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_take__Suc__conv__app__nth,axiom,
% 168.50/168.35 ! [V_xs,T_a,V_i] :
% 168.50/168.35 ( 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)))
% 168.50/168.35 => 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))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_snoc__listrel1__snoc__iff,axiom,
% 168.50/168.35 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),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)))
% 168.50/168.35 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 168.50/168.35 & V_x_2 = V_y_2 )
% 168.50/168.35 | ( V_xs_2 = V_ys_2
% 168.50/168.35 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_listrel1E,axiom,
% 168.50/168.35 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 168.50/168.35 => ~ ! [B_x,B_y] :
% 168.50/168.35 ( 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))
% 168.50/168.35 => ! [B_us,B_vs] :
% 168.50/168.35 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_vs))
% 168.50/168.35 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_vs)) ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_lexord__append__leftD,axiom,
% 168.50/168.35 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_b] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),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)))
% 168.50/168.35 => ( ! [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))
% 168.50/168.35 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_u_2),V_v_2)),c_List_Olexord(T_b,V_r_2))) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_rotate1__def,axiom,
% 168.50/168.35 ! [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) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_upd__conv__take__nth__drop,axiom,
% 168.50/168.35 ! [V_a,V_xs,T_a,V_i] :
% 168.50/168.35 ( 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)))
% 168.50/168.35 => 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))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_append__take__drop__id,axiom,
% 168.50/168.35 ! [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 ).
% 168.50/168.35
% 168.50/168.35 fof(fact_drop__Suc__Cons,axiom,
% 168.50/168.35 ! [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) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_drop__1__Cons,axiom,
% 168.50/168.35 ! [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 ).
% 168.50/168.35
% 168.50/168.35 fof(fact_nth__via__drop,axiom,
% 168.50/168.35 ! [V_ys,V_y,V_xs,V_n,T_a] :
% 168.50/168.35 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)
% 168.50/168.35 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_distinct__drop,axiom,
% 168.50/168.35 ! [V_i,V_xs,T_a] :
% 168.50/168.35 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 168.50/168.35 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_distinct1__rotate,axiom,
% 168.50/168.35 ! [V_xs_2,T_b] :
% 168.50/168.35 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)))
% 168.50/168.35 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_butlast__drop,axiom,
% 168.50/168.35 ! [V_xs,V_n,T_a] : c_List_Obutlast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Obutlast(T_a,V_xs)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_drop__butlast,axiom,
% 168.50/168.35 ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Obutlast(T_a,V_xs)) = c_List_Obutlast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_drop__take,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_take__drop,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_drop__0,axiom,
% 168.50/168.35 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ).
% 168.50/168.35
% 168.50/168.35 fof(fact_drop__drop,axiom,
% 168.50/168.35 ! [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) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_drop__zip,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_length__rotate1,axiom,
% 168.50/168.35 ! [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) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_length__drop,axiom,
% 168.50/168.35 ! [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) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_set__rotate1,axiom,
% 168.50/168.35 ! [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) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_in__set__dropD,axiom,
% 168.50/168.35 ! [V_xs_2,V_n_2,V_x_2,T_b] :
% 168.50/168.35 ( 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))))
% 168.50/168.35 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_set__drop__subset,axiom,
% 168.50/168.35 ! [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))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_drop__Nil,axiom,
% 168.50/168.35 ! [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) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_rotate1__is__Nil__conv,axiom,
% 168.50/168.35 ! [V_xs_2,T_b] :
% 168.50/168.35 ( hAPP(c_List_Orotate1(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
% 168.50/168.35 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_set__drop__subset__set__drop,axiom,
% 168.50/168.35 ! [V_xs_2,T_b,V_m_2,V_n_2] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2))
% 168.50/168.35 => 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)))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_drop__all,axiom,
% 168.50/168.35 ! [V_n,V_xs,T_a] :
% 168.50/168.35 ( 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))
% 168.50/168.35 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_drop__eq__Nil,axiom,
% 168.50/168.35 ! [V_xs_2,V_n_2,T_b] :
% 168.50/168.35 ( hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 168.50/168.35 <=> 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)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_drop__append,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_append__eq__conv__conj,axiom,
% 168.50/168.35 ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
% 168.50/168.35 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_zs_2
% 168.50/168.35 <=> ( 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)
% 168.50/168.35 & 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) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_drop__Cons,axiom,
% 168.50/168.35 ! [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) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_drop__Cons_H,axiom,
% 168.50/168.35 ! [V_xs,V_x,T_a,V_n] :
% 168.50/168.35 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.50/168.35 => 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) )
% 168.50/168.35 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.50/168.35 => 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) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_nth__drop,axiom,
% 168.50/168.35 ! [V_xs,T_a,V_i,V_n] :
% 168.50/168.35 ( 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)))
% 168.50/168.35 => 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)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_append__eq__append__conv__if,axiom,
% 168.50/168.35 ! [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] :
% 168.50/168.35 ( 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)
% 168.50/168.35 <=> ( ( 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)))
% 168.50/168.35 => ( 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)
% 168.50/168.35 & 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) ) )
% 168.50/168.35 & ( ~ 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)))
% 168.50/168.35 => ( 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
% 168.50/168.35 & 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 ) ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_nth__drop_H,axiom,
% 168.50/168.35 ! [V_xs,T_a,V_i] :
% 168.50/168.35 ( 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)))
% 168.50/168.35 => 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) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_rotate__simps,axiom,
% 168.50/168.35 ! [V_xs,V_x,T_b,T_a] :
% 168.50/168.35 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a)
% 168.50/168.35 & 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))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_drop__Cons__number__of,axiom,
% 168.50/168.35 ! [V_xs,V_x,T_a,V_v] :
% 168.50/168.35 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.50/168.35 => 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) )
% 168.50/168.35 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.50/168.35 => 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) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_take__add,axiom,
% 168.50/168.35 ! [V_xs,T_a,V_j,V_i] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 168.50/168.35 => 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))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_rotate1__length01,axiom,
% 168.50/168.35 ! [V_xs,T_a] :
% 168.50/168.35 ( 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)))
% 168.50/168.35 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_zip__append1,axiom,
% 168.50/168.35 ! [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))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_zip__append2,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_id__take__nth__drop,axiom,
% 168.50/168.35 ! [V_xs,T_a,V_i] :
% 168.50/168.35 ( 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)))
% 168.50/168.35 => 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))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_take__hd__drop,axiom,
% 168.50/168.35 ! [V_xs,T_a,V_n] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 168.50/168.35 => 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) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_hd__drop__conv__nth,axiom,
% 168.50/168.35 ! [V_n,T_a,V_xs] :
% 168.50/168.35 ( V_xs != c_List_Olist_ONil(T_a)
% 168.50/168.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 168.50/168.35 => 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) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_hd_Osimps,axiom,
% 168.50/168.35 ! [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 ).
% 168.50/168.35
% 168.50/168.35 fof(fact_hd__append2,axiom,
% 168.50/168.35 ! [V_ys,T_a,V_xs] :
% 168.50/168.35 ( V_xs != c_List_Olist_ONil(T_a)
% 168.50/168.35 => 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) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_hd__append,axiom,
% 168.50/168.35 ! [V_ys,T_a,V_xs] :
% 168.50/168.35 ( ( V_xs = c_List_Olist_ONil(T_a)
% 168.50/168.35 => 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) )
% 168.50/168.35 & ( V_xs != c_List_Olist_ONil(T_a)
% 168.50/168.35 => 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) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_hd__in__set,axiom,
% 168.50/168.35 ! [T_b,V_xs_2] :
% 168.50/168.35 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 168.50/168.35 => 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))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_hd__conv__nth,axiom,
% 168.50/168.35 ! [T_a,V_xs] :
% 168.50/168.35 ( V_xs != c_List_Olist_ONil(T_a)
% 168.50/168.35 => 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)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_rotate1__hd__tl,axiom,
% 168.50/168.35 ! [T_a,V_xs] :
% 168.50/168.35 ( V_xs != c_List_Olist_ONil(T_a)
% 168.50/168.35 => 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))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_hd__rotate__conv__nth,axiom,
% 168.50/168.35 ! [V_n,T_a,V_xs] :
% 168.50/168.35 ( V_xs != c_List_Olist_ONil(T_a)
% 168.50/168.35 => 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))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_drop__tl,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_tl__drop,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_tl_Osimps_I2_J,axiom,
% 168.50/168.35 ! [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 ).
% 168.50/168.35
% 168.50/168.35 fof(fact_distinct__tl,axiom,
% 168.50/168.35 ! [V_xs,T_a] :
% 168.50/168.35 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 168.50/168.35 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_distinct__rotate,axiom,
% 168.50/168.35 ! [V_xs_2,V_n_2,T_b] :
% 168.50/168.35 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)))
% 168.50/168.35 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_rotate__rotate,axiom,
% 168.50/168.35 ! [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) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_rotate0,axiom,
% 168.50/168.35 ! [T_b] : c_List_Orotate(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_rotate__add,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_length__rotate,axiom,
% 168.50/168.35 ! [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) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_set__rotate,axiom,
% 168.50/168.35 ! [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) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_tl_Osimps_I1_J,axiom,
% 168.50/168.35 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_rotate__is__Nil__conv,axiom,
% 168.50/168.35 ! [V_xs_2,V_n_2,T_b] :
% 168.50/168.35 ( hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 168.50/168.35 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_rotate1__rotate__swap,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_rotate__def,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_tl__append2,axiom,
% 168.50/168.35 ! [V_ys,T_a,V_xs] :
% 168.50/168.35 ( V_xs != c_List_Olist_ONil(T_a)
% 168.50/168.35 => 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) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_take__tl,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_rotate__conv__mod,axiom,
% 168.50/168.35 ! [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) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_drop__Suc,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_rotate__Suc,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_tl__append,axiom,
% 168.50/168.35 ! [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) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_rotate__id,axiom,
% 168.50/168.35 ! [V_xs,T_a,V_n] :
% 168.50/168.35 ( 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)
% 168.50/168.35 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_rotate__length01,axiom,
% 168.50/168.35 ! [V_n,V_xs,T_a] :
% 168.50/168.35 ( 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)))
% 168.50/168.35 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_length__tl,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_tl__take,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_take__Suc,axiom,
% 168.50/168.35 ! [V_n,T_a,V_xs] :
% 168.50/168.35 ( V_xs != c_List_Olist_ONil(T_a)
% 168.50/168.35 => 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))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_rotate__drop__take,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_fold1__set,axiom,
% 168.50/168.35 ! [V_xs_2,T_b] :
% 168.50/168.35 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 168.50/168.35 => ( V_xs_2 != c_List_Olist_ONil(T_b)
% 168.50/168.35 => 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)) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_lexord__append__rightI,axiom,
% 168.50/168.35 ! [V_r_2,V_x_2,T_b,V_y_2] :
% 168.50/168.35 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_b),B_z)
% 168.50/168.35 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_y_2))),c_List_Olexord(T_b,V_r_2))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_foldl__Nil,axiom,
% 168.50/168.35 ! [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 ).
% 168.50/168.35
% 168.50/168.35 fof(fact_start__le__sum,axiom,
% 168.50/168.35 ! [V_ns_2,V_n_2,V_m_2] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 168.50/168.35 => 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))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_foldl__absorb0,axiom,
% 168.50/168.35 ! [V_zs_2,V_x_2,T_b] :
% 168.50/168.35 ( class_Groups_Omonoid__add(T_b)
% 168.50/168.35 => 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) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_foldl__assoc,axiom,
% 168.50/168.35 ! [V_zs_2,V_y_2,V_x_2,T_b] :
% 168.50/168.35 ( class_Groups_Osemigroup__add(T_b)
% 168.50/168.35 => 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)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_foldl__Cons,axiom,
% 168.50/168.35 ! [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) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_foldl__append,axiom,
% 168.50/168.35 ! [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) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_listsum__foldl,axiom,
% 168.50/168.35 ! [T_b] :
% 168.50/168.35 ( class_Groups_Omonoid__add(T_b)
% 168.50/168.35 => 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)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sum__eq__0__conv,axiom,
% 168.50/168.35 ! [V_ns_2,V_m_2] :
% 168.50/168.35 ( 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)
% 168.50/168.35 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.50/168.35 & ! [B_x] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 168.50/168.35 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_fun__left__comm__idem_Ofold__set,axiom,
% 168.50/168.35 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
% 168.50/168.35 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 168.50/168.35 => 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) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_Sup__set__fold,axiom,
% 168.50/168.35 ! [V_xs_2,T_b] :
% 168.50/168.35 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 168.50/168.35 => 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) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_Inf__set__fold,axiom,
% 168.50/168.35 ! [V_xs_2,T_b] :
% 168.50/168.35 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 168.50/168.35 => 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) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_Sup__fin__set__fold,axiom,
% 168.50/168.35 ! [V_xs_2,V_x_2,T_b] :
% 168.50/168.35 ( class_Lattices_Olattice(T_b)
% 168.50/168.35 => 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) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_Inf__fin__set__fold,axiom,
% 168.50/168.35 ! [V_xs_2,V_x_2,T_b] :
% 168.50/168.35 ( class_Lattices_Olattice(T_b)
% 168.50/168.35 => 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) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_Min__fin__set__fold,axiom,
% 168.50/168.35 ! [V_xs_2,V_x_2,T_b] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_b)
% 168.50/168.35 => 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) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_Max__fin__set__fold,axiom,
% 168.50/168.35 ! [V_xs_2,V_x_2,T_b] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_b)
% 168.50/168.35 => 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) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_min__max_OInf__fin__set__fold,axiom,
% 168.50/168.35 ! [V_xs_2,V_x_2,T_b] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_b)
% 168.50/168.35 => 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) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_min__max_OSup__fin__set__fold,axiom,
% 168.50/168.35 ! [V_xs_2,V_x_2,T_b] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_b)
% 168.50/168.35 => 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) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_SUPR__set__fold,axiom,
% 168.50/168.35 ! [V_f_2,V_xs_2,T_c,T_b] :
% 168.50/168.35 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 168.50/168.35 => 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) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_INFI__set__fold,axiom,
% 168.50/168.35 ! [V_f_2,V_xs_2,T_c,T_b] :
% 168.50/168.35 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 168.50/168.35 => 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) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_elem__le__sum,axiom,
% 168.50/168.35 ! [V_ns_2,V_n_2] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 168.50/168.35 => 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))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sorted__list__of__set__insert,axiom,
% 168.50/168.35 ! [V_x_2,V_A_2,T_b] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_b)
% 168.50/168.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.35 => 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)))))) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_lexord__Nil__left,axiom,
% 168.50/168.35 ! [V_r_2,V_y_2,T_b] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_y_2)),c_List_Olexord(T_b,V_r_2)))
% 168.50/168.35 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_x) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_insort__key_Osimps_I1_J,axiom,
% 168.50/168.35 ! [V_x_2,V_f_2,T_b,T_c] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_c)
% 168.50/168.35 => 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)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_insort__key_Osimps_I2_J,axiom,
% 168.50/168.35 ! [V_ys_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_b)
% 168.50/168.35 => ( ( 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)))
% 168.50/168.35 => 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)) )
% 168.50/168.35 & ( ~ 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)))
% 168.50/168.35 => 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)) ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_set__insort,axiom,
% 168.50/168.35 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_c)
% 168.50/168.35 => 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)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_length__insort,axiom,
% 168.50/168.35 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_c)
% 168.50/168.35 => 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)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_insort__key__left__comm,axiom,
% 168.50/168.35 ! [V_xs_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_b)
% 168.50/168.35 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
% 168.50/168.35 => 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)) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_fun__left__comm__insort,axiom,
% 168.50/168.35 ! [T_b] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_b)
% 168.50/168.35 => 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))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_insort__left__comm,axiom,
% 168.50/168.35 ! [V_xs_2,V_y_2,V_x_2,T_b] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_b)
% 168.50/168.35 => 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)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_remove1__insort,axiom,
% 168.50/168.35 ! [V_xs_2,V_x_2,T_b] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_b)
% 168.50/168.35 => 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 ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_insort__not__Nil,axiom,
% 168.50/168.35 ! [V_xs_2,V_a_2,V_f_2,T_b,T_c] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_c)
% 168.50/168.35 => 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) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_distinct__insort,axiom,
% 168.50/168.35 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_c)
% 168.50/168.35 => ( 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)))
% 168.50/168.35 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.35 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_insort__insert__insort__key,axiom,
% 168.50/168.35 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_b)
% 168.50/168.35 => ( ~ 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))))
% 168.50/168.35 => 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) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_insort__insert__insort,axiom,
% 168.50/168.35 ! [V_xs_2,V_x_2,T_b] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_b)
% 168.50/168.35 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.35 => 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) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_distinct__insort__insert,axiom,
% 168.50/168.35 ! [V_x_2,V_f_2,V_xs_2,T_b,T_c] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_c)
% 168.50/168.35 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 168.50/168.35 => 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))) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_insort__insert__triv,axiom,
% 168.50/168.35 ! [V_xs_2,V_x_2,T_b] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_b)
% 168.50/168.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.35 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_set__insort__insert,axiom,
% 168.50/168.35 ! [V_xs_2,V_x_2,T_b] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_b)
% 168.50/168.35 => 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)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_insort__insert__key__triv,axiom,
% 168.50/168.35 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_b)
% 168.50/168.35 => ( 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))))
% 168.50/168.35 => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_last__list__update,axiom,
% 168.50/168.35 ! [V_x,V_k,T_a,V_xs] :
% 168.50/168.35 ( V_xs != c_List_Olist_ONil(T_a)
% 168.50/168.35 => ( ( V_k = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
% 168.50/168.35 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x )
% 168.50/168.35 & ( V_k != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
% 168.50/168.35 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = c_List_Olast(T_a,V_xs) ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_last__conv__nth,axiom,
% 168.50/168.35 ! [T_a,V_xs] :
% 168.50/168.35 ( V_xs != c_List_Olist_ONil(T_a)
% 168.50/168.35 => c_List_Olast(T_a,V_xs) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_last_Osimps,axiom,
% 168.50/168.35 ! [V_x,T_a,V_xs] :
% 168.50/168.35 ( ( V_xs = c_List_Olist_ONil(T_a)
% 168.50/168.35 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x )
% 168.50/168.35 & ( V_xs != c_List_Olist_ONil(T_a)
% 168.50/168.35 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_last__ConsR,axiom,
% 168.50/168.35 ! [V_x,T_a,V_xs] :
% 168.50/168.35 ( V_xs != c_List_Olist_ONil(T_a)
% 168.50/168.35 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_last__ConsL,axiom,
% 168.50/168.35 ! [V_x,T_a,V_xs] :
% 168.50/168.35 ( V_xs = c_List_Olist_ONil(T_a)
% 168.50/168.35 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_last__append,axiom,
% 168.50/168.35 ! [V_xs,T_a,V_ys] :
% 168.50/168.35 ( ( V_ys = c_List_Olist_ONil(T_a)
% 168.50/168.35 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) )
% 168.50/168.35 & ( V_ys != c_List_Olist_ONil(T_a)
% 168.50/168.35 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_last__appendR,axiom,
% 168.50/168.35 ! [V_xs,T_a,V_ys] :
% 168.50/168.35 ( V_ys != c_List_Olist_ONil(T_a)
% 168.50/168.35 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_last__appendL,axiom,
% 168.50/168.35 ! [V_xs,T_a,V_ys] :
% 168.50/168.35 ( V_ys = c_List_Olist_ONil(T_a)
% 168.50/168.35 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_last__in__set,axiom,
% 168.50/168.35 ! [T_b,V_as_2] :
% 168.50/168.35 ( V_as_2 != c_List_Olist_ONil(T_b)
% 168.50/168.35 => hBOOL(hAPP(hAPP(c_member(T_b),c_List_Olast(T_b,V_as_2)),hAPP(c_List_Oset(T_b),V_as_2))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_last__snoc,axiom,
% 168.50/168.35 ! [V_x,V_xs,T_a] : c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)))) = V_x ).
% 168.50/168.35
% 168.50/168.35 fof(fact_last__drop,axiom,
% 168.50/168.35 ! [V_xs,T_a,V_n] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 168.50/168.35 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_append__butlast__last__id,axiom,
% 168.50/168.35 ! [T_a,V_xs] :
% 168.50/168.35 ( V_xs != c_List_Olist_ONil(T_a)
% 168.50/168.35 => hAPP(hAPP(c_List_Oappend(T_a),c_List_Obutlast(T_a,V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),c_List_Olast(T_a,V_xs)),c_List_Olist_ONil(T_a))) = V_xs ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_snoc__eq__iff__butlast,axiom,
% 168.50/168.35 ! [V_ys_2,V_x_2,V_xs_2,T_b] :
% 168.50/168.35 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))) = V_ys_2
% 168.50/168.35 <=> ( V_ys_2 != c_List_Olist_ONil(T_b)
% 168.50/168.35 & c_List_Obutlast(T_b,V_ys_2) = V_xs_2
% 168.50/168.35 & c_List_Olast(T_b,V_ys_2) = V_x_2 ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_lists_Osimps,axiom,
% 168.50/168.35 ! [V_A_2,V_a_2,T_b] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_a_2),c_List_Olists(T_b,V_A_2)))
% 168.50/168.35 <=> ( V_a_2 = c_List_Olist_ONil(T_b)
% 168.50/168.35 | ? [B_a,B_l] :
% 168.50/168.35 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_l)
% 168.50/168.35 & hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 168.50/168.35 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_l),c_List_Olists(T_b,V_A_2))) ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_select__weigth__select,axiom,
% 168.50/168.35 ! [T_b,V_xs_2] :
% 168.50/168.35 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 168.50/168.35 => 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) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_inj__mapI,axiom,
% 168.50/168.35 ! [V_f_2,T_c,T_b] :
% 168.50/168.35 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 168.50/168.35 => 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))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_last__map,axiom,
% 168.50/168.35 ! [V_f_2,T_c,T_b,V_xs_2] :
% 168.50/168.35 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 168.50/168.35 => c_List_Olast(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(V_f_2,c_List_Olast(T_b,V_xs_2)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_List_Omap_Oid,axiom,
% 168.50/168.35 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_foldl__map,axiom,
% 168.50/168.35 ! [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) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_rotate__map,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_map__tl,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_zip__map2,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_map__zip__map2,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_map__zip__map,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_zip__map1,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_zip__map__map,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_zip__same__conv__map,axiom,
% 168.50/168.35 ! [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) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_map__is__Nil__conv,axiom,
% 168.50/168.35 ! [V_xs_2,V_f_2,T_b,T_c] :
% 168.50/168.35 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 168.50/168.35 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_map_Osimps_I1_J,axiom,
% 168.50/168.35 ! [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) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_Nil__is__map__conv,axiom,
% 168.50/168.35 ! [V_xs_2,V_f_2,T_c,T_b] :
% 168.50/168.35 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)
% 168.50/168.35 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_map__update,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_map__eq__conv,axiom,
% 168.50/168.35 ! [V_g_2,V_xs_2,V_f_2,T_b,T_c] :
% 168.50/168.35 ( 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)
% 168.50/168.35 <=> ! [B_x] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
% 168.50/168.35 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_length__map,axiom,
% 168.50/168.35 ! [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) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_map__eq__imp__length__eq,axiom,
% 168.50/168.35 ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_b,T_c] :
% 168.50/168.35 ( 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)
% 168.50/168.35 => 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) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_listsum__addf,axiom,
% 168.50/168.35 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 168.50/168.35 ( class_Groups_Ocomm__monoid__add(T_b)
% 168.50/168.35 => 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))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_listsum__0,axiom,
% 168.50/168.35 ! [V_xs_2,T_c,T_b] :
% 168.50/168.35 ( class_Groups_Omonoid__add(T_b)
% 168.50/168.35 => 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) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_listsum__mult__const,axiom,
% 168.50/168.35 ! [V_xs_2,V_c_2,V_f_2,T_c,T_b] :
% 168.50/168.35 ( class_Rings_Osemiring__0(T_b)
% 168.50/168.35 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_c_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),V_c_2) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_listsum__const__mult,axiom,
% 168.50/168.35 ! [V_xs_2,V_f_2,V_c_2,T_c,T_b] :
% 168.50/168.35 ( class_Rings_Osemiring__0(T_b)
% 168.50/168.35 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2)),V_f_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_listsum__subtractf,axiom,
% 168.50/168.35 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 168.50/168.35 ( class_Groups_Oab__group__add(T_b)
% 168.50/168.35 => 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))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_inj__map__eq__map,axiom,
% 168.50/168.35 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
% 168.50/168.35 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 168.50/168.35 => ( 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)
% 168.50/168.35 <=> V_xs_2 = V_ys_2 ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_map__injective,axiom,
% 168.50/168.35 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 168.50/168.35 ( 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)
% 168.50/168.35 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 168.50/168.35 => V_xs_2 = V_ys_2 ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_map__ident,axiom,
% 168.50/168.35 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)),V_xs_2) = V_xs_2 ).
% 168.50/168.35
% 168.50/168.35 fof(fact_take__map,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_map__butlast,axiom,
% 168.50/168.35 ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Obutlast(T_c,V_xs_2)) = c_List_Obutlast(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_set__map,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_map_Osimps_I2_J,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_map__append,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_hd__map,axiom,
% 168.50/168.35 ! [V_f_2,T_c,T_b,V_xs_2] :
% 168.50/168.35 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 168.50/168.35 => 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)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_drop__map,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_List_Omap_Oidentity,axiom,
% 168.50/168.35 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_List_Omap_Ocomp,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_map__comp__map,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_List_Omap_Ocompositionality,axiom,
% 168.50/168.35 ! [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) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_map__map,axiom,
% 168.50/168.35 ! [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) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_list__size__map,axiom,
% 168.50/168.35 ! [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) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_inj__on__map__eq__map,axiom,
% 168.50/168.35 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
% 168.50/168.35 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)))
% 168.50/168.35 => ( 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)
% 168.50/168.35 <=> V_xs_2 = V_ys_2 ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_map__inj__on,axiom,
% 168.50/168.35 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 168.50/168.35 ( 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)
% 168.50/168.35 => ( 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)))
% 168.50/168.35 => V_xs_2 = V_ys_2 ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_nth__map,axiom,
% 168.50/168.35 ! [V_f_2,T_c,V_xs_2,T_b,V_n_2] :
% 168.50/168.35 ( 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)))
% 168.50/168.35 => 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)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_map__fun__upd,axiom,
% 168.50/168.35 ! [V_v_2,V_f_2,T_c,V_xs_2,V_y_2,T_b] :
% 168.50/168.35 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.35 => hAPP(hAPP(c_List_Omap(T_b,T_c),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) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_distinct__map,axiom,
% 168.50/168.35 ! [V_xs_2,V_f_2,T_c,T_b] :
% 168.50/168.35 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
% 168.50/168.35 <=> ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
% 168.50/168.35 & c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(c_List_Oset(T_c),V_xs_2)) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_listsum__abs,axiom,
% 168.50/168.35 ! [V_xs_2,T_b] :
% 168.50/168.35 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 168.50/168.35 => 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)))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_uminus__listsum__map,axiom,
% 168.50/168.35 ! [V_xs_2,V_f_2,T_c,T_b] :
% 168.50/168.35 ( class_Groups_Oab__group__add(T_b)
% 168.50/168.35 => 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)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_inj__on__mapI,axiom,
% 168.50/168.35 ! [V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.35 ( 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)))
% 168.50/168.35 => 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) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_inj__mapD,axiom,
% 168.50/168.35 ! [V_f_2,T_c,T_b] :
% 168.50/168.35 ( 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)))
% 168.50/168.35 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_inj__map,axiom,
% 168.50/168.35 ! [V_f_2,T_c,T_b] :
% 168.50/168.35 ( 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)))
% 168.50/168.35 <=> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_listsum__distinct__conv__setsum__set,axiom,
% 168.50/168.35 ! [V_f_2,V_xs_2,T_b,T_c] :
% 168.50/168.35 ( class_Groups_Ocomm__monoid__add(T_c)
% 168.50/168.35 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 168.50/168.35 => 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)) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_listsum__triv,axiom,
% 168.50/168.35 ! [V_xs_2,V_r_2,T_c,T_b] :
% 168.50/168.35 ( class_Rings_Osemiring__1(T_b)
% 168.50/168.35 => 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) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_listsum__map__remove1,axiom,
% 168.50/168.35 ! [V_f_2,V_xs_2,V_x_2,T_b,T_c] :
% 168.50/168.35 ( class_Groups_Ocomm__monoid__add(T_c)
% 168.50/168.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.35 => 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)))) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_Nitpick_Osetsum_H__def,axiom,
% 168.50/168.35 ! [V_f_2,V_A_2,T_b,T_c] :
% 168.50/168.35 ( class_Groups_Ocomm__monoid__add(T_c)
% 168.50/168.35 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.35 => 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))))) )
% 168.50/168.35 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.35 => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_pick__same,axiom,
% 168.50/168.35 ! [V_xs_2,T_b,V_l_2] :
% 168.50/168.35 ( 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)))
% 168.50/168.35 => 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) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_zero__code__numeral__def,axiom,
% 168.50/168.35 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_Code__Numeral_Oof__nat__inject,axiom,
% 168.50/168.35 ! [V_m_2,V_n_2] :
% 168.50/168.35 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2)
% 168.50/168.35 <=> V_n_2 = V_m_2 ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_Code__Numeral_Oof__nat__code,axiom,
% 168.50/168.35 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_times__code__numeral__code,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_one__code__numeral__def,axiom,
% 168.50/168.35 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_less__code__numeral__code,axiom,
% 168.50/168.35 ! [V_m_2,V_n_2] :
% 168.50/168.35 ( 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)))
% 168.50/168.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_code__numeral_Oof__nat__inject,axiom,
% 168.50/168.35 ! [V_y_2,V_x_2] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 168.50/168.35 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 168.50/168.35 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2)
% 168.50/168.35 <=> V_x_2 = V_y_2 ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_map__fst__zip,axiom,
% 168.50/168.35 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 168.50/168.35 ( 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)
% 168.50/168.35 => 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 ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_map__snd__zip,axiom,
% 168.50/168.35 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 168.50/168.35 ( 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)
% 168.50/168.35 => 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 ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_number__of__code__numeral__def,axiom,
% 168.50/168.35 c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Int_Oint,c_Code__Numeral_Oof__nat),c_Int_Onat) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_zip__map__fst__snd,axiom,
% 168.50/168.35 ! [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 ).
% 168.50/168.35
% 168.50/168.35 fof(fact_plus__code__numeral__code,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_less__eq__code__numeral__code,axiom,
% 168.50/168.35 ! [V_m_2,V_n_2] :
% 168.50/168.35 ( 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)))
% 168.50/168.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_subtract__code__numeral__code,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_pick__member,axiom,
% 168.50/168.35 ! [V_xs_2,T_b,V_i_2] :
% 168.50/168.35 ( 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))))
% 168.50/168.35 => 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)))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_zip__eq__conv,axiom,
% 168.50/168.35 ! [V_zs_2,V_ys_2,T_c,V_xs_2,T_b] :
% 168.50/168.35 ( 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)
% 168.50/168.35 => ( hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2) = V_zs_2
% 168.50/168.35 <=> ( 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
% 168.50/168.35 & 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 ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_list__size__conv__listsum,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_code__numeral__not__eq__zero,axiom,
% 168.50/168.35 ! [V_i_2] :
% 168.50/168.35 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 168.50/168.35 <=> 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)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_interv__listsum__conv__setsum__set__int,axiom,
% 168.50/168.35 ! [V_l_2,V_k_2,V_f_2,T_b] :
% 168.50/168.35 ( class_Groups_Ocomm__monoid__add(T_b)
% 168.50/168.35 => 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))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_setsum__set__upto__conv__listsum__int,axiom,
% 168.50/168.35 ! [V_j_2,V_i_2,V_f_2,T_b] :
% 168.50/168.35 ( class_Groups_Ocomm__monoid__add(T_b)
% 168.50/168.35 => 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))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_select__weight__member,axiom,
% 168.50/168.35 ! [V_s_2,V_xs_2,T_b] :
% 168.50/168.35 ( 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))))
% 168.50/168.35 => 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)))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_select__weight__def,axiom,
% 168.50/168.35 ! [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))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_select__def,axiom,
% 168.50/168.35 ! [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))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_listsum__mono,axiom,
% 168.50/168.35 ! [V_g_2,V_f_2,V_xs_2,T_b,T_c] :
% 168.50/168.35 ( ( class_Groups_Omonoid__add(T_c)
% 168.50/168.35 & class_Groups_Oordered__ab__semigroup__add(T_c) )
% 168.50/168.35 => ( ! [B_x] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 168.50/168.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_g_2),V_xs_2)))) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_nat__of__inverse,axiom,
% 168.50/168.35 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ).
% 168.50/168.35
% 168.50/168.35 fof(fact_of__nat__nat__of,axiom,
% 168.50/168.35 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ).
% 168.50/168.35
% 168.50/168.35 fof(fact_nat__of__of__nat,axiom,
% 168.50/168.35 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ).
% 168.50/168.35
% 168.50/168.35 fof(fact_Code__Numeral_Onat__of__inject,axiom,
% 168.50/168.35 ! [V_l_2,V_k_2] :
% 168.50/168.35 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2)
% 168.50/168.35 <=> V_k_2 = V_l_2 ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_code__numeral_Onat__of__inject,axiom,
% 168.50/168.35 ! [V_y_2,V_x_2] :
% 168.50/168.35 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2)
% 168.50/168.35 <=> V_x_2 = V_y_2 ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_times__code__numeral__def,axiom,
% 168.50/168.35 ! [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))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_type__definition__code__numeral,axiom,
% 168.50/168.35 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))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_less__code__numeral__def,axiom,
% 168.50/168.35 ! [V_m_2,V_n_2] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 168.50/168.35 <=> 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))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_nat__of,axiom,
% 168.50/168.35 ! [V_x_2] : hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_x_2)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_nat__of__number,axiom,
% 168.50/168.35 ! [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) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_int__of__def,axiom,
% 168.50/168.35 c_Code__Numeral_Oint__of = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Int_Oint,tc_Code__Numeral_Ocode__numeral,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Code__Numeral_Onat__of) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_less__eq__code__numeral__def,axiom,
% 168.50/168.35 ! [V_m_2,V_n_2] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 168.50/168.35 <=> 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))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_nat__of__code,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_nat__of__aux__def,axiom,
% 168.50/168.35 ! [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) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_Suc__code__numeral__def,axiom,
% 168.50/168.35 ! [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))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_minus__code__numeral__def,axiom,
% 168.50/168.35 ! [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))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_of__nat__inverse,axiom,
% 168.50/168.35 ! [V_y_2] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 168.50/168.35 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_plus__code__numeral__def,axiom,
% 168.50/168.35 ! [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))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_div__code__numeral__def,axiom,
% 168.50/168.35 ! [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))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_mod__code__numeral__def,axiom,
% 168.50/168.35 ! [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))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_code__numeral__decr,axiom,
% 168.50/168.35 ! [V_k] :
% 168.50/168.35 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 168.50/168.35 => 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))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_New__DSequence_Opos__not__seq__def,axiom,
% 168.50/168.35 ! [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))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_partition__set,axiom,
% 168.50/168.35 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_b] :
% 168.50/168.35 ( c_List_Opartition(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2)
% 168.50/168.35 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_yes_2)),hAPP(c_List_Oset(T_b),V_no_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_partition__P,axiom,
% 168.50/168.35 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_b] :
% 168.50/168.35 ( c_List_Opartition(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2)
% 168.50/168.35 => ( ! [B_x] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_yes_2)))
% 168.50/168.35 => hBOOL(hAPP(V_P_2,B_x)) )
% 168.50/168.35 & ! [B_x] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_no_2)))
% 168.50/168.35 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_partition_Osimps_I1_J,axiom,
% 168.50/168.35 ! [V_P_2,T_b] : c_List_Opartition(T_b,V_P_2,c_List_Olist_ONil(T_b)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olist_ONil(T_b)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_partition_Osimps_I2_J,axiom,
% 168.50/168.35 ! [V_xs_2,V_x_2,V_P_2,T_b] : c_List_Opartition(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),hAPP(c_If(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(V_P_2,V_x_2)))),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_List_Olist_OCons(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBB(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_List_Olist(T_b))),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(c_List_Olist_OCons(T_b),V_x_2)))),c_List_Opartition(T_b,V_P_2,V_xs_2)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_lists__Int__eq,axiom,
% 168.50/168.35 ! [V_B_2,V_A_2,T_b] : c_List_Olistsp(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_b))),c_List_Olists(T_b,V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_b))),c_List_Olists(T_b,V_B_2))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_lists__IntI,axiom,
% 168.50/168.35 ! [V_B_2,V_A_2,V_l_2,T_b] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_A_2)))
% 168.50/168.35 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_B_2)))
% 168.50/168.35 => hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_l_2)) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_listsp_ONil,axiom,
% 168.50/168.35 ! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_listsp_Oequations_I1_J,axiom,
% 168.50/168.35 ! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_in__listsp__conv__set,axiom,
% 168.50/168.35 ! [V_xs_2,V_A_2,T_b] :
% 168.50/168.35 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2))
% 168.50/168.35 <=> ! [B_x] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.35 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_listsp__conj__eq,axiom,
% 168.50/168.35 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 168.50/168.35 ( hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_A_2)),V_B_2)),V_x_2))
% 168.50/168.35 <=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_x_2))
% 168.50/168.35 & hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_x_2)) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_listsp__infI,axiom,
% 168.50/168.35 ! [V_B_2,V_l_2,V_A_2,T_b] :
% 168.50/168.35 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_l_2))
% 168.50/168.35 => ( hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_l_2))
% 168.50/168.35 => hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_l_2)) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_listsp__inf__eq,axiom,
% 168.50/168.35 ! [V_B_2,V_A_2,T_b] : c_List_Olistsp(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),c_List_Olistsp(T_b,V_A_2)),c_List_Olistsp(T_b,V_B_2)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_listsp_Oequations_I2_J,axiom,
% 168.50/168.35 ! [V_a2_2,V_a1_2,V_A_2,T_b] :
% 168.50/168.35 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a2_2)))
% 168.50/168.35 <=> ( hBOOL(hAPP(V_A_2,V_a1_2))
% 168.50/168.35 & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_a2_2)) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_append__in__listsp__conv,axiom,
% 168.50/168.35 ! [V_ys_2,V_xs_2,V_A_2,T_b] :
% 168.50/168.35 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
% 168.50/168.35 <=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2))
% 168.50/168.35 & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_ys_2)) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_listsp__mono,axiom,
% 168.50/168.35 ! [V_B_2,V_A_2,T_b] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.50/168.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),c_List_Olistsp(T_b,V_A_2)),c_List_Olistsp(T_b,V_B_2))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_listsp__lists__eq,axiom,
% 168.50/168.35 ! [V_x_2,V_A_2,T_b] :
% 168.50/168.35 ( hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),V_x_2))
% 168.50/168.35 <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_x_2),c_List_Olists(T_b,V_A_2))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_product_Osimps_I2_J,axiom,
% 168.50/168.35 ! [V_ys_2,V_xs_2,V_x_2,T_c,T_b] : c_Enum_Oproduct(T_b,T_c,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Omap(T_c,tc_prod(T_b,T_c)),hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2)),V_ys_2)),c_Enum_Oproduct(T_b,T_c,V_xs_2,V_ys_2)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_list__all2__def,axiom,
% 168.50/168.35 ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 168.50/168.35 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 168.50/168.35 <=> ( 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)
% 168.50/168.35 & ! [B_x] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
% 168.50/168.35 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2),B_x)) ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_list__all2__map2,axiom,
% 168.50/168.35 ! [V_bs_2,V_f_2,T_d,V_as_2,V_P_2,T_c,T_b] :
% 168.50/168.35 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_as_2,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_bs_2))
% 168.50/168.35 <=> c_List_Olist__all2(T_b,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBB(T_c,tc_HOL_Obool,T_d)),V_P_2)),V_f_2),V_as_2,V_bs_2) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_list__all2__map1,axiom,
% 168.50/168.35 ! [V_bs_2,V_as_2,V_f_2,T_d,V_P_2,T_c,T_b] :
% 168.50/168.35 ( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_as_2),V_bs_2)
% 168.50/168.35 <=> c_List_Olist__all2(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),V_P_2),V_f_2),V_as_2,V_bs_2) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_list__all2__dropI,axiom,
% 168.50/168.35 ! [V_n_2,V_bs_2,V_as_2,V_P_2,T_c,T_b] :
% 168.50/168.35 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_as_2,V_bs_2)
% 168.50/168.35 => c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_as_2),hAPP(hAPP(c_List_Odrop(T_c),V_n_2),V_bs_2)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_list__all2__appendI,axiom,
% 168.50/168.35 ! [V_d_2,V_c_2,V_b_2,V_a_2,V_P_2,T_c,T_b] :
% 168.50/168.35 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_a_2,V_b_2)
% 168.50/168.35 => ( c_List_Olist__all2(T_b,T_c,V_P_2,V_c_2,V_d_2)
% 168.50/168.35 => c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_a_2),V_c_2),hAPP(hAPP(c_List_Oappend(T_c),V_b_2),V_d_2)) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_list__all2__append,axiom,
% 168.50/168.35 ! [V_vs_2,V_us_2,V_P_2,V_ys_2,T_c,V_xs_2,T_b] :
% 168.50/168.35 ( 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)
% 168.50/168.35 => ( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_us_2),hAPP(hAPP(c_List_Oappend(T_c),V_ys_2),V_vs_2))
% 168.50/168.35 <=> ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 168.50/168.35 & c_List_Olist__all2(T_b,T_c,V_P_2,V_us_2,V_vs_2) ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_list__all2__Cons,axiom,
% 168.50/168.35 ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_P_2,T_c,T_b] :
% 168.50/168.35 ( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2))
% 168.50/168.35 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 168.50/168.35 & c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_list__all2__takeI,axiom,
% 168.50/168.35 ! [V_n_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 168.50/168.35 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 168.50/168.35 => c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2),hAPP(hAPP(c_List_Otake(T_c),V_n_2),V_ys_2)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_list__all2__eq,axiom,
% 168.50/168.35 ! [T_b,V_ys_2,V_xs_2] :
% 168.50/168.35 ( V_xs_2 = V_ys_2
% 168.50/168.35 <=> c_List_Olist__all2(T_b,T_b,c_fequal,V_xs_2,V_ys_2) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_list__all2__lengthD,axiom,
% 168.50/168.35 ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 168.50/168.35 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 168.50/168.35 => 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) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_list__all2__Nil,axiom,
% 168.50/168.35 ! [V_ys_2,V_P_2,T_c,T_b] :
% 168.50/168.35 ( c_List_Olist__all2(T_b,T_c,V_P_2,c_List_Olist_ONil(T_b),V_ys_2)
% 168.50/168.35 <=> V_ys_2 = c_List_Olist_ONil(T_c) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_list__all2__Nil2,axiom,
% 168.50/168.35 ! [V_xs_2,V_P_2,T_c,T_b] :
% 168.50/168.35 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,c_List_Olist_ONil(T_c))
% 168.50/168.35 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_product_Osimps_I1_J,axiom,
% 168.50/168.35 ! [V_uu,T_b,T_a] : c_Enum_Oproduct(T_a,T_b,c_List_Olist_ONil(T_a),V_uu) = c_List_Olist_ONil(tc_prod(T_a,T_b)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_list__all2__nthD2,axiom,
% 168.50/168.35 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 168.50/168.35 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 168.50/168.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_p_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))
% 168.50/168.35 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),V_p_2))) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_list__all2__nthD,axiom,
% 168.50/168.35 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 168.50/168.35 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 168.50/168.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_p_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 168.50/168.35 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),V_p_2))) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_list__all2__conv__all__nth,axiom,
% 168.50/168.35 ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 168.50/168.35 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 168.50/168.35 <=> ( 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)
% 168.50/168.35 & ! [B_i] :
% 168.50/168.35 ( 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)))
% 168.50/168.35 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),B_i))) ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_list__all2__update__cong2,axiom,
% 168.50/168.35 ! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 168.50/168.35 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 168.50/168.35 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 168.50/168.35 => ( 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)))
% 168.50/168.35 => c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_c,V_ys_2),V_i_2),V_y_2)) ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_list__all2__update__cong,axiom,
% 168.50/168.35 ! [V_y_2,V_x_2,V_ys_2,V_P_2,T_c,V_xs_2,T_b,V_i_2] :
% 168.50/168.35 ( 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)))
% 168.50/168.35 => ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 168.50/168.35 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 168.50/168.35 => c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_c,V_ys_2),V_i_2),V_y_2)) ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_distinct__product,axiom,
% 168.50/168.35 ! [V_ys,T_b,V_xs,T_a] :
% 168.50/168.35 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 168.50/168.35 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys))
% 168.50/168.35 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys))) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_product__list__set,axiom,
% 168.50/168.35 ! [V_ys_2,V_xs_2,T_c,T_b] : hAPP(c_List_Oset(tc_prod(T_b,T_c)),c_Enum_Oproduct(T_b,T_c,V_xs_2,V_ys_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_List_Oset(T_c),V_ys_2))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sublists__powset,axiom,
% 168.50/168.35 ! [V_xs_2,T_b] : hAPP(c_Set_Oimage(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),c_List_Oset(T_b)),hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_Osublists(T_b,V_xs_2))) = hAPP(c_Set_OPow(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_length__sublists,axiom,
% 168.50/168.35 ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_Enum_Osublists(T_a,V_xs)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sublists_Osimps_I1_J,axiom,
% 168.50/168.35 ! [T_a] : c_Enum_Osublists(T_a,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sublists_Osimps_I2_J,axiom,
% 168.50/168.35 ! [V_xs_2,V_x_2,T_b] : c_Enum_Osublists(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_Enum_Osublists(T_b,V_xs_2)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(T_b)),tc_fun(tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),tc_List_Olist(tc_List_Olist(T_b))),c_List_Oappend(tc_List_Olist(T_b))),hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(c_List_Olist_OCons(T_b),V_x_2)))),c_COMBI(tc_List_Olist(tc_List_Olist(T_b))))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_distinct__set__sublists,axiom,
% 168.50/168.35 ! [V_xs_2,T_b] :
% 168.50/168.35 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 168.50/168.35 => hBOOL(hAPP(c_List_Odistinct(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),c_List_Oset(T_b)),c_Enum_Osublists(T_b,V_xs_2)))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_set__n__lists,axiom,
% 168.50/168.35 ! [V_xs_2,V_n_2,T_b] : hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_On__lists(T_b,V_n_2,V_xs_2)) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),hAPP(c_List_Oset(T_b),V_xs_2)))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_enum__the__def,axiom,
% 168.50/168.35 ! [V_P_2,T_b] : c_Enum_Oenum__the(T_b,V_P_2) = c_HOL_OThe(T_b,V_P_2) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_distinct__n__lists,axiom,
% 168.50/168.35 ! [V_n,V_xs,T_a] :
% 168.50/168.35 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 168.50/168.35 => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_n__lists__Nil,axiom,
% 168.50/168.35 ! [T_a,V_n] :
% 168.50/168.35 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.50/168.35 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a))) )
% 168.50/168.35 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.50/168.35 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_n__lists_Osimps_I1_J,axiom,
% 168.50/168.35 ! [V_xs,T_a] : c_Enum_On__lists(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_xs) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_length__n__lists,axiom,
% 168.50/168.35 ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_Enum_On__lists(T_a,V_n,V_xs)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_length__n__lists__elem,axiom,
% 168.50/168.35 ! [V_xs_2,V_n_2,V_ys_2,T_b] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_On__lists(T_b,V_n_2,V_xs_2))))
% 168.50/168.35 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_list__all2I,axiom,
% 168.50/168.35 ! [V_P_2,V_b_2,V_a_2,T_c,T_b] :
% 168.50/168.35 ( ! [B_x] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_a_2),V_b_2))))
% 168.50/168.35 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2),B_x)) )
% 168.50/168.35 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_b_2)
% 168.50/168.35 => c_List_Olist__all2(T_b,T_c,V_P_2,V_a_2,V_b_2) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_all__nth__imp__all__set,axiom,
% 168.50/168.35 ! [V_x_2,V_P_2,V_xs_2,T_b] :
% 168.50/168.35 ( ! [B_i] :
% 168.50/168.35 ( 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)))
% 168.50/168.35 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) )
% 168.50/168.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.35 => hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_fun__left__comm_Ofold__set__remdups,axiom,
% 168.50/168.35 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
% 168.50/168.35 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 168.50/168.35 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_f_2),V_y_2),c_List_Oremdups(T_b,V_xs_2)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_map__removeAll__inj__on,axiom,
% 168.50/168.35 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 168.50/168.35 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.35 => hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_c,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_distinct__remdups,axiom,
% 168.50/168.35 ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_length__remdups__leq,axiom,
% 168.50/168.35 ! [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))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_distinct__remdups__id,axiom,
% 168.50/168.35 ! [V_xs,T_a] :
% 168.50/168.35 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 168.50/168.35 => c_List_Oremdups(T_a,V_xs) = V_xs ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_distinct__removeAll,axiom,
% 168.50/168.35 ! [V_x,V_xs,T_a] :
% 168.50/168.35 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 168.50/168.35 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_remdups__id__iff__distinct,axiom,
% 168.50/168.35 ! [V_xs_2,T_b] :
% 168.50/168.35 ( c_List_Oremdups(T_b,V_xs_2) = V_xs_2
% 168.50/168.35 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_set__remdups,axiom,
% 168.50/168.35 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_length__remdups__eq,axiom,
% 168.50/168.35 ! [V_xs_2,T_b] :
% 168.50/168.35 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)
% 168.50/168.35 <=> c_List_Oremdups(T_b,V_xs_2) = V_xs_2 ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_remdups__remdups,axiom,
% 168.50/168.35 ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_remdups__eq__nil__iff,axiom,
% 168.50/168.35 ! [V_x_2,T_b] :
% 168.50/168.35 ( c_List_Oremdups(T_b,V_x_2) = c_List_Olist_ONil(T_b)
% 168.50/168.35 <=> V_x_2 = c_List_Olist_ONil(T_b) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_removeAll_Osimps_I1_J,axiom,
% 168.50/168.35 ! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_remdups__eq__nil__right__iff,axiom,
% 168.50/168.35 ! [V_x_2,T_b] :
% 168.50/168.35 ( c_List_Olist_ONil(T_b) = c_List_Oremdups(T_b,V_x_2)
% 168.50/168.35 <=> V_x_2 = c_List_Olist_ONil(T_b) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_remdups_Osimps_I1_J,axiom,
% 168.50/168.35 ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_removeAll_Osimps_I2_J,axiom,
% 168.50/168.35 ! [V_xs,T_a,V_y,V_x] :
% 168.50/168.35 ( ( V_x = V_y
% 168.50/168.35 => hAPP(c_List_OremoveAll(T_a,V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) )
% 168.50/168.35 & ( V_x != V_y
% 168.50/168.35 => hAPP(c_List_OremoveAll(T_a,V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),hAPP(c_List_OremoveAll(T_a,V_x),V_xs)) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_removeAll__append,axiom,
% 168.50/168.35 ! [V_ys,V_xs,V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs)),hAPP(c_List_OremoveAll(T_a,V_x),V_ys)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_remdups__map__remdups,axiom,
% 168.50/168.35 ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oremdups(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oremdups(T_c,V_xs_2))) = c_List_Oremdups(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_remove1__remdups,axiom,
% 168.50/168.35 ! [V_x,V_xs,T_a] :
% 168.50/168.35 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 168.50/168.35 => c_List_Oremove1(T_a,V_x,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,c_List_Oremove1(T_a,V_x,V_xs)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_removeAll__id,axiom,
% 168.50/168.35 ! [V_xs_2,V_x_2,T_b] :
% 168.50/168.35 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.35 => hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2) = V_xs_2 ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_distinct__remove1__removeAll,axiom,
% 168.50/168.35 ! [V_x,V_xs,T_a] :
% 168.50/168.35 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 168.50/168.35 => c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_remdups_Osimps_I2_J,axiom,
% 168.50/168.35 ! [V_xs_2,V_x_2,T_b] :
% 168.50/168.35 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.35 => c_List_Oremdups(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Oremdups(T_b,V_xs_2) )
% 168.50/168.35 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.35 => c_List_Oremdups(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oremdups(T_b,V_xs_2)) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_length__remdups__card__conv,axiom,
% 168.50/168.35 ! [V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_map__removeAll__inj,axiom,
% 168.50/168.35 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 168.50/168.35 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 168.50/168.35 => hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_c,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_set__removeAll,axiom,
% 168.50/168.35 ! [V_xs_2,V_x_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_length__remdups__concat,axiom,
% 168.50/168.35 ! [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))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sorted__list__of__set__sort__remdups,axiom,
% 168.50/168.35 ! [V_xs_2,T_b] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_b)
% 168.50/168.35 => c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),c_List_Oremdups(T_b,V_xs_2)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_concat__conv__foldl,axiom,
% 168.50/168.35 ! [V_xss_2,T_b] : c_List_Oconcat(T_b,V_xss_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Oappend(T_b),c_List_Olist_ONil(T_b)),V_xss_2) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sort__key__simps_I1_J,axiom,
% 168.50/168.35 ! [V_f_2,T_b,T_c] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_c)
% 168.50/168.35 => c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_foldl__conv__concat,axiom,
% 168.50/168.35 ! [V_xss_2,V_xs_2,T_b] : hAPP(c_List_Ofoldl(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Oappend(T_b),V_xs_2),V_xss_2) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_Oconcat(T_b,V_xss_2)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_length__sort,axiom,
% 168.50/168.35 ! [V_xs_2,V_f_2,T_b,T_c] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_c)
% 168.50/168.35 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_set__sort,axiom,
% 168.50/168.35 ! [V_xs_2,V_f_2,T_b,T_c] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_c)
% 168.50/168.35 => hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_distinct__sort,axiom,
% 168.50/168.35 ! [V_xs_2,V_f_2,T_b,T_c] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_c)
% 168.50/168.35 => ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)))
% 168.50/168.35 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_concat_Osimps_I1_J,axiom,
% 168.50/168.35 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_concat_Osimps_I2_J,axiom,
% 168.50/168.35 ! [V_xs,V_x,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_a),V_x),c_List_Oconcat(T_a,V_xs)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_concat__eq__Nil__conv,axiom,
% 168.50/168.35 ! [V_xss_2,T_b] :
% 168.50/168.35 ( c_List_Oconcat(T_b,V_xss_2) = c_List_Olist_ONil(T_b)
% 168.50/168.35 <=> ! [B_x] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
% 168.50/168.35 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_Nil__eq__concat__conv,axiom,
% 168.50/168.35 ! [V_xss_2,T_b] :
% 168.50/168.35 ( c_List_Olist_ONil(T_b) = c_List_Oconcat(T_b,V_xss_2)
% 168.50/168.35 <=> ! [B_x] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
% 168.50/168.35 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_map__concat,axiom,
% 168.50/168.35 ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oconcat(T_c,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),V_xs_2)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_length__concat,axiom,
% 168.50/168.35 ! [V_xss_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oconcat(T_b,V_xss_2)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xss_2)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_set__concat,axiom,
% 168.50/168.35 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oconcat(T_b,V_xs_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)),c_List_Oset(T_b)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sort__key__simps_I2_J,axiom,
% 168.50/168.35 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_c)
% 168.50/168.35 => c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_concat__append,axiom,
% 168.50/168.35 ! [V_ys,V_xs,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Oappend(tc_List_Olist(T_a)),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oconcat(T_a,V_xs)),c_List_Oconcat(T_a,V_ys)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sort__foldl__insort,axiom,
% 168.50/168.35 ! [V_xs_2,T_b] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_b)
% 168.50/168.35 => c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),T_b,hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b))),c_List_Olist_ONil(T_b)),V_xs_2) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_concat__injective,axiom,
% 168.50/168.35 ! [V_ys_2,V_xs_2,T_b] :
% 168.50/168.35 ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
% 168.50/168.35 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_ys_2)
% 168.50/168.35 => ( ! [B_x] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2))))
% 168.50/168.35 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),B_x)) )
% 168.50/168.35 => V_xs_2 = V_ys_2 ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_concat__eq__concat__iff,axiom,
% 168.50/168.35 ! [V_ys_2,V_xs_2,T_b] :
% 168.50/168.35 ( ! [B_x] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2))))
% 168.50/168.35 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),B_x)) )
% 168.50/168.35 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_ys_2)
% 168.50/168.35 => ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
% 168.50/168.35 <=> V_xs_2 = V_ys_2 ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_concat__map__singleton,axiom,
% 168.50/168.35 ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_c),c_List_Olist_OCons(T_b)),V_f_2)),c_List_Olist_ONil(T_b))),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_n__lists_Osimps_I2_J,axiom,
% 168.50/168.35 ! [V_xs_2,V_n_2,T_b] : c_Enum_On__lists(T_b,hAPP(c_Nat_OSuc,V_n_2),V_xs_2) = c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_List_Omap(T_b,tc_List_Olist(T_b))),hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)))),V_xs_2)),c_Enum_On__lists(T_b,V_n_2,V_xs_2))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_transpose_Osimps_I3_J,axiom,
% 168.50/168.35 ! [V_xss_2,V_xs_2,V_x_2,T_b] : c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)))),c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2))))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_transpose__aux__filter__head,axiom,
% 168.50/168.35 ! [V_xss_2,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),c_List_Ohd(T_b)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xss_2)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_filter__concat,axiom,
% 168.50/168.35 ! [V_xs_2,V_p_2,T_b] : hAPP(c_List_Ofilter(T_b,V_p_2),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Ofilter(T_b,V_p_2)),V_xs_2)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_filter__sort,axiom,
% 168.50/168.35 ! [V_xs_2,V_f_2,V_P_2,T_b,T_c] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_c)
% 168.50/168.35 => hAPP(c_List_Ofilter(T_b,V_P_2),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) = c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_distinct__filter,axiom,
% 168.50/168.35 ! [V_P_2,V_xs_2,T_b] :
% 168.50/168.35 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 168.50/168.35 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sum__length__filter__compl,axiom,
% 168.50/168.35 ! [V_xs_2,V_P_2,T_b] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2)),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_filter__is__subset,axiom,
% 168.50/168.35 ! [V_xs_2,V_P_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_filter__id__conv,axiom,
% 168.50/168.35 ! [V_xs_2,V_P_2,T_b] :
% 168.50/168.35 ( hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) = V_xs_2
% 168.50/168.35 <=> ! [B_x] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.35 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_length__filter__le,axiom,
% 168.50/168.35 ! [V_xs_2,V_P_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_filter__filter,axiom,
% 168.50/168.35 ! [V_xs_2,V_Q_2,V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(c_List_Ofilter(T_b,V_Q_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Q_2)),V_P_2)),V_xs_2) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_filter__remove1,axiom,
% 168.50/168.35 ! [V_xs_2,V_x_2,V_Q_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Q_2),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_Q_2),V_xs_2)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_remove1__filter__not,axiom,
% 168.50/168.35 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 168.50/168.35 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 168.50/168.35 => c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_filter__insort__triv,axiom,
% 168.50/168.35 ! [V_xs_2,V_f_2,T_b,V_x_2,V_P_2,T_c] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_c)
% 168.50/168.35 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 168.50/168.35 => hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_partition__filter1,axiom,
% 168.50/168.35 ! [V_xs_2,V_P_2,T_b] : hAPP(c_Product__Type_Ofst(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_P_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_partition__filter2,axiom,
% 168.50/168.35 ! [V_xs_2,V_P_2,T_b] : hAPP(c_Product__Type_Osnd(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_P_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_b,c_fNot),V_P_2)),V_xs_2) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_partition__filter__conv,axiom,
% 168.50/168.35 ! [V_xs_2,V_f_2,T_b] : c_List_Opartition(T_b,V_f_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_f_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_b,c_fNot),V_f_2)),V_xs_2)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_filter__map,axiom,
% 168.50/168.35 ! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_P_2),V_f_2)),V_xs_2)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_filter_Osimps_I1_J,axiom,
% 168.50/168.35 ! [V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_2),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_transpose_Osimps_I1_J,axiom,
% 168.50/168.35 ! [T_a] : c_List_Otranspose(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(tc_List_Olist(T_a)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_filter_Osimps_I2_J,axiom,
% 168.50/168.35 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 168.50/168.35 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 168.50/168.35 => hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) )
% 168.50/168.35 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 168.50/168.35 => hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_filter__append,axiom,
% 168.50/168.35 ! [V_ys_2,V_xs_2,V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,V_P_2),V_ys_2)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_filter__empty__conv,axiom,
% 168.50/168.35 ! [V_xs_2,V_P_2,T_b] :
% 168.50/168.35 ( hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 168.50/168.35 <=> ! [B_x] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.35 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_length__filter__map,axiom,
% 168.50/168.35 ! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_P_2),V_f_2)),V_xs_2)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_removeAll__filter__not__eq,axiom,
% 168.50/168.35 ! [V_x_2,T_b] : c_List_OremoveAll(T_b,V_x_2) = c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(c_fequal,V_x_2))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_remdups__filter,axiom,
% 168.50/168.35 ! [V_xs_2,V_P_2,T_b] : c_List_Oremdups(T_b,hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),c_List_Oremdups(T_b,V_xs_2)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_removeAll__filter__not,axiom,
% 168.50/168.35 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 168.50/168.35 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 168.50/168.35 => hAPP(c_List_OremoveAll(T_b,V_x_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_transpose_Osimps_I2_J,axiom,
% 168.50/168.35 ! [V_xss,T_a] : c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xss)) = c_List_Otranspose(T_a,V_xss) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_nth__transpose,axiom,
% 168.50/168.35 ! [V_xs_2,T_b,V_i_2] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2))))
% 168.50/168.35 => hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),c_List_Otranspose(T_b,V_xs_2)),V_i_2) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,T_b),c_List_Onth(T_b)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_xs_2)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_transpose__map__map,axiom,
% 168.50/168.35 ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Otranspose(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),V_xs_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),c_List_Otranspose(T_c,V_xs_2)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_set__filter,axiom,
% 168.50/168.35 ! [V_xs_2,V_P_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)))),V_P_2)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_length__filter__less,axiom,
% 168.50/168.35 ! [V_P_2,V_xs_2,V_x_2,T_b] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.35 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 168.50/168.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_set__minus__filter__out,axiom,
% 168.50/168.35 ! [V_y_2,V_xs_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_y_2))),V_xs_2)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_filter__in__sublist,axiom,
% 168.50/168.35 ! [V_s_2,V_xs_2,T_b] :
% 168.50/168.35 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 168.50/168.35 => hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_s_2)))),V_xs_2) = c_List_Osublist(T_b,V_xs_2,V_s_2) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_transpose__empty,axiom,
% 168.50/168.35 ! [V_xs_2,T_b] :
% 168.50/168.35 ( c_List_Otranspose(T_b,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_b))
% 168.50/168.35 <=> ! [B_x] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 168.50/168.35 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_length__filter__conv__card,axiom,
% 168.50/168.35 ! [V_xs_2,V_p_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_p_2),V_xs_2)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat),V_p_2),hAPP(c_List_Onth(T_b),V_xs_2))))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_transpose__aux__filter__tail,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_transpose_Opsimps_I3_J,axiom,
% 168.50/168.35 ! [V_xss_2,V_xs_2,V_x_2,T_b] :
% 168.50/168.35 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)))
% 168.50/168.35 => c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)))),c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2))))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_transpose_Opsimps_I2_J,axiom,
% 168.50/168.35 ! [V_xss_2,T_b] :
% 168.50/168.35 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xss_2)))
% 168.50/168.35 => c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xss_2)) = c_List_Otranspose(T_b,V_xss_2) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sublist__shift__lemma__Suc,axiom,
% 168.50/168.35 ! [V_is_2,V_xs_2,V_P_2,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_P_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(T_b,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(T_b,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),V_is_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_P_2),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),V_is_2)))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_select__weigth__drop__zero,axiom,
% 168.50/168.35 ! [V_xs_2,T_b] : c_Random_Oselect__weight(T_b,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),V_xs_2)) = c_Random_Oselect__weight(T_b,V_xs_2) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_pick__drop__zero,axiom,
% 168.50/168.35 ! [V_xs_2,T_b] : c_Random_Opick(T_b,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),V_xs_2)) = c_Random_Opick(T_b,V_xs_2) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_transpose_Opsimps_I1_J,axiom,
% 168.50/168.35 ! [T_b] :
% 168.50/168.35 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),c_List_Olist_ONil(tc_List_Olist(T_b))))
% 168.50/168.35 => c_List_Otranspose(T_b,c_List_Olist_ONil(tc_List_Olist(T_b))) = c_List_Olist_ONil(tc_List_Olist(T_b)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_transpose__max__length,axiom,
% 168.50/168.35 ! [V_xs_2,T_b] : c_List_Ofoldr(tc_List_Olist(T_b),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xs_2)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_transpose__aux__max,axiom,
% 168.50/168.35 ! [V_xss_2,T_c,V_xs_2,T_b] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),c_List_Ofoldr(tc_List_Olist(T_c),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c))),V_xss_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),c_List_Ofoldr(tc_List_Olist(T_c),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_c)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_c)))),V_xss_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_foldr_Osimps_I1_J,axiom,
% 168.50/168.35 ! [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 ).
% 168.50/168.35
% 168.50/168.35 fof(fact_foldr_Osimps_I2_J,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_foldr__append,axiom,
% 168.50/168.35 ! [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)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_foldr__conv__foldl,axiom,
% 168.50/168.35 ! [V_a_2,V_xs_2,T_b] :
% 168.50/168.35 ( class_Groups_Oab__semigroup__add(T_b)
% 168.50/168.35 => 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) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_foldr__map,axiom,
% 168.50/168.35 ! [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) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_foldl__foldr1,axiom,
% 168.50/168.35 ! [V_xs_2,T_b] :
% 168.50/168.35 ( class_Groups_Omonoid__add(T_b)
% 168.50/168.35 => 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)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_foldl__foldr1__lemma,axiom,
% 168.50/168.35 ! [V_xs_2,V_a_2,T_b] :
% 168.50/168.35 ( class_Groups_Omonoid__add(T_b)
% 168.50/168.35 => 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))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_length__transpose,axiom,
% 168.50/168.35 ! [V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = c_List_Ofoldr(tc_List_Olist(T_b),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sublist__def,axiom,
% 168.50/168.35 ! [V_A_2,V_xs_2,T_b] : c_List_Osublist(T_b,V_xs_2,V_A_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sublist__shift__lemma,axiom,
% 168.50/168.35 ! [V_i_2,V_xs_2,V_A_2,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(V_i_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(T_b,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_i_2))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_set__upt,axiom,
% 168.50/168.35 ! [V_j_2,V_i_2] : hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_i_2,V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_atLeastLessThan__upt,axiom,
% 168.50/168.35 ! [V_j_2,V_i_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_i_2,V_j_2)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_upt__Suc__append,axiom,
% 168.50/168.35 ! [V_j,V_i] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 168.50/168.35 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_j),c_List_Olist_ONil(tc_Nat_Onat))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_upt__Suc,axiom,
% 168.50/168.35 ! [V_j,V_i] :
% 168.50/168.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 168.50/168.35 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_j),c_List_Olist_ONil(tc_Nat_Onat))) )
% 168.50/168.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 168.50/168.35 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_upt__add__eq__append,axiom,
% 168.50/168.35 ! [V_k,V_j,V_i] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 168.50/168.35 => c_List_Oupt(V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),c_List_Oupt(V_j,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_upt__rec,axiom,
% 168.50/168.35 ! [V_j,V_i] :
% 168.50/168.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 168.50/168.35 => c_List_Oupt(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_i),c_List_Oupt(hAPP(c_Nat_OSuc,V_i),V_j)) )
% 168.50/168.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 168.50/168.35 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_upt__conv__Cons,axiom,
% 168.50/168.35 ! [V_j,V_i] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 168.50/168.35 => c_List_Oupt(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_i),c_List_Oupt(hAPP(c_Nat_OSuc,V_i),V_j)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_upt__eq__Nil__conv,axiom,
% 168.50/168.35 ! [V_j_2,V_i_2] :
% 168.50/168.35 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat)
% 168.50/168.35 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.50/168.35 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_upt__conv__Nil,axiom,
% 168.50/168.35 ! [V_i,V_j] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 168.50/168.35 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_upt__0,axiom,
% 168.50/168.35 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_take__upt,axiom,
% 168.50/168.35 ! [V_n,V_m,V_i] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)),V_n))
% 168.50/168.35 => hAPP(hAPP(c_List_Otake(tc_Nat_Onat),V_m),c_List_Oupt(V_i,V_n)) = c_List_Oupt(V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sorted__list__of__set__range,axiom,
% 168.50/168.35 ! [V_n_2,V_m_2] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) = c_List_Oupt(V_m_2,V_n_2) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_hd__upt,axiom,
% 168.50/168.35 ! [V_j,V_i] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 168.50/168.35 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_drop__upt,axiom,
% 168.50/168.35 ! [V_j,V_i,V_m] : hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),V_m),c_List_Oupt(V_i,V_j)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m),V_j) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_distinct__upt,axiom,
% 168.50/168.35 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_length__upt,axiom,
% 168.50/168.35 ! [V_j,V_i] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(V_i,V_j)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_i) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_upt__rec__number__of,axiom,
% 168.50/168.35 ! [V_n,V_m] :
% 168.50/168.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)))
% 168.50/168.35 => c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n))) )
% 168.50/168.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)))
% 168.50/168.35 => c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_upt__eq__Cons__conv,axiom,
% 168.50/168.35 ! [V_xs_2,V_x_2,V_j_2,V_i_2] :
% 168.50/168.35 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2)
% 168.50/168.35 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2))
% 168.50/168.35 & V_i_2 = V_x_2
% 168.50/168.35 & c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_j_2) = V_xs_2 ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_last__upt,axiom,
% 168.50/168.35 ! [V_j,V_i] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 168.50/168.35 => c_List_Olast(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_map__Suc__upt,axiom,
% 168.50/168.35 ! [V_n_2,V_m_2] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(V_m_2,V_n_2)) = c_List_Oupt(hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_n_2)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_atLeastAtMost__upt,axiom,
% 168.50/168.35 ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_n_2,hAPP(c_Nat_OSuc,V_m_2))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_atLeast__upt,axiom,
% 168.50/168.35 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_nth__upt,axiom,
% 168.50/168.35 ! [V_j,V_k,V_i] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),V_j))
% 168.50/168.35 => hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_greaterThanAtMost__upt,axiom,
% 168.50/168.35 ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_greaterThanLessThan__upt,axiom,
% 168.50/168.35 ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,V_n_2),V_m_2)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_atMost__upto,axiom,
% 168.50/168.35 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_map__nth,axiom,
% 168.50/168.35 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),hAPP(c_List_Onth(T_b),V_xs_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) = V_xs_2 ).
% 168.50/168.35
% 168.50/168.35 fof(fact_interv__listsum__conv__setsum__set__nat,axiom,
% 168.50/168.35 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 168.50/168.35 ( class_Groups_Ocomm__monoid__add(T_b)
% 168.50/168.35 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_setsum__set__upt__conv__listsum__nat,axiom,
% 168.50/168.35 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 168.50/168.35 ( class_Groups_Ocomm__monoid__add(T_b)
% 168.50/168.35 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_nth__map__upt,axiom,
% 168.50/168.35 ! [V_f_2,T_b,V_m_2,V_n_2,V_i_2] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_m_2)))
% 168.50/168.35 => hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2))),V_i_2) = hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_i_2)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_transpose__rectangle,axiom,
% 168.50/168.35 ! [V_n_2,T_b,V_xs_2] :
% 168.50/168.35 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
% 168.50/168.35 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 168.50/168.35 => ( ! [B_i] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))
% 168.50/168.35 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),B_i)) = V_n_2 )
% 168.50/168.35 => c_List_Otranspose(T_b,V_xs_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_b)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,T_b)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_Nat_Onat,T_b),tc_Nat_Onat),c_List_Onth(T_b)),hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_insort__key__remove1,axiom,
% 168.50/168.35 ! [V_f_2,V_xs_2,V_a_2,T_b,T_c] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_c)
% 168.50/168.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.35 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
% 168.50/168.35 => ( hAPP(c_List_Ohd(T_b),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),hAPP(c_fequal,hAPP(V_f_2,V_a_2))),V_f_2)),V_xs_2)) = V_a_2
% 168.50/168.35 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),c_List_Oremove1(T_b,V_a_2,V_xs_2)) = V_xs_2 ) ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sorted_ONil,axiom,
% 168.50/168.35 ! [T_a] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_a)
% 168.50/168.35 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sorted__single,axiom,
% 168.50/168.35 ! [V_x,T_a] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_a)
% 168.50/168.35 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sorted__upt,axiom,
% 168.50/168.35 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sorted__sort,axiom,
% 168.50/168.35 ! [V_xs_2,T_b] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_b)
% 168.50/168.35 => c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),V_xs_2)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sorted__insort__insert,axiom,
% 168.50/168.35 ! [V_x_2,V_xs_2,T_b] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_b)
% 168.50/168.35 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 168.50/168.35 => c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2)) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sorted__drop,axiom,
% 168.50/168.35 ! [V_n,V_xs,T_a] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_a)
% 168.50/168.35 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 168.50/168.35 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sorted__upto,axiom,
% 168.50/168.35 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sorted__take,axiom,
% 168.50/168.35 ! [V_n,V_xs,T_a] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_a)
% 168.50/168.35 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 168.50/168.35 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sorted__remove1,axiom,
% 168.50/168.35 ! [V_a,V_xs,T_a] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_a)
% 168.50/168.35 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 168.50/168.35 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sorted__tl,axiom,
% 168.50/168.35 ! [V_xs,T_a] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_a)
% 168.50/168.35 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 168.50/168.35 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sorted__insort,axiom,
% 168.50/168.35 ! [V_xs_2,V_x_2,T_b] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_b)
% 168.50/168.35 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2))
% 168.50/168.35 <=> c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sorted__butlast,axiom,
% 168.50/168.35 ! [V_xs,T_a] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_a)
% 168.50/168.35 => ( V_xs != c_List_Olist_ONil(T_a)
% 168.50/168.35 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 168.50/168.35 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sorted_Oequations_I1_J,axiom,
% 168.50/168.35 ! [T_a] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_a)
% 168.50/168.35 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sorted__many,axiom,
% 168.50/168.35 ! [V_zs,V_y,V_x,T_a] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_a)
% 168.50/168.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 168.50/168.35 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))
% 168.50/168.35 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))) ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sorted__many__eq,axiom,
% 168.50/168.35 ! [V_zs_2,V_y_2,V_x_2,T_b] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_b)
% 168.50/168.35 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2)))
% 168.50/168.35 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 168.50/168.35 & c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2)) ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sorted__remdups,axiom,
% 168.50/168.35 ! [V_l,T_a] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_a)
% 168.50/168.35 => ( c_List_Olinorder__class_Osorted(T_a,V_l)
% 168.50/168.35 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sorted__distinct__set__unique,axiom,
% 168.50/168.35 ! [V_ys_2,V_xs_2,T_b] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_b)
% 168.50/168.35 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 168.50/168.35 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 168.50/168.35 => ( c_List_Olinorder__class_Osorted(T_b,V_ys_2)
% 168.50/168.35 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
% 168.50/168.35 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
% 168.50/168.35 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sorted__sort__key,axiom,
% 168.50/168.35 ! [V_xs_2,V_f_2,T_c,T_b] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_b)
% 168.50/168.35 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olinorder__class_Osort__key(T_c,T_b,V_f_2,V_xs_2))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sorted__insort__insert__key,axiom,
% 168.50/168.35 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_b)
% 168.50/168.35 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 168.50/168.35 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2))) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sorted__map__remove1,axiom,
% 168.50/168.35 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_b)
% 168.50/168.35 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 168.50/168.35 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oremove1(T_c,V_x_2,V_xs_2))) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sorted__insort__key,axiom,
% 168.50/168.35 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_b)
% 168.50/168.35 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)))
% 168.50/168.35 <=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sorted__map__same,axiom,
% 168.50/168.35 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_b)
% 168.50/168.35 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_c),c_fequal),V_f_2)),hAPP(V_g_2,V_xs_2))),V_xs_2))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sorted__filter,axiom,
% 168.50/168.35 ! [V_P_2,V_xs_2,V_f_2,T_c,T_b] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_b)
% 168.50/168.35 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 168.50/168.35 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,V_P_2),V_xs_2))) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sorted__same,axiom,
% 168.50/168.35 ! [V_xs_2,V_g_2,T_b] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_b)
% 168.50/168.35 => c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),hAPP(V_g_2,V_xs_2))),V_xs_2)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sorted__Cons,axiom,
% 168.50/168.35 ! [V_xs_2,V_x_2,T_b] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_b)
% 168.50/168.35 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 168.50/168.35 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 168.50/168.35 & ! [B_x] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sorted__append,axiom,
% 168.50/168.35 ! [V_ys_2,V_xs_2,T_b] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_b)
% 168.50/168.35 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 168.50/168.35 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 168.50/168.35 & c_List_Olinorder__class_Osorted(T_b,V_ys_2)
% 168.50/168.35 & ! [B_x] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.35 => ! [B_xa] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),V_ys_2)))
% 168.50/168.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) ) ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_filter__insort,axiom,
% 168.50/168.35 ! [V_x_2,V_P_2,V_xs_2,V_f_2,T_c,T_b] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_b)
% 168.50/168.35 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 168.50/168.35 => ( hBOOL(hAPP(V_P_2,V_x_2))
% 168.50/168.35 => hAPP(c_List_Ofilter(T_c,V_P_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(c_List_Ofilter(T_c,V_P_2),V_xs_2)) ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sorted_Oequations_I2_J,axiom,
% 168.50/168.35 ! [V_a1_2,V_a2_2,T_b] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_b)
% 168.50/168.35 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a1_2))
% 168.50/168.35 <=> ( ! [B_x] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_a1_2)))
% 168.50/168.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a2_2),B_x)) )
% 168.50/168.35 & c_List_Olinorder__class_Osorted(T_b,V_a1_2) ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sorted__list__of__set,axiom,
% 168.50/168.35 ! [V_A_2,T_b] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_b)
% 168.50/168.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.35 => ( hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) = V_A_2
% 168.50/168.35 & c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))
% 168.50/168.35 & hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))) ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_insort__remove1,axiom,
% 168.50/168.35 ! [V_xs_2,V_a_2,T_b] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_b)
% 168.50/168.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.35 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 168.50/168.35 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_a_2),c_List_Oremove1(T_b,V_a_2,V_xs_2)) = V_xs_2 ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sorted__equals__nth__mono,axiom,
% 168.50/168.35 ! [V_xs_2,T_b] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_b)
% 168.50/168.35 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 168.50/168.35 <=> ! [B_j] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 168.50/168.35 => ! [B_i] :
% 168.50/168.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 168.50/168.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j))) ) ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sorted__nth__mono,axiom,
% 168.50/168.35 ! [V_j,V_i,V_xs,T_a] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_a)
% 168.50/168.35 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 168.50/168.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 168.50/168.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 168.50/168.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j))) ) ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_map__sorted__distinct__set__unique,axiom,
% 168.50/168.35 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 168.50/168.35 ( class_Orderings_Olinorder(T_c)
% 168.50/168.35 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)))
% 168.50/168.35 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
% 168.50/168.35 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)))
% 168.50/168.35 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2))
% 168.50/168.35 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)))
% 168.50/168.35 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
% 168.50/168.35 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_transpose__column,axiom,
% 168.50/168.35 ! [V_i_2,V_xs_2,T_b] :
% 168.50/168.35 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
% 168.50/168.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))
% 168.50/168.35 => hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,T_b),c_List_Onth(T_b)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_List_Otranspose(T_b,V_xs_2))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_i_2) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_nth__nth__transpose__sorted,axiom,
% 168.50/168.35 ! [V_j_2,V_i_2,V_xs_2,T_b] :
% 168.50/168.35 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
% 168.50/168.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2))))
% 168.50/168.35 => ( 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))))
% 168.50/168.35 => 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) ) ) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_inj__on__rev,axiom,
% 168.50/168.35 ! [V_A_2,T_b] : c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Orev(T_b),V_A_2) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_distinct__rev,axiom,
% 168.50/168.35 ! [V_xs_2,T_b] :
% 168.50/168.35 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orev(T_b),V_xs_2)))
% 168.50/168.35 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_rev__is__Nil__conv,axiom,
% 168.50/168.35 ! [V_xs_2,T_b] :
% 168.50/168.35 ( hAPP(c_List_Orev(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
% 168.50/168.35 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_Nil__is__rev__conv,axiom,
% 168.50/168.35 ! [V_xs_2,T_b] :
% 168.50/168.35 ( c_List_Olist_ONil(T_b) = hAPP(c_List_Orev(T_b),V_xs_2)
% 168.50/168.35 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_rev_Osimps_I1_J,axiom,
% 168.50/168.35 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_singleton__rev__conv,axiom,
% 168.50/168.35 ! [V_xs_2,V_x_2,T_b] :
% 168.50/168.35 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) = hAPP(c_List_Orev(T_b),V_xs_2)
% 168.50/168.35 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_rev__singleton__conv,axiom,
% 168.50/168.35 ! [V_x_2,V_xs_2,T_b] :
% 168.50/168.35 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))
% 168.50/168.35 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_rev__append,axiom,
% 168.50/168.35 ! [V_ys,V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Orev(T_a),V_ys)),hAPP(c_List_Orev(T_a),V_xs)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_rev__concat,axiom,
% 168.50/168.35 ! [V_xs_2,T_b] : hAPP(c_List_Orev(T_b),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Orev(T_b)),hAPP(c_List_Orev(tc_List_Olist(T_b)),V_xs_2))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_rev__map,axiom,
% 168.50/168.35 ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_List_Orev(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Orev(T_c),V_xs_2)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_rev__filter,axiom,
% 168.50/168.35 ! [V_xs_2,V_P_2,T_b] : hAPP(c_List_Orev(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(c_List_Orev(T_b),V_xs_2)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_zip__rev,axiom,
% 168.50/168.35 ! [V_ys,T_b,V_xs,T_a] :
% 168.50/168.35 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)
% 168.50/168.35 => hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(c_List_Orev(T_a),V_xs)),hAPP(c_List_Orev(T_b),V_ys)) = hAPP(c_List_Orev(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_set__rev,axiom,
% 168.50/168.35 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_list__all2__rev,axiom,
% 168.50/168.35 ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 168.50/168.35 ( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2),hAPP(c_List_Orev(T_c),V_ys_2))
% 168.50/168.35 <=> c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_list__all2__rev1,axiom,
% 168.50/168.35 ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 168.50/168.35 ( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2),V_ys_2)
% 168.50/168.35 <=> c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,hAPP(c_List_Orev(T_c),V_ys_2)) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_rev__rev__ident,axiom,
% 168.50/168.35 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ).
% 168.50/168.35
% 168.50/168.35 fof(fact_rev__swap,axiom,
% 168.50/168.35 ! [V_ys_2,V_xs_2,T_b] :
% 168.50/168.35 ( hAPP(c_List_Orev(T_b),V_xs_2) = V_ys_2
% 168.50/168.35 <=> V_xs_2 = hAPP(c_List_Orev(T_b),V_ys_2) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_rev__is__rev__conv,axiom,
% 168.50/168.35 ! [V_ys_2,V_xs_2,T_b] :
% 168.50/168.35 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Orev(T_b),V_ys_2)
% 168.50/168.35 <=> V_xs_2 = V_ys_2 ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_listsum__rev,axiom,
% 168.50/168.35 ! [V_xs,T_a] :
% 168.50/168.35 ( class_Groups_Ocomm__monoid__add(T_a)
% 168.50/168.35 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_length__rev,axiom,
% 168.50/168.35 ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_foldl__foldr,axiom,
% 168.50/168.35 ! [V_xs_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),V_xs_2) = c_List_Ofoldr(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_b),V_f_2),hAPP(c_List_Orev(T_c),V_xs_2),V_a_2) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_foldr__foldl,axiom,
% 168.50/168.35 ! [V_a_2,V_xs_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),V_f_2),V_a_2),hAPP(c_List_Orev(T_c),V_xs_2)) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_rev__eq__Cons__iff,axiom,
% 168.50/168.35 ! [V_ys_2,V_y_2,V_xs_2,T_b] :
% 168.50/168.35 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
% 168.50/168.35 <=> V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),hAPP(c_List_Orev(T_b),V_ys_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b))) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_rev_Osimps_I2_J,axiom,
% 168.50/168.35 ! [V_xs,V_x,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Orev(T_a),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_hd__rev,axiom,
% 168.50/168.35 ! [T_a,V_xs] :
% 168.50/168.35 ( V_xs != c_List_Olist_ONil(T_a)
% 168.50/168.35 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_last__rev,axiom,
% 168.50/168.35 ! [T_a,V_xs] :
% 168.50/168.35 ( V_xs != c_List_Olist_ONil(T_a)
% 168.50/168.35 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_sorted__transpose,axiom,
% 168.50/168.35 ! [V_xs_2,T_b] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)))) ).
% 168.50/168.35
% 168.50/168.35 fof(fact_rev__foldl__cons,axiom,
% 168.50/168.35 ! [V_xs_2,T_b] : hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),T_b,hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b)),V_xs_2) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_rev__take,axiom,
% 168.50/168.36 ! [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)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_rev__drop,axiom,
% 168.50/168.36 ! [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)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_rotate__rev,axiom,
% 168.50/168.36 ! [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)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_rev__nth,axiom,
% 168.50/168.36 ! [V_xs,T_a,V_n] :
% 168.50/168.36 ( 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)))
% 168.50/168.36 => 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))) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_rev__update,axiom,
% 168.50/168.36 ! [V_y,V_xs,T_a,V_k] :
% 168.50/168.36 ( 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)))
% 168.50/168.36 => 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) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_sorted__rev__nth__mono,axiom,
% 168.50/168.36 ! [V_j,V_i,V_xs,T_a] :
% 168.50/168.36 ( class_Orderings_Olinorder(T_a)
% 168.50/168.36 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 168.50/168.36 => ( 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)))
% 168.50/168.36 => 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))) ) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_foldr__max__sorted,axiom,
% 168.50/168.36 ! [V_y_2,V_xs_2,T_b] :
% 168.50/168.36 ( class_Orderings_Olinorder(T_b)
% 168.50/168.36 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),V_xs_2))
% 168.50/168.36 => ( ( V_xs_2 = c_List_Olist_ONil(T_b)
% 168.50/168.36 => c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = V_y_2 )
% 168.50/168.36 & ( V_xs_2 != c_List_Olist_ONil(T_b)
% 168.50/168.36 => 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) ) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_length__transpose__sorted,axiom,
% 168.50/168.36 ! [V_xs_2,T_b] :
% 168.50/168.36 ( 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)))
% 168.50/168.36 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
% 168.50/168.36 => 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) )
% 168.50/168.36 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_b))
% 168.50/168.36 => 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))) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_transpose__column__length,axiom,
% 168.50/168.36 ! [V_i_2,V_xs_2,T_b] :
% 168.50/168.36 ( 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)))
% 168.50/168.36 => ( 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)))
% 168.50/168.36 => 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)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_transpose__transpose,axiom,
% 168.50/168.36 ! [V_xs_2,T_b] :
% 168.50/168.36 ( 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)))
% 168.50/168.36 => 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) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_transfer__nat__int__list__functions_I2_J,axiom,
% 168.50/168.36 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_sorted__takeWhile,axiom,
% 168.50/168.36 ! [V_P_2,V_xs_2,T_b] :
% 168.50/168.36 ( class_Orderings_Olinorder(T_b)
% 168.50/168.36 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 168.50/168.36 => c_List_Olinorder__class_Osorted(T_b,c_List_OtakeWhile(T_b,V_P_2,V_xs_2)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_length__takeWhile__le,axiom,
% 168.50/168.36 ! [V_xs_2,V_P_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_set__takeWhileD,axiom,
% 168.50/168.36 ! [V_xs_2,V_P_2,V_x_2,T_b] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.36 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_takeWhile__eq__all__conv,axiom,
% 168.50/168.36 ! [V_xs_2,V_P_2,T_b] :
% 168.50/168.36 ( c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = V_xs_2
% 168.50/168.36 <=> ! [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.36 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_zip__takeWhile__snd,axiom,
% 168.50/168.36 ! [V_ys_2,V_P_2,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),c_List_OtakeWhile(T_c,V_P_2,V_ys_2)) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_c,tc_HOL_Obool,tc_prod(T_b,T_c),V_P_2),c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_zip__takeWhile__fst,axiom,
% 168.50/168.36 ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)),V_ys_2) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,tc_prod(T_b,T_c),V_P_2),c_Product__Type_Ofst(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_takeWhile__map,axiom,
% 168.50/168.36 ! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OtakeWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_P_2),V_f_2),V_xs_2)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_takeWhile__tail,axiom,
% 168.50/168.36 ! [V_l_2,V_xs_2,T_b,V_x_2,V_P_2] :
% 168.50/168.36 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 168.50/168.36 => c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_l_2))) = c_List_OtakeWhile(T_b,V_P_2,V_xs_2) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_takeWhile_Osimps_I2_J,axiom,
% 168.50/168.36 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 168.50/168.36 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 168.50/168.36 => c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)) )
% 168.50/168.36 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 168.50/168.36 => c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Olist_ONil(T_b) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_takeWhile_Osimps_I1_J,axiom,
% 168.50/168.36 ! [V_P_2,T_b] : c_List_OtakeWhile(T_b,V_P_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_takeWhile__eq__take,axiom,
% 168.50/168.36 ! [V_xs_2,V_P_2,T_b] : c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))),V_xs_2) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_distinct__takeWhile,axiom,
% 168.50/168.36 ! [V_P_2,V_xs_2,T_b] :
% 168.50/168.36 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 168.50/168.36 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_return__list__def,axiom,
% 168.50/168.36 ! [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) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_takeWhile__append1,axiom,
% 168.50/168.36 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_b] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.36 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 168.50/168.36 => c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OtakeWhile(T_b,V_P_2,V_xs_2) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_nth__length__takeWhile,axiom,
% 168.50/168.36 ! [V_xs_2,V_P_2,T_b] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 168.50/168.36 => ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))))) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_takeWhile__nth,axiom,
% 168.50/168.36 ! [V_xs_2,V_P_2,T_b,V_j_2] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))))
% 168.50/168.36 => hAPP(hAPP(c_List_Onth(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_j_2) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_takeWhile__not__last,axiom,
% 168.50/168.36 ! [T_b,V_xs_2] :
% 168.50/168.36 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 168.50/168.36 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 168.50/168.36 => 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) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_filter__equals__takeWhile__sorted__rev,axiom,
% 168.50/168.36 ! [V_t_2,V_xs_2,V_f_2,T_c,T_b] :
% 168.50/168.36 ( class_Orderings_Olinorder(T_b)
% 168.50/168.36 => ( 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)))
% 168.50/168.36 => 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) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_transfer__nat__int__list__return__embed,axiom,
% 168.50/168.36 ! [V_l] :
% 168.50/168.36 ( c_List_Onat__list(V_l)
% 168.50/168.36 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_transfer__nat__int__list__functions_I1_J,axiom,
% 168.50/168.36 ! [V_m,V_l] : hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),V_l),V_m) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(V_l)),c_List_Oembed__list(V_m))) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_embed__list__def,axiom,
% 168.50/168.36 ! [V_l_2] : c_List_Oembed__list(V_l_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_l_2) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_takeWhile__neq__rev,axiom,
% 168.50/168.36 ! [V_x_2,V_xs_2,T_b] :
% 168.50/168.36 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.36 => c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(c_List_Orev(T_b),hAPP(c_List_Otl(T_b),c_List_OdropWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2))) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dropWhile__neq__rev,axiom,
% 168.50/168.36 ! [V_x_2,V_xs_2,T_b] :
% 168.50/168.36 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.36 => c_List_OdropWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(c_List_Orev(T_b),c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2))) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_takeWhile__dropWhile__id,axiom,
% 168.50/168.36 ! [V_xs_2,V_P_2,T_b] : hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)),c_List_OdropWhile(T_b,V_P_2,V_xs_2)) = V_xs_2 ).
% 168.50/168.36
% 168.50/168.36 fof(fact_sorted__dropWhile,axiom,
% 168.50/168.36 ! [V_P_2,V_xs_2,T_b] :
% 168.50/168.36 ( class_Orderings_Olinorder(T_b)
% 168.50/168.36 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 168.50/168.36 => c_List_Olinorder__class_Osorted(T_b,c_List_OdropWhile(T_b,V_P_2,V_xs_2)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_length__dropWhile__le,axiom,
% 168.50/168.36 ! [V_xs_2,V_P_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OdropWhile(T_b,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dropWhile__eq__Nil__conv,axiom,
% 168.50/168.36 ! [V_xs_2,V_P_2,T_b] :
% 168.50/168.36 ( c_List_OdropWhile(T_b,V_P_2,V_xs_2) = c_List_Olist_ONil(T_b)
% 168.50/168.36 <=> ! [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.36 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dropWhile_Osimps_I2_J,axiom,
% 168.50/168.36 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 168.50/168.36 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 168.50/168.36 => c_List_OdropWhile(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_OdropWhile(T_b,V_P_2,V_xs_2) )
% 168.50/168.36 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 168.50/168.36 => c_List_OdropWhile(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dropWhile_Osimps_I1_J,axiom,
% 168.50/168.36 ! [V_P_2,T_b] : c_List_OdropWhile(T_b,V_P_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_distinct__dropWhile,axiom,
% 168.50/168.36 ! [V_P_2,V_xs_2,T_b] :
% 168.50/168.36 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 168.50/168.36 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2))) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_hd__dropWhile,axiom,
% 168.50/168.36 ! [V_xs_2,V_P_2,T_b] :
% 168.50/168.36 ( c_List_OdropWhile(T_b,V_P_2,V_xs_2) != c_List_Olist_ONil(T_b)
% 168.50/168.36 => ~ hBOOL(hAPP(V_P_2,hAPP(c_List_Ohd(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2)))) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dropWhile__map,axiom,
% 168.50/168.36 ! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : c_List_OdropWhile(T_b,V_P_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OdropWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_P_2),V_f_2),V_xs_2)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dropWhile__append1,axiom,
% 168.50/168.36 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_b] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.36 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 168.50/168.36 => c_List_OdropWhile(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2)),V_ys_2) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dropWhile__eq__Cons__conv,axiom,
% 168.50/168.36 ! [V_ys_2,V_y_2,V_xs_2,V_P_2,T_b] :
% 168.50/168.36 ( c_List_OdropWhile(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
% 168.50/168.36 <=> ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))
% 168.50/168.36 & ~ hBOOL(hAPP(V_P_2,V_y_2)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dropWhile__eq__drop,axiom,
% 168.50/168.36 ! [V_xs_2,V_P_2,T_b] : c_List_OdropWhile(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))),V_xs_2) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dropWhile__nth,axiom,
% 168.50/168.36 ! [V_xs_2,V_P_2,T_b,V_j_2] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OdropWhile(T_b,V_P_2,V_xs_2))))
% 168.50/168.36 => hAPP(hAPP(c_List_Onth(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)))) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_listsum__map__filter,axiom,
% 168.50/168.36 ! [V_f_2,V_P_2,V_xs_2,T_b,T_c] :
% 168.50/168.36 ( class_Groups_Omonoid__add(T_c)
% 168.50/168.36 => ( ! [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.36 => ( ~ hBOOL(hAPP(V_P_2,B_x))
% 168.50/168.36 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) )
% 168.50/168.36 => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_sorted__nth__monoI,axiom,
% 168.50/168.36 ! [V_xs,T_a] :
% 168.50/168.36 ( class_Orderings_Olinorder(T_a)
% 168.50/168.36 => ( ! [B_i,B_j] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 168.50/168.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i)),hAPP(hAPP(c_List_Onth(T_a),V_xs),B_j))) ) )
% 168.50/168.36 => c_List_Olinorder__class_Osorted(T_a,V_xs) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_takeWhile__eq__filter,axiom,
% 168.50/168.36 ! [V_xs_2,V_P_2,T_b] :
% 168.50/168.36 ( ! [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2))))
% 168.50/168.36 => ~ hBOOL(hAPP(V_P_2,B_x)) )
% 168.50/168.36 => c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_takeWhile__eq__take__P__nth,axiom,
% 168.50/168.36 ! [V_P_2,V_xs_2,T_b,V_n_2] :
% 168.50/168.36 ( ! [B_i] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 168.50/168.36 => ( 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)))
% 168.50/168.36 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) )
% 168.50/168.36 => ( ( 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)))
% 168.50/168.36 => ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2))) )
% 168.50/168.36 => c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_length__takeWhile__less__P__nth,axiom,
% 168.50/168.36 ! [V_xs_2,T_b,V_P_2,V_j_2] :
% 168.50/168.36 ( ! [B_i] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2))
% 168.50/168.36 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) )
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 168.50/168.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)))) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_sorted_Osimps,axiom,
% 168.50/168.36 ! [V_a_2,T_b] :
% 168.50/168.36 ( class_Orderings_Olinorder(T_b)
% 168.50/168.36 => ( c_List_Olinorder__class_Osorted(T_b,V_a_2)
% 168.50/168.36 <=> ( V_a_2 = c_List_Olist_ONil(T_b)
% 168.50/168.36 | ? [B_xs,B_x] :
% 168.50/168.36 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs)
% 168.50/168.36 & ! [B_xa] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),B_xs)))
% 168.50/168.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) )
% 168.50/168.36 & c_List_Olinorder__class_Osorted(T_b,B_xs) ) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_List_Oinsert__def,axiom,
% 168.50/168.36 ! [V_xs_2,V_x_2,T_b] :
% 168.50/168.36 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.36 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 )
% 168.50/168.36 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.36 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_not__in__set__insert,axiom,
% 168.50/168.36 ! [V_xs_2,V_x_2,T_b] :
% 168.50/168.36 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.36 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_insert__remdups,axiom,
% 168.50/168.36 ! [V_xs,V_x,T_a] : c_List_Oinsert(T_a,V_x,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,c_List_Oinsert(T_a,V_x,V_xs)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_distinct__insert,axiom,
% 168.50/168.36 ! [V_x,V_xs,T_a] :
% 168.50/168.36 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 168.50/168.36 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs))) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_in__set__insert,axiom,
% 168.50/168.36 ! [V_xs_2,V_x_2,T_b] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.36 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_List_Oset__insert,axiom,
% 168.50/168.36 ! [V_xs_2,V_x_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oinsert(T_b,V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_insert__Nil,axiom,
% 168.50/168.36 ! [V_x,T_a] : c_List_Oinsert(T_a,V_x,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_maps__def,axiom,
% 168.50/168.36 ! [V_xs_2,V_f_2,T_b,T_c] : c_List_Omaps(T_c,T_b,V_f_2,V_xs_2) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),V_f_2),V_xs_2)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_concat__map__maps,axiom,
% 168.50/168.36 ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),V_f_2),V_xs_2)) = c_List_Omaps(T_c,T_b,V_f_2,V_xs_2) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_maps__simps_I2_J,axiom,
% 168.50/168.36 ! [V_f_2,T_b,T_c] : c_List_Omaps(T_c,T_b,V_f_2,c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_b) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_maps__simps_I1_J,axiom,
% 168.50/168.36 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : c_List_Omaps(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(V_f_2,V_x_2)),c_List_Omaps(T_c,T_b,V_f_2,V_xs_2)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_distinct__concat,axiom,
% 168.50/168.36 ! [V_xs_2,T_b] :
% 168.50/168.36 ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_b)),V_xs_2))
% 168.50/168.36 => ( ! [B_ys] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 168.50/168.36 => hBOOL(hAPP(c_List_Odistinct(T_b),B_ys)) )
% 168.50/168.36 => ( ! [B_ys] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 168.50/168.36 => ! [B_zs] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 168.50/168.36 => ( B_ys != B_zs
% 168.50/168.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),B_ys)),hAPP(c_List_Oset(T_b),B_zs)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) )
% 168.50/168.36 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Oconcat(T_b,V_xs_2))) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_measures__lesseq,axiom,
% 168.50/168.36 ! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] :
% 168.50/168.36 ( 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)))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,V_fs_2)))
% 168.50/168.36 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2)))) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_wf__measures,axiom,
% 168.50/168.36 ! [V_fs_2,T_b] : c_Wellfounded_Owf(T_b,c_List_Omeasures(T_b,V_fs_2)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_in__measures_I1_J,axiom,
% 168.50/168.36 ! [V_y_2,V_x_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,c_List_Olist_ONil(tc_fun(T_b,tc_Nat_Onat))))) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_measures__def,axiom,
% 168.50/168.36 ! [V_fs_2,T_b] : c_List_Omeasures(T_b,V_fs_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),T_b),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(tc_fun(T_b,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(T_b,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),T_b),c_List_Omap(tc_fun(T_b,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(T_b,tc_Nat_Onat),T_b,tc_Nat_Onat),c_COMBI(tc_fun(T_b,tc_Nat_Onat))))),V_fs_2)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_in__measures_I2_J,axiom,
% 168.50/168.36 ! [V_fs_2,V_f_2,V_y_2,V_x_2,T_b] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2))))
% 168.50/168.36 <=> ( 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)))
% 168.50/168.36 | ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 168.50/168.36 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,V_fs_2))) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_measures__less,axiom,
% 168.50/168.36 ! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] :
% 168.50/168.36 ( 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)))
% 168.50/168.36 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2)))) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_foldl__apply,axiom,
% 168.50/168.36 ! [V_s_2,V_g_2,V_h_2,V_f_2,T_c,T_d,V_xs_2,T_b] :
% 168.50/168.36 ( ! [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.36 => hAPP(c_Fun_Ocomp(T_d,T_d,T_c,hAPP(V_f_2,B_x)),V_h_2) = hAPP(c_Fun_Ocomp(T_c,T_d,T_c,V_h_2),hAPP(V_g_2,B_x)) )
% 168.50/168.36 => hAPP(c_List_Ofoldl(T_d,T_b,hAPP(c_COMBC(T_b,T_d,T_d),V_f_2),hAPP(V_h_2,V_s_2)),V_xs_2) = hAPP(V_h_2,hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_g_2),V_s_2),V_xs_2)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_order__fun_I2_J,axiom,
% 168.50/168.36 ! [V_g_2,V_f_2,T_b,T_c] :
% 168.50/168.36 ( ( class_Orderings_Oorder(T_c)
% 168.50/168.36 & class_Enum_Oenum(T_b) )
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 168.50/168.36 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 168.50/168.36 & hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBS(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_g_2)))) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_enum__ex__prod__def,axiom,
% 168.50/168.36 ! [V_P_2,T_b,T_c] :
% 168.50/168.36 ( ( class_Enum_Oenum(T_c)
% 168.50/168.36 & class_Enum_Oenum(T_b) )
% 168.50/168.36 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_b,T_c)),V_P_2))
% 168.50/168.36 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_Enum_Oenum__class_Oenum__ex(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_P_2)),c_Product__Type_OPair(T_b,T_c))))) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_enum__ex,axiom,
% 168.50/168.36 ! [V_P_2,T_b] :
% 168.50/168.36 ( class_Enum_Oenum(T_b)
% 168.50/168.36 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_P_2))
% 168.50/168.36 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_exists__code,axiom,
% 168.50/168.36 ! [V_P_2,T_b] :
% 168.50/168.36 ( class_Enum_Oenum(T_b)
% 168.50/168.36 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 168.50/168.36 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_P_2)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_zip__obtain__same__length,axiom,
% 168.50/168.36 ! [V_P_2,V_ys_2,T_c,V_xs_2,T_b] :
% 168.50/168.36 ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Otake(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(hAPP(c_List_Otake(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_ys_2))
% 168.50/168.36 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Otake(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_xs_2)),hAPP(hAPP(c_List_Otake(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_ys_2)))) )
% 168.50/168.36 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_pos__not__random__dseq__def,axiom,
% 168.50/168.36 ! [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)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dropWhile__append2,axiom,
% 168.50/168.36 ! [V_ys_2,V_P_2,V_xs_2,T_b] :
% 168.50/168.36 ( ! [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.36 => hBOOL(hAPP(V_P_2,B_x)) )
% 168.50/168.36 => c_List_OdropWhile(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OdropWhile(T_b,V_P_2,V_ys_2) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_list__all2__all__nthI,axiom,
% 168.50/168.36 ! [V_P_2,V_b_2,T_c,V_a_2,T_b] :
% 168.50/168.36 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_b_2)
% 168.50/168.36 => ( ! [B_n] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_a_2)))
% 168.50/168.36 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_a_2),B_n)),hAPP(hAPP(c_List_Onth(T_c),V_b_2),B_n))) )
% 168.50/168.36 => c_List_Olist__all2(T_b,T_c,V_P_2,V_a_2,V_b_2) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_finite__sorted__distinct__unique,axiom,
% 168.50/168.36 ! [V_A_2,T_b] :
% 168.50/168.36 ( class_Orderings_Olinorder(T_b)
% 168.50/168.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.36 => ? [B_x] :
% 168.50/168.36 ( hAPP(c_List_Oset(T_b),B_x) = V_A_2
% 168.50/168.36 & c_List_Olinorder__class_Osorted(T_b,B_x)
% 168.50/168.36 & hBOOL(hAPP(c_List_Odistinct(T_b),B_x))
% 168.50/168.36 & ! [B_y] :
% 168.50/168.36 ( ( hAPP(c_List_Oset(T_b),B_y) = V_A_2
% 168.50/168.36 & c_List_Olinorder__class_Osorted(T_b,B_y)
% 168.50/168.36 & hBOOL(hAPP(c_List_Odistinct(T_b),B_y)) )
% 168.50/168.36 => B_y = B_x ) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_takeWhile__append2,axiom,
% 168.50/168.36 ! [V_ys_2,V_P_2,V_xs_2,T_b] :
% 168.50/168.36 ( ! [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.36 => hBOOL(hAPP(V_P_2,B_x)) )
% 168.50/168.36 => c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_OtakeWhile(T_b,V_P_2,V_ys_2)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_insort__is__Cons,axiom,
% 168.50/168.36 ! [V_a_2,V_f_2,V_xs_2,T_b,T_c] :
% 168.50/168.36 ( class_Orderings_Olinorder(T_c)
% 168.50/168.36 => ( ! [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) )
% 168.50/168.36 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_xs_2) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_Cons__eq__filter__iff,axiom,
% 168.50/168.36 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_b] :
% 168.50/168.36 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = hAPP(c_List_Ofilter(T_b,V_P_2),V_ys_2)
% 168.50/168.36 <=> ? [B_us,B_vs] :
% 168.50/168.36 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_vs))
% 168.50/168.36 & ! [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us)))
% 168.50/168.36 => ~ hBOOL(hAPP(V_P_2,B_x)) )
% 168.50/168.36 & hBOOL(hAPP(V_P_2,V_x_2))
% 168.50/168.36 & V_xs_2 = hAPP(c_List_Ofilter(T_b,V_P_2),B_vs) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_filter__eq__Cons__iff,axiom,
% 168.50/168.36 ! [V_xs_2,V_x_2,V_ys_2,V_P_2,T_b] :
% 168.50/168.36 ( hAPP(c_List_Ofilter(T_b,V_P_2),V_ys_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)
% 168.50/168.36 <=> ? [B_us,B_vs] :
% 168.50/168.36 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_vs))
% 168.50/168.36 & ! [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us)))
% 168.50/168.36 => ~ hBOOL(hAPP(V_P_2,B_x)) )
% 168.50/168.36 & hBOOL(hAPP(V_P_2,V_x_2))
% 168.50/168.36 & V_xs_2 = hAPP(c_List_Ofilter(T_b,V_P_2),B_vs) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_order__fun_I1_J,axiom,
% 168.50/168.36 ! [V_g_2,V_f_2,T_b,T_c] :
% 168.50/168.36 ( ( class_Orderings_Oorder(T_c)
% 168.50/168.36 & class_Enum_Oenum(T_b) )
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 168.50/168.36 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),hAPP(hAPP(c_COMBS(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Oord__class_Oless__eq(T_c)),V_f_2)),V_g_2))) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_all__code,axiom,
% 168.50/168.36 ! [V_P_2,T_b] :
% 168.50/168.36 ( class_Enum_Oenum(T_b)
% 168.50/168.36 => ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 168.50/168.36 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_P_2)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_enum__all,axiom,
% 168.50/168.36 ! [V_P_2,T_b] :
% 168.50/168.36 ( class_Enum_Oenum(T_b)
% 168.50/168.36 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_P_2))
% 168.50/168.36 <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_enum__all__prod__def,axiom,
% 168.50/168.36 ! [V_P_2,T_b,T_c] :
% 168.50/168.36 ( ( class_Enum_Oenum(T_c)
% 168.50/168.36 & class_Enum_Oenum(T_b) )
% 168.50/168.36 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_b,T_c)),V_P_2))
% 168.50/168.36 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_Enum_Oenum__class_Oenum__all(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_P_2)),c_Product__Type_OPair(T_b,T_c))))) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_list__ball__nth,axiom,
% 168.50/168.36 ! [V_P_2,V_xs_2,T_b,V_n_2] :
% 168.50/168.36 ( 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)))
% 168.50/168.36 => ( ! [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.36 => hBOOL(hAPP(V_P_2,B_x)) )
% 168.50/168.36 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2))) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_sorted_OCons,axiom,
% 168.50/168.36 ! [V_x_2,V_xs_2,T_b] :
% 168.50/168.36 ( class_Orderings_Olinorder(T_b)
% 168.50/168.36 => ( ! [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) )
% 168.50/168.36 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 168.50/168.36 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_list__ex__length,axiom,
% 168.50/168.36 ! [V_xs_2,V_P_2,T_b] :
% 168.50/168.36 ( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
% 168.50/168.36 <=> ? [B_n] :
% 168.50/168.36 ( 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)))
% 168.50/168.36 & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_in__set__conv__decomp,axiom,
% 168.50/168.36 ! [V_xs_2,V_x_2,T_b] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.36 <=> ? [B_ys,B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_list__ex__simps_I2_J,axiom,
% 168.50/168.36 ! [V_P_2,T_b] : ~ c_List_Olist__ex(T_b,V_P_2,c_List_Olist_ONil(T_b)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_list__ex__append,axiom,
% 168.50/168.36 ! [V_ys_2,V_xs_2,V_P_2,T_b] :
% 168.50/168.36 ( c_List_Olist__ex(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 168.50/168.36 <=> ( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
% 168.50/168.36 | c_List_Olist__ex(T_b,V_P_2,V_ys_2) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_list__ex__iff,axiom,
% 168.50/168.36 ! [V_xs_2,V_P_2,T_b] :
% 168.50/168.36 ( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
% 168.50/168.36 <=> ? [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.36 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_list__ex__rev,axiom,
% 168.50/168.36 ! [V_xs_2,V_P_2,T_b] :
% 168.50/168.36 ( c_List_Olist__ex(T_b,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2))
% 168.50/168.36 <=> c_List_Olist__ex(T_b,V_P_2,V_xs_2) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_list__ex__simps_I1_J,axiom,
% 168.50/168.36 ! [V_xs_2,V_x_2,V_P_2,T_b] :
% 168.50/168.36 ( c_List_Olist__ex(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 168.50/168.36 <=> ( hBOOL(hAPP(V_P_2,V_x_2))
% 168.50/168.36 | c_List_Olist__ex(T_b,V_P_2,V_xs_2) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_in__set__conv__decomp__first,axiom,
% 168.50/168.36 ! [V_xs_2,V_x_2,T_b] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.36 <=> ? [B_ys] :
% 168.50/168.36 ( ? [B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs))
% 168.50/168.36 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_ys))) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_in__set__conv__decomp__last,axiom,
% 168.50/168.36 ! [V_xs_2,V_x_2,T_b] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.36 <=> ? [B_ys,B_zs] :
% 168.50/168.36 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs))
% 168.50/168.36 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_zs))) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_list__all__length,axiom,
% 168.50/168.36 ! [V_xs_2,V_P_2,T_b] :
% 168.50/168.36 ( c_List_Olist__all(T_b,V_P_2,V_xs_2)
% 168.50/168.36 <=> ! [B_n] :
% 168.50/168.36 ( 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)))
% 168.50/168.36 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_measure__function__int,axiom,
% 168.50/168.36 c_FunDef_Ois__measure(tc_Int_Oint,hAPP(c_Fun_Ocomp(tc_Int_Oint,tc_Nat_Onat,tc_Int_Oint,c_Int_Onat),c_Groups_Oabs__class_Oabs(tc_Int_Oint))) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_list__all__simps_I2_J,axiom,
% 168.50/168.36 ! [V_P_2,T_b] : c_List_Olist__all(T_b,V_P_2,c_List_Olist_ONil(T_b)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_list__all__append,axiom,
% 168.50/168.36 ! [V_ys_2,V_xs_2,V_P_2,T_b] :
% 168.50/168.36 ( c_List_Olist__all(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 168.50/168.36 <=> ( c_List_Olist__all(T_b,V_P_2,V_xs_2)
% 168.50/168.36 & c_List_Olist__all(T_b,V_P_2,V_ys_2) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_measure__size,axiom,
% 168.50/168.36 ! [T_b] :
% 168.50/168.36 ( class_Nat_Osize(T_b)
% 168.50/168.36 => c_FunDef_Ois__measure(T_b,c_Nat_Osize__class_Osize(T_b)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_is__measure_Osimps,axiom,
% 168.50/168.36 ! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_is__measure_Oequations,axiom,
% 168.50/168.36 ! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_is__measure_Ointros,axiom,
% 168.50/168.36 ! [V_f_2,T_b] : c_FunDef_Ois__measure(T_b,V_f_2) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_list__all__iff,axiom,
% 168.50/168.36 ! [V_xs_2,V_P_2,T_b] :
% 168.50/168.36 ( c_List_Olist__all(T_b,V_P_2,V_xs_2)
% 168.50/168.36 <=> ! [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.36 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_measure__fst,axiom,
% 168.50/168.36 ! [T_c,V_f_2,T_b] :
% 168.50/168.36 ( c_FunDef_Ois__measure(T_b,V_f_2)
% 168.50/168.36 => c_FunDef_Ois__measure(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBB(T_b,tc_Nat_Onat,tc_prod(T_b,T_c)),V_f_2),c_Product__Type_Ofst(T_b,T_c))) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_measure__snd,axiom,
% 168.50/168.36 ! [T_c,V_f_2,T_b] :
% 168.50/168.36 ( c_FunDef_Ois__measure(T_b,V_f_2)
% 168.50/168.36 => c_FunDef_Ois__measure(tc_prod(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,tc_Nat_Onat,tc_prod(T_c,T_b)),V_f_2),c_Product__Type_Osnd(T_c,T_b))) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_list__all__rev,axiom,
% 168.50/168.36 ! [V_xs_2,V_P_2,T_b] :
% 168.50/168.36 ( c_List_Olist__all(T_b,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2))
% 168.50/168.36 <=> c_List_Olist__all(T_b,V_P_2,V_xs_2) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_list__all__simps_I1_J,axiom,
% 168.50/168.36 ! [V_xs_2,V_x_2,V_P_2,T_b] :
% 168.50/168.36 ( c_List_Olist__all(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 168.50/168.36 <=> ( hBOOL(hAPP(V_P_2,V_x_2))
% 168.50/168.36 & c_List_Olist__all(T_b,V_P_2,V_xs_2) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_Ball__set__list__all,axiom,
% 168.50/168.36 ! [V_P_2,V_xs_2,T_b] :
% 168.50/168.36 ( ! [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.36 => hBOOL(hAPP(V_P_2,B_x)) )
% 168.50/168.36 <=> c_List_Olist__all(T_b,V_P_2,V_xs_2) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_list__all__iff__raw,axiom,
% 168.50/168.36 ! [V_xs_2,V_P_2,T_b] :
% 168.50/168.36 ( c_List_Olist__all(T_b,V_P_2,V_xs_2)
% 168.50/168.36 <=> ! [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.36 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_list__ex1__simps_I2_J,axiom,
% 168.50/168.36 ! [V_xs_2,V_x_2,V_P_2,T_b] :
% 168.50/168.36 ( c_List_Olist__ex1(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 168.50/168.36 <=> ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 168.50/168.36 => c_List_Olist__all(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2))),hAPP(c_fequal,V_x_2)),V_xs_2) )
% 168.50/168.36 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 168.50/168.36 => c_List_Olist__ex1(T_b,V_P_2,V_xs_2) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_transfer__morphism__int__nat,axiom,
% 168.50/168.36 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)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_list__ex1__simps_I1_J,axiom,
% 168.50/168.36 ! [V_P_2,T_b] : ~ c_List_Olist__ex1(T_b,V_P_2,c_List_Olist_ONil(T_b)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_bool_Osize_I3_J,axiom,
% 168.50/168.36 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_bool_Osize_I4_J,axiom,
% 168.50/168.36 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_list__ex1__iff,axiom,
% 168.50/168.36 ! [V_xs_2,V_P_2,T_b] :
% 168.50/168.36 ( c_List_Olist__ex1(T_b,V_P_2,V_xs_2)
% 168.50/168.36 <=> ? [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.36 & hBOOL(hAPP(V_P_2,B_x))
% 168.50/168.36 & ! [B_y] :
% 168.50/168.36 ( ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.36 & hBOOL(hAPP(V_P_2,B_y)) )
% 168.50/168.36 => B_y = B_x ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom,
% 168.50/168.36 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
% 168.50/168.36 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 168.50/168.36 => 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) )
% 168.50/168.36 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 168.50/168.36 => 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)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_New__DSequence_Opos__decr__bind__def,axiom,
% 168.50/168.36 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
% 168.50/168.36 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 168.50/168.36 => 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) )
% 168.50/168.36 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 168.50/168.36 => hAPP(c_New__DSequence_Opos__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = hAPP(c_Lazy__Sequence_Obind(T_c,T_b,hAPP(V_x_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2),V_i_2)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom,
% 168.50/168.36 ! [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)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom,
% 168.50/168.36 ! [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)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_New__DSequence_Oneg__bind__def,axiom,
% 168.50/168.36 ! [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)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_New__DSequence_Opos__empty__def,axiom,
% 168.50/168.36 ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_pos__empty__def,axiom,
% 168.50/168.36 ! [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) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_neg__bind__def,axiom,
% 168.50/168.36 ! [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)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_New__DSequence_Opos__bind__def,axiom,
% 168.50/168.36 ! [V_i_2,V_f_2,V_x_2,T_b,T_c] : hAPP(c_New__DSequence_Opos__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = hAPP(c_Lazy__Sequence_Obind(T_c,T_b,hAPP(V_x_2,V_i_2)),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2),V_i_2)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_neg__map__def,axiom,
% 168.50/168.36 ! [V_P_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Oneg__map(T_c,T_b,V_f_2,V_P_2) = c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_P_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),T_c,c_New__Random__Sequence_Oneg__single(T_b)),V_f_2)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_neg__single__def,axiom,
% 168.50/168.36 ! [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) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_pos__bind__def,axiom,
% 168.50/168.36 ! [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)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_New__DSequence_Oneg__single__def,axiom,
% 168.50/168.36 ! [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) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_pos__map__def,axiom,
% 168.50/168.36 ! [V_P_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Opos__map(T_c,T_b,V_f_2,V_P_2) = c_New__Random__Sequence_Opos__bind(T_c,T_b,V_P_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),T_c,c_New__Random__Sequence_Opos__single(T_b)),V_f_2)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_pos__single__def,axiom,
% 168.50/168.36 ! [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) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_length__splice,axiom,
% 168.50/168.36 ! [V_ys,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Osplice(T_a,V_xs,V_ys)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_splice_Osimps_I3_J,axiom,
% 168.50/168.36 ! [V_ys,V_y,V_xs,V_x,T_a] : c_List_Osplice(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),c_List_Osplice(T_a,V_xs,V_ys))) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_splice_Osimps_I1_J,axiom,
% 168.50/168.36 ! [V_ys,T_a] : c_List_Osplice(T_a,c_List_Olist_ONil(T_a),V_ys) = V_ys ).
% 168.50/168.36
% 168.50/168.36 fof(fact_splice__Nil2,axiom,
% 168.50/168.36 ! [V_xs,T_a] : c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a)) = V_xs ).
% 168.50/168.36
% 168.50/168.36 fof(fact_splice_Osimps_I2_J,axiom,
% 168.50/168.36 ! [V_va,V_v,T_a] : c_List_Osplice(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_v),V_va),c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_v),V_va) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_New__DSequence_Opos__single__def,axiom,
% 168.50/168.36 ! [V_i_1,V_x,T_a] : hAPP(c_New__DSequence_Opos__single(T_a,V_x),V_i_1) = hAPP(c_Lazy__Sequence_Osingle(T_a),V_x) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_acyclicP__converse,axiom,
% 168.50/168.36 ! [V_r_2,T_b] :
% 168.50/168.36 ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_Predicate_Oconversep(T_b,T_b,V_r_2))))
% 168.50/168.36 <=> 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))) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_converse__meet,axiom,
% 168.50/168.36 ! [V_s_2,V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Predicate_Oconversep(T_c,T_b,V_r_2)),c_Predicate_Oconversep(T_c,T_b,V_s_2)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_converse__join,axiom,
% 168.50/168.36 ! [V_s_2,V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Predicate_Oconversep(T_c,T_b,V_r_2)),c_Predicate_Oconversep(T_c,T_b,V_s_2)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_converse__pred__comp,axiom,
% 168.50/168.36 ! [V_s_2,V_r_2,T_d,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,c_Predicate_Opred__comp(T_c,T_d,T_b,V_r_2,V_s_2)) = c_Predicate_Opred__comp(T_b,T_d,T_c,c_Predicate_Oconversep(T_d,T_b,V_s_2),c_Predicate_Oconversep(T_c,T_d,V_r_2)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_conversep__noteq,axiom,
% 168.50/168.36 ! [V_y_2,V_x_2,T_b] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_b,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot)),c_fequal)),V_x_2),V_y_2))
% 168.50/168.36 <=> V_x_2 != V_y_2 ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_conversepD,axiom,
% 168.50/168.36 ! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2))
% 168.50/168.36 => hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_conversep_Ointros,axiom,
% 168.50/168.36 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 168.50/168.36 => hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_b_2),V_a_2)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_conversep_Oequations,axiom,
% 168.50/168.36 ! [V_a1_2,V_a2_2,V_r_2,T_c,T_b] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a2_2),V_a1_2))
% 168.50/168.36 <=> hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_conversep__iff,axiom,
% 168.50/168.36 ! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2))
% 168.50/168.36 <=> hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_conversep__conversep,axiom,
% 168.50/168.36 ! [V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,c_Predicate_Oconversep(T_b,T_c,V_r_2)) = V_r_2 ).
% 168.50/168.36
% 168.50/168.36 fof(fact_conversep__eq,axiom,
% 168.50/168.36 ! [T_b] : c_Predicate_Oconversep(T_b,T_b,c_fequal) = c_fequal ).
% 168.50/168.36
% 168.50/168.36 fof(fact_conversep__converse__eq,axiom,
% 168.50/168.36 ! [V_y_2,V_x_2,V_r_2,T_c,T_b] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2),V_y_2))
% 168.50/168.36 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2))) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_,axiom,
% 168.50/168.36 ! [V_s2_2,V_s1_2,T_c,T_b] : c_Lazy__Sequence_Oproduct(T_b,T_c,V_s1_2,V_s2_2) = hAPP(c_Lazy__Sequence_Obind(T_b,tc_prod(T_b,T_c),V_s1_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c)),T_b),c_Lazy__Sequence_Obind(T_c,tc_prod(T_b,T_c),V_s2_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c))),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c)),T_c),c_Lazy__Sequence_Osingle(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_tl__replicate,axiom,
% 168.50/168.36 ! [V_x,T_a,V_n] :
% 168.50/168.36 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.50/168.36 => hAPP(c_List_Otl(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_x) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_replicate__length__filter,axiom,
% 168.50/168.36 ! [V_xs_2,V_x_2,T_b] : c_List_Oreplicate(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(c_fequal,V_x_2)),V_xs_2)),V_x_2) = hAPP(c_List_Ofilter(T_b,hAPP(c_fequal,V_x_2)),V_xs_2) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_length__replicate,axiom,
% 168.50/168.36 ! [V_x,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oreplicate(T_a,V_n,V_x)) = V_n ).
% 168.50/168.36
% 168.50/168.36 fof(fact_map__replicate__const,axiom,
% 168.50/168.36 ! [V_lst_2,V_k_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_k_2)),V_lst_2) = c_List_Oreplicate(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_lst_2),V_k_2) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_replicate__app__Cons__same,axiom,
% 168.50/168.36 ! [V_xs,V_x,V_n,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_xs)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_replicate__Suc,axiom,
% 168.50/168.36 ! [V_x,V_n,T_a] : c_List_Oreplicate(T_a,hAPP(c_Nat_OSuc,V_n),V_x) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Oreplicate(T_a,V_n,V_x)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_rev__replicate,axiom,
% 168.50/168.36 ! [V_x,V_n,T_a] : hAPP(c_List_Orev(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = c_List_Oreplicate(T_a,V_n,V_x) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_take__replicate,axiom,
% 168.50/168.36 ! [V_x,V_k,V_i,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_i),c_List_Oreplicate(T_a,V_k,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_i),V_k),V_x) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_drop__replicate,axiom,
% 168.50/168.36 ! [V_x,V_k,V_i,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_i),c_List_Oreplicate(T_a,V_k,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_k),V_i),V_x) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_hd__replicate,axiom,
% 168.50/168.36 ! [V_x,T_a,V_n] :
% 168.50/168.36 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.50/168.36 => hAPP(c_List_Ohd(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_last__replicate,axiom,
% 168.50/168.36 ! [V_x,T_a,V_n] :
% 168.50/168.36 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.50/168.36 => c_List_Olast(T_a,c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_zip__replicate,axiom,
% 168.50/168.36 ! [V_y,V_j,V_x,V_i,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),c_List_Oreplicate(T_a,V_i,V_x)),c_List_Oreplicate(T_b,V_j,V_y)) = c_List_Oreplicate(tc_prod(T_a,T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_i),V_j),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_Bex__set__replicate,axiom,
% 168.50/168.36 ! [V_P_2,V_a_2,V_n_2,T_b] :
% 168.50/168.36 ( ? [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_a_2))))
% 168.50/168.36 & hBOOL(hAPP(V_P_2,B_x)) )
% 168.50/168.36 <=> ( hBOOL(hAPP(V_P_2,V_a_2))
% 168.50/168.36 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_Ball__set__replicate,axiom,
% 168.50/168.36 ! [V_P_2,V_a_2,V_n_2,T_b] :
% 168.50/168.36 ( ! [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_a_2))))
% 168.50/168.36 => hBOOL(hAPP(V_P_2,B_x)) )
% 168.50/168.36 <=> ( hBOOL(hAPP(V_P_2,V_a_2))
% 168.50/168.36 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_replicate__eq__replicate,axiom,
% 168.50/168.36 ! [V_y_2,V_n_2,V_x_2,V_m_2,T_b] :
% 168.50/168.36 ( c_List_Oreplicate(T_b,V_m_2,V_x_2) = c_List_Oreplicate(T_b,V_n_2,V_y_2)
% 168.50/168.36 <=> ( V_m_2 = V_n_2
% 168.50/168.36 & ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.50/168.36 => V_x_2 = V_y_2 ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_nth__replicate,axiom,
% 168.50/168.36 ! [V_x,T_a,V_n,V_i] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
% 168.50/168.36 => hAPP(hAPP(c_List_Onth(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_i) = V_x ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_append__replicate__commute,axiom,
% 168.50/168.36 ! [V_k,V_x,V_n,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),c_List_Oreplicate(T_a,V_k,V_x)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_k,V_x)),c_List_Oreplicate(T_a,V_n,V_x)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_replicate__add,axiom,
% 168.50/168.36 ! [V_x,V_m,V_n,T_a] : c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),V_x) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),c_List_Oreplicate(T_a,V_m,V_x)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_filter__replicate,axiom,
% 168.50/168.36 ! [V_n_2,T_b,V_x_2,V_P_2] :
% 168.50/168.36 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 168.50/168.36 => hAPP(c_List_Ofilter(T_b,V_P_2),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_List_Oreplicate(T_b,V_n_2,V_x_2) )
% 168.50/168.36 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 168.50/168.36 => hAPP(c_List_Ofilter(T_b,V_P_2),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_List_Olist_ONil(T_b) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_concat__replicate__trivial,axiom,
% 168.50/168.36 ! [V_i,T_a] : c_List_Oconcat(T_a,c_List_Oreplicate(tc_List_Olist(T_a),V_i,c_List_Olist_ONil(T_a))) = c_List_Olist_ONil(T_a) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_replicate__0,axiom,
% 168.50/168.36 ! [V_x,T_a] : c_List_Oreplicate(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x) = c_List_Olist_ONil(T_a) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_empty__replicate,axiom,
% 168.50/168.36 ! [V_x_2,V_n_2,T_b] :
% 168.50/168.36 ( c_List_Olist_ONil(T_b) = c_List_Oreplicate(T_b,V_n_2,V_x_2)
% 168.50/168.36 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_replicate__empty,axiom,
% 168.50/168.36 ! [V_x_2,V_n_2,T_b] :
% 168.50/168.36 ( c_List_Oreplicate(T_b,V_n_2,V_x_2) = c_List_Olist_ONil(T_b)
% 168.50/168.36 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_map__replicate,axiom,
% 168.50/168.36 ! [V_x_2,V_n_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oreplicate(T_c,V_n_2,V_x_2)) = c_List_Oreplicate(T_b,V_n_2,hAPP(V_f_2,V_x_2)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_in__set__replicate,axiom,
% 168.50/168.36 ! [V_y_2,V_n_2,V_x_2,T_b] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_y_2))))
% 168.50/168.36 <=> ( V_x_2 = V_y_2
% 168.50/168.36 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_replicate__append__same,axiom,
% 168.50/168.36 ! [V_x,V_i,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_i,V_x)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Oreplicate(T_a,V_i,V_x)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_map__replicate__trivial,axiom,
% 168.50/168.36 ! [V_i_2,V_x_2,T_b] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),hAPP(c_COMBK(T_b,tc_Nat_Onat),V_x_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2)) = c_List_Oreplicate(T_b,V_i_2,V_x_2) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_set__replicate,axiom,
% 168.50/168.36 ! [V_x_2,T_b,V_n_2] :
% 168.50/168.36 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.50/168.36 => hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_set__replicate__conv__if,axiom,
% 168.50/168.36 ! [V_x_2,T_b,V_n_2] :
% 168.50/168.36 ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.50/168.36 => hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
% 168.50/168.36 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.50/168.36 => hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_set__replicate__Suc,axiom,
% 168.50/168.36 ! [V_x_2,V_n_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,hAPP(c_Nat_OSuc,V_n_2),V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_small__lazy__list_Osimps,axiom,
% 168.50/168.36 ! [V_d_2,T_b] :
% 168.50/168.36 ( class_Lazy__Sequence_Osmall__lazy(T_b)
% 168.50/168.36 => c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(T_b),V_d_2) = c_Lazy__Sequence_Oappend(tc_List_Olist(T_b),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)),hAPP(c_Lazy__Sequence_Obind(tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),c_Lazy__Sequence_Oproduct(T_b,tc_List_Olist(T_b),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_d_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_d_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b))),T_b),hAPP(c_COMBB(tc_List_Olist(T_b),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b)),tc_List_Olist(T_b)),c_Lazy__Sequence_Osingle(tc_List_Olist(T_b)))),c_List_Olist_OCons(T_b))))),c_Lazy__Sequence_Oempty(tc_List_Olist(T_b)))) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_eq__comp__r,axiom,
% 168.50/168.36 ! [V_R_2,T_b] : c_Predicate_Opred__comp(T_b,T_b,T_b,c_fequal,c_Predicate_Opred__comp(T_b,T_b,T_b,V_R_2,c_fequal)) = V_R_2 ).
% 168.50/168.36
% 168.50/168.36 fof(fact_small__lazy__prod__def,axiom,
% 168.50/168.36 ! [V_d,T_b,T_a] :
% 168.50/168.36 ( ( class_Lazy__Sequence_Osmall__lazy(T_a)
% 168.50/168.36 & class_Lazy__Sequence_Osmall__lazy(T_b) )
% 168.50/168.36 => c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(T_a,T_b),V_d) = c_Lazy__Sequence_Oproduct(T_a,T_b,c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_a,V_d),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_b,V_d)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_New__DSequence_Opos__union__def,axiom,
% 168.50/168.36 ! [V_i_2,V_yq_2,V_xq_2,T_b] : hAPP(c_New__DSequence_Opos__union(T_b,V_xq_2,V_yq_2),V_i_2) = c_Lazy__Sequence_Oappend(T_b,hAPP(V_xq_2,V_i_2),hAPP(V_yq_2,V_i_2)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_lazy__sequence_Osize_I4_J,axiom,
% 168.50/168.36 ! [V_lazy__sequence,V_a,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a,V_lazy__sequence)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),V_lazy__sequence)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 168.50/168.36
% 168.50/168.36 fof(fact__01,axiom,
% 168.50/168.36 ! [V_yq,V_xq,V_x,T_a] : c_Lazy__Sequence_Oappend(T_a,c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_x,V_xq),V_yq) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_x,c_Lazy__Sequence_Oappend(T_a,V_xq,V_yq)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_lazy__sequence_Oinject,axiom,
% 168.50/168.36 ! [V_lazy__sequence_H_2,V_a_H_2,V_lazy__sequence_2,V_a_2,T_b] :
% 168.50/168.36 ( c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_2,V_lazy__sequence_2) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_H_2,V_lazy__sequence_H_2)
% 168.50/168.36 <=> ( V_a_2 = V_a_H_2
% 168.50/168.36 & V_lazy__sequence_2 = V_lazy__sequence_H_2 ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_pos__union__def,axiom,
% 168.50/168.36 ! [V_seed_2,V_size_2,V_nrandom_2,V_R2_2,V_R1_2,T_b] : c_New__Random__Sequence_Opos__union(T_b,V_R1_2,V_R2_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__union(T_b,hAPP(hAPP(hAPP(V_R1_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(hAPP(V_R2_2,V_nrandom_2),V_size_2),V_seed_2)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_lazy__sequence_Osize_I2_J,axiom,
% 168.50/168.36 ! [V_lazy__sequence_2,V_a_2,V_fa_2,T_b] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_fa_2),c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_fa_2),V_lazy__sequence_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_small__lazy_H_Osimps,axiom,
% 168.50/168.36 ! [V_i,V_d] :
% 168.50/168.36 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i))
% 168.50/168.36 => c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
% 168.50/168.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i))
% 168.50/168.36 => c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),V_i),c_Lazy__Sequence_Osmall__lazy_H(V_d,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_small__lazy_H_Opsimps,axiom,
% 168.50/168.36 ! [V_i_2,V_d_2] :
% 168.50/168.36 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_d_2),V_i_2)))
% 168.50/168.36 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 168.50/168.36 => c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
% 168.50/168.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 168.50/168.36 => c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),V_i_2),c_Lazy__Sequence_Osmall__lazy_H(V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_small__lazy__int__def,axiom,
% 168.50/168.36 ! [V_d] : c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint,V_d) = c_Lazy__Sequence_Osmall__lazy_H(V_d,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_d)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_small__lazy_H_Opinduct,axiom,
% 168.50/168.36 ! [V_P_2,V_a1_2,V_a0_2] :
% 168.50/168.36 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
% 168.50/168.36 => ( ! [B_d,B_i] :
% 168.50/168.36 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_d),B_i)))
% 168.50/168.36 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i))
% 168.50/168.36 => hBOOL(hAPP(hAPP(V_P_2,B_d),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint)))) )
% 168.50/168.36 => hBOOL(hAPP(hAPP(V_P_2,B_d),B_i)) ) )
% 168.50/168.36 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_size__code,axiom,
% 168.50/168.36 ! [V_xq_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_b)),V_xq_2) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),T_b),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_b)))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(T_b),V_xq_2)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_lazy__sequence__size__code,axiom,
% 168.50/168.36 ! [V_xq_2,V_s_2,T_b] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_s_2),V_xq_2) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),hAPP(hAPP(c_COMBC(T_b,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),T_b),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),T_b),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),T_b),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),T_b),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_s_2))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_s_2))))),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Lazy__Sequence_Oyield(T_b),V_xq_2)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_seq__case,axiom,
% 168.50/168.36 ! [V_xq_2,V_g_2,V_f_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_b,T_c,V_f_2,V_g_2,V_xq_2) = c_Option_Ooption_Ooption__case(T_b,tc_prod(T_c,tc_Lazy__Sequence_Olazy__sequence(T_c)),V_f_2,hAPP(c_Product__Type_Oprod_Oprod__case(T_c,tc_Lazy__Sequence_Olazy__sequence(T_c),T_b),V_g_2),hAPP(c_Lazy__Sequence_Oyield(T_c),V_xq_2)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_yieldn__def,axiom,
% 168.50/168.36 ! [T_b] : c_Lazy__Sequence_Oyieldn(T_b) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(T_b),T_b,c_Lazy__Sequence_Oyield(T_b)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_lazy__sequence_Osimps_I5_J,axiom,
% 168.50/168.36 ! [V_lazy__sequence_2,V_a_2,V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_lazy__sequence_2) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_refl__on__INTER,axiom,
% 168.50/168.36 ! [V_r_2,V_A_2,T_c,V_S_2,T_b] :
% 168.50/168.36 ( ! [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 168.50/168.36 => c_Relation_Orefl__on(T_c,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) )
% 168.50/168.36 => c_Relation_Orefl__on(T_c,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_S_2),V_r_2)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_List_Omember__def,axiom,
% 168.50/168.36 ! [V_x_2,V_xs_2,T_b] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2))
% 168.50/168.36 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_member__rec_I2_J,axiom,
% 168.50/168.36 ! [V_y,T_a] : ~ hBOOL(hAPP(hAPP(c_List_Omember(T_a),c_List_Olist_ONil(T_a)),V_y)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_member__set,axiom,
% 168.50/168.36 ! [T_b] : c_List_Omember(T_b) = c_List_Oset(T_b) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_member__rec_I1_J,axiom,
% 168.50/168.36 ! [V_y_2,V_xs_2,V_x_2,T_b] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_List_Omember(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_y_2))
% 168.50/168.36 <=> ( V_x_2 = V_y_2
% 168.50/168.36 | hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_y_2)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_in__set__member,axiom,
% 168.50/168.36 ! [V_xs_2,V_x_2,T_b] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.36 <=> hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_list__ex1__iff__raw,axiom,
% 168.50/168.36 ! [V_xs_2,V_P_2,T_b] :
% 168.50/168.36 ( c_List_Olist__ex1(T_b,V_P_2,V_xs_2)
% 168.50/168.36 <=> ? [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.36 & hBOOL(hAPP(V_P_2,B_x))
% 168.50/168.36 & ! [B_y] :
% 168.50/168.36 ( ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.36 & hBOOL(hAPP(V_P_2,B_y)) )
% 168.50/168.36 => B_y = B_x ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_setsum__UNION__zero,axiom,
% 168.50/168.36 ! [V_f_2,V_S_2,T_b,T_c] :
% 168.50/168.36 ( class_Groups_Ocomm__monoid__add(T_c)
% 168.50/168.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_S_2))
% 168.50/168.36 => ( ! [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_S_2))
% 168.50/168.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) )
% 168.50/168.36 => ( ! [B_T1] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T1),V_S_2))
% 168.50/168.36 => ! [B_T2] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T2),V_S_2))
% 168.50/168.36 => ( B_T1 != B_T2
% 168.50/168.36 => ! [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T1))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T2))
% 168.50/168.36 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) )
% 168.50/168.36 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2)),V_S_2) ) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_THE__default__def,axiom,
% 168.50/168.36 ! [V_d_2,T_b,V_P_2] :
% 168.50/168.36 ( ( ? [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(V_P_2,B_x))
% 168.50/168.36 & ! [B_y] :
% 168.50/168.36 ( hBOOL(hAPP(V_P_2,B_y))
% 168.50/168.36 => B_y = B_x ) )
% 168.50/168.36 => c_FunDef_OTHE__default(T_b,V_d_2,V_P_2) = c_HOL_OThe(T_b,V_P_2) )
% 168.50/168.36 & ( ~ ? [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(V_P_2,B_x))
% 168.50/168.36 & ! [B_y] :
% 168.50/168.36 ( hBOOL(hAPP(V_P_2,B_y))
% 168.50/168.36 => B_y = B_x ) )
% 168.50/168.36 => c_FunDef_OTHE__default(T_b,V_d_2,V_P_2) = V_d_2 ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_SUP2__E,axiom,
% 168.50/168.36 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
% 168.50/168.36 => ~ ! [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.50/168.36 => ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_INF2__I,axiom,
% 168.50/168.36 ! [T_d,T_c,V_c_2,V_b_2,V_B_2,V_A_2,T_b] :
% 168.50/168.36 ( ! [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.50/168.36 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) )
% 168.50/168.36 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_finite__maxlen,axiom,
% 168.50/168.36 ! [V_M_2,T_b] :
% 168.50/168.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),V_M_2))
% 168.50/168.36 => ? [B_n] :
% 168.50/168.36 ! [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),V_M_2))
% 168.50/168.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),B_x)),B_n)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_lazy__sequence_Osize_I3_J,axiom,
% 168.50/168.36 ! [T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_lazy__sequence_Osize_I1_J,axiom,
% 168.50/168.36 ! [V_fa_2,T_b] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_fa_2),c_Lazy__Sequence_Olazy__sequence_OEmpty(T_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 168.50/168.36
% 168.50/168.36 fof(fact__02,axiom,
% 168.50/168.36 ! [V_yq,T_a] : c_Lazy__Sequence_Oappend(T_a,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a),V_yq) = V_yq ).
% 168.50/168.36
% 168.50/168.36 fof(fact_lazy__sequence_Osimps_I2_J,axiom,
% 168.50/168.36 ! [V_lazy__sequence_H,V_a_H,T_a] : c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a) != c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_H,V_lazy__sequence_H) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_lazy__sequence_Osimps_I3_J,axiom,
% 168.50/168.36 ! [V_lazy__sequence_H,V_a_H,T_a] : c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_H,V_lazy__sequence_H) != c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_lazy__sequence_Osimps_I4_J,axiom,
% 168.50/168.36 ! [V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_c)) = V_f1_2 ).
% 168.50/168.36
% 168.50/168.36 fof(fact_list__all__iff__all__interval__int,axiom,
% 168.50/168.36 ! [V_j_2,V_i_2,V_P_2] :
% 168.50/168.36 ( c_List_Olist__all(tc_Int_Oint,V_P_2,c_List_Oupto(V_i_2,V_j_2))
% 168.50/168.36 <=> c_List_Oall__interval__int(V_P_2,V_i_2,V_j_2) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_list__ex__iff__not__all__inverval__int,axiom,
% 168.50/168.36 ! [V_j_2,V_i_2,V_P_2] :
% 168.50/168.36 ( c_List_Olist__ex(tc_Int_Oint,V_P_2,c_List_Oupto(V_i_2,V_j_2))
% 168.50/168.36 <=> ~ c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),V_P_2),V_i_2,V_j_2) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_all__interval__int__def,axiom,
% 168.50/168.36 ! [V_j_2,V_i_2,V_P_2] :
% 168.50/168.36 ( c_List_Oall__interval__int(V_P_2,V_i_2,V_j_2)
% 168.50/168.36 <=> ! [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2)))
% 168.50/168.36 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_code__numeral_Orecs_I2_J,axiom,
% 168.50/168.36 ! [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)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_Random_Osimps,axiom,
% 168.50/168.36 ! [V_size_2,V_g_2,T_b,V_nrandom_2] :
% 168.50/168.36 ( ( 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)))
% 168.50/168.36 => 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)) )
% 168.50/168.36 & ( ~ 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)))
% 168.50/168.36 => 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))))))) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_code__numeral_Orecs_I1_J,axiom,
% 168.50/168.36 ! [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 ).
% 168.50/168.36
% 168.50/168.36 fof(fact_Random__Sequence_Oempty__def,axiom,
% 168.50/168.36 ! [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)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_Random__Sequence_Osingle__def,axiom,
% 168.50/168.36 ! [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)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_Random__Sequence_Omap__def,axiom,
% 168.50/168.36 ! [V_P_2,V_f_2,T_b,T_c] : c_Random__Sequence_Omap(T_c,T_b,V_f_2,V_P_2) = c_Random__Sequence_Obind(T_c,T_b,V_P_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),T_c,c_Random__Sequence_Osingle(T_b)),V_f_2)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_exE__realizer,axiom,
% 168.50/168.36 ! [T_d,V_f_2,V_Q_2,V_p_2,T_b,T_c,V_P_2] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Osnd(T_c,T_b),V_p_2)),hAPP(c_Product__Type_Ofst(T_c,T_b),V_p_2)))
% 168.50/168.36 => ( ! [B_x,B_y] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(V_P_2,B_y),B_x))
% 168.50/168.36 => hBOOL(hAPP(V_Q_2,hAPP(hAPP(V_f_2,B_x),B_y))) )
% 168.50/168.36 => 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))) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_Image__Collect__split,axiom,
% 168.50/168.36 ! [V_A_2,V_P_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,hAPP(c_Set_OCollect(tc_prod(T_c,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_P_2))),V_A_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_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_A_2)))),hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_P_2)))) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_lexord__trans,axiom,
% 168.50/168.36 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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_z_2)),c_List_Olexord(T_b,V_r_2)))
% 168.50/168.36 => ( c_Relation_Otrans(T_b,V_r_2)
% 168.50/168.36 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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_z_2)),c_List_Olexord(T_b,V_r_2))) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_trans__less__than,axiom,
% 168.50/168.36 c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_trans__lex__prod,axiom,
% 168.50/168.36 ! [V_R2_2,T_c,V_R1_2,T_b] :
% 168.50/168.36 ( c_Relation_Otrans(T_b,V_R1_2)
% 168.50/168.36 => ( c_Relation_Otrans(T_c,V_R2_2)
% 168.50/168.36 => c_Relation_Otrans(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_R1_2,V_R2_2)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_transD,axiom,
% 168.50/168.36 ! [V_c_2,V_b_2,V_a_2,V_r_2,T_b] :
% 168.50/168.36 ( c_Relation_Otrans(T_b,V_r_2)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2))
% 168.50/168.36 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),V_r_2)) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_trans__def,axiom,
% 168.50/168.36 ! [V_r_2,T_b] :
% 168.50/168.36 ( c_Relation_Otrans(T_b,V_r_2)
% 168.50/168.36 <=> ! [B_x,B_y] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2))
% 168.50/168.36 => ! [B_z] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_z)),V_r_2))
% 168.50/168.36 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_z)),V_r_2)) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_Union__eq,axiom,
% 168.50/168.36 ! [V_A_2,T_b] : c_Complete__Lattice_OSup__class_OSup(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_OEx(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_fconj),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)))) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_trans__rtrancl,axiom,
% 168.50/168.36 ! [V_r_2,T_b] : c_Relation_Otrans(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_trans__finite__psubset,axiom,
% 168.50/168.36 ! [T_b] : c_Relation_Otrans(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_trans__Id__on,axiom,
% 168.50/168.36 ! [V_A_2,T_b] : c_Relation_Otrans(T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_trancl__id,axiom,
% 168.50/168.36 ! [V_r_2,T_b] :
% 168.50/168.36 ( c_Relation_Otrans(T_b,V_r_2)
% 168.50/168.36 => c_Transitive__Closure_Otrancl(T_b,V_r_2) = V_r_2 ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_trans__trancl,axiom,
% 168.50/168.36 ! [V_r_2,T_b] : c_Relation_Otrans(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_trans__Id,axiom,
% 168.50/168.36 ! [T_b] : c_Relation_Otrans(T_b,c_Relation_OId(T_b)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_lexord__transI,axiom,
% 168.50/168.36 ! [V_r_2,T_b] :
% 168.50/168.36 ( c_Relation_Otrans(T_b,V_r_2)
% 168.50/168.36 => c_Relation_Otrans(tc_List_Olist(T_b),c_List_Olexord(T_b,V_r_2)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_trans__converse,axiom,
% 168.50/168.36 ! [V_r_2,T_b] :
% 168.50/168.36 ( c_Relation_Otrans(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 168.50/168.36 <=> c_Relation_Otrans(T_b,V_r_2) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_bex__empty,axiom,
% 168.50/168.36 ! [V_P_2,T_b] :
% 168.50/168.36 ~ ? [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 168.50/168.36 & hBOOL(hAPP(V_P_2,B_x)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_listrel__trans,axiom,
% 168.50/168.36 ! [V_r_2,T_b] :
% 168.50/168.36 ( c_Relation_Otrans(T_b,V_r_2)
% 168.50/168.36 => c_Relation_Otrans(tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_finite__Collect__bex,axiom,
% 168.50/168.36 ! [V_Q_2,T_c,V_A_2,T_b] :
% 168.50/168.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.36 => ( 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),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),V_Q_2)))))
% 168.50/168.36 <=> ! [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.50/168.36 => 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_x)))) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_bex__UNIV,axiom,
% 168.50/168.36 ! [V_P_2,T_b] :
% 168.50/168.36 ( ? [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 168.50/168.36 & hBOOL(hAPP(V_P_2,B_x)) )
% 168.50/168.36 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_trans__Int,axiom,
% 168.50/168.36 ! [V_s_2,V_r_2,T_b] :
% 168.50/168.36 ( c_Relation_Otrans(T_b,V_r_2)
% 168.50/168.36 => ( c_Relation_Otrans(T_b,V_s_2)
% 168.50/168.36 => c_Relation_Otrans(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_s_2)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_SUPR__bool__eq,axiom,
% 168.50/168.36 ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_HOL_Obool) = c_Set_OBex(T_b) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_trans__O__subset,axiom,
% 168.50/168.36 ! [V_r_2,T_b] :
% 168.50/168.36 ( c_Relation_Otrans(T_b,V_r_2)
% 168.50/168.36 => 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_r_2)),V_r_2)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_trans__inv__image,axiom,
% 168.50/168.36 ! [V_f_2,T_c,V_r_2,T_b] :
% 168.50/168.36 ( c_Relation_Otrans(T_b,V_r_2)
% 168.50/168.36 => c_Relation_Otrans(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_trans__reflclI,axiom,
% 168.50/168.36 ! [V_r_2,T_b] :
% 168.50/168.36 ( c_Relation_Otrans(T_b,V_r_2)
% 168.50/168.36 => c_Relation_Otrans(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))) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_list__ex__iff__raw,axiom,
% 168.50/168.36 ! [V_xs_2,V_P_2,T_b] :
% 168.50/168.36 ( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
% 168.50/168.36 <=> ? [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.36 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_Bex__set__list__ex,axiom,
% 168.50/168.36 ! [V_P_2,V_xs_2,T_b] :
% 168.50/168.36 ( ? [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 168.50/168.36 & hBOOL(hAPP(V_P_2,B_x)) )
% 168.50/168.36 <=> c_List_Olist__ex(T_b,V_P_2,V_xs_2) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_UN__eq,axiom,
% 168.50/168.36 ! [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_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),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_A_2)))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),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)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_fequal)),V_B_2))))) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_INT__eq,axiom,
% 168.50/168.36 ! [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_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),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_A_2)))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),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)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_fequal)),V_B_2))))) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_Sup__apply,axiom,
% 168.50/168.36 ! [V_x_2,V_A_2,T_c,T_b] :
% 168.50/168.36 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 168.50/168.36 => hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_Sup__fun__def,axiom,
% 168.50/168.36 ! [V_x_2,V_A_2,T_c,T_b] :
% 168.50/168.36 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 168.50/168.36 => hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_Inf__fun__def,axiom,
% 168.50/168.36 ! [V_x_2,V_A_2,T_c,T_b] :
% 168.50/168.36 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 168.50/168.36 => hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_Inf__apply,axiom,
% 168.50/168.36 ! [V_x_2,V_A_2,T_c,T_b] :
% 168.50/168.36 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 168.50/168.36 => hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_max__extp_Ointros,axiom,
% 168.50/168.36 ! [V_R_2,V_Y_2,V_X_2,T_b] :
% 168.50/168.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2))
% 168.50/168.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2))
% 168.50/168.36 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.36 => ( ! [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2))
% 168.50/168.36 => ? [B_xa] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2))
% 168.50/168.36 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) )
% 168.50/168.36 => c_Wellfounded_Omax__extp(T_b,V_R_2,V_X_2,V_Y_2) ) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_transp__def,axiom,
% 168.50/168.36 ! [V_r_2,T_b] :
% 168.50/168.36 ( c_Predicate_Otransp(T_b,V_r_2)
% 168.50/168.36 <=> c_Relation_Otrans(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))) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_transpE,axiom,
% 168.50/168.36 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
% 168.50/168.36 ( c_Predicate_Otransp(T_b,V_r_2)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_z_2))
% 168.50/168.36 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_z_2)) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_equivpE,axiom,
% 168.50/168.36 ! [V_R_2,T_b] :
% 168.50/168.36 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 168.50/168.36 => ~ ( c_Predicate_Oreflp(T_b,V_R_2)
% 168.50/168.36 => ( c_Predicate_Osymp(T_b,V_R_2)
% 168.50/168.36 => ~ c_Predicate_Otransp(T_b,V_R_2) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_equivpI,axiom,
% 168.50/168.36 ! [V_R_2,T_b] :
% 168.50/168.36 ( c_Predicate_Oreflp(T_b,V_R_2)
% 168.50/168.36 => ( c_Predicate_Osymp(T_b,V_R_2)
% 168.50/168.36 => ( c_Predicate_Otransp(T_b,V_R_2)
% 168.50/168.36 => c_Equiv__Relations_Oequivp(T_b,V_R_2) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_sympE,axiom,
% 168.50/168.36 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 168.50/168.36 ( c_Predicate_Osymp(T_b,V_r_2)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 168.50/168.36 => hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_x_2)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_equivp__reflp__symp__transp,axiom,
% 168.50/168.36 ! [V_R_2,T_b] :
% 168.50/168.36 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 168.50/168.36 <=> ( c_Predicate_Oreflp(T_b,V_R_2)
% 168.50/168.36 & c_Predicate_Osymp(T_b,V_R_2)
% 168.50/168.36 & c_Predicate_Otransp(T_b,V_R_2) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_max__extp_Osimps,axiom,
% 168.50/168.36 ! [V_a2_2,V_a1_2,V_R_2,T_b] :
% 168.50/168.36 ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2)
% 168.50/168.36 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 168.50/168.36 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 168.50/168.36 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.36 & ! [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 168.50/168.36 => ? [B_xa] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 168.50/168.36 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_trans__diff__Id,axiom,
% 168.50/168.36 ! [V_r_2,T_b] :
% 168.50/168.36 ( c_Relation_Otrans(T_b,V_r_2)
% 168.50/168.36 => ( c_Relation_Oantisym(T_b,V_r_2)
% 168.50/168.36 => c_Relation_Otrans(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))) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_antisym__Id__on,axiom,
% 168.50/168.36 ! [V_A_2,T_b] : c_Relation_Oantisym(T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_antisym__empty,axiom,
% 168.50/168.36 ! [T_b] : c_Relation_Oantisym(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_antisym__converse,axiom,
% 168.50/168.36 ! [V_r_2,T_b] :
% 168.50/168.36 ( c_Relation_Oantisym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 168.50/168.36 <=> c_Relation_Oantisym(T_b,V_r_2) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_antisym__Id,axiom,
% 168.50/168.36 ! [T_b] : c_Relation_Oantisym(T_b,c_Relation_OId(T_b)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_antisym__subset,axiom,
% 168.50/168.36 ! [V_s_2,V_r_2,T_b] :
% 168.50/168.36 ( 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))
% 168.50/168.36 => ( c_Relation_Oantisym(T_b,V_s_2)
% 168.50/168.36 => c_Relation_Oantisym(T_b,V_r_2) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_antisymD,axiom,
% 168.50/168.36 ! [V_b_2,V_a_2,V_r_2,T_b] :
% 168.50/168.36 ( c_Relation_Oantisym(T_b,V_r_2)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),V_r_2))
% 168.50/168.36 => V_a_2 = V_b_2 ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_antisym__def,axiom,
% 168.50/168.36 ! [V_r_2,T_b] :
% 168.50/168.36 ( c_Relation_Oantisym(T_b,V_r_2)
% 168.50/168.36 <=> ! [B_x,B_y] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2))
% 168.50/168.36 => ( 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))
% 168.50/168.36 => B_x = B_y ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_antisym__reflcl,axiom,
% 168.50/168.36 ! [V_r_2,T_b] :
% 168.50/168.36 ( c_Relation_Oantisym(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)))
% 168.50/168.36 <=> c_Relation_Oantisym(T_b,V_r_2) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_acyclic__impl__antisym__rtrancl,axiom,
% 168.50/168.36 ! [V_r_2,T_b] :
% 168.50/168.36 ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 168.50/168.36 => c_Relation_Oantisym(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_fun__lub__def,axiom,
% 168.50/168.36 ! [V_x_2,V_A_2,V_L_2,T_d,T_b,T_c] : c_Partial__Function_Ofun__lub(T_c,T_b,T_d,V_L_2,V_A_2,V_x_2) = hAPP(V_L_2,hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(tc_fun(T_d,T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),T_c),hAPP(c_COMBS(tc_fun(T_d,T_c),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_d,T_c)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_d,T_c),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_d,T_c))),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_fun(T_d,T_c),T_c),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_d,T_c),T_c),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,tc_fun(T_d,T_c))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_d,T_c),T_d,T_c),c_COMBI(tc_fun(T_d,T_c))),V_x_2)))))) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_sym__trans__comp__subset,axiom,
% 168.50/168.36 ! [V_r_2,T_b] :
% 168.50/168.36 ( c_Relation_Osym(T_b,V_r_2)
% 168.50/168.36 => ( c_Relation_Otrans(T_b,V_r_2)
% 168.50/168.36 => 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_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2)),V_r_2)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_symD,axiom,
% 168.50/168.36 ! [V_b_2,V_a_2,V_r_2,T_b] :
% 168.50/168.36 ( c_Relation_Osym(T_b,V_r_2)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 168.50/168.36 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),V_r_2)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_sym__def,axiom,
% 168.50/168.36 ! [V_r_2,T_b] :
% 168.50/168.36 ( c_Relation_Osym(T_b,V_r_2)
% 168.50/168.36 <=> ! [B_x,B_y] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2))
% 168.50/168.36 => 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)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_sym__Un__converse,axiom,
% 168.50/168.36 ! [V_r_2,T_b] : c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_sym__rtrancl,axiom,
% 168.50/168.36 ! [V_r_2,T_b] :
% 168.50/168.36 ( c_Relation_Osym(T_b,V_r_2)
% 168.50/168.36 => c_Relation_Osym(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_sym__Id__on,axiom,
% 168.50/168.36 ! [V_A_2,T_b] : c_Relation_Osym(T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_sym__trancl,axiom,
% 168.50/168.36 ! [V_r_2,T_b] :
% 168.50/168.36 ( c_Relation_Osym(T_b,V_r_2)
% 168.50/168.36 => c_Relation_Osym(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_sym__Un,axiom,
% 168.50/168.36 ! [V_s_2,V_r_2,T_b] :
% 168.50/168.36 ( c_Relation_Osym(T_b,V_r_2)
% 168.50/168.36 => ( c_Relation_Osym(T_b,V_s_2)
% 168.50/168.36 => c_Relation_Osym(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)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_sym__Id,axiom,
% 168.50/168.36 ! [T_b] : c_Relation_Osym(T_b,c_Relation_OId(T_b)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_sym__conv__converse__eq,axiom,
% 168.50/168.36 ! [V_r_2,T_b] :
% 168.50/168.36 ( c_Relation_Osym(T_b,V_r_2)
% 168.50/168.36 <=> hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2) = V_r_2 ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_sym__converse,axiom,
% 168.50/168.36 ! [V_r_2,T_b] :
% 168.50/168.36 ( c_Relation_Osym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 168.50/168.36 <=> c_Relation_Osym(T_b,V_r_2) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_listrel__sym,axiom,
% 168.50/168.36 ! [V_r_2,T_b] :
% 168.50/168.36 ( c_Relation_Osym(T_b,V_r_2)
% 168.50/168.36 => c_Relation_Osym(tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_sym__Int,axiom,
% 168.50/168.36 ! [V_s_2,V_r_2,T_b] :
% 168.50/168.36 ( c_Relation_Osym(T_b,V_r_2)
% 168.50/168.36 => ( c_Relation_Osym(T_b,V_s_2)
% 168.50/168.36 => c_Relation_Osym(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_s_2)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_sym__inv__image,axiom,
% 168.50/168.36 ! [V_f_2,T_c,V_r_2,T_b] :
% 168.50/168.36 ( c_Relation_Osym(T_b,V_r_2)
% 168.50/168.36 => c_Relation_Osym(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_sym__Int__converse,axiom,
% 168.50/168.36 ! [V_r_2,T_b] : c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_equiv__def,axiom,
% 168.50/168.36 ! [V_r_2,V_A_2,T_b] :
% 168.50/168.36 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 168.50/168.36 <=> ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 168.50/168.36 & c_Relation_Osym(T_b,V_r_2)
% 168.50/168.36 & c_Relation_Otrans(T_b,V_r_2) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_equivI,axiom,
% 168.50/168.36 ! [V_r_2,V_A_2,T_b] :
% 168.50/168.36 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 168.50/168.36 => ( c_Relation_Osym(T_b,V_r_2)
% 168.50/168.36 => ( c_Relation_Otrans(T_b,V_r_2)
% 168.50/168.36 => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_equivE,axiom,
% 168.50/168.36 ! [V_r_2,V_A_2,T_b] :
% 168.50/168.36 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 168.50/168.36 => ~ ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 168.50/168.36 => ( c_Relation_Osym(T_b,V_r_2)
% 168.50/168.36 => ~ c_Relation_Otrans(T_b,V_r_2) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_symp__def,axiom,
% 168.50/168.36 ! [V_r_2,T_b] :
% 168.50/168.36 ( c_Predicate_Osymp(T_b,V_r_2)
% 168.50/168.36 <=> c_Relation_Osym(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))) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_part__equivpI,axiom,
% 168.50/168.36 ! [T_b,V_R_2] :
% 168.50/168.36 ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 168.50/168.36 => ( c_Predicate_Osymp(T_b,V_R_2)
% 168.50/168.36 => ( c_Predicate_Otransp(T_b,V_R_2)
% 168.50/168.36 => c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_part__equivp__refl__symp__transp,axiom,
% 168.50/168.36 ! [V_R_2,T_b] :
% 168.50/168.36 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 168.50/168.36 <=> ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 168.50/168.36 & c_Predicate_Osymp(T_b,V_R_2)
% 168.50/168.36 & c_Predicate_Otransp(T_b,V_R_2) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_part__equivp__transp,axiom,
% 168.50/168.36 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] :
% 168.50/168.36 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
% 168.50/168.36 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_part__equivp__symp,axiom,
% 168.50/168.36 ! [V_y_2,V_x_2,V_R_2,T_b] :
% 168.50/168.36 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 168.50/168.36 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_part__equivp__def,axiom,
% 168.50/168.36 ! [V_R_2,T_b] :
% 168.50/168.36 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 168.50/168.36 <=> ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 168.50/168.36 & ! [B_x,B_y] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
% 168.50/168.36 <=> ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 168.50/168.36 & hBOOL(hAPP(hAPP(V_R_2,B_y),B_y))
% 168.50/168.36 & hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_equivp__implies__part__equivp,axiom,
% 168.50/168.36 ! [V_R_2,T_b] :
% 168.50/168.36 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 168.50/168.36 => c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_part__equivpE,axiom,
% 168.50/168.36 ! [V_R_2,T_b] :
% 168.50/168.36 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 168.50/168.36 => ~ ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 168.50/168.36 => ( c_Predicate_Osymp(T_b,V_R_2)
% 168.50/168.36 => ~ c_Predicate_Otransp(T_b,V_R_2) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_part__equivp__typedef,axiom,
% 168.50/168.36 ! [V_R_2,T_b] :
% 168.50/168.36 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 168.50/168.36 => ? [B_d] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),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_COMBS(T_b,T_b,tc_HOL_Obool),V_R_2),c_COMBI(T_b))))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),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_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b)),c_fequal)),V_R_2))))) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_inv__o__cancel,axiom,
% 168.50/168.36 ! [V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 168.50/168.36 => hAPP(c_Fun_Ocomp(T_c,T_b,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),V_f_2) = c_Fun_Oid(T_b) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_inj__iff,axiom,
% 168.50/168.36 ! [V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 168.50/168.36 <=> hAPP(c_Fun_Ocomp(T_c,T_b,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),V_f_2) = c_Fun_Oid(T_b) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_o__inv__o__cancel,axiom,
% 168.50/168.36 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 168.50/168.36 => hAPP(c_Fun_Ocomp(T_c,T_d,T_b,hAPP(c_Fun_Ocomp(T_b,T_d,T_c,V_g_2),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2))),V_f_2) = V_g_2 ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_inv__into__def,axiom,
% 168.50/168.36 ! [V_x_2,V_f_2,V_A_2,T_c,T_b] : hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_x_2) = c_Hilbert__Choice_OEps(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_x_2))) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_inv__id,axiom,
% 168.50/168.36 ! [T_b] : c_Hilbert__Choice_Oinv__into(T_b,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Fun_Oid(T_b)) = c_Fun_Oid(T_b) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_inv__f__f,axiom,
% 168.50/168.36 ! [V_x_2,V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 168.50/168.36 => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_inv__f__eq,axiom,
% 168.50/168.36 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 168.50/168.36 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 168.50/168.36 => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),V_y_2) = V_x_2 ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_inv__into__f__eq,axiom,
% 168.50/168.36 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.50/168.36 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 168.50/168.36 => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_inv__into__f__f,axiom,
% 168.50/168.36 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 168.50/168.36 => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_inv__into__injective,axiom,
% 168.50/168.36 ! [V_y_2,V_x_2,V_f_2,V_A_2,T_c,T_b] :
% 168.50/168.36 ( hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_x_2) = hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_y_2)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 168.50/168.36 => V_x_2 = V_y_2 ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_inv__into__into,axiom,
% 168.50/168.36 ! [V_A_2,V_f_2,T_c,V_x_2,T_b] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 168.50/168.36 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2),V_x_2)),V_A_2)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_f__inv__into__f,axiom,
% 168.50/168.36 ! [V_A_2,V_f_2,T_c,V_y_2,T_b] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 168.50/168.36 => hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2),V_y_2)) = V_y_2 ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_surj__iff__all,axiom,
% 168.50/168.36 ! [V_f_2,T_b,T_c] :
% 168.50/168.36 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.36 <=> ! [B_x] : hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),B_x)) = B_x ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_surj__f__inv__f,axiom,
% 168.50/168.36 ! [V_y_2,V_f_2,T_b,T_c] :
% 168.50/168.36 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.36 => hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),V_y_2)) = V_y_2 ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_image__surj__f__inv__f,axiom,
% 168.50/168.36 ! [V_A_2,V_f_2,T_b,T_c] :
% 168.50/168.36 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.36 => hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2)),V_A_2)) = V_A_2 ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_image__inv__into__cancel,axiom,
% 168.50/168.36 ! [V_B_H_2,V_A_H_2,V_A_2,V_f_2,T_b,T_c] :
% 168.50/168.36 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_H_2),V_A_H_2))
% 168.50/168.36 => hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2)),V_B_H_2)) = V_B_H_2 ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_inv__def,axiom,
% 168.50/168.36 ! [V_y_2,V_f_2,T_c,T_b] : hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),V_y_2) = c_Hilbert__Choice_OEps(T_b,hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_y_2)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_surj__imp__inj__inv,axiom,
% 168.50/168.36 ! [V_f_2,T_b,T_c] :
% 168.50/168.36 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.36 => c_Fun_Oinj__on(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_inv__image__comp,axiom,
% 168.50/168.36 ! [V_X_2,V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 168.50/168.36 => hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_X_2)) = V_X_2 ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_image__inv__f__f,axiom,
% 168.50/168.36 ! [V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 168.50/168.36 => hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2 ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_inj__imp__surj__inv,axiom,
% 168.50/168.36 ! [V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 168.50/168.36 => hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_inj__on__inv__into,axiom,
% 168.50/168.36 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 168.50/168.36 => c_Fun_Oinj__on(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2),V_B_2) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_inv__into__image__cancel,axiom,
% 168.50/168.36 ! [V_S_2,V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_A_2))
% 168.50/168.36 => hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_S_2)) = V_S_2 ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_inv__into__comp,axiom,
% 168.50/168.36 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2))
% 168.50/168.36 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2))))
% 168.50/168.36 => hAPP(c_Hilbert__Choice_Oinv__into(T_d,T_c,V_A_2,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_b,T_d,T_c,c_Hilbert__Choice_Oinv__into(T_d,T_b,V_A_2,V_g_2)),c_Hilbert__Choice_Oinv__into(T_b,T_c,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2),V_f_2)),V_x_2) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_surj__iff,axiom,
% 168.50/168.36 ! [V_f_2,T_b,T_c] :
% 168.50/168.36 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.36 <=> hAPP(c_Fun_Ocomp(T_c,T_b,T_b,V_f_2),c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2)) = c_Fun_Oid(T_b) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_inj__transfer,axiom,
% 168.50/168.36 ! [V_x_2,V_P_2,V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 168.50/168.36 => ( ! [B_y] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))
% 168.50/168.36 => hBOOL(hAPP(V_P_2,hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),B_y))) )
% 168.50/168.36 => hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_fold__image__UN__disjoint,axiom,
% 168.50/168.36 ! [V_g_2,V_A_2,T_c,V_I_2,T_b,T_d] :
% 168.50/168.36 ( class_Groups_Ocomm__monoid__mult(T_d)
% 168.50/168.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_I_2))
% 168.50/168.36 => ( ! [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 168.50/168.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) )
% 168.50/168.36 => ( ! [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 168.50/168.36 => ! [B_xa] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_I_2))
% 168.50/168.36 => ( B_x != B_xa
% 168.50/168.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,B_x)),hAPP(V_A_2,B_xa)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) )
% 168.50/168.36 => hAPP(hAPP(hAPP(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)),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(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),T_d,T_b),hAPP(hAPP(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_A_2)),c_Groups_Oone__class_Oone(T_d)),V_I_2) ) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_nat__of__induct,axiom,
% 168.50/168.36 ! [V_P_2,V_y_2] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 168.50/168.36 => ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Code__Numeral_Onat__of,B_x)))
% 168.50/168.36 => hBOOL(hAPP(V_P_2,V_y_2)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_nat__of__cases,axiom,
% 168.50/168.36 ! [V_y_2] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 168.50/168.36 => ~ ! [B_x] : V_y_2 != hAPP(c_Code__Numeral_Onat__of,B_x) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_of__nat__induct,axiom,
% 168.50/168.36 ! [V_x_2,V_P_2] :
% 168.50/168.36 ( ! [B_y] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_y),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 168.50/168.36 => hBOOL(hAPP(V_P_2,hAPP(c_Code__Numeral_Oof__nat,B_y))) )
% 168.50/168.36 => hBOOL(hAPP(V_P_2,V_x_2)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_of__nat__cases,axiom,
% 168.50/168.36 ! [V_x_2] :
% 168.50/168.36 ~ ! [B_y] :
% 168.50/168.36 ( V_x_2 = hAPP(c_Code__Numeral_Oof__nat,B_y)
% 168.50/168.36 => ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_y),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_lazy__sequence_Orecs_I1_J,axiom,
% 168.50/168.36 ! [V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_c)) = V_f1_2 ).
% 168.50/168.36
% 168.50/168.36 fof(fact_beyond__def,axiom,
% 168.50/168.36 ! [V_l,V_k] :
% 168.50/168.36 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 168.50/168.36 => c_Quickcheck_Obeyond(V_k,V_l) = V_l )
% 168.50/168.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 168.50/168.36 => c_Quickcheck_Obeyond(V_k,V_l) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_beyond__zero,axiom,
% 168.50/168.36 ! [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) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_lazy__sequence_Orecs_I2_J,axiom,
% 168.50/168.36 ! [V_lazy__sequence_2,V_a_2,V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(hAPP(V_f2_2,V_a_2),V_lazy__sequence_2),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(T_b,T_c,V_f1_2,V_f2_2,V_lazy__sequence_2)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_bij__image__Collect__eq,axiom,
% 168.50/168.36 ! [V_P_2,V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 168.50/168.36 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Set_OCollect(T_b),V_P_2)) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),V_P_2),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2))) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_curry__def,axiom,
% 168.50/168.36 ! [V_y_2,V_x_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_c_2),V_x_2),V_y_2) = hAPP(V_c_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_curryI,axiom,
% 168.50/168.36 ! [V_b_2,V_a_2,T_c,T_b,V_f_2] :
% 168.50/168.36 ( hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))
% 168.50/168.36 => hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_bij__betw__id,axiom,
% 168.50/168.36 ! [V_A_2,T_b] : c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_A_2) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_bij__betw__inv__into,axiom,
% 168.50/168.36 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 168.50/168.36 => c_Fun_Obij__betw(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_B_2,V_A_2) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_inv__into__inv__into__eq,axiom,
% 168.50/168.36 ! [V_a_2,V_A_H_2,V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 168.50/168.36 => hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_H_2,c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2)),V_a_2) = hAPP(V_f_2,V_a_2) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_inv__inv__eq,axiom,
% 168.50/168.36 ! [V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 168.50/168.36 => c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)) = V_f_2 ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_bij__imp__bij__inv,axiom,
% 168.50/168.36 ! [V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 168.50/168.36 => c_Fun_Obij__betw(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_o__inv__distrib,axiom,
% 168.50/168.36 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 168.50/168.36 => ( c_Fun_Obij__betw(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 168.50/168.36 => c_Hilbert__Choice_Oinv__into(T_d,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_d,T_c,c_Hilbert__Choice_Oinv__into(T_d,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),V_g_2)),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_bij__betw__trans,axiom,
% 168.50/168.36 ! [V_C_2,V_g_2,T_d,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 168.50/168.36 => ( c_Fun_Obij__betw(T_c,T_d,V_g_2,V_B_2,V_C_2)
% 168.50/168.36 => c_Fun_Obij__betw(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_f_2),V_A_2,V_C_2) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_bij__betw__comp__iff,axiom,
% 168.50/168.36 ! [V_A_H_H_2,V_f_H_2,T_d,V_A_H_2,V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 168.50/168.36 => ( c_Fun_Obij__betw(T_c,T_d,V_f_H_2,V_A_H_2,V_A_H_H_2)
% 168.50/168.36 <=> c_Fun_Obij__betw(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_f_H_2),V_f_2),V_A_2,V_A_H_H_2) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_bij__comp,axiom,
% 168.50/168.36 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 168.50/168.36 => ( c_Fun_Obij__betw(T_c,T_d,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))
% 168.50/168.36 => c_Fun_Obij__betw(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_bij__betw__comp__iff2,axiom,
% 168.50/168.36 ! [V_A_2,V_f_2,T_d,V_A_H_H_2,V_A_H_2,V_f_H_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Obij__betw(T_b,T_c,V_f_H_2,V_A_H_2,V_A_H_H_2)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_b,V_f_2),V_A_2)),V_A_H_2))
% 168.50/168.36 => ( c_Fun_Obij__betw(T_d,T_b,V_f_2,V_A_2,V_A_H_2)
% 168.50/168.36 <=> c_Fun_Obij__betw(T_d,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_H_2),V_f_2),V_A_2,V_A_H_H_2) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_curry__conv,axiom,
% 168.50/168.36 ! [V_b_2,V_a_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_f_2),V_a_2),V_b_2) = hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_curryE,axiom,
% 168.50/168.36 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
% 168.50/168.36 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_curryD,axiom,
% 168.50/168.36 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
% 168.50/168.36 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_bij__image__Compl__eq,axiom,
% 168.50/168.36 ! [V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 168.50/168.36 => 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)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_finite__vimage__iff,axiom,
% 168.50/168.36 ! [V_F_2,V_h_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Obij__betw(T_b,T_c,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 168.50/168.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2)))
% 168.50/168.36 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_bij__def,axiom,
% 168.50/168.36 ! [V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 168.50/168.36 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 168.50/168.36 & hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_bijI,axiom,
% 168.50/168.36 ! [V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 168.50/168.36 => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
% 168.50/168.36 => c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_bij__betw__subset,axiom,
% 168.50/168.36 ! [V_B_H_2,V_B_2,V_A_H_2,V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 168.50/168.36 => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2) = V_B_H_2
% 168.50/168.36 => c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_bij__is__surj,axiom,
% 168.50/168.36 ! [V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 168.50/168.36 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_bij__betw__imp__surj,axiom,
% 168.50/168.36 ! [V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 168.50/168.36 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_bij__betw__def,axiom,
% 168.50/168.36 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 168.50/168.36 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 168.50/168.36 & hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = V_B_2 ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_inj__on__imp__bij__betw,axiom,
% 168.50/168.36 ! [V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 168.50/168.36 => c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_bij__betw__imp__inj__on,axiom,
% 168.50/168.36 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 168.50/168.36 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_bij__is__inj,axiom,
% 168.50/168.36 ! [V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 168.50/168.36 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_bij__betw__the__inv__into,axiom,
% 168.50/168.36 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 168.50/168.36 => c_Fun_Obij__betw(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_B_2,V_A_2) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_bij__betw__same__card,axiom,
% 168.50/168.36 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 168.50/168.36 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_bij__betw__empty2,axiom,
% 168.50/168.36 ! [V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))
% 168.50/168.36 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_bij__betw__empty1,axiom,
% 168.50/168.36 ! [V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_A_2)
% 168.50/168.36 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_BIJ,axiom,
% 168.50/168.36 ! [V_B_2,T_c,V_A_2,T_b] :
% 168.50/168.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 168.50/168.36 => ( ? [B_f] : c_Fun_Obij__betw(T_b,T_c,B_f,V_A_2,V_B_2)
% 168.50/168.36 <=> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_bij__betw__finite,axiom,
% 168.50/168.36 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 168.50/168.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.36 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_bij__betw__id__iff,axiom,
% 168.50/168.36 ! [V_B_2,V_A_2,T_b] :
% 168.50/168.36 ( c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_B_2)
% 168.50/168.36 <=> V_A_2 = V_B_2 ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_bij__id,axiom,
% 168.50/168.36 ! [T_b] : c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_bij__betw__combine,axiom,
% 168.50/168.36 ! [V_D_2,V_C_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 168.50/168.36 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_C_2,V_D_2)
% 168.50/168.36 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_D_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
% 168.50/168.36 => c_Fun_Obij__betw(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_D_2)) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_bij__betw__Disj__Un,axiom,
% 168.50/168.36 ! [V_f_2,V_B_H_2,V_A_H_2,T_c,V_B_2,V_A_2,T_b] :
% 168.50/168.36 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 168.50/168.36 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_H_2),V_B_H_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
% 168.50/168.36 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 168.50/168.36 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2)
% 168.50/168.36 => c_Fun_Obij__betw(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_H_2),V_B_H_2)) ) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_curry__split,axiom,
% 168.50/168.36 ! [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 ).
% 168.50/168.36
% 168.50/168.36 fof(fact_split__curry,axiom,
% 168.50/168.36 ! [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 ).
% 168.50/168.36
% 168.50/168.36 fof(fact_bij__image__INT,axiom,
% 168.50/168.36 ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 168.50/168.36 => 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)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_vimage__subset__eq,axiom,
% 168.50/168.36 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),V_A_2))
% 168.50/168.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_bij__vimage__eq__inv__image,axiom,
% 168.50/168.36 ! [V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 168.50/168.36 => hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),V_A_2) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_ex__bij__betw__nat__finite__1,axiom,
% 168.50/168.36 ! [V_M_2,T_b] :
% 168.50/168.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
% 168.50/168.36 => ? [B_h] : c_Fun_Obij__betw(tc_Nat_Onat,T_b,B_h,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_M_2)),V_M_2) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_Cantor__Bernstein,axiom,
% 168.50/168.36 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2))
% 168.50/168.36 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),V_B_2)),V_A_2))
% 168.50/168.36 => ? [B_h] : c_Fun_Obij__betw(T_b,T_c,B_h,V_A_2,V_B_2) ) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_ex__bij__betw__nat__finite,axiom,
% 168.50/168.36 ! [V_M_2,T_b] :
% 168.50/168.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
% 168.50/168.36 => ? [B_h] : c_Fun_Obij__betw(tc_Nat_Onat,T_b,B_h,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_M_2)),V_M_2) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_ex__bij__betw__finite__nat,axiom,
% 168.50/168.36 ! [V_M_2,T_b] :
% 168.50/168.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
% 168.50/168.36 => ? [B_h] : c_Fun_Obij__betw(T_b,tc_Nat_Onat,B_h,V_M_2,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_M_2))) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_refl__on__UNION,axiom,
% 168.50/168.36 ! [V_r_2,V_A_2,T_c,V_S_2,T_b] :
% 168.50/168.36 ( ! [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 168.50/168.36 => c_Relation_Orefl__on(T_c,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) )
% 168.50/168.36 => c_Relation_Orefl__on(T_c,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_S_2),V_r_2)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_bex__reg__eqv,axiom,
% 168.50/168.36 ! [V_P_2,V_R_2,T_b] :
% 168.50/168.36 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 168.50/168.36 => ( ? [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Quotient_ORespects(T_b,V_R_2)))
% 168.50/168.36 & hBOOL(hAPP(V_P_2,B_x)) )
% 168.50/168.36 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_in__respects,axiom,
% 168.50/168.36 ! [V_R_2,V_x_2,T_b] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Quotient_ORespects(T_b,V_R_2)))
% 168.50/168.36 <=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_Respects__def,axiom,
% 168.50/168.36 ! [V_x_2,V_R_2,T_b] :
% 168.50/168.36 ( hBOOL(hAPP(c_Quotient_ORespects(T_b,V_R_2),V_x_2))
% 168.50/168.36 <=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_bex__reg__right,axiom,
% 168.50/168.36 ! [V_P_2,V_Q_2,V_R_2,T_b] :
% 168.50/168.36 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 168.50/168.36 => ( ! [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(V_Q_2,B_x))
% 168.50/168.36 => hBOOL(hAPP(V_P_2,B_x)) )
% 168.50/168.36 => ( ? [B_x1] : hBOOL(hAPP(V_Q_2,B_x1))
% 168.50/168.36 => ? [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Quotient_ORespects(T_b,V_R_2)))
% 168.50/168.36 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_babs__reg__eqv,axiom,
% 168.50/168.36 ! [V_P_2,T_c,V_R_2,T_b] :
% 168.50/168.36 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 168.50/168.36 => c_Quotient_OBabs(T_b,T_c,c_Quotient_ORespects(T_b,V_R_2),V_P_2) = V_P_2 ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_Babs__def,axiom,
% 168.50/168.36 ! [V_m_2,T_c,V_p_2,V_x_2,T_b] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_p_2))
% 168.50/168.36 => hAPP(c_Quotient_OBabs(T_b,T_c,V_p_2,V_m_2),V_x_2) = hAPP(V_m_2,V_x_2) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_wf__weak__decr__stable,axiom,
% 168.50/168.36 ! [V_r_2,V_f_2,T_b] :
% 168.50/168.36 ( ! [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)))
% 168.50/168.36 => ( c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2))
% 168.50/168.36 => ? [B_i] :
% 168.50/168.36 ! [B_k] : hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),B_k)) = hAPP(V_f_2,B_i) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_INT__greatest,axiom,
% 168.50/168.36 ! [V_B_2,V_C_2,T_c,V_A_2,T_b] :
% 168.50/168.36 ( ! [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.50/168.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(V_B_2,B_x))) )
% 168.50/168.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_C_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))) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_INT__anti__mono,axiom,
% 168.50/168.36 ! [V_g_2,V_f_2,T_c,V_A_2,V_B_2,T_b] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 168.50/168.36 => ( ! [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 168.50/168.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 168.50/168.36 => 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_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_g_2))) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_rtrancl__induct2,axiom,
% 168.50/168.36 ! [V_P_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_c,T_b] :
% 168.50/168.36 ( 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_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2)))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(V_P_2,V_ax_2),V_ay_2))
% 168.50/168.36 => ( ! [B_a,B_b] :
% 168.50/168.36 ( 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_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2)))
% 168.50/168.36 => ! [B_aa,B_ba] :
% 168.50/168.36 ( 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),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_aa),B_ba))),V_r_2))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(V_P_2,B_a),B_b))
% 168.50/168.36 => hBOOL(hAPP(hAPP(V_P_2,B_aa),B_ba)) ) ) )
% 168.50/168.36 => hBOOL(hAPP(hAPP(V_P_2,V_bx_2),V_by_2)) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_converse__rtranclE2,axiom,
% 168.50/168.36 ! [V_r_2,V_zb_2,V_za_2,V_xb_2,V_xa_2,T_c,T_b] :
% 168.50/168.36 ( 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_xa_2),V_xb_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_za_2),V_zb_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2)))
% 168.50/168.36 => ( hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_xa_2),V_xb_2) != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_za_2),V_zb_2)
% 168.50/168.36 => ~ ! [B_a,B_b] :
% 168.50/168.36 ( 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_xa_2),V_xb_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))),V_r_2))
% 168.50/168.36 => ~ 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),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_za_2),V_zb_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2))) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_converse__rtrancl__induct2,axiom,
% 168.50/168.36 ! [V_P_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_c,T_b] :
% 168.50/168.36 ( 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_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2)))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(V_P_2,V_bx_2),V_by_2))
% 168.50/168.36 => ( ! [B_a,B_b,B_aa,B_ba] :
% 168.50/168.36 ( 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),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_aa),B_ba))),V_r_2))
% 168.50/168.36 => ( 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),B_aa),B_ba)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2)))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(V_P_2,B_aa),B_ba))
% 168.50/168.36 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) ) )
% 168.50/168.36 => hBOOL(hAPP(hAPP(V_P_2,V_ax_2),V_ay_2)) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_congruentI,axiom,
% 168.50/168.36 ! [T_c,V_f_2,V_r_2,T_b] :
% 168.50/168.36 ( ! [B_y,B_z] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_z)),V_r_2))
% 168.50/168.36 => hAPP(V_f_2,B_y) = hAPP(V_f_2,B_z) )
% 168.50/168.36 => c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_congruent2I_H,axiom,
% 168.50/168.36 ! [T_d,V_f_2,V_r2_2,T_c,V_r1_2,T_b] :
% 168.50/168.36 ( ! [B_y1,B_z1] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y1),B_z1)),V_r1_2))
% 168.50/168.36 => ! [B_y2,B_z2] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_y2),B_z2)),V_r2_2))
% 168.50/168.36 => hAPP(hAPP(V_f_2,B_y1),B_y2) = hAPP(hAPP(V_f_2,B_z1),B_z2) ) )
% 168.50/168.36 => c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact__03,axiom,
% 168.50/168.36 ! [V_xqq,V_xq,T_a] : c_Lazy__Sequence_Oflat(T_a,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(T_a),V_xq,V_xqq)) = c_Lazy__Sequence_Oappend(T_a,V_xq,c_Lazy__Sequence_Oflat(T_a,V_xqq)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_all__interval__nat__def,axiom,
% 168.50/168.36 ! [V_j_2,V_i_2,V_P_2] :
% 168.50/168.36 ( c_List_Oall__interval__nat(V_P_2,V_i_2,V_j_2)
% 168.50/168.36 <=> ! [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)))
% 168.50/168.36 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact__04,axiom,
% 168.50/168.36 ! [T_a] : c_Lazy__Sequence_Oflat(T_a,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(T_a))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_list__all__iff__all__interval__nat,axiom,
% 168.50/168.36 ! [V_j_2,V_i_2,V_P_2] :
% 168.50/168.36 ( c_List_Olist__all(tc_Nat_Onat,V_P_2,c_List_Oupt(V_i_2,V_j_2))
% 168.50/168.36 <=> c_List_Oall__interval__nat(V_P_2,V_i_2,V_j_2) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_list__ex__iff__not__all__inverval__nat,axiom,
% 168.50/168.36 ! [V_j_2,V_i_2,V_P_2] :
% 168.50/168.36 ( c_List_Olist__ex(tc_Nat_Onat,V_P_2,c_List_Oupt(V_i_2,V_j_2))
% 168.50/168.36 <=> ~ c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),V_P_2),V_i_2,V_j_2) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact__05,axiom,
% 168.50/168.36 ! [V_f_2,V_xq_2,T_b,T_c] : hAPP(c_Lazy__Sequence_Obind(T_c,T_b,V_xq_2),V_f_2) = c_Lazy__Sequence_Oflat(T_b,c_Lazy__Sequence_Omap(T_c,tc_Lazy__Sequence_Olazy__sequence(T_b),V_f_2,V_xq_2)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_folding__image_Ocong,axiom,
% 168.50/168.36 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 168.50/168.36 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 168.50/168.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 168.50/168.36 => ( ! [B_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 168.50/168.36 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) )
% 168.50/168.36 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(V_F_2,V_h_2),V_A_2) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact__06,axiom,
% 168.50/168.36 ! [V_xq_2,V_x_2,V_f_2,T_b,T_c] : c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,V_x_2,V_xq_2)) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,hAPP(V_f_2,V_x_2),c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,V_xq_2)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact__07,axiom,
% 168.50/168.36 ! [V_f_2,T_b,T_c] : c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_c)) = c_Lazy__Sequence_Olazy__sequence_OEmpty(T_b) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_New__DSequence_Opos__map__def,axiom,
% 168.50/168.36 ! [V_i_2,V_xq_2,V_f_2,T_b,T_c] : c_New__DSequence_Opos__map(T_c,T_b,V_f_2,V_xq_2,V_i_2) = c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,hAPP(V_xq_2,V_i_2)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_power__dvd__imp__le,axiom,
% 168.50/168.36 ! [V_n,V_m,V_i] :
% 168.50/168.36 ( 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)))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_i))
% 168.50/168.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_Oorder__refl,axiom,
% 168.50/168.36 ! [V_x] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_x)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd__0__right,axiom,
% 168.50/168.36 ! [V_a,T_a] :
% 168.50/168.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.50/168.36 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd__1__left,axiom,
% 168.50/168.36 ! [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)) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_setprod__dvd__setprod__subset,axiom,
% 168.50/168.36 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 168.50/168.36 ( ( class_Groups_Ocomm__monoid__mult(T_c)
% 168.50/168.36 & class_Rings_Odvd(T_c) )
% 168.50/168.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 168.50/168.36 => 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))) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd__setprod,axiom,
% 168.50/168.36 ! [V_f_2,V_i_2,V_A_2,T_b,T_c] :
% 168.50/168.36 ( class_Rings_Ocomm__semiring__1(T_c)
% 168.50/168.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 168.50/168.36 => 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))) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_unity__coeff__ex,axiom,
% 168.50/168.36 ! [V_l_2,V_P_2,T_b] :
% 168.50/168.36 ( ( class_Rings_Odvd(T_b)
% 168.50/168.36 & class_Rings_Osemiring__0(T_b) )
% 168.50/168.36 => ( ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_l_2),B_x)))
% 168.50/168.36 <=> ? [B_x] :
% 168.50/168.36 ( 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))))
% 168.50/168.36 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd__mult__cancel__left,axiom,
% 168.50/168.36 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 168.50/168.36 ( class_Rings_Oidom(T_b)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
% 168.50/168.36 <=> ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 168.50/168.36 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd__mult__cancel__right,axiom,
% 168.50/168.36 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 168.50/168.36 ( class_Rings_Oidom(T_b)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2)))
% 168.50/168.36 <=> ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 168.50/168.36 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd__mult__right,axiom,
% 168.50/168.36 ! [V_c,V_b,V_a,T_a] :
% 168.50/168.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.50/168.36 => ( 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))
% 168.50/168.36 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd__mult__left,axiom,
% 168.50/168.36 ! [V_c,V_b,V_a,T_a] :
% 168.50/168.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.50/168.36 => ( 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))
% 168.50/168.36 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvdI,axiom,
% 168.50/168.36 ! [V_k,V_b,V_a,T_a] :
% 168.50/168.36 ( class_Rings_Odvd(T_a)
% 168.50/168.36 => ( V_a = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k)
% 168.50/168.36 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_a)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_mult__dvd__mono,axiom,
% 168.50/168.36 ! [V_d,V_c,V_b,V_a,T_a] :
% 168.50/168.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_d))
% 168.50/168.36 => 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))) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd__mult,axiom,
% 168.50/168.36 ! [V_b,V_c,V_a,T_a] :
% 168.50/168.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))
% 168.50/168.36 => 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))) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd__mult2,axiom,
% 168.50/168.36 ! [V_c,V_b,V_a,T_a] :
% 168.50/168.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 168.50/168.36 => 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))) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd__triv__right,axiom,
% 168.50/168.36 ! [V_b,V_a,T_a] :
% 168.50/168.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.50/168.36 => 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))) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd__triv__left,axiom,
% 168.50/168.36 ! [V_b,V_a,T_a] :
% 168.50/168.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.50/168.36 => 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))) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd__mult__div__cancel,axiom,
% 168.50/168.36 ! [V_b,V_a,T_a] :
% 168.50/168.36 ( class_Divides_Osemiring__div(T_a)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 168.50/168.36 => 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 ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_div__mult__swap,axiom,
% 168.50/168.36 ! [V_a,V_b,V_c,T_a] :
% 168.50/168.36 ( class_Divides_Osemiring__div(T_a)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))
% 168.50/168.36 => 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) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd__div__mult__self,axiom,
% 168.50/168.36 ! [V_b,V_a,T_a] :
% 168.50/168.36 ( class_Divides_Osemiring__div(T_a)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 168.50/168.36 => 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 ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd__div__mult,axiom,
% 168.50/168.36 ! [V_c,V_b,V_a,T_a] :
% 168.50/168.36 ( class_Divides_Osemiring__div(T_a)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 168.50/168.36 => 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) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_div__mult__div__if__dvd,axiom,
% 168.50/168.36 ! [V_w,V_z,V_x,V_y,T_a] :
% 168.50/168.36 ( class_Divides_Osemiring__div(T_a)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_w))
% 168.50/168.36 => 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)) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_nat__mult__dvd__cancel__disj,axiom,
% 168.50/168.36 ! [V_n_2,V_m_2,V_k_2] :
% 168.50/168.36 ( 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)))
% 168.50/168.36 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 168.50/168.36 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_inf__period_I4_J,axiom,
% 168.50/168.36 ! [V_t_2,V_D_2,V_d_2,T_b] :
% 168.50/168.36 ( ( class_Rings_Ocomm__ring(T_b)
% 168.50/168.36 & class_Rings_Odvd(T_b) )
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))
% 168.50/168.36 => ! [B_x,B_k] :
% 168.50/168.36 ( 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)))
% 168.50/168.36 <=> 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))) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_inf__period_I3_J,axiom,
% 168.50/168.36 ! [V_t_2,V_D_2,V_d_2,T_b] :
% 168.50/168.36 ( ( class_Rings_Ocomm__ring(T_b)
% 168.50/168.36 & class_Rings_Odvd(T_b) )
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))
% 168.50/168.36 => ! [B_x,B_k] :
% 168.50/168.36 ( 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)))
% 168.50/168.36 <=> 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))) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_OatLeastAtMost__singleton__iff,axiom,
% 168.50/168.36 ! [V_c_2,V_b_2,V_a_2] :
% 168.50/168.36 ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
% 168.50/168.36 <=> ( V_a_2 = V_b_2
% 168.50/168.36 & V_b_2 = V_c_2 ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_OatLeastAtMost__singleton,axiom,
% 168.50/168.36 ! [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))) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_OatLeastAtMost__singleton_H,axiom,
% 168.50/168.36 ! [V_b_2,V_a_2] :
% 168.50/168.36 ( V_a_2 = V_b_2
% 168.50/168.36 => c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_OgreaterThanAtMost__empty,axiom,
% 168.50/168.36 ! [V_k_2,V_l_2] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
% 168.50/168.36 => 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)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_OatLeastLessThan__empty,axiom,
% 168.50/168.36 ! [V_a_2,V_b_2] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2))
% 168.50/168.36 => c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_OgreaterThanLessThan__empty,axiom,
% 168.50/168.36 ! [V_k_2,V_l_2] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
% 168.50/168.36 => 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)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_OgreaterThanAtMost__empty__iff,axiom,
% 168.50/168.36 ! [V_l_2,V_k_2] :
% 168.50/168.36 ( 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))
% 168.50/168.36 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2))
% 168.50/168.36 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_OatLeastLessThan__empty__iff,axiom,
% 168.50/168.36 ! [V_b_2,V_a_2] :
% 168.50/168.36 ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
% 168.50/168.36 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
% 168.50/168.36 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_OgreaterThanAtMost__empty__iff2,axiom,
% 168.50/168.36 ! [V_l_2,V_k_2] :
% 168.50/168.36 ( 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)
% 168.50/168.36 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2))
% 168.50/168.36 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_OatLeastLessThan__empty__iff2,axiom,
% 168.50/168.36 ! [V_b_2,V_a_2] :
% 168.50/168.36 ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2)
% 168.50/168.36 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
% 168.50/168.36 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_OatLeastatMost__empty__iff2,axiom,
% 168.50/168.36 ! [V_b_2,V_a_2] :
% 168.50/168.36 ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)
% 168.50/168.36 <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_OatLeastatMost__empty__iff,axiom,
% 168.50/168.36 ! [V_b_2,V_a_2] :
% 168.50/168.36 ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
% 168.50/168.36 <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_OatLeastatMost__empty,axiom,
% 168.50/168.36 ! [V_a_2,V_b_2] :
% 168.50/168.36 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2))
% 168.50/168.36 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) )
% 168.50/168.36 => c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd__1__iff__1,axiom,
% 168.50/168.36 ! [V_m_2] :
% 168.50/168.36 ( 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))))
% 168.50/168.36 <=> V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_nat__dvd__not__less,axiom,
% 168.50/168.36 ! [V_n,V_m] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 168.50/168.36 => ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_div__power,axiom,
% 168.50/168.36 ! [V_n,V_x,V_y,T_a] :
% 168.50/168.36 ( class_Divides_Osemiring__div(T_a)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 168.50/168.36 => 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)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd__diff__nat,axiom,
% 168.50/168.36 ! [V_n,V_m,V_k] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
% 168.50/168.36 => 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))) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd__diff,axiom,
% 168.50/168.36 ! [V_z,V_y,V_x,T_a] :
% 168.50/168.36 ( class_Rings_Ocomm__ring__1(T_a)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_z))
% 168.50/168.36 => 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))) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_minus__dvd__iff,axiom,
% 168.50/168.36 ! [V_y_2,V_x_2,T_b] :
% 168.50/168.36 ( class_Rings_Ocomm__ring__1(T_b)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),V_y_2))
% 168.50/168.36 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd__minus__iff,axiom,
% 168.50/168.36 ! [V_y_2,V_x_2,T_b] :
% 168.50/168.36 ( class_Rings_Ocomm__ring__1(T_b)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)))
% 168.50/168.36 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_div__add,axiom,
% 168.50/168.36 ! [V_y,V_x,V_z,T_a] :
% 168.50/168.36 ( class_Divides_Osemiring__div(T_a)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_x))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_y))
% 168.50/168.36 => 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)) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd__add,axiom,
% 168.50/168.36 ! [V_c,V_b,V_a,T_a] :
% 168.50/168.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))
% 168.50/168.36 => 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))) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd__reduce,axiom,
% 168.50/168.36 ! [V_n_2,V_k_2] :
% 168.50/168.36 ( 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)))
% 168.50/168.36 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_n_2)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_nat__dvd__1__iff__1,axiom,
% 168.50/168.36 ! [V_m_2] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
% 168.50/168.36 <=> V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd__power__same,axiom,
% 168.50/168.36 ! [V_n,V_y,V_x,T_a] :
% 168.50/168.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
% 168.50/168.36 => 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))) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd__mod__iff,axiom,
% 168.50/168.36 ! [V_m_2,V_n_2,V_k_2,T_b] :
% 168.50/168.36 ( class_Divides_Osemiring__div(T_b)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_n_2))
% 168.50/168.36 => ( 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)))
% 168.50/168.36 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_m_2)) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_mod__mod__cancel,axiom,
% 168.50/168.36 ! [V_a,V_b,V_c,T_a] :
% 168.50/168.36 ( class_Divides_Osemiring__div(T_a)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))
% 168.50/168.36 => 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) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd__mod,axiom,
% 168.50/168.36 ! [V_n,V_m,V_k,T_a] :
% 168.50/168.36 ( class_Divides_Osemiring__div(T_a)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))
% 168.50/168.36 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n))) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd__mod__imp__dvd,axiom,
% 168.50/168.36 ! [V_n,V_m,V_k,T_a] :
% 168.50/168.36 ( class_Divides_Osemiring__div(T_a)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n)))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))
% 168.50/168.36 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m)) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_div__dvd__div,axiom,
% 168.50/168.36 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 168.50/168.36 ( class_Divides_Osemiring__div(T_b)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_c_2))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_c_2),V_a_2)))
% 168.50/168.36 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_b_2),V_c_2)) ) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd__abs__iff,axiom,
% 168.50/168.36 ! [V_k_2,V_m_2,T_b] :
% 168.50/168.36 ( class_Rings_Olinordered__idom(T_b)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_k_2)))
% 168.50/168.36 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_abs__dvd__iff,axiom,
% 168.50/168.36 ! [V_k_2,V_m_2,T_b] :
% 168.50/168.36 ( class_Rings_Olinordered__idom(T_b)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_m_2)),V_k_2))
% 168.50/168.36 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd__if__abs__eq,axiom,
% 168.50/168.36 ! [V_k,V_l,T_a] :
% 168.50/168.36 ( class_Rings_Olinordered__idom(T_a)
% 168.50/168.36 => ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_l) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_k)
% 168.50/168.36 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_l),V_k)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd__trans,axiom,
% 168.50/168.36 ! [V_c,V_b,V_a,T_a] :
% 168.50/168.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c))
% 168.50/168.36 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd__refl,axiom,
% 168.50/168.36 ! [V_a,T_a] :
% 168.50/168.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.50/168.36 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_a)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_Oless__asym,axiom,
% 168.50/168.36 ! [V_y,V_x] :
% 168.50/168.36 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 168.50/168.36 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 168.50/168.36 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 168.50/168.36 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_Oless__trans,axiom,
% 168.50/168.36 ! [V_z,V_y,V_x] :
% 168.50/168.36 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 168.50/168.36 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 168.50/168.36 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 168.50/168.36 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y)) )
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))
% 168.50/168.36 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_Oless__asym_H,axiom,
% 168.50/168.36 ! [V_b,V_a] :
% 168.50/168.36 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 168.50/168.36 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) )
% 168.50/168.36 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
% 168.50/168.36 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_Oless__le__trans,axiom,
% 168.50/168.36 ! [V_z,V_y,V_x] :
% 168.50/168.36 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 168.50/168.36 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))
% 168.50/168.36 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_Oord__less__eq__trans,axiom,
% 168.50/168.36 ! [V_c,V_b,V_a] :
% 168.50/168.36 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 168.50/168.36 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) )
% 168.50/168.36 => ( V_b = V_c
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c))
% 168.50/168.36 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a)) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_Oless__imp__not__eq2,axiom,
% 168.50/168.36 ! [V_y,V_x] :
% 168.50/168.36 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 168.50/168.36 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 168.50/168.36 => V_y != V_x ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_Oless__imp__not__eq,axiom,
% 168.50/168.36 ! [V_y,V_x] :
% 168.50/168.36 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 168.50/168.36 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 168.50/168.36 => V_x != V_y ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_Oless__imp__not__less,axiom,
% 168.50/168.36 ! [V_y,V_x] :
% 168.50/168.36 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 168.50/168.36 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 168.50/168.36 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 168.50/168.36 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_Oless__imp__le,axiom,
% 168.50/168.36 ! [V_y,V_x] :
% 168.50/168.36 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 168.50/168.36 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 168.50/168.36 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_Oless__not__sym,axiom,
% 168.50/168.36 ! [V_y,V_x] :
% 168.50/168.36 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 168.50/168.36 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 168.50/168.36 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 168.50/168.36 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_Oless__imp__neq,axiom,
% 168.50/168.36 ! [V_y,V_x] :
% 168.50/168.36 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 168.50/168.36 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 168.50/168.36 => V_x != V_y ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_Ole__less__trans,axiom,
% 168.50/168.36 ! [V_z,V_y,V_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 168.50/168.36 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 168.50/168.36 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y)) )
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))
% 168.50/168.36 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_Oord__eq__less__trans,axiom,
% 168.50/168.36 ! [V_c,V_b,V_a] :
% 168.50/168.36 ( V_a = V_b
% 168.50/168.36 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))
% 168.50/168.36 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_b)) )
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c))
% 168.50/168.36 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a)) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_Oorder__trans,axiom,
% 168.50/168.36 ! [V_z,V_y,V_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 168.50/168.36 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_Oantisym,axiom,
% 168.50/168.36 ! [V_y,V_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 168.50/168.36 => V_x = V_y ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd__antisym,axiom,
% 168.50/168.36 ! [V_n,V_m] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m))
% 168.50/168.36 => V_m = V_n ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_Oord__le__eq__trans,axiom,
% 168.50/168.36 ! [V_c,V_b,V_a] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 168.50/168.36 => ( V_b = V_c
% 168.50/168.36 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_Oord__eq__le__trans,axiom,
% 168.50/168.36 ! [V_c,V_b,V_a] :
% 168.50/168.36 ( V_a = V_b
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))
% 168.50/168.36 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_Ole__neq__trans,axiom,
% 168.50/168.36 ! [V_b,V_a] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 168.50/168.36 => ( V_a != V_b
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 168.50/168.36 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_Ole__imp__less__or__eq,axiom,
% 168.50/168.36 ! [V_y,V_x] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 168.50/168.36 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 168.50/168.36 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 168.50/168.36 | V_x = V_y ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_Oantisym__conv,axiom,
% 168.50/168.36 ! [V_x_2,V_y_2] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 168.50/168.36 <=> V_x_2 = V_y_2 ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_Oeq__refl,axiom,
% 168.50/168.36 ! [V_y,V_x] :
% 168.50/168.36 ( V_x = V_y
% 168.50/168.36 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_Oneq__le__trans,axiom,
% 168.50/168.36 ! [V_b,V_a] :
% 168.50/168.36 ( V_a != V_b
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 168.50/168.36 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_Oless__le,axiom,
% 168.50/168.36 ! [V_y_2,V_x_2] :
% 168.50/168.36 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 168.50/168.36 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) )
% 168.50/168.36 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 168.50/168.36 & V_x_2 != V_y_2 ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_Ole__less,axiom,
% 168.50/168.36 ! [V_y_2,V_x_2] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 168.50/168.36 <=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 168.50/168.36 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) )
% 168.50/168.36 | V_x_2 = V_y_2 ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_Oeq__iff,axiom,
% 168.50/168.36 ! [V_y_2,V_x_2] :
% 168.50/168.36 ( V_x_2 = V_y_2
% 168.50/168.36 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 168.50/168.36 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_one__dvd,axiom,
% 168.50/168.36 ! [V_a,T_a] :
% 168.50/168.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.50/168.36 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd__0__left,axiom,
% 168.50/168.36 ! [V_a,T_a] :
% 168.50/168.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 168.50/168.36 => V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_OatLeastatMost__psubset__iff,axiom,
% 168.50/168.36 ! [V_d_2,V_c_2,V_b_2,V_a_2] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2,V_d_2)))
% 168.50/168.36 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
% 168.50/168.36 | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2))
% 168.50/168.36 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2))
% 168.50/168.36 & ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2))
% 168.50/168.36 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_c_2)) )
% 168.50/168.36 | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2))
% 168.50/168.36 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_d_2),V_b_2)) ) ) ) )
% 168.50/168.36 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_d_2)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd__eq__mod__eq__0,axiom,
% 168.50/168.36 ! [V_b_2,V_a_2,T_b] :
% 168.50/168.36 ( class_Divides_Osemiring__div(T_b)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 168.50/168.36 <=> c_Divides_Odiv__class_Omod(T_b,V_b_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd__imp__mod__0,axiom,
% 168.50/168.36 ! [V_b,V_a,T_a] :
% 168.50/168.36 ( class_Divides_Osemiring__div(T_a)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 168.50/168.36 => c_Divides_Odiv__class_Omod(T_a,V_b,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd__neg__div,axiom,
% 168.50/168.36 ! [V_x,V_y,T_a] :
% 168.50/168.36 ( class_Divides_Oring__div(T_a)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 168.50/168.36 => 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)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd__div__neg,axiom,
% 168.50/168.36 ! [V_x,V_y,T_a] :
% 168.50/168.36 ( class_Divides_Oring__div(T_a)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 168.50/168.36 => 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)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_OatMost__iff,axiom,
% 168.50/168.36 ! [V_k_2,V_i_2] :
% 168.50/168.36 ( 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)))
% 168.50/168.36 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_OatLeast__iff,axiom,
% 168.50/168.36 ! [V_k_2,V_i_2] :
% 168.50/168.36 ( 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)))
% 168.50/168.36 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_OlessThan__iff,axiom,
% 168.50/168.36 ! [V_k_2,V_i_2] :
% 168.50/168.36 ( 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)))
% 168.50/168.36 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2))
% 168.50/168.36 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_OgreaterThan__iff,axiom,
% 168.50/168.36 ! [V_k_2,V_i_2] :
% 168.50/168.36 ( 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)))
% 168.50/168.36 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2))
% 168.50/168.36 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd__diffD,axiom,
% 168.50/168.36 ! [V_n,V_m,V_k] :
% 168.50/168.36 ( 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)))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 168.50/168.36 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m)) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd__diffD1,axiom,
% 168.50/168.36 ! [V_n,V_m,V_k] :
% 168.50/168.36 ( 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)))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 168.50/168.36 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd_OatLeastatMost__subset__iff,axiom,
% 168.50/168.36 ! [V_d_2,V_c_2,V_b_2,V_a_2] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2,V_d_2)))
% 168.50/168.36 <=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
% 168.50/168.36 | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2))
% 168.50/168.36 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2)) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_le__imp__power__dvd,axiom,
% 168.50/168.36 ! [V_a,V_n,V_m,T_a] :
% 168.50/168.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 168.50/168.36 => 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))) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd__power__le,axiom,
% 168.50/168.36 ! [V_m,V_n,V_y,V_x,T_a] :
% 168.50/168.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 168.50/168.36 => 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))) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_power__le__dvd,axiom,
% 168.50/168.36 ! [V_m,V_b,V_n,V_a,T_a] :
% 168.50/168.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 168.50/168.36 => ( 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))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 168.50/168.36 => 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)) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd__div__eq__mult,axiom,
% 168.50/168.36 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 168.50/168.36 ( class_Divides_Osemiring__div(T_b)
% 168.50/168.36 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 168.50/168.36 => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) = V_c_2
% 168.50/168.36 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2) ) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd__div__div__eq__mult,axiom,
% 168.50/168.36 ! [V_d_2,V_b_2,V_c_2,V_a_2,T_b] :
% 168.50/168.36 ( class_Divides_Osemiring__div(T_b)
% 168.50/168.36 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
% 168.50/168.36 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_c_2),V_d_2))
% 168.50/168.36 => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_d_2),V_c_2)
% 168.50/168.36 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2) ) ) ) ) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd__eq__mod__eq__0__number__of,axiom,
% 168.50/168.36 ! [V_y_2,V_x_2,T_b] :
% 168.50/168.36 ( ( class_Divides_Osemiring__div(T_b)
% 168.50/168.36 & class_Int_Onumber(T_b) )
% 168.50/168.36 => ( 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)))
% 168.50/168.36 <=> 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) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_nat__mult__dvd__cancel1,axiom,
% 168.50/168.36 ! [V_n_2,V_m_2,V_k_2] :
% 168.50/168.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 168.50/168.36 => ( 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)))
% 168.50/168.36 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 168.50/168.36
% 168.50/168.36 fof(fact_dvd__mult__cancel,axiom,
% 168.50/168.36 ! [V_n,V_m,V_k] :
% 168.50/168.36 ( 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)))
% 168.50/168.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 168.50/168.36 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 168.50/168.36
% 168.50/168.36 %----Arity declarations (220)
% 168.50/168.36 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom,
% 168.50/168.36 class_Lattices_Obounded__lattice(tc_HOL_Obool) ).
% 168.50/168.36
% 168.50/168.36 fof(arity_fun__Lattices_Obounded__lattice,axiom,
% 168.50/168.36 ! [T_2,T_1] :
% 168.50/168.36 ( class_Lattices_Obounded__lattice(T_1)
% 168.50/168.36 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
% 168.50/168.36 ! [T_2,T_1] :
% 168.50/168.36 ( class_Complete__Lattice_Ocomplete__lattice(T_1)
% 168.50/168.36 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ).
% 168.50/168.36
% 168.50/168.36 fof(arity_fun__Lattices_Obounded__lattice__top,axiom,
% 168.50/168.36 ! [T_2,T_1] :
% 168.50/168.36 ( class_Lattices_Obounded__lattice(T_1)
% 168.50/168.36 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom,
% 168.50/168.37 ! [T_2,T_1] :
% 168.50/168.37 ( class_Lattices_Obounded__lattice(T_1)
% 168.50/168.37 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_fun__Lattices_Osemilattice__sup,axiom,
% 168.50/168.37 ! [T_2,T_1] :
% 168.50/168.37 ( class_Lattices_Olattice(T_1)
% 168.50/168.37 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_fun__Lattices_Osemilattice__inf,axiom,
% 168.50/168.37 ! [T_2,T_1] :
% 168.50/168.37 ( class_Lattices_Olattice(T_1)
% 168.50/168.37 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_fun__Lattices_Odistrib__lattice,axiom,
% 168.50/168.37 ! [T_2,T_1] :
% 168.50/168.37 ( class_Lattices_Odistrib__lattice(T_1)
% 168.50/168.37 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_fun__Lattices_Oboolean__algebra,axiom,
% 168.50/168.37 ! [T_2,T_1] :
% 168.50/168.37 ( class_Lattices_Oboolean__algebra(T_1)
% 168.50/168.37 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_fun__Orderings_Opreorder,axiom,
% 168.50/168.37 ! [T_2,T_1] :
% 168.50/168.37 ( class_Orderings_Opreorder(T_1)
% 168.50/168.37 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_fun__Finite__Set_Ofinite,axiom,
% 168.50/168.37 ! [T_1,T_2] :
% 168.50/168.37 ( ( class_Finite__Set_Ofinite(T_2)
% 168.50/168.37 & class_Finite__Set_Ofinite(T_1) )
% 168.50/168.37 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_fun__Lattices_Olattice,axiom,
% 168.50/168.37 ! [T_2,T_1] :
% 168.50/168.37 ( class_Lattices_Olattice(T_1)
% 168.50/168.37 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_fun__Orderings_Oorder,axiom,
% 168.50/168.37 ! [T_2,T_1] :
% 168.50/168.37 ( class_Orderings_Oorder(T_1)
% 168.50/168.37 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_fun__Orderings_Otop,axiom,
% 168.50/168.37 ! [T_2,T_1] :
% 168.50/168.37 ( class_Orderings_Otop(T_1)
% 168.50/168.37 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_fun__Orderings_Oord,axiom,
% 168.50/168.37 ! [T_2,T_1] :
% 168.50/168.37 ( class_Orderings_Oord(T_1)
% 168.50/168.37 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_fun__Orderings_Obot,axiom,
% 168.50/168.37 ! [T_2,T_1] :
% 168.50/168.37 ( class_Orderings_Obot(T_1)
% 168.50/168.37 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_fun__Groups_Ouminus,axiom,
% 168.50/168.37 ! [T_2,T_1] :
% 168.50/168.37 ( class_Groups_Ouminus(T_1)
% 168.50/168.37 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_fun__Groups_Ominus,axiom,
% 168.50/168.37 ! [T_2,T_1] :
% 168.50/168.37 ( class_Groups_Ominus(T_1)
% 168.50/168.37 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_fun__Enum_Oenum,axiom,
% 168.50/168.37 ! [T_1,T_2] :
% 168.50/168.37 ( ( class_Enum_Oenum(T_2)
% 168.50/168.37 & class_Enum_Oenum(T_1) )
% 168.50/168.37 => class_Enum_Oenum(tc_fun(T_2,T_1)) ) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 168.50/168.37 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 168.50/168.37 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 168.50/168.37 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
% 168.50/168.37 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
% 168.50/168.37 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom,
% 168.50/168.37 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
% 168.50/168.37 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
% 168.50/168.37 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
% 168.50/168.37 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
% 168.50/168.37 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
% 168.50/168.37 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
% 168.50/168.37 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
% 168.50/168.37 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
% 168.50/168.37 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
% 168.50/168.37 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
% 168.50/168.37 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
% 168.50/168.37 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
% 168.50/168.37 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
% 168.50/168.37 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
% 168.50/168.37 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
% 168.50/168.37 class_Rings_Olinordered__semiring(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
% 168.50/168.37 class_Rings_Olinordered__semidom(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Lazy__Sequence_Osmall__lazy,axiom,
% 168.50/168.37 class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom,
% 168.50/168.37 class_Lattices_Osemilattice__sup(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom,
% 168.50/168.37 class_Lattices_Osemilattice__inf(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom,
% 168.50/168.37 class_Lattices_Odistrib__lattice(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
% 168.50/168.37 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
% 168.50/168.37 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
% 168.50/168.37 class_Groups_Oab__semigroup__add(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
% 168.50/168.37 class_Rings_Oordered__semiring(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
% 168.50/168.37 class_Rings_Oordered__ring__abs(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
% 168.50/168.37 class_Rings_Ono__zero__divisors(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
% 168.50/168.37 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
% 168.50/168.37 class_Rings_Olinordered__ring(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
% 168.50/168.37 class_Rings_Olinordered__idom(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
% 168.50/168.37 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom,
% 168.50/168.37 class_Groups_Osemigroup__add(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
% 168.50/168.37 class_Divides_Osemiring__div(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
% 168.50/168.37 class_Rings_Ocomm__semiring(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom,
% 168.50/168.37 class_Nat_Osemiring__char__0(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
% 168.50/168.37 class_Groups_Oab__group__add(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
% 168.50/168.37 class_Rings_Ozero__neq__one(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
% 168.50/168.37 class_Rings_Oordered__ring(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Orderings_Opreorder,axiom,
% 168.50/168.37 class_Orderings_Opreorder(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Orderings_Olinorder,axiom,
% 168.50/168.37 class_Orderings_Olinorder(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
% 168.50/168.37 class_Groups_Omonoid__mult(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
% 168.50/168.37 class_Rings_Ocomm__ring__1(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
% 168.50/168.37 class_Groups_Omonoid__add(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
% 168.50/168.37 class_Rings_Osemiring__1(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
% 168.50/168.37 class_Rings_Osemiring__0(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Lattices_Olattice,axiom,
% 168.50/168.37 class_Lattices_Olattice(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
% 168.50/168.37 class_Groups_Ogroup__add(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Divides_Oring__div,axiom,
% 168.50/168.37 class_Divides_Oring__div(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Rings_Omult__zero,axiom,
% 168.50/168.37 class_Rings_Omult__zero(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
% 168.50/168.37 class_Rings_Ocomm__ring(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Orderings_Oorder,axiom,
% 168.50/168.37 class_Orderings_Oorder(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Int_Oring__char__0,axiom,
% 168.50/168.37 class_Int_Oring__char__0(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Int_Onumber__ring,axiom,
% 168.50/168.37 class_Int_Onumber__ring(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Rings_Osemiring,axiom,
% 168.50/168.37 class_Rings_Osemiring(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Orderings_Oord,axiom,
% 168.50/168.37 class_Orderings_Oord(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Groups_Ouminus,axiom,
% 168.50/168.37 class_Groups_Ouminus(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Groups_Osgn__if,axiom,
% 168.50/168.37 class_Groups_Osgn__if(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Groups_Oabs__if,axiom,
% 168.50/168.37 class_Groups_Oabs__if(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Rings_Oring__1,axiom,
% 168.50/168.37 class_Rings_Oring__1(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Groups_Ominus,axiom,
% 168.50/168.37 class_Groups_Ominus(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Power_Opower,axiom,
% 168.50/168.37 class_Power_Opower(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Groups_Ozero,axiom,
% 168.50/168.37 class_Groups_Ozero(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Rings_Oring,axiom,
% 168.50/168.37 class_Rings_Oring(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Rings_Oidom,axiom,
% 168.50/168.37 class_Rings_Oidom(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Int_Onumber,axiom,
% 168.50/168.37 class_Int_Onumber(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Groups_Oone,axiom,
% 168.50/168.37 class_Groups_Oone(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Int__Oint__Rings_Odvd,axiom,
% 168.50/168.37 class_Rings_Odvd(tc_Int_Oint) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 168.50/168.37 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 168.50/168.37 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 168.50/168.37 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
% 168.50/168.37 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom,
% 168.50/168.37 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
% 168.50/168.37 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 168.50/168.37 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 168.50/168.37 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 168.50/168.37 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
% 168.50/168.37 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
% 168.50/168.37 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 168.50/168.37 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
% 168.50/168.37 class_Rings_Olinordered__semiring(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 168.50/168.37 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom,
% 168.50/168.37 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom,
% 168.50/168.37 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom,
% 168.50/168.37 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
% 168.50/168.37 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
% 168.50/168.37 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 168.50/168.37 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
% 168.50/168.37 class_Rings_Oordered__semiring(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
% 168.50/168.37 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 168.50/168.37 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 168.50/168.37 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom,
% 168.50/168.37 class_Groups_Osemigroup__add(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
% 168.50/168.37 class_Divides_Osemiring__div(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
% 168.50/168.37 class_Rings_Ocomm__semiring(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Orderings_Owellorder,axiom,
% 168.50/168.37 class_Orderings_Owellorder(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom,
% 168.50/168.37 class_Nat_Osemiring__char__0(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 168.50/168.37 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 168.50/168.37 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 168.50/168.37 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
% 168.50/168.37 class_Groups_Omonoid__mult(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 168.50/168.37 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
% 168.50/168.37 class_Rings_Osemiring__1(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
% 168.50/168.37 class_Rings_Osemiring__0(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Lattices_Olattice,axiom,
% 168.50/168.37 class_Lattices_Olattice(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
% 168.50/168.37 class_Rings_Omult__zero(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 168.50/168.37 class_Orderings_Oorder(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Rings_Osemiring,axiom,
% 168.50/168.37 class_Rings_Osemiring(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 168.50/168.37 class_Orderings_Oord(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Orderings_Obot,axiom,
% 168.50/168.37 class_Orderings_Obot(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Groups_Ominus,axiom,
% 168.50/168.37 class_Groups_Ominus(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Power_Opower,axiom,
% 168.50/168.37 class_Power_Opower(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 168.50/168.37 class_Groups_Ozero(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Int_Onumber,axiom,
% 168.50/168.37 class_Int_Onumber(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 168.50/168.37 class_Groups_Oone(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Rings_Odvd,axiom,
% 168.50/168.37 class_Rings_Odvd(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nat__Onat__Nat_Osize,axiom,
% 168.50/168.37 class_Nat_Osize(tc_Nat_Onat) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom,
% 168.50/168.37 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom,
% 168.50/168.37 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom,
% 168.50/168.37 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom,
% 168.50/168.37 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom,
% 168.50/168.37 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom,
% 168.50/168.37 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
% 168.50/168.37 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 168.50/168.37 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom,
% 168.50/168.37 class_Finite__Set_Ofinite(tc_HOL_Obool) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_HOL__Obool__Lattices_Olattice,axiom,
% 168.50/168.37 class_Lattices_Olattice(tc_HOL_Obool) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 168.50/168.37 class_Orderings_Oorder(tc_HOL_Obool) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_HOL__Obool__Orderings_Otop,axiom,
% 168.50/168.37 class_Orderings_Otop(tc_HOL_Obool) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 168.50/168.37 class_Orderings_Oord(tc_HOL_Obool) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_HOL__Obool__Orderings_Obot,axiom,
% 168.50/168.37 class_Orderings_Obot(tc_HOL_Obool) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_HOL__Obool__Groups_Ouminus,axiom,
% 168.50/168.37 class_Groups_Ouminus(tc_HOL_Obool) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_HOL__Obool__Groups_Ominus,axiom,
% 168.50/168.37 class_Groups_Ominus(tc_HOL_Obool) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_HOL__Obool__Enum_Oenum,axiom,
% 168.50/168.37 class_Enum_Oenum(tc_HOL_Obool) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_HOL__Obool__Nat_Osize,axiom,
% 168.50/168.37 class_Nat_Osize(tc_HOL_Obool) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_List__Olist__Lazy__Sequence_Osmall__lazy,axiom,
% 168.50/168.37 ! [T_1] :
% 168.50/168.37 ( class_Lazy__Sequence_Osmall__lazy(T_1)
% 168.50/168.37 => class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(T_1)) ) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_List__Olist__Nat_Osize,axiom,
% 168.50/168.37 ! [T_1] : class_Nat_Osize(tc_List_Olist(T_1)) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_sum__Finite__Set_Ofinite,axiom,
% 168.50/168.37 ! [T_1,T_2] :
% 168.50/168.37 ( ( class_Finite__Set_Ofinite(T_2)
% 168.50/168.37 & class_Finite__Set_Ofinite(T_1) )
% 168.50/168.37 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_sum__Enum_Oenum,axiom,
% 168.50/168.37 ! [T_1,T_2] :
% 168.50/168.37 ( ( class_Enum_Oenum(T_2)
% 168.50/168.37 & class_Enum_Oenum(T_1) )
% 168.50/168.37 => class_Enum_Oenum(tc_sum(T_2,T_1)) ) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_sum__Nat_Osize,axiom,
% 168.50/168.37 ! [T_1,T_2] : class_Nat_Osize(tc_sum(T_2,T_1)) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
% 168.50/168.37 ! [T_1] :
% 168.50/168.37 ( class_Finite__Set_Ofinite(T_1)
% 168.50/168.37 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Option__Ooption__Enum_Oenum,axiom,
% 168.50/168.37 ! [T_1] :
% 168.50/168.37 ( class_Enum_Oenum(T_1)
% 168.50/168.37 => class_Enum_Oenum(tc_Option_Ooption(T_1)) ) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Option__Ooption__Nat_Osize,axiom,
% 168.50/168.37 ! [T_1] : class_Nat_Osize(tc_Option_Ooption(T_1)) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Nitpick__Opair____box__Nat_Osize,axiom,
% 168.50/168.37 ! [T_1,T_2] : class_Nat_Osize(tc_Nitpick_Opair__box(T_2,T_1)) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_prod__Lazy__Sequence_Osmall__lazy,axiom,
% 168.50/168.37 ! [T_1,T_2] :
% 168.50/168.37 ( ( class_Lazy__Sequence_Osmall__lazy(T_2)
% 168.50/168.37 & class_Lazy__Sequence_Osmall__lazy(T_1) )
% 168.50/168.37 => class_Lazy__Sequence_Osmall__lazy(tc_prod(T_2,T_1)) ) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_prod__Finite__Set_Ofinite,axiom,
% 168.50/168.37 ! [T_1,T_2] :
% 168.50/168.37 ( ( class_Finite__Set_Ofinite(T_2)
% 168.50/168.37 & class_Finite__Set_Ofinite(T_1) )
% 168.50/168.37 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_prod__Enum_Oenum,axiom,
% 168.50/168.37 ! [T_1,T_2] :
% 168.50/168.37 ( ( class_Enum_Oenum(T_2)
% 168.50/168.37 & class_Enum_Oenum(T_1) )
% 168.50/168.37 => class_Enum_Oenum(tc_prod(T_2,T_1)) ) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_prod__Nat_Osize,axiom,
% 168.50/168.37 ! [T_1,T_2] : class_Nat_Osize(tc_prod(T_2,T_1)) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy,axiom,
% 168.50/168.37 class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
% 168.50/168.37 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Product____Type__Ounit__Enum_Oenum,axiom,
% 168.50/168.37 class_Enum_Oenum(tc_Product__Type_Ounit) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Product____Type__Ounit__Nat_Osize,axiom,
% 168.50/168.37 class_Nat_Osize(tc_Product__Type_Ounit) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Evaluation__Oterm__Nat_Osize,axiom,
% 168.50/168.37 class_Nat_Osize(tc_Code__Evaluation_Oterm) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Hoare____Mirabelle__Otriple__Nat_Osize,axiom,
% 168.50/168.37 ! [T_1] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(T_1)) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 168.50/168.37 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 168.50/168.37 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom,
% 168.50/168.37 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom,
% 168.50/168.37 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom,
% 168.50/168.37 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom,
% 168.50/168.37 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom,
% 168.50/168.37 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom,
% 168.50/168.37 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom,
% 168.50/168.37 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom,
% 168.50/168.37 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom,
% 168.50/168.37 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom,
% 168.50/168.37 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom,
% 168.50/168.37 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom,
% 168.50/168.37 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom,
% 168.50/168.37 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom,
% 168.50/168.37 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom,
% 168.50/168.37 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom,
% 168.50/168.37 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom,
% 168.50/168.37 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom,
% 168.50/168.37 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom,
% 168.50/168.37 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom,
% 168.50/168.37 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom,
% 168.50/168.37 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom,
% 168.50/168.37 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom,
% 168.50/168.37 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom,
% 168.50/168.37 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom,
% 168.50/168.37 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom,
% 168.50/168.37 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom,
% 168.50/168.37 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom,
% 168.50/168.37 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom,
% 168.50/168.37 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom,
% 168.50/168.37 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom,
% 168.50/168.37 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom,
% 168.50/168.37 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom,
% 168.50/168.37 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom,
% 168.50/168.37 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom,
% 168.50/168.37 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom,
% 168.50/168.37 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom,
% 168.50/168.37 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom,
% 168.50/168.37 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Rings_Odvd,axiom,
% 168.50/168.37 class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osize,axiom,
% 168.50/168.37 class_Nat_Osize(tc_Code__Numeral_Ocode__numeral) ).
% 168.50/168.37
% 168.50/168.37 fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize,axiom,
% 168.50/168.37 ! [T_1] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(T_1)) ).
% 168.50/168.37
% 168.50/168.37 %----Helper facts (20)
% 168.50/168.37 fof(help_c__COMBI__1,axiom,
% 168.50/168.37 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ).
% 168.50/168.37
% 168.50/168.37 fof(help_c__COMBK__1,axiom,
% 168.50/168.37 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ).
% 168.50/168.37
% 168.50/168.37 fof(help_c__COMBB__1,axiom,
% 168.50/168.37 ! [V_R_2,V_Q_2,V_P_2,T_d,T_b,T_c] : hAPP(hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_P_2),V_Q_2),V_R_2) = hAPP(V_P_2,hAPP(V_Q_2,V_R_2)) ).
% 168.50/168.37
% 168.50/168.37 fof(help_c__COMBC__1,axiom,
% 168.50/168.37 ! [V_R_2,V_Q_2,V_P_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_P_2),V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),V_Q_2) ).
% 168.50/168.37
% 168.50/168.37 fof(help_c__COMBS__1,axiom,
% 168.50/168.37 ! [V_R_2,V_Q_2,V_P_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBS(T_c,T_d,T_b),V_P_2),V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),hAPP(V_Q_2,V_R_2)) ).
% 168.50/168.37
% 168.50/168.37 fof(help_c__fequal__1,axiom,
% 168.50/168.37 ! [V_y_2,V_x_2] :
% 168.50/168.37 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2))
% 168.50/168.37 | V_x_2 = V_y_2 ) ).
% 168.50/168.37
% 168.50/168.37 fof(help_c__fequal__2,axiom,
% 168.50/168.37 ! [V_y_2,V_x_2] :
% 168.50/168.37 ( V_x_2 != V_y_2
% 168.50/168.37 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ).
% 168.50/168.37
% 168.50/168.37 fof(help_c__fFalse__1,axiom,
% 168.50/168.37 ~ hBOOL(c_fFalse) ).
% 168.50/168.37
% 168.50/168.37 fof(help_c__fTrue__1,axiom,
% 168.50/168.37 hBOOL(c_fTrue) ).
% 168.50/168.37
% 168.50/168.37 fof(help_c__fNot__1,axiom,
% 168.50/168.37 ! [V_P_2] :
% 168.50/168.37 ( ~ hBOOL(hAPP(c_fNot,V_P_2))
% 168.50/168.37 | ~ hBOOL(V_P_2) ) ).
% 168.50/168.37
% 168.50/168.37 fof(help_c__fNot__2,axiom,
% 168.50/168.37 ! [V_P_2] :
% 168.50/168.37 ( ~ ~ hBOOL(V_P_2)
% 168.50/168.37 | hBOOL(hAPP(c_fNot,V_P_2)) ) ).
% 168.50/168.37
% 168.50/168.37 fof(help_c__fconj__1,axiom,
% 168.50/168.37 ! [V_Q_2,V_P_2] :
% 168.50/168.37 ( ~ hBOOL(V_P_2)
% 168.50/168.37 | ~ hBOOL(V_Q_2)
% 168.50/168.37 | hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ) ).
% 168.50/168.37
% 168.50/168.37 fof(help_c__fconj__2,axiom,
% 168.50/168.37 ! [V_Q_2,V_P_2] :
% 168.50/168.37 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))
% 168.50/168.37 | hBOOL(V_P_2) ) ).
% 168.50/168.37
% 168.50/168.37 fof(help_c__fconj__3,axiom,
% 168.50/168.37 ! [V_Q_2,V_P_2] :
% 168.50/168.37 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))
% 168.50/168.37 | hBOOL(V_Q_2) ) ).
% 168.50/168.37
% 168.50/168.37 fof(help_c__fdisj__1,axiom,
% 168.50/168.37 ! [V_Q_2,V_P_2] :
% 168.50/168.37 ( ~ hBOOL(V_P_2)
% 168.50/168.37 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ).
% 168.50/168.37
% 168.50/168.37 fof(help_c__fdisj__2,axiom,
% 168.50/168.37 ! [V_P_2,V_Q_2] :
% 168.50/168.37 ( ~ hBOOL(V_Q_2)
% 168.50/168.37 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ).
% 168.50/168.37
% 168.50/168.37 fof(help_c__fdisj__3,axiom,
% 168.50/168.37 ! [V_Q_2,V_P_2] :
% 168.50/168.37 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2))
% 168.50/168.37 | hBOOL(V_P_2)
% 168.50/168.37 | hBOOL(V_Q_2) ) ).
% 168.50/168.37
% 168.50/168.37 fof(help_c__fimplies__1,axiom,
% 168.50/168.37 ! [V_Q_2,V_P_2] :
% 168.50/168.37 ( hBOOL(V_P_2)
% 168.50/168.37 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ).
% 168.50/168.37
% 168.50/168.37 fof(help_c__fimplies__2,axiom,
% 168.50/168.37 ! [V_P_2,V_Q_2] :
% 168.50/168.37 ( ~ hBOOL(V_Q_2)
% 168.50/168.37 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ).
% 168.50/168.37
% 168.50/168.37 fof(help_c__fimplies__3,axiom,
% 168.50/168.37 ! [V_Q_2,V_P_2] :
% 168.50/168.37 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2))
% 168.50/168.37 | ~ hBOOL(V_P_2)
% 168.50/168.37 | hBOOL(V_Q_2) ) ).
% 168.50/168.37
% 168.50/168.37 %----Conjectures (5)
% 168.50/168.37 fof(conj_0,hypothesis,
% 168.50/168.37 c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ).
% 168.50/168.37
% 168.50/168.37 fof(conj_1,hypothesis,
% 168.50/168.37 ! [B_n] :
% 168.50/168.37 ( ! [B_x] :
% 168.50/168.37 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_G))
% 168.50/168.37 => c_Hoare__Mirabelle_Otriple__valid(t_a,B_n,B_x) )
% 168.50/168.37 => ! [B_x] :
% 168.50/168.37 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))))
% 168.50/168.37 => c_Hoare__Mirabelle_Otriple__valid(t_a,B_n,B_x) ) ) ).
% 168.50/168.37
% 168.50/168.37 fof(conj_2,hypothesis,
% 168.50/168.37 c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G,v_ts) ).
% 168.50/168.37
% 168.50/168.37 fof(conj_3,hypothesis,
% 168.50/168.37 ! [B_n] :
% 168.50/168.37 ( ! [B_x] :
% 168.50/168.37 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_G))
% 168.50/168.37 => c_Hoare__Mirabelle_Otriple__valid(t_a,B_n,B_x) )
% 168.50/168.37 => ! [B_x] :
% 168.50/168.37 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_ts))
% 168.50/168.37 => c_Hoare__Mirabelle_Otriple__valid(t_a,B_n,B_x) ) ) ).
% 168.50/168.37
% 168.50/168.37 fof(conj_4,conjecture,
% 168.50/168.37 ! [B_n] :
% 168.50/168.37 ( ! [B_x] :
% 168.50/168.37 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_G))
% 168.50/168.37 => c_Hoare__Mirabelle_Otriple__valid(t_a,B_n,B_x) )
% 168.50/168.37 => ! [B_x] :
% 168.50/168.37 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),v_ts)))
% 168.50/168.37 => c_Hoare__Mirabelle_Otriple__valid(t_a,B_n,B_x) ) ) ).
% 168.50/168.37
% 168.50/168.37 %------------------------------------------------------------------------------
% 168.50/168.37 %-------------------------------------------
% 168.50/168.37 % Proof found
% 168.50/168.37 % SZS status Theorem for theBenchmark
% 168.50/168.37 % SZS output start Proof
% 168.50/168.37 %ClaNum:10409(EqnAxiom:3044)
% 168.50/168.37 %VarNum:70846(SingletonVarNum:20437)
% 168.50/168.37 %MaxLitNum:8
% 168.50/168.37 %MaxfuncDepth:13
% 168.50/168.37 %SharedTerms:1000
% 168.50/168.37 %goalClause: 3783 4595 5677
% 168.50/168.37 %singleGoalClaCount:2
% 168.50/168.37 [3048]P1(a176)
% 168.50/168.37 [3049]P2(a899)
% 168.50/168.37 [3050]P2(a901)
% 168.50/168.37 [3051]P108(a899)
% 168.50/168.37 [3052]P108(a901)
% 168.50/168.37 [3053]P108(a1)
% 168.50/168.37 [3054]P108(a88)
% 168.50/168.37 [3055]P109(a899)
% 168.50/168.37 [3056]P109(a901)
% 168.50/168.37 [3057]P109(a1)
% 168.50/168.37 [3058]P109(a88)
% 168.50/168.37 [3059]P110(a901)
% 168.50/168.37 [3060]P110(a1)
% 168.50/168.37 [3061]P110(a88)
% 168.50/168.37 [3062]P111(a899)
% 168.50/168.37 [3063]P111(a901)
% 168.50/168.37 [3064]P111(a1)
% 168.50/168.37 [3065]P111(a88)
% 168.50/168.37 [3066]P3(a899)
% 168.50/168.37 [3067]P3(a901)
% 168.50/168.37 [3068]P3(a1)
% 168.50/168.37 [3069]P3(a88)
% 168.50/168.37 [3070]P80(a899)
% 168.50/168.37 [3071]P80(a901)
% 168.50/168.37 [3072]P80(a1)
% 168.50/168.37 [3073]P81(a899)
% 168.50/168.37 [3074]P103(a899)
% 168.50/168.37 [3075]P103(a901)
% 168.50/168.37 [3076]P103(a1)
% 168.50/168.37 [3077]P82(a1)
% 168.50/168.37 [3078]P4(a899)
% 168.50/168.37 [3079]P4(a904)
% 168.50/168.37 [3080]P69(a1)
% 168.50/168.37 [3081]P112(a1)
% 168.50/168.37 [3082]P70(a901)
% 168.50/168.37 [3083]P70(a1)
% 168.50/168.37 [3084]P70(a88)
% 168.50/168.37 [3085]P104(a899)
% 168.50/168.37 [3086]P104(a901)
% 168.50/168.37 [3087]P104(a1)
% 168.50/168.37 [3088]P101(a899)
% 168.50/168.37 [3089]P101(a901)
% 168.50/168.37 [3090]P101(a1)
% 168.50/168.37 [3091]P72(a901)
% 168.50/168.37 [3092]P72(a1)
% 168.50/168.37 [3093]P72(a88)
% 168.50/168.37 [3094]P86(a901)
% 168.50/168.37 [3095]P86(a1)
% 168.50/168.37 [3096]P86(a88)
% 168.50/168.37 [3097]P73(a901)
% 168.50/168.37 [3098]P73(a1)
% 168.50/168.37 [3099]P73(a88)
% 168.50/168.37 [3100]P74(a901)
% 168.50/168.37 [3101]P74(a1)
% 168.50/168.37 [3102]P74(a88)
% 168.50/168.37 [3103]P71(a901)
% 168.50/168.37 [3104]P71(a1)
% 168.50/168.37 [3105]P71(a88)
% 168.50/168.37 [3106]P83(a901)
% 168.50/168.37 [3107]P83(a1)
% 168.50/168.37 [3108]P83(a88)
% 168.50/168.37 [3109]P87(a901)
% 168.50/168.37 [3110]P87(a1)
% 168.50/168.37 [3111]P87(a88)
% 168.50/168.37 [3112]P88(a901)
% 168.50/168.37 [3113]P88(a1)
% 168.50/168.37 [3114]P88(a88)
% 168.50/168.37 [3115]P76(a1)
% 168.50/168.37 [3116]P77(a901)
% 168.50/168.37 [3117]P77(a1)
% 168.50/168.37 [3118]P77(a88)
% 168.50/168.37 [3119]P84(a901)
% 168.50/168.37 [3120]P84(a1)
% 168.50/168.37 [3121]P84(a88)
% 168.50/168.37 [3122]P113(a1)
% 168.50/168.37 [3123]P114(a1)
% 168.50/168.37 [3124]P141(a901)
% 168.50/168.37 [3125]P141(a1)
% 168.50/168.37 [3126]P141(a88)
% 168.50/168.37 [3127]P115(a901)
% 168.50/168.37 [3128]P115(a1)
% 168.50/168.37 [3129]P115(a88)
% 168.50/168.37 [3130]P128(a901)
% 168.50/168.37 [3131]P128(a1)
% 168.50/168.37 [3132]P128(a88)
% 168.50/168.37 [3133]P121(a901)
% 168.50/168.37 [3134]P121(a1)
% 168.50/168.37 [3135]P121(a88)
% 168.50/168.37 [3136]P145(a901)
% 168.50/168.37 [3137]P145(a1)
% 168.50/168.37 [3138]P131(a1)
% 168.50/168.37 [3139]P134(a901)
% 168.50/168.37 [3140]P134(a1)
% 168.50/168.37 [3141]P134(a88)
% 168.50/168.37 [3142]P90(a901)
% 168.50/168.37 [3143]P90(a1)
% 168.50/168.37 [3144]P90(a88)
% 168.50/168.37 [3145]P85(a901)
% 168.50/168.37 [3146]P85(a1)
% 168.50/168.37 [3147]P85(a88)
% 168.50/168.37 [3148]P78(a1)
% 168.50/168.37 [3149]P142(a1)
% 168.50/168.37 [3150]P135(a901)
% 168.50/168.37 [3151]P135(a1)
% 168.50/168.37 [3152]P135(a88)
% 168.50/168.37 [3153]P146(a901)
% 168.50/168.37 [3154]P146(a1)
% 168.50/168.37 [3155]P146(a88)
% 168.50/168.37 [3156]P91(a901)
% 168.50/168.37 [3157]P91(a1)
% 168.50/168.37 [3158]P91(a88)
% 168.50/168.37 [3159]P129(a1)
% 168.50/168.37 [3160]P130(a1)
% 168.50/168.37 [3161]P137(a901)
% 168.50/168.37 [3162]P137(a1)
% 168.50/168.37 [3163]P137(a88)
% 168.50/168.37 [3164]P139(a901)
% 168.50/168.37 [3165]P139(a1)
% 168.50/168.37 [3166]P139(a88)
% 168.50/168.37 [3167]P138(a901)
% 168.50/168.37 [3168]P138(a1)
% 168.50/168.37 [3169]P138(a88)
% 168.50/168.37 [3170]P122(a901)
% 168.50/168.37 [3171]P122(a1)
% 168.50/168.37 [3172]P122(a88)
% 168.50/168.37 [3173]P136(a901)
% 168.50/168.37 [3174]P136(a1)
% 168.50/168.37 [3175]P136(a88)
% 168.50/168.37 [3176]P132(a901)
% 168.50/168.37 [3177]P132(a1)
% 168.50/168.37 [3178]P132(a88)
% 168.50/168.37 [3179]P133(a1)
% 168.50/168.37 [3180]P5(a899)
% 168.50/168.37 [3181]P143(a1)
% 168.50/168.37 [3182]P95(a1)
% 168.50/168.37 [3183]P96(a901)
% 168.50/168.37 [3184]P96(a1)
% 168.50/168.37 [3185]P96(a88)
% 168.50/168.37 [3186]P97(a1)
% 168.50/168.37 [3187]P105(a901)
% 168.50/168.37 [3188]P105(a1)
% 168.50/168.37 [3189]P105(a88)
% 168.50/168.37 [3190]P147(a901)
% 168.50/168.37 [3191]P147(a1)
% 168.50/168.37 [3192]P147(a88)
% 168.50/168.37 [3193]P89(a1)
% 168.50/168.37 [3194]P140(a1)
% 168.50/168.37 [3195]P98(a899)
% 168.50/168.37 [3196]P92(a899)
% 168.50/168.37 [3197]P92(a1)
% 168.50/168.37 [3198]P123(a1)
% 168.50/168.37 [3199]P116(a1)
% 168.50/168.37 [3200]P144(a1)
% 168.50/168.37 [3201]P75(a1)
% 168.50/168.37 [3202]P62(a901)
% 168.50/168.37 [3203]P62(a1)
% 168.50/168.37 [3204]P62(a88)
% 168.50/168.37 [3205]P63(a1)
% 168.50/168.37 [3206]P117(a901)
% 168.50/168.37 [3207]P117(a1)
% 168.50/168.37 [3208]P117(a88)
% 168.50/168.37 [3209]P148(a901)
% 168.50/168.37 [3210]P148(a1)
% 168.50/168.37 [3211]P148(a88)
% 168.50/168.37 [3212]P93(a1)
% 168.50/168.37 [3213]P118(a899)
% 168.50/168.37 [3214]P102(a899)
% 168.50/168.37 [3215]P79(a901)
% 168.50/168.37 [3216]P79(a1)
% 168.50/168.37 [3217]P79(a88)
% 168.50/168.37 [3218]P119(a901)
% 168.50/168.37 [3219]P94(a901)
% 168.50/168.37 [3220]P94(a1)
% 168.50/168.37 [3221]P94(a88)
% 168.50/168.37 [3222]P64(a899)
% 168.50/168.37 [3223]P64(a904)
% 168.50/168.37 [3224]P107(a899)
% 168.50/168.37 [3225]P107(a901)
% 168.50/168.37 [3226]P107(a88)
% 168.50/168.37 [3227]P107(a904)
% 168.50/168.37 [3228]P107(a311)
% 168.50/168.37 [3229]P106(a1)
% 168.50/168.37 [3230]P106(a904)
% 168.50/168.37 [3231]P124(a901)
% 168.50/168.37 [3232]P124(a1)
% 168.50/168.37 [3233]P124(a88)
% 168.50/168.37 [3234]P120(a1)
% 168.50/168.37 [3235]P100(a899)
% 168.50/168.37 [3250]P39(a901,a228)
% 168.50/168.37 [3251]P39(a901,a305)
% 168.50/168.37 [3252]P40(a901,a228)
% 168.50/168.37 [3332]P14(a898,a910,a911)
% 168.50/168.37 [4579]~E(a86,a76)
% 168.50/168.37 [4580]~P1(a227)
% 168.50/168.37 [4595]~P28(a898,a801,a800)
% 168.50/168.37 [3045]E(f2(a1),a76)
% 168.50/168.37 [3046]E(f3(a88),a4)
% 168.50/168.37 [3047]E(f89(a88),a5)
% 168.50/168.37 [3236]E(f177(a901),f2(a901))
% 168.50/168.37 [3237]E(f90(a901),f221(a901))
% 168.50/168.37 [3238]E(f99(a901),f222(a901))
% 168.50/168.37 [3239]E(f91(a1),f25(a1))
% 168.50/168.37 [3240]E(f77(a227),f2(a901))
% 168.50/168.37 [3241]E(f77(a176),f2(a901))
% 168.50/168.37 [3242]P6(f71(a1))
% 168.50/168.37 [3243]P6(f2(a1))
% 168.50/168.37 [3298]P39(f908(a901,a901),a26)
% 168.50/168.37 [3641]E(f307(a901,a901,a228,a228),a26)
% 168.50/168.37 [4581]~E(f71(a1),f2(a1))
% 168.50/168.37 [3244]E(f6(f2(a88)),f2(a901))
% 168.50/168.37 [3245]E(f100(f2(a901)),f2(a901))
% 168.50/168.37 [3254]E(f315(f72(a1),a76),a76)
% 168.50/168.37 [3257]E(f315(a101,f2(a901)),f71(a901))
% 168.50/168.37 [3258]E(f315(a93,f71(a1)),f71(a901))
% 168.50/168.37 [3259]E(f315(a5,f71(a901)),f71(a88))
% 168.50/168.37 [3261]E(f315(a5,f2(a901)),f2(a88))
% 168.50/168.37 [3263]E(f315(f92(a1),a76),f2(a1))
% 168.50/168.37 [3264]E(f315(f92(a88),a76),f2(a88))
% 168.50/168.37 [3265]E(f315(a93,f2(a1)),f2(a901))
% 168.50/168.37 [3266]E(f315(f92(a901),a76),f2(a901))
% 168.50/168.37 [3267]E(f315(f178(a899),a227),f2(a901))
% 168.50/168.37 [3268]E(f315(f178(a899),a176),f2(a901))
% 168.50/168.37 [3274]E(f315(f72(a1),f71(a1)),a86)
% 168.50/168.37 [3281]E(f315(f89(a1),f71(a901)),f71(a1))
% 168.50/168.37 [3282]E(f315(f89(a1),f2(a901)),f2(a1))
% 168.50/168.37 [3283]E(f315(f72(a1),f2(a1)),f2(a1))
% 168.50/168.37 [3285]E(f315(f178(a88),f2(a88)),f2(a901))
% 168.50/168.37 [3295]E(f315(a93,f71(a1)),f315(a101,f2(a901)))
% 168.50/168.37 [3296]E(f306(f908(a901,a901),a26),a27)
% 168.50/168.37 [3297]E(f308(f908(a901,a901),a26),a62)
% 168.50/168.37 [3324]E(f315(f270(a901),f2(a901)),f177(f909(a901,a899)))
% 168.50/168.37 [3325]E(f315(f271(a901),f2(a901)),f230(f909(a901,a899)))
% 168.50/168.37 [3334]P42(f177(f909(a1,a899)))
% 168.50/168.37 [3368]E(f315(f315(f3(a88),f2(a88)),f71(a88)),f2(a88))
% 168.50/168.37 [3443]P1(f315(f315(f224(a1),a86),f2(a1)))
% 168.50/168.37 [3467]P1(f315(f315(f223(a1),f2(a1)),f71(a1)))
% 168.50/168.37 [3469]P1(f315(f315(f224(a1),f2(a1)),f71(a1)))
% 168.50/168.37 [3672]E(f315(f315(f277(a901,a901,a901),a305),f295(a901,a305)),a228)
% 168.50/168.37 [3709]P43(a1,a901,a93,f315(f223(a1),f2(a1)))
% 168.50/168.37 [3713]E(f315(f315(f32(a901,f909(a901,a899)),f230(f909(a901,a899))),f292(a901)),f177(f909(a901,a899)))
% 168.50/168.37 [3714]E(f315(f315(f33(a901,f909(a901,a899)),f230(f909(a901,a899))),f270(a901)),f230(f909(a901,a899)))
% 168.50/168.37 [3715]E(f315(f315(f33(a901,f909(a901,a899)),f230(f909(a901,a899))),f289(a901)),f230(f909(a901,a899)))
% 168.50/168.37 [3716]E(f315(f315(f33(a901,f909(a901,a899)),f230(f909(a901,a899))),f271(a901)),f230(f909(a901,a899)))
% 168.50/168.37 [3731]P25(a901,a1,f89(a1),f230(f909(a901,a899)))
% 168.50/168.37 [3746]P43(a901,a1,f89(a1),f315(f18(a899,a901),a176))
% 168.50/168.37 [3882]E(f315(f66(a901,a88,a1,a5),a93),f92(a88))
% 168.50/168.37 [4101]P58(a88,a901,a22,a5,f230(f909(a901,a899)))
% 168.50/168.37 [4105]P58(a1,f909(f908(a901,a901),a899),a95,a82,a87)
% 168.50/168.37 [4359]E(f246(a1,a1,a1,a1,f25(a1),f72(a1)),a44)
% 168.50/168.37 [4590]~E(f315(f92(a1),a86),f315(f92(a1),a76))
% 168.50/168.37 [4591]~P1(f315(a182,f71(a1)))
% 168.50/168.37 [4592]~P1(f315(a182,f2(a1)))
% 168.50/168.37 [4618]~P1(f315(f315(f224(a1),a76),f2(a1)))
% 168.50/168.37 [3316]E(f315(f315(f3(a1),a86),a86),a76)
% 168.50/168.37 [3331]E(f315(f89(a1),f315(a101,f2(a901))),f71(a1))
% 168.50/168.37 [3397]E(f315(f28(a904),f230(f909(a904,a899))),f71(a901))
% 168.50/168.37 [3417]P1(f315(a182,f315(f92(a1),a86)))
% 168.50/168.37 [3419]P1(f315(f315(f223(a1),a86),a76))
% 168.50/168.37 [3421]P1(f315(f315(f224(a1),a86),a76))
% 168.50/168.37 [3477]E(f315(f315(f297(a901),f2(a901)),f177(f909(a901,a899))),f315(f289(a901),f2(a901)))
% 168.50/168.37 [3532]P1(f315(f315(f223(a1),f2(a1)),f315(f92(a1),a76)))
% 168.50/168.37 [3544]E(f315(f298(a901,a901,a101),f230(f909(a901,a899))),f315(f292(a901),f2(a901)))
% 168.50/168.37 [3579]P8(f908(a901,a901),f230(f909(f908(a901,a901),a899)),a97)
% 168.50/168.37 [3889]E(f315(f66(a901,a1,a88,f89(a1)),a22),a24)
% 168.50/168.37 [3948]P39(a901,f315(f250(f908(a901,a901)),f315(f245(a901,a901,a899),f224(a901))))
% 168.50/168.37 [4609]~P1(f315(a182,f315(f92(a1),a76)))
% 168.50/168.37 [4610]~P1(f315(f315(f223(a1),a76),a86))
% 168.50/168.37 [4611]~P1(f315(f315(f224(a1),a76),a76))
% 168.50/168.37 [4612]~P1(f315(f315(f224(a1),a76),a86))
% 168.50/168.37 [4613]~P1(f315(f315(f224(a1),a86),a86))
% 168.50/168.37 [4622]~P1(f315(f54(a901),f230(f909(a901,a899))))
% 168.50/168.37 [4623]~P1(f315(f54(a1),f230(f909(a1,a899))))
% 168.50/168.37 [3735]P14(a898,a910,f315(f315(f297(f900(a898)),a912),f177(f909(f900(a898),a899))))
% 168.50/168.37 [4525]E(f315(f245(a1,a1,a899),f315(f315(f10(f909(a1,a899),f909(a1,a899),a1),f315(f20(a1,a899,a899),f315(f315(f10(a899,f909(a899,a899),a1),a313),f315(f224(a1),f2(a1))))),f315(f315(f9(a1,a1,f909(a1,a899)),f315(f315(f10(f909(a1,f909(a1,a899)),f909(a1,f909(a1,a899)),a1),f9(a1,a1,a899)),f315(f315(f10(f909(a1,a1),f909(a1,f909(a1,a899)),a1),f315(f10(a1,f909(a1,a899),a1),a312)),a206))),f71(a1)))),a202)
% 168.50/168.37 [3616]E(f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86),f315(f72(a1),a86))
% 168.50/168.37 [3654]E(f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86),f315(f315(f3(a1),a76),a86))
% 168.50/168.37 [3783]P1(f315(f315(f317(f900(a898)),a800),f315(f315(f297(f900(a898)),a912),a911)))
% 168.50/168.37 [3816]E(f315(f315(f53(f908(a901,a901)),f230(f909(f908(a901,a901),a899))),a97),a87)
% 168.50/168.37 [3845]E(f315(f92(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f71(a1))
% 168.50/168.37 [3846]E(f315(f92(a88),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f71(a88))
% 168.50/168.37 [3847]E(f315(f92(a901),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f71(a901))
% 168.50/168.37 [3850]E(f315(f92(a901),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(a101,f2(a901)))
% 168.50/168.37 [4227]E(f315(f315(f99(f909(f908(f908(a901,a901),f908(a901,a901)),a899)),a26),f295(f908(a901,a901),f177(f909(f908(f908(a901,a901),f908(a901,a901)),a899)))),a64)
% 168.50/168.37 [4293]E(f315(a82,f315(f273(f908(a901,a901),f908(a901,a901),a97),f315(f315(f297(f908(a901,a901)),f315(f315(f240(a901,a901),f71(a901)),f2(a901))),f177(f909(f908(a901,a901),a899))))),f71(a1))
% 168.50/168.37 [4294]E(f315(a82,f315(f273(f908(a901,a901),f908(a901,a901),a97),f315(f315(f297(f908(a901,a901)),f315(f315(f240(a901,a901),f2(a901)),f2(a901))),f177(f909(f908(a901,a901),a899))))),f2(a1))
% 168.50/168.37 [4307]E(f315(f250(f908(a901,a901)),f315(f245(a901,a901,a899),f315(f315(f10(a901,f909(a901,a899),a901),f315(f9(a901,a901,a899),a312)),a101))),a305)
% 168.50/168.37 [4279]E(f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))),f315(a101,f315(a101,f2(a901))))
% 168.50/168.37 [4282]E(f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))),f315(f315(f73(a901),f71(a901)),f71(a901)))
% 168.50/168.37 [4283]E(f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))),f315(f28(a899),f230(f909(a899,a899))))
% 168.50/168.37 [4346]P6(f315(f92(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))))
% 168.50/168.37 [4415]P27(f909(f908(a901,a901),a899),f315(f315(f240(f909(f908(f909(f908(a901,a901),a899),f909(f908(a901,a901),a899)),a899),f909(f908(f909(f908(a901,a901),a899),f909(f908(a901,a901),a899)),a899)),a27),a63))
% 168.50/168.37 [4416]P27(f909(f908(a901,a901),a899),f315(f315(f240(f909(f908(f909(f908(a901,a901),a899),f909(f908(a901,a901),a899)),a899),f909(f908(f909(f908(a901,a901),a899),f909(f908(a901,a901),a899)),a899)),a62),a65))
% 168.50/168.37 [4456]E(f315(f315(f99(f909(f908(f909(f908(a901,a901),a899),f909(f908(a901,a901),a899)),a899)),f308(f908(a901,a901),a64)),f315(f315(f297(f908(f909(f908(a901,a901),a899),f909(f908(a901,a901),a899))),f315(f315(f240(f909(f908(a901,a901),a899),f909(f908(a901,a901),a899)),f177(f909(f908(a901,a901),a899))),f177(f909(f908(a901,a901),a899)))),f177(f909(f908(f909(f908(a901,a901),a899),f909(f908(a901,a901),a899)),a899)))),a65)
% 168.50/168.37 [4457]E(f315(f315(f99(f909(f908(f909(f908(a901,a901),a899),f909(f908(a901,a901),a899)),a899)),f306(f908(a901,a901),a64)),f315(f315(f297(f908(f909(f908(a901,a901),a899),f909(f908(a901,a901),a899))),f315(f315(f240(f909(f908(a901,a901),a899),f909(f908(a901,a901),a899)),f177(f909(f908(a901,a901),a899))),f177(f909(f908(a901,a901),a899)))),f177(f909(f908(f909(f908(a901,a901),a899),f909(f908(a901,a901),a899)),a899)))),a63)
% 168.50/168.37 [4348]E(f315(a93,f315(f92(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),f315(a101,f315(a101,f2(a901))))
% 168.50/168.37 [4393]E(f315(f89(a1),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),f315(f92(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))))
% 168.50/168.37 [4426]P1(f315(f315(f223(a1),f2(a1)),f315(f92(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))))
% 168.50/168.37 [4427]E(f315(f92(a901),f315(f315(f3(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))),a86)),f315(a101,f315(a101,f315(a101,f2(a901)))))
% 168.50/168.37 [4471]P6(f315(f92(a1),f315(f315(f3(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))),a86)))
% 168.50/168.37 [4497]E(f315(f89(a1),f315(f92(a901),f315(f315(f3(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))),a86))),f315(f92(a1),f315(f315(f3(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))),a86)))
% 168.50/168.37 [4510]P1(f315(f315(f223(a1),f2(a1)),f315(f92(a1),f315(f315(f3(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))),a86))))
% 168.50/168.37 [3253]P7(x32531,a312)
% 168.50/168.37 [3642]P25(a901,a901,a101,x36421)
% 168.50/168.37 [3246]P107(f900(x32461))
% 168.50/168.37 [3247]P107(f905(x32471))
% 168.50/168.37 [3248]P107(f902(x32481))
% 168.50/168.37 [3249]P107(f903(x32491))
% 168.50/168.37 [3269]P39(a1,f94(x32691))
% 168.50/168.37 [3270]P39(a1,f96(x32701))
% 168.50/168.37 [3320]P39(f909(x33201,a899),f302(x33201))
% 168.50/168.37 [3321]P40(f909(x33211,a899),f302(x33211))
% 168.50/168.37 [3346]E(f231(x33461,x33461,a312),a312)
% 168.50/168.37 [3361]E(f38(a1,x33611,x33611),f2(a1))
% 168.50/168.37 [3414]P15(x34141,f909(x34141,a899),f297(x34141))
% 168.50/168.37 [4583]~E(f315(a101,x45831),x45831)
% 168.50/168.37 [4589]~E(f315(a101,x45891),f2(a901))
% 168.50/168.37 [3255]E(f315(f92(a1),x32551),x32551)
% 168.50/168.37 [3256]E(f315(f178(a901),x32561),x32561)
% 168.50/168.37 [3271]E(f315(a82,f316(x32711)),x32711)
% 168.50/168.37 [3272]E(f315(a5,f561(x32721)),x32721)
% 168.50/168.37 [3273]E(f229(x32731,f2(a88)),f2(a88))
% 168.50/168.37 [3286]E(f103(x32861,f102(x32861)),f102(x32861))
% 168.50/168.37 [3287]E(f141(x32871,f102(x32871)),f102(x32871))
% 168.50/168.37 [3292]E(f315(f156(x32921),f102(x32921)),f102(x32921))
% 168.50/168.37 [3293]E(f315(f160(x32931),f102(x32931)),f102(x32931))
% 168.50/168.37 [3294]E(f315(f157(x32941),f102(x32941)),f102(x32941))
% 168.50/168.37 [3299]E(f315(f92(a1),x32991),f315(f91(a1),x32991))
% 168.50/168.37 [3300]E(f315(a82,f315(a95,x33001)),x33001)
% 168.50/168.37 [3302]E(f315(a5,f315(a22,x33021)),x33021)
% 168.50/168.37 [3303]E(f315(a22,f315(a5,x33031)),x33031)
% 168.50/168.37 [3305]P6(f315(f89(a1),x33051))
% 168.50/168.37 [3314]E(f315(f178(f902(x33141)),f102(x33141)),f2(a901))
% 168.50/168.37 [3315]E(f315(f178(f903(x33151)),f108(x33151)),f2(a901))
% 168.50/168.37 [3337]E(f315(f315(f3(a901),x33371),f2(a901)),x33371)
% 168.50/168.37 [3338]E(f315(f315(f74(a901),x33381),f71(a901)),x33381)
% 168.50/168.37 [3339]E(f315(f315(f74(a1),x33391),f71(a1)),x33391)
% 168.50/168.37 [3340]E(f315(f315(f73(a901),x33401),f2(a901)),x33401)
% 168.50/168.37 [3341]E(f315(f315(f73(a1),x33411),f2(a1)),x33411)
% 168.50/168.37 [3342]E(f315(f315(f222(a901),x33421),f2(a901)),x33421)
% 168.50/168.37 [3343]E(f315(f315(f74(a901),x33431),f2(a901)),f2(a901))
% 168.50/168.37 [3344]E(f315(f315(f221(a901),x33441),f2(a901)),f2(a901))
% 168.50/168.37 [3345]E(f315(f315(f29(a1),x33451),f2(a1)),f2(a1))
% 168.50/168.37 [3352]E(f315(f161(x33521),f102(x33521)),f177(f909(x33521,a899)))
% 168.50/168.37 [3356]P1(f315(f126(x33561),f102(x33561)))
% 168.50/168.37 [3362]E(f315(f143(x33621,x33621),f7(x33621)),f25(f902(x33621)))
% 168.50/168.37 [3363]E(f315(f143(x33631,x33631),f25(x33631)),f25(f902(x33631)))
% 168.50/168.37 [3364]E(f38(a1,x33641,f2(a1)),x33641)
% 168.50/168.37 [3365]E(f315(f223(a901),f315(a101,x33651)),f315(f224(a901),x33651))
% 168.50/168.37 [3366]E(f315(f270(a901),f315(a101,x33661)),f315(f289(a901),x33661))
% 168.50/168.37 [3367]E(f315(f271(a901),f315(a101,x33671)),f315(f292(a901),x33671))
% 168.50/168.37 [3369]E(f38(a1,f2(a1),x33691),f2(a1))
% 168.50/168.37 [3382]E(f315(f315(f73(a901),x33821),f71(a901)),f315(a101,x33821))
% 168.50/168.37 [3391]E(f315(f290(a901,x33911),f2(a901)),f177(f909(a901,a899)))
% 168.50/168.37 [3403]E(f291(a901,f2(a901),x34031),f315(f289(a901),x34031))
% 168.50/168.37 [3446]E(f315(f315(f3(a901),f315(a101,x34461)),f71(a901)),x34461)
% 168.50/168.37 [3458]E(f40(f2(a1),x34581),f315(f315(f240(a1,a1),f2(a1)),f2(a1)))
% 168.50/168.37 [3507]P1(f315(f315(f224(a901),x35071),f315(a101,x35071)))
% 168.50/168.37 [3519]P1(f315(f315(f224(a901),f2(a901)),f315(a101,x35191)))
% 168.50/168.37 [3745]E(f84(x37451,x37451,f230(f909(x37451,a899)),f25(x37451)),f25(x37451))
% 168.50/168.37 [3803]E(f315(f315(f3(a88),f315(a5,f315(a101,f315(a22,x38031)))),f71(a88)),x38031)
% 168.50/168.37 [3873]P1(f315(f315(f223(a1),f315(f72(a1),f315(f89(a1),x38731))),f2(a1)))
% 168.50/168.37 [4016]P1(f315(f315(f224(a1),f315(f72(a1),f315(f89(a1),f315(a101,x40161)))),f2(a1)))
% 168.50/168.37 [4598]~E(f230(f909(x45981,a899)),f177(f909(x45981,a899)))
% 168.50/168.37 [4621]~P1(f315(f315(f224(a901),x46211),f2(a901)))
% 168.50/168.37 [4632]~P1(f315(f315(f224(a1),f315(f89(a1),x46321)),f2(a1)))
% 168.50/168.37 [3304]E(f109(x33041,f108(f903(x33041))),f108(x33041))
% 168.50/168.37 [3319]E(f168(x33191,f102(f902(x33191))),f102(f902(x33191)))
% 168.50/168.37 [3322]E(f315(f315(f74(a1),a76),x33221),a76)
% 168.50/168.37 [3323]E(f315(f315(f73(a1),a76),x33231),x33231)
% 168.50/168.37 [3326]E(f315(a93,f315(f89(a1),x33261)),x33261)
% 168.50/168.37 [3327]E(f315(f315(f3(a1),x33271),a76),x33271)
% 168.50/168.37 [3328]E(f315(f315(f73(a1),x33281),a76),x33281)
% 168.50/168.37 [3330]E(f315(f315(f3(a901),x33301),x33301),f2(a901))
% 168.50/168.37 [3335]E(f315(f28(a901),f315(f270(a901),x33351)),x33351)
% 168.50/168.37 [3336]E(f315(f72(a1),f315(f72(a1),x33361)),x33361)
% 168.50/168.37 [3347]E(f315(f315(f74(a901),f71(a901)),x33471),x33471)
% 168.50/168.37 [3348]E(f315(f315(f74(a1),f71(a1)),x33481),x33481)
% 168.50/168.37 [3349]E(f315(f315(f73(a901),f2(a901)),x33491),x33491)
% 168.50/168.37 [3350]E(f315(f315(f73(a1),f2(a1)),x33501),x33501)
% 168.50/168.37 [3351]E(f315(f315(f222(a901),f2(a901)),x33511),x33511)
% 168.50/168.37 [3357]E(f315(f315(f3(a901),f2(a901)),x33571),f2(a901))
% 168.50/168.37 [3358]E(f315(f315(f74(a901),f2(a901)),x33581),f2(a901))
% 168.50/168.37 [3359]E(f315(f315(f221(a901),f2(a901)),x33591),f2(a901))
% 168.50/168.37 [3360]E(f315(f315(f29(a1),f2(a1)),x33601),f2(a1))
% 168.50/168.37 [3370]E(f117(x33701,f315(f72(a1),x33701)),f121(a1,x33701))
% 168.50/168.37 [3375]E(f315(f290(a901,f2(a901)),x33751),f315(f270(a901),x33751))
% 168.50/168.37 [3376]E(f315(f315(f74(a1),a86),x33761),f315(f72(a1),x33761))
% 168.50/168.37 [3384]E(f315(a93,f315(f92(a1),x33841)),f315(f92(a901),x33841))
% 168.50/168.37 [3385]E(f315(a22,f315(f92(a88),x33851)),f315(f92(a901),x33851))
% 168.50/168.37 [3386]E(f315(f28(a901),f315(f289(a901),x33861)),f315(a101,x33861))
% 168.50/168.37 [3395]E(f315(f315(f73(a901),f71(a901)),x33951),f315(a101,x33951))
% 168.50/168.37 [3399]E(f315(f69(a1),f315(f89(a1),x33991)),f315(f89(a1),x33991))
% 168.50/168.37 [3400]E(f315(f91(a1),f315(f89(a1),x34001)),f315(f89(a1),x34001))
% 168.50/168.37 [3404]E(f315(f28(x34041),f177(f909(x34041,a899))),f2(a901))
% 168.50/168.37 [3406]E(f315(f315(f29(a901),x34061),f315(a101,f2(a901))),x34061)
% 168.50/168.37 [3415]E(f38(a901,x34151,f315(a101,f2(a901))),f2(a901))
% 168.50/168.37 [3416]E(f38(a1,x34161,f315(f92(a1),a86)),f2(a1))
% 168.50/168.37 [3430]E(f315(f315(f29(a1),x34301),f315(f92(a1),a86)),f315(f72(a1),x34301))
% 168.50/168.37 [3434]E(f128(a901,f315(f290(a901,x34341),f2(a901))),f102(a901))
% 168.50/168.37 [3435]E(f315(f315(f73(a1),x34351),f71(a1)),f315(f315(f3(a1),x34351),a86))
% 168.50/168.37 [3436]E(f315(f315(f3(a1),x34361),f71(a1)),f315(f315(f73(a1),x34361),a86))
% 168.50/168.37 [3440]P1(f315(f315(f223(a901),x34401),x34401))
% 168.50/168.37 [3441]P1(f315(f315(f223(a1),x34411),x34411))
% 168.50/168.37 [3442]P1(f315(f315(f275(a901),x34421),x34421))
% 168.50/168.37 [3447]E(f315(f72(a1),f315(f92(a1),x34471)),f315(f92(a1),f315(f72(a1),x34471)))
% 168.50/168.37 [3448]P1(f315(f54(a901),f315(f270(a901),x34481)))
% 168.50/168.37 [3449]P1(f315(f54(a901),f315(f289(a901),x34491)))
% 168.50/168.37 [3456]E(f150(x34561,f230(f909(x34561,a899))),f230(f909(f902(x34561),a899)))
% 168.50/168.37 [3461]P1(f315(f315(f223(a901),f2(a901)),x34611))
% 168.50/168.37 [3471]E(f315(f315(f73(a901),f100(x34711)),f315(a101,f2(a901))),f100(f315(a101,x34711)))
% 168.50/168.37 [3472]E(f315(f250(x34721),f315(f18(a899,x34721),a227)),f177(f909(x34721,a899)))
% 168.50/168.37 [3473]E(f315(f250(x34731),f315(f18(a899,x34731),a176)),f230(f909(x34731,a899)))
% 168.50/168.37 [3476]E(f315(f315(f297(a901),x34761),f315(f270(a901),x34761)),f315(f270(a901),f315(a101,x34761)))
% 168.50/168.37 [3488]E(f315(f315(f73(a1),f71(a1)),f315(f89(a1),x34881)),f315(f89(a1),f315(a101,x34881)))
% 168.50/168.37 [3490]E(f315(f315(f140(f902(x34901)),f102(x34901)),f102(f902(x34901))),f47(x34901,f102(x34901)))
% 168.50/168.37 [3510]E(f177(f909(f908(x35101,x35101),a899)),f251(x35101,f177(f909(x35101,a899))))
% 168.50/168.37 [3511]E(f315(f296(x35111),f230(f909(x35111,a899))),f230(f909(f909(x35111,a899),a899)))
% 168.50/168.37 [3512]E(f315(f72(f909(x35121,a899)),f177(f909(x35121,a899))),f230(f909(x35121,a899)))
% 168.50/168.37 [3513]E(f315(f72(f909(x35131,a899)),f230(f909(x35131,a899))),f177(f909(x35131,a899)))
% 168.50/168.37 [3515]P1(f315(f54(x35151),f177(f909(x35151,a899))))
% 168.50/168.37 [3517]E(f315(f290(a901,x35171),f315(a101,x35171)),f315(f315(f297(a901),x35171),f177(f909(a901,a899))))
% 168.50/168.37 [3518]E(f78(f908(a901,a901),f41(x35181,f2(a901))),f315(f315(f240(a901,a901),f2(a901)),x35181))
% 168.50/168.37 [3531]E(f315(f315(f297(a901),f315(a101,x35311)),f315(f289(a901),x35311)),f315(f289(a901),f315(a101,x35311)))
% 168.50/168.37 [3535]P39(x35351,f177(f909(f908(x35351,x35351),a899)))
% 168.50/168.37 [3536]P41(x35361,f177(f909(f908(x35361,x35361),a899)))
% 168.50/168.37 [3539]P1(f315(f315(f223(a1),f2(a1)),f315(f89(a1),x35391)))
% 168.50/168.37 [3546]E(f315(f315(f73(a901),f315(f178(a901),x35461)),f315(a101,f2(a901))),f315(f178(a901),f315(a101,x35461)))
% 168.50/168.37 [3649]P42(f315(f298(a901,a1,f89(a1)),x36491))
% 168.50/168.37 [3687]P54(x36871,f177(f909(x36871,a899)),f177(f909(f908(x36871,x36871),a899)))
% 168.50/168.37 [3705]E(f315(f315(f240(a1,a1),f315(f92(a1),a86)),f315(f315(f3(a1),x37051),f71(a1))),f43(f315(f92(a1),a86),x37051))
% 168.50/168.37 [3758]P61(x37581,f315(f18(f909(x37581,a899),x37581),f315(f18(a899,x37581),a227)))
% 168.50/168.37 [3770]E(f278(a901,f275(a901),x37701,x37701),f315(f315(f297(a901),x37701),f177(f909(a901,a899))))
% 168.50/168.37 [3960]P1(f315(f315(f317(f909(f908(a901,a901),a899)),f316(x39601)),a87))
% 168.50/168.37 [3985]P1(f315(f315(f317(f909(f908(a901,a901),a899)),f315(a95,x39851)),a87))
% 168.50/168.37 [4114]P25(x41141,f909(x41141,a899),f315(f315(f9(x41141,f909(x41141,a899),f909(x41141,a899)),f297(x41141)),f177(f909(x41141,a899))),f230(f909(x41141,a899)))
% 168.50/168.37 [4594]~E(f315(f315(f73(a1),x45941),x45941),a86)
% 168.50/168.37 [4608]~E(f315(a5,f315(a101,f315(a22,x46081))),f2(a88))
% 168.50/168.37 [4614]~P1(f315(a182,f315(f89(a1),x46141)))
% 168.50/168.37 [4617]~P1(f315(f315(f224(a901),x46171),x46171))
% 168.50/168.37 [4625]~P1(f315(f315(f223(a901),f315(a101,x46251)),x46251))
% 168.50/168.37 [3463]E(f315(a93,f315(f72(a1),f315(f89(a1),x34631))),f2(a901))
% 168.50/168.37 [3466]E(f315(f315(f73(a1),f315(f72(a1),x34661)),x34661),f2(a1))
% 168.50/168.37 [3470]E(f315(f28(a1),f315(f290(a1,f2(a1)),x34701)),f315(a93,x34701))
% 168.50/168.37 [3481]E(f315(f315(f232(a901),f315(a101,f2(a901))),x34811),f315(a101,f2(a901)))
% 168.50/168.37 [3576]E(f315(f269(x35761),f177(f909(f908(x35761,x35761),a899))),f177(f909(x35761,a899)))
% 168.50/168.37 [3584]E(f30(f909(x35841,a899),f177(f909(f909(x35841,a899),a899))),f177(f909(x35841,a899)))
% 168.50/168.37 [3585]E(f30(f909(x35851,a899),f230(f909(f909(x35851,a899),a899))),f230(f909(x35851,a899)))
% 168.50/168.37 [3586]E(f31(f909(x35861,a899),f177(f909(f909(x35861,a899),a899))),f230(f909(x35861,a899)))
% 168.50/168.37 [3587]E(f31(f909(x35871,a899),f230(f909(f909(x35871,a899),a899))),f177(f909(x35871,a899)))
% 168.50/168.37 [3591]P1(f315(f315(f275(a901),f315(a101,f2(a901))),x35911))
% 168.50/168.37 [3632]E(f315(f315(f297(f902(x36321)),f102(x36321)),f177(f909(f902(x36321),a899))),f150(x36321,f177(f909(x36321,a899))))
% 168.50/168.37 [3633]E(f315(f315(f297(f902(x36331)),f102(x36331)),f177(f909(f902(x36331),a899))),f151(x36331,f102(f909(x36331,a899))))
% 168.50/168.37 [3671]E(f315(f315(f73(a901),f6(x36711)),f315(a101,f2(a901))),f6(f315(a5,f315(a101,f315(a22,x36711)))))
% 168.50/168.37 [3696]E(f315(f28(a1),f315(f298(a901,a1,f89(a1)),x36961)),f315(f28(a901),x36961))
% 168.50/168.37 [3697]P1(f315(f315(f223(a901),x36971),f315(f315(f74(a901),x36971),x36971)))
% 168.50/168.37 [3736]E(f315(f298(a1,a901,a93),f291(a1,f2(a1),f315(f89(a1),x37361))),f315(f289(a901),x37361))
% 168.50/168.37 [3753]E(f315(f315(f29(a901),f315(a101,f2(a901))),f315(f92(a901),x37531)),f315(a93,f315(f315(f29(a1),f71(a1)),f315(f92(a1),x37531))))
% 168.50/168.37 [3755]E(f315(f161(a901),f128(a901,f315(f290(a901,f2(a901)),f315(a101,x37551)))),f315(f289(a901),x37551))
% 168.50/168.37 [3756]E(f315(f315(f73(a901),f315(f178(a88),x37561)),f315(a101,f2(a901))),f315(f178(a88),f315(a5,f315(a101,f315(a22,x37561)))))
% 168.50/168.37 [3776]P41(x37761,f295(x37761,f177(f909(f908(x37761,x37761),a899))))
% 168.50/168.37 [3777]P53(x37771,f295(x37771,f177(f909(f908(x37771,x37771),a899))))
% 168.50/168.37 [3778]E(f315(f298(a1,a901,a93),f315(f298(a901,a1,f89(a1)),x37781)),x37781)
% 168.50/168.37 [3809]E(f315(f315(f297(a901),f2(a901)),f315(f298(a901,a901,a101),f315(f270(a901),x38091))),f315(f270(a901),f315(a101,x38091)))
% 168.50/168.37 [3815]P56(x38151,x38151,f295(x38151,f177(f909(f908(x38151,x38151),a899))))
% 168.50/168.37 [3821]P1(f315(a182,f315(f72(a1),f315(f89(a1),f315(a101,x38211)))))
% 168.50/168.37 [3831]E(f315(f315(f3(f909(a901,a899)),f315(f271(a901),x38311)),f315(f315(f297(a901),x38311),f177(f909(a901,a899)))),f315(f271(a901),f315(a101,x38311)))
% 168.50/168.37 [3848]E(f315(f315(f73(a1),f315(f315(f3(a1),a76),x38481)),f315(f315(f3(a1),a76),x38481)),f315(f315(f3(a1),a76),f315(f315(f73(a1),x38481),x38481)))
% 168.50/168.37 [3862]E(f315(f315(f297(f909(x38621,a899)),f177(f909(x38621,a899))),f177(f909(f909(x38621,a899),a899))),f315(f296(x38621),f177(f909(x38621,a899))))
% 168.50/168.37 [3890]E(f315(f315(f3(f909(a901,a899)),f315(f292(a901),x38901)),f315(f315(f297(a901),f315(a101,x38901)),f177(f909(a901,a899)))),f315(f292(a901),f315(a101,x38901)))
% 168.50/168.37 [3997]E(f315(f92(a901),f315(f315(f73(a1),x39971),x39971)),f315(f315(f79(a901,a901),f315(f92(a901),x39971)),f315(f315(f20(a901,a901,a901),f73(a901)),f7(a901))))
% 168.50/168.37 [4368]P15(x43681,f909(x43681,a899),f315(f315(f10(f909(x43681,a899),f909(f909(x43681,a899),f909(x43681,a899)),x43681),f315(f9(f909(x43681,a899),f909(x43681,a899),f909(x43681,a899)),f3(f909(x43681,a899)))),f315(f315(f9(x43681,f909(x43681,a899),f909(x43681,a899)),f297(x43681)),f177(f909(x43681,a899)))))
% 168.50/168.37 [4455]E(f315(f250(f908(a1,a1)),f315(f245(a1,a1,a899),f315(f315(f10(f909(a1,a899),f909(a1,a899),a1),f315(f20(a1,a899,a899),f315(f315(f10(a899,f909(a899,a899),a1),a313),f315(f223(a1),x44551)))),f224(a1)))),f96(x44551))
% 168.50/168.37 [4488]E(f315(f250(f908(a1,a1)),f315(f245(a1,a1,a899),f315(f315(f20(a1,f909(a1,a899),f909(a1,a899)),f315(f315(f10(f909(a899,a899),f909(f909(a1,a899),f909(a1,a899)),a1),f10(a899,a899,a1)),f315(f315(f10(a899,f909(a899,a899),a1),a313),f315(f223(a1),x44881)))),f224(a1)))),f94(x44881))
% 168.50/168.37 [4541]E(f315(f250(f908(f909(x45411,a899),f909(x45411,a899))),f315(f245(f909(x45411,a899),f909(x45411,a899),a899),f315(f315(f9(f909(x45411,a899),f909(f909(x45411,a899),a899),f909(f909(x45411,a899),a899)),f315(f315(f10(f909(f909(x45411,a899),f909(a899,a899)),f909(f909(f909(x45411,a899),a899),f909(f909(x45411,a899),a899)),f909(x45411,a899)),f20(f909(x45411,a899),a899,a899)),f315(f315(f10(f909(f909(x45411,a899),a899),f909(f909(x45411,a899),f909(a899,a899)),f909(x45411,a899)),f315(f10(a899,f909(a899,a899),f909(x45411,a899)),a313)),f224(f909(x45411,a899))))),f54(x45411)))),f302(x45411))
% 168.50/168.37 [4629]~P1(f315(f54(f902(x46291)),f230(f909(f902(x46291),a899))))
% 168.50/168.37 [4641]~P1(f315(f315(f223(a1),f2(a1)),f315(f72(a1),f315(f89(a1),f315(a101,x46411)))))
% 168.50/168.37 [3611]E(f315(f315(f3(a1),f315(f315(f73(a1),x36111),a86)),a86),x36111)
% 168.50/168.37 [3625]E(f315(f161(a901),f128(a901,f315(f290(a901,f2(a901)),x36251))),f315(f270(a901),x36251))
% 168.50/168.37 [3869]E(f315(f315(f73(a1),f315(f315(f73(a1),f71(a1)),x38691)),x38691),f315(f315(f3(a1),f315(f315(f73(a1),x38691),x38691)),a86))
% 168.50/168.37 [3917]E(f315(f274(x39171,x39171),f295(x39171,f177(f909(f908(x39171,x39171),a899)))),f295(x39171,f177(f909(f908(x39171,x39171),a899))))
% 168.50/168.37 [3963]P1(f315(f315(f223(a901),x39631),f315(f315(f74(a901),x39631),f315(f315(f74(a901),x39631),x39631))))
% 168.50/168.37 [4231]P1(f315(f54(a901),f315(f250(a901),f315(f315(f9(a901,a901,a899),f223(a901)),x42311))))
% 168.50/168.37 [4232]P1(f315(f54(a901),f315(f250(a901),f315(f315(f9(a901,a901,a899),f224(a901)),x42321))))
% 168.50/168.37 [4504]E(f315(f250(f908(x45041,x45041)),f315(f315(f10(f909(x45041,a899),a899,f908(x45041,x45041)),f80(x45041)),f315(f315(f9(f908(x45041,x45041),f909(x45041,f908(x45041,x45041)),f909(x45041,a899)),f315(f315(f10(f909(f908(x45041,x45041),a899),f909(f909(x45041,f908(x45041,x45041)),f909(x45041,a899)),f908(x45041,x45041)),f10(f908(x45041,x45041),a899,x45041)),a312)),f315(f315(f20(x45041,x45041,f908(x45041,x45041)),f240(x45041,x45041)),f7(x45041))))),f295(x45041,f177(f909(f908(x45041,x45041),a899))))
% 168.50/168.37 [4631]~E(f315(f315(f3(a1),f315(f315(f73(a1),x46311),x46311)),a86),a76)
% 168.50/168.37 [4633]~E(f315(f315(f73(a1),f315(f315(f73(a1),f71(a1)),x46331)),x46331),f2(a1))
% 168.50/168.37 [4007]E(f315(f315(f73(a1),f315(f315(f3(a1),a86),x40071)),f315(f315(f3(a1),a86),x40071)),f315(f315(f3(a1),a86),f315(f315(f3(a1),f315(f315(f73(a1),x40071),x40071)),a86)))
% 168.50/168.37 [4122]E(f315(f315(f3(a1),f315(f315(f73(a1),f315(f315(f3(a1),a86),x41221)),f315(f315(f3(a1),a86),x41221))),a86),f315(f315(f3(a1),a86),f315(f315(f73(a1),x41221),x41221)))
% 168.50/168.37 [4154]E(f315(f315(f3(a1),f315(f315(f73(a1),f315(f315(f73(a1),x41541),a86)),f315(f315(f73(a1),x41541),a86))),a86),f315(f315(f73(a1),f315(f315(f73(a1),x41541),x41541)),a86))
% 168.50/168.37 [4192]E(f315(f315(f3(a1),f315(f315(f73(a1),f315(f315(f3(a1),a86),x41921)),f315(f315(f3(a1),a86),x41921))),a86),f315(f315(f3(a1),a76),f315(f315(f3(a1),f315(f315(f73(a1),x41921),x41921)),a86)))
% 168.50/168.37 [4289]E(f315(a82,f315(f273(f908(a901,a901),f908(a901,a901),a97),f315(f315(f297(f908(a901,a901)),f315(f315(f240(a901,a901),x42891),f2(a901))),f177(f909(f908(a901,a901),a899))))),f315(f89(a1),x42891))
% 168.50/168.37 [4299]E(f315(a82,f315(f273(f908(a901,a901),f908(a901,a901),a97),f315(f315(f297(f908(a901,a901)),f315(f315(f240(a901,a901),f320(x42991)),f391(x42991))),f177(f909(f908(a901,a901),a899))))),x42991)
% 168.50/168.37 [4332]E(f315(f250(a1),f315(f315(f20(a1,a899,a899),f315(f315(f10(a899,f909(a899,a899),a1),a313),f315(f223(a1),f2(a1)))),x43321)),f315(f298(a901,a1,f89(a1)),f315(f250(a901),f315(f315(f10(a1,a899,a901),x43321),f89(a1)))))
% 168.50/168.37 [4376]P42(f315(f250(a1),f315(f315(f20(a1,a899,a899),f315(f315(f10(a899,f909(a899,a899),a1),a313),f315(f223(a1),f2(a1)))),x43761)))
% 168.50/168.37 [4396]P1(f315(f315(f317(f908(f909(f908(a901,a901),a899),f909(f908(a901,a901),a899))),f315(f315(f240(f909(f908(a901,a901),a899),f909(f908(a901,a901),a899)),x43961),f177(f909(f908(a901,a901),a899)))),a65))
% 168.50/168.37 [4401]E(f315(f298(a1,a901,a93),f315(f250(a1),f315(f315(f20(a1,a899,a899),f315(f315(f10(a899,f909(a899,a899),a1),a313),f315(f223(a1),f2(a1)))),f315(f315(f10(a901,a899,a1),x44011),a93)))),f315(f250(a901),x44011))
% 168.50/168.37 [4556]E(f300(a901,f315(f315(f33(f908(a901,a901),f909(a901,a899)),f315(a95,x45561)),f315(f245(a901,a901,f909(a901,a899)),f315(f315(f9(a901,f909(a901,a899),f909(a901,f909(a901,a899))),f315(f315(f10(f909(a901,f909(f909(a901,a899),f909(a901,a899))),f909(f909(a901,a899),f909(a901,f909(a901,a899))),a901),f9(a901,f909(a901,a899),f909(a901,a899))),f315(f315(f10(f909(a901,a901),f909(a901,f909(f909(a901,a899),f909(a901,a899))),a901),f315(f10(a901,f909(f909(a901,a899),f909(a901,a899)),a901),f297(a901))),f3(a901)))),f177(f909(a901,a899)))))),f315(a93,x45561))
% 168.50/168.37 [4052]E(f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),x40521),x40521)),a86)),a86),f315(f315(f73(a1),x40521),x40521))
% 168.50/168.37 [4102]E(f315(f315(f3(a1),f315(f315(f3(a1),f315(f315(f73(a1),x41021),x41021)),a86)),a86),f315(f315(f73(a1),f315(f315(f3(a1),x41021),a86)),f315(f315(f3(a1),x41021),a86)))
% 168.50/168.37 [4305]E(f315(f315(f3(a1),f315(f315(f73(a1),f315(f315(f73(a1),f315(f72(a1),x43051)),a86)),f315(f315(f73(a1),f315(f72(a1),x43051)),a86))),a86),f315(f72(a1),f315(f315(f3(a1),f315(f315(f73(a1),x43051),x43051)),a86)))
% 168.50/168.37 [4349]E(f315(f315(f73(a901),x43491),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),f315(a101,f315(a101,x43491)))
% 168.50/168.37 [4350]E(f315(f315(f74(a901),x43501),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),f315(f315(f73(a901),x43501),x43501))
% 168.50/168.37 [4351]E(f315(f315(f29(a901),f315(f315(f73(a901),x43511),x43511)),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),x43511)
% 168.50/168.37 [4429]E(f38(a901,f315(a101,f315(a101,x44291)),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),f38(a901,x44291,f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))))
% 168.50/168.37 [4570]E(f315(a82,f315(f315(f33(f908(a901,a901),f909(f908(a901,a901),a899)),f315(a95,x45701)),f315(f245(a901,a901,f909(f908(a901,a901),a899)),f315(f315(f10(f909(a901,f909(f908(a901,a901),a899)),f909(a901,f909(f908(a901,a901),a899)),a901),f315(f10(f909(f908(a901,a901),a899),f909(f908(a901,a901),a899),a901),f273(f908(a901,a901),f908(a901,a901),a97))),f315(f315(f9(a901,f909(f908(a901,a901),a899),f909(a901,f909(f908(a901,a901),a899))),f315(f315(f10(f909(a901,f909(f909(f908(a901,a901),a899),f909(f908(a901,a901),a899))),f909(f909(f908(a901,a901),a899),f909(a901,f909(f908(a901,a901),a899))),a901),f9(a901,f909(f908(a901,a901),a899),f909(f908(a901,a901),a899))),f315(f315(f10(f909(a901,f908(a901,a901)),f909(a901,f909(f909(f908(a901,a901),a899),f909(f908(a901,a901),a899))),a901),f315(f10(f908(a901,a901),f909(f909(f908(a901,a901),a899),f909(f908(a901,a901),a899)),a901),f297(f908(a901,a901)))),f315(f9(a901,a901,f908(a901,a901)),f240(a901,a901))))),f177(f909(f908(a901,a901),a899))))))),f315(f72(a1),x45701))
% 168.50/168.37 [4424]E(f315(f315(f73(a901),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),x44241),f315(a101,f315(a101,x44241)))
% 168.50/168.37 [4425]E(f315(f315(f74(a901),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),x44251),f315(f315(f73(a901),x44251),x44251))
% 168.50/168.37 [4461]E(f315(f315(f29(a901),f315(a101,f315(a101,x44611))),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),f315(a101,f315(f315(f29(a901),x44611),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))))))
% 168.50/168.37 [4511]E(f315(f315(f73(a901),f315(f92(a901),f315(f315(f3(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))),a86))),x45111),f315(a101,f315(a101,f315(a101,x45111))))
% 168.50/168.37 [4577]E(f315(f245(a1,a1,f908(a1,a1)),f315(f315(f20(a1,f909(a1,f908(a1,a1)),f909(a1,f908(a1,a1))),f315(f315(f10(f909(a1,f909(f908(a1,a1),f908(a1,a1))),f909(f909(a1,f908(a1,a1)),f909(a1,f908(a1,a1))),a1),f20(a1,f908(a1,a1),f908(a1,a1))),f315(f315(f10(f909(a1,f908(a1,a1)),f909(a1,f909(f908(a1,a1),f908(a1,a1))),a1),f315(f20(a1,f908(a1,a1),f909(f908(a1,a1),f908(a1,a1))),f315(f315(f10(a899,f909(f908(a1,a1),f909(f908(a1,a1),f908(a1,a1))),a1),f85(f908(a1,a1))),f315(f315(f10(a1,a899,a1),f315(f223(a1),f2(a1))),f315(f315(f9(a1,a1,a1),f3(a1)),x45771))))),f315(f315(f9(a1,f909(a1,a1),f909(a1,f908(a1,a1))),f315(f315(f10(f909(a1,f908(a1,a1)),f909(f909(a1,a1),f909(a1,f908(a1,a1))),a1),f10(a1,f908(a1,a1),a1)),f315(f315(f10(a1,f909(a1,f908(a1,a1)),a1),f240(a1,a1)),f315(f315(f9(a1,a1,a1),f315(f315(f10(a1,f909(a1,a1),a1),f73(a1)),f315(f74(a1),f315(f92(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))))),f71(a1))))),f315(f315(f9(a1,a1,a1),f3(a1)),x45771))))),f315(f315(f10(a1,f909(a1,f908(a1,a1)),a1),f240(a1,a1)),f315(f74(a1),f315(f92(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))))))),f36(x45771))
% 168.50/168.37 [3289]P107(f907(x32891,x32892))
% 168.50/168.37 [3290]P107(f908(x32901,x32902))
% 168.50/168.37 [3291]P107(f906(x32911,x32912))
% 168.50/168.37 [3308]P13(a1,f167(x33081,x33082))
% 168.50/168.37 [3309]P39(x33091,f142(x33091,x33092))
% 168.50/168.37 [3310]P40(x33101,f251(x33101,x33102))
% 168.50/168.37 [3311]P40(x33111,f295(x33111,x33112))
% 168.50/168.37 [3312]P41(x33121,f251(x33121,x33122))
% 168.50/168.37 [3313]P53(x33131,f251(x33131,x33132))
% 168.50/168.37 [3377]P33(x33771,x33772,f102(x33771))
% 168.50/168.37 [3410]P54(x34101,x34102,f251(x34101,x34102))
% 168.50/168.37 [3411]P56(x34111,x34111,f251(x34111,x34112))
% 168.50/168.37 [3674]P25(x36741,x36741,f7(x36741),x36742)
% 168.50/168.37 [3675]P25(x36751,x36751,f25(x36751),x36752)
% 168.50/168.37 [3683]P34(x36831,x36832,f102(x36831),f102(x36831))
% 168.50/168.37 [3690]P25(f902(x36901),f902(x36901),f157(x36901),x36902)
% 168.50/168.37 [4092]P26(x40921,x40921,f25(x40921),x40922,x40922)
% 168.50/168.37 [4603]~P35(x46031,x46032,f102(x46031))
% 168.50/168.37 [4604]~P37(x46041,x46042,f102(x46041))
% 168.50/168.37 [3275]E(f315(f7(x32751),x32752),x32752)
% 168.50/168.37 [3276]E(f315(f250(x32761),x32762),x32762)
% 168.50/168.37 [3278]E(f315(f25(x32781),x32782),x32782)
% 168.50/168.37 [3288]E(f315(f180(x32881),x32882),f104(x32881))
% 168.50/168.37 [3306]E(f78(x33061,f315(a312,x33062)),x33062)
% 168.50/168.37 [3307]E(f83(x33071,f315(a312,x33072)),x33072)
% 168.50/168.37 [3329]E(f315(f114(x33291,x33292),f108(x33291)),f2(a901))
% 168.50/168.37 [3333]E(f315(f125(x33331,x33332),f102(x33331)),f102(x33331))
% 168.50/168.37 [3353]E(f295(x33531,f295(x33531,x33532)),f295(x33531,x33532))
% 168.50/168.37 [3354]E(f141(x33541,f141(x33541,x33542)),f141(x33541,x33542))
% 168.50/168.37 [3372]E(f315(f315(f123(x33721),x33722),f102(x33721)),x33722)
% 168.50/168.37 [3378]E(f162(x33781,x33782,f102(x33781)),x33782)
% 168.50/168.37 [3379]E(f162(x33791,f102(x33791),x33792),x33792)
% 168.50/168.37 [3380]E(f105(x33801,f108(x33801),x33802),x33802)
% 168.50/168.37 [3381]E(f158(x33811,f2(a901),x33812),f102(x33811))
% 168.50/168.37 [3387]E(f315(f315(f164(x33871),x33872),f102(x33871)),f102(x33871))
% 168.50/168.37 [3388]E(f315(f315(f127(x33881),x33882),f102(x33881)),f102(x33881))
% 168.50/168.37 [3390]E(f144(x33901,x33902,f102(x33901)),f2(a901))
% 168.50/168.37 [3392]E(f159(x33921,x33922,f102(x33921)),f102(x33921))
% 168.50/168.37 [3393]E(f166(x33931,x33932,f102(x33931)),f102(x33931))
% 168.50/168.37 [3394]E(f165(x33941,f102(x33941),x33942),f102(x33941))
% 168.50/168.37 [3398]E(f315(f161(x33981),f141(x33981,x33982)),f315(f161(x33981),x33982))
% 168.50/168.37 [3401]E(f315(f272(x34011,x34011),f251(x34011,x34012)),x34012)
% 168.50/168.37 [3402]E(f315(f252(x34021,x34021),f251(x34021,x34022)),x34022)
% 168.50/168.37 [3409]E(f315(f274(x34091,x34091),f251(x34091,x34092)),f251(x34091,x34092))
% 168.50/168.37 [3422]E(f295(f902(x34221),f146(x34221,x34222)),f147(x34221,f295(x34221,x34222)))
% 168.50/168.37 [3424]P1(f315(f126(a1),f167(x34241,x34242)))
% 168.50/168.37 [3432]E(f315(f272(x34321,x34321),f295(x34321,x34322)),f230(f909(x34321,a899)))
% 168.50/168.37 [3433]E(f315(f252(x34331,x34331),f295(x34331,x34332)),f230(f909(x34331,a899)))
% 168.50/168.37 [3437]P1(f315(f126(x34371),f141(x34371,x34372)))
% 168.50/168.37 [3439]P1(f315(f149(x34391,x34392),f102(x34391)))
% 168.50/168.37 [3445]E(f315(f161(a1),f167(x34451,x34452)),f291(a1,x34451,x34452))
% 168.50/168.37 [3459]P57(x34591,f177(f909(x34591,a899)),x34592)
% 168.50/168.37 [3464]E(f315(f244(a1,a1),f39(x34641,x34642)),f38(a1,x34641,x34642))
% 168.50/168.37 [3465]E(f315(f290(a901,x34651),f315(a101,x34652)),f291(a901,x34651,x34652))
% 168.50/168.37 [3480]E(f315(f315(f140(x34801),x34802),f102(x34801)),f129(x34801,x34802,f102(x34801)))
% 168.50/168.37 [3492]E(f291(a901,f315(a101,x34921),x34922),f293(a901,x34921,x34922))
% 168.50/168.37 [3495]P54(x34951,f230(f909(x34951,a899)),f295(x34951,x34952))
% 168.50/168.37 [3557]E(f315(f315(f3(a901),x35571),f315(a101,x35572)),f315(f28(a901),f294(a901,x35572,x35571)))
% 168.50/168.37 [3612]E(f155(x36121,x36122,f102(x36121)),f315(f315(f240(f902(x36121),f902(x36121)),f102(x36121)),f102(x36121)))
% 168.50/168.37 [3630]E(f315(f245(x36301,x36302,f908(x36301,x36302)),f240(x36301,x36302)),f25(f908(x36301,x36302)))
% 168.50/168.37 [3634]P1(f315(f315(f317(f902(x36341)),f102(x36341)),f150(x36341,x36342)))
% 168.50/168.37 [3635]E(f315(f178(f902(x36351)),f103(x36351,x36352)),f315(f315(f3(a901),f315(f178(f902(x36351)),x36352)),f71(a901)))
% 168.50/168.37 [3643]P1(f315(f54(a901),f291(a901,x36431,x36432)))
% 168.50/168.37 [3644]P1(f315(f54(a901),f294(a901,x36441,x36442)))
% 168.50/168.37 [3645]P1(f315(f54(a901),f293(a901,x36451,x36452)))
% 168.50/168.37 [3646]P1(f315(f54(a1),f291(a1,x36461,x36462)))
% 168.50/168.37 [3647]P1(f315(f54(a1),f294(a1,x36471,x36472)))
% 168.50/168.37 [3648]P1(f315(f54(a1),f293(a1,x36481,x36482)))
% 168.50/168.37 [3752]E(f315(f298(a901,a901,a101),f291(a901,x37521,x37522)),f291(a901,f315(a101,x37521),f315(a101,x37522)))
% 168.50/168.37 [3772]E(f315(f315(f277(x37721,x37721,x37721),f295(x37721,x37722)),f295(x37721,x37722)),f295(x37721,x37722))
% 168.50/168.37 [3807]E(f315(f315(f240(a88,a88),f315(f315(f29(a88),x38071),x38072)),f38(a88,x38071,x38072)),f23(x38071,x38072))
% 168.50/168.37 [3808]E(f315(f315(f240(a1,a1),f315(f315(f29(a1),x38081),x38082)),f38(a1,x38081,x38082)),f39(x38081,x38082))
% 168.50/168.37 [3835]E(f315(f315(f240(a901,a901),f315(f315(f29(a901),x38351),x38352)),f38(a901,x38351,x38352)),f78(f908(a901,a901),f41(x38351,x38352)))
% 168.50/168.37 [3886]P1(f315(f315(f224(a901),f315(f315(f3(a901),x38861),x38862)),f315(a101,x38861)))
% 168.50/168.37 [3934]P40(x39341,f315(f315(f277(x39341,x39341,x39341),x39342),f295(x39341,x39342)))
% 168.50/168.37 [3984]E(f315(f315(f73(a1),f315(f315(f74(a1),x39841),f315(f315(f29(a1),x39842),x39841))),f38(a1,x39842,x39841)),x39842)
% 168.50/168.37 [3988]E(f315(f315(f33(a901,f909(f908(f902(x39881),f902(x39881)),a899)),f230(f909(a901,a899))),f132(x39881,x39882)),f134(x39881,x39882))
% 168.50/168.37 [4208]P1(f315(f315(f317(f908(f902(x42081),f902(x42081))),f315(f315(f240(f902(x42081),f902(x42081)),f102(x42081)),f102(x42081))),f147(x42081,x42082)))
% 168.50/168.37 [4317]E(f241(x43171,x43171,x43171,a312,f241(x43171,x43171,x43171,x43172,a312)),x43172)
% 168.50/168.37 [4361]E(f246(x43611,x43611,x43612,x43612,f7(x43611),f7(x43612)),f25(f908(x43611,x43612)))
% 168.50/168.37 [4363]E(f246(x43631,x43631,x43632,x43632,f25(x43631),f25(x43632)),f25(f908(x43631,x43632)))
% 168.50/168.37 [3371]E(f315(f157(x33711),f315(f157(x33711),x33712)),x33712)
% 168.50/168.37 [3373]E(f315(f315(f127(x33731),f2(a901)),x33732),x33732)
% 168.50/168.37 [3389]E(f315(f315(f164(x33891),f2(a901)),x33892),f102(x33891))
% 168.50/168.37 [3396]E(f315(f315(f123(x33961),f102(x33961)),x33962),x33962)
% 168.50/168.37 [3405]E(f30(f909(x34051,a899),f315(f296(x34051),x34052)),x34052)
% 168.50/168.37 [3407]E(f315(f161(x34071),f315(f156(x34071),x34072)),f315(f161(x34071),x34072))
% 168.50/168.37 [3408]E(f315(f161(x34081),f315(f157(x34081),x34082)),f315(f161(x34081),x34082))
% 168.50/168.37 [3413]E(f315(f315(f3(a88),x34131),x34132),f315(f315(a4,x34131),x34132))
% 168.50/168.37 [3426]E(f315(f315(f74(a901),x34261),x34262),f315(f315(f74(a901),x34262),x34261))
% 168.50/168.37 [3427]E(f315(f315(f74(a1),x34271),x34272),f315(f315(f74(a1),x34272),x34271))
% 168.50/168.37 [3428]E(f315(f315(f73(a901),x34281),x34282),f315(f315(f73(a901),x34282),x34281))
% 168.50/168.37 [3429]E(f315(f315(f73(a1),x34291),x34292),f315(f315(f73(a1),x34292),x34291))
% 168.50/168.37 [3451]E(f315(f315(f172(x34511,x34511),f2(a901)),x34512),f25(x34511))
% 168.50/168.37 [3452]E(f315(f178(f902(x34521)),f315(f156(x34521),x34522)),f315(f178(f902(x34521)),x34522))
% 168.50/168.37 [3453]E(f315(f178(f902(x34531)),f315(f157(x34531),x34532)),f315(f178(f902(x34531)),x34532))
% 168.50/168.37 [3454]E(f165(x34541,x34542,f177(f909(a901,a899))),f102(x34541))
% 168.50/168.37 [3455]E(f315(f315(f143(x34551,x34551),f7(x34551)),x34552),x34552)
% 168.50/168.37 [3457]E(f315(f239(a1,a1),f39(x34571,x34572)),f315(f315(f29(a1),x34571),x34572))
% 168.50/168.37 [3474]E(f315(f178(f902(x34741)),f141(x34741,x34742)),f315(f28(x34741),f315(f161(x34741),x34742)))
% 168.50/168.37 [3475]E(f315(f269(x34751),f315(f274(x34751,x34751),x34752)),f315(f269(x34751),x34752))
% 168.50/168.37 [3479]P1(f315(f54(x34791),f315(f161(x34791),x34792)))
% 168.50/168.37 [3487]E(f315(f315(f73(a1),x34871),f315(f72(a1),x34872)),f315(f315(f3(a1),x34871),x34872))
% 168.50/168.37 [3494]P14(x34941,x34942,f177(f909(f900(x34941),a899)))
% 168.50/168.37 [3496]E(f315(f298(x34961,x34961,f7(x34961)),x34962),x34962)
% 168.50/168.37 [3497]E(f315(f298(x34971,x34971,f25(x34971)),x34972),x34972)
% 168.50/168.37 [3498]E(f315(f299(x34981,x34981,f7(x34981)),x34982),x34982)
% 168.50/168.37 [3499]E(f315(f299(x34991,x34991,f25(x34991)),x34992),x34992)
% 168.50/168.37 [3500]P1(f315(f230(f909(x35001,a899)),x35002))
% 168.50/168.37 [3502]E(f315(f28(a901),f315(f290(a901,x35021),x35022)),f315(f315(f3(a901),x35022),x35021))
% 168.50/168.37 [3503]E(f315(f290(a901,f315(a101,x35031)),x35032),f294(a901,x35031,x35032))
% 168.50/168.37 [3516]E(f315(f315(f297(x35161),x35162),f177(f909(x35161,a899))),f315(f250(x35161),f315(a312,x35162)))
% 168.50/168.37 [3521]E(f295(x35211,f315(f274(x35211,x35211),x35212)),f315(f274(x35211,x35211),f295(x35211,x35212)))
% 168.50/168.37 [3526]E(f315(f315(f73(a901),f315(a101,x35261)),x35262),f315(f315(f73(a901),x35261),f315(a101,x35262)))
% 168.50/168.37 [3527]E(f315(f315(f3(a901),f315(a101,x35271)),f315(a101,x35272)),f315(f315(f3(a901),x35271),x35272))
% 168.50/168.37 [3533]E(f48(x35331,f2(a901),x35332),f315(f315(f140(f902(x35331)),f102(x35331)),f102(f902(x35331))))
% 168.50/168.37 [3534]E(f315(f28(a901),f293(a901,x35341,x35342)),f315(f315(f3(a901),x35342),x35341))
% 168.50/168.37 [3543]P39(x35431,f315(f315(f276(a901,x35431),a228),x35432))
% 168.50/168.37 [3545]P13(a901,f128(a901,f315(f290(a901,x35451),x35452)))
% 168.50/168.37 [3547]P1(f315(f54(a901),f315(f290(a901,x35471),x35472)))
% 168.50/168.37 [3548]P1(f315(f54(a1),f315(f290(a1,x35481),x35482)))
% 168.50/168.37 [3551]E(f315(f274(f902(x35511),f902(x35511)),f146(x35511,x35512)),f146(x35511,f315(f274(x35511,x35511),x35512)))
% 168.50/168.37 [3553]E(f315(f290(a1,x35531),f315(f315(f73(a1),x35532),f71(a1))),f291(a1,x35531,x35532))
% 168.50/168.37 [3556]E(f315(f315(f29(a1),f315(f72(a1),x35561)),f315(f72(a1),x35562)),f315(f315(f29(a1),x35561),x35562))
% 168.50/168.37 [3564]E(f315(f315(f172(f908(x35641,x35641),a899),f71(a901)),x35642),x35642)
% 168.50/168.37 [3566]E(f315(f315(f99(f909(x35661,a899)),x35662),f177(f909(x35661,a899))),x35662)
% 168.50/168.37 [3567]E(f315(f315(f3(f909(x35671,a899)),x35672),f177(f909(x35671,a899))),x35672)
% 168.50/168.37 [3568]E(f315(f315(f90(f909(x35681,a899)),x35682),f230(f909(x35681,a899))),x35682)
% 168.50/168.37 [3569]E(f315(f239(a901,a901),f78(f908(a901,a901),f41(x35691,x35692))),f315(f315(f29(a901),x35691),x35692))
% 168.50/168.37 [3575]E(f291(a1,f315(f315(f73(a1),x35751),f71(a1)),x35752),f293(a1,x35751,x35752))
% 168.50/168.37 [3580]E(f315(f244(a901,a901),f78(f908(a901,a901),f41(x35801,x35802))),f38(a901,x35801,x35802))
% 168.50/168.37 [3590]P1(f315(f315(f317(x35901),x35902),f230(f909(x35901,a899))))
% 168.50/168.37 [3595]E(f315(f315(f3(a901),f315(a101,x35951)),x35952),f315(f28(a901),f291(a901,x35952,x35951)))
% 168.50/168.37 [3621]E(f315(f315(f99(f909(x36211,a899)),x36212),f230(f909(x36211,a899))),f230(f909(x36211,a899)))
% 168.50/168.37 [3622]E(f315(f315(f3(f909(x36221,a899)),x36222),f230(f909(x36221,a899))),f177(f909(x36221,a899)))
% 168.50/168.37 [3623]E(f315(f315(f90(f909(x36231,a899)),x36232),f177(f909(x36231,a899))),f177(f909(x36231,a899)))
% 168.50/168.37 [3638]E(f38(a1,f315(f89(a1),x36381),f315(f89(a1),x36382)),f315(f89(a1),f38(a901,x36381,x36382)))
% 168.50/168.37 [3639]E(f38(a1,f315(f72(a1),x36391),f315(f72(a1),x36392)),f315(f72(a1),f38(a1,x36391,x36392)))
% 168.50/168.37 [3650]E(f315(f178(f902(x36501)),f315(f160(x36501),x36502)),f315(f315(f3(a901),f315(f178(f902(x36501)),x36502)),f71(a901)))
% 168.50/168.37 [3676]E(f315(f315(f29(a1),f38(a1,x36761,x36762)),x36762),f2(a1))
% 168.50/168.37 [3685]E(f315(a5,f38(a901,f315(a22,x36851),f315(a22,x36852))),f38(a88,x36851,x36852))
% 168.50/168.37 [3718]E(f315(a5,f315(f315(f3(a901),f315(a22,x37181)),f315(a22,x37182))),f315(f315(f3(a88),x37181),x37182))
% 168.50/168.37 [3719]E(f315(a5,f315(f315(f74(a901),f315(a22,x37191)),f315(a22,x37192))),f315(f315(f74(a88),x37191),x37192))
% 168.50/168.37 [3720]E(f315(a5,f315(f315(f73(a901),f315(a22,x37201)),f315(a22,x37202))),f315(f315(f73(a88),x37201),x37202))
% 168.50/168.37 [3721]E(f315(a5,f315(f315(f29(a901),f315(a22,x37211)),f315(a22,x37212))),f315(f315(f29(a88),x37211),x37212))
% 168.50/168.37 [3729]E(f315(f298(a901,a901,a101),f315(f290(a901,x37291),x37292)),f315(f290(a901,f315(a101,x37291)),f315(a101,x37292)))
% 168.50/168.37 [3757]P1(f315(f41(x37571,x37572),f78(f908(a901,a901),f41(x37571,x37572))))
% 168.50/168.37 [3781]E(f38(a901,f315(a101,f38(a901,x37811,x37812)),x37812),f38(a901,f315(a101,x37811),x37812))
% 168.50/168.37 [3794]E(f315(f315(f33(f909(x37941,a899),f909(x37941,a899)),x37942),f7(f909(x37941,a899))),f30(f909(x37941,a899),x37942))
% 168.50/168.37 [3795]E(f315(f315(f32(f909(x37951,a899),f909(x37951,a899)),x37952),f7(f909(x37951,a899))),f31(f909(x37951,a899),x37952))
% 168.50/168.37 [3796]E(f315(f298(f902(x37961),f909(x37961,a899),f161(x37961)),f315(f161(f902(x37961)),f47(x37961,x37962))),f315(f296(x37961),f315(f161(x37961),x37962)))
% 168.50/168.37 [3800]P1(f315(f315(f317(f909(x38001,a899)),x38002),f315(f296(x38001),x38002)))
% 168.50/168.37 [3806]E(f38(a1,f315(f72(a1),f38(a1,x38061,x38062)),x38062),f38(a1,f315(f72(a1),x38061),x38062))
% 168.50/168.37 [3817]P1(f315(f315(f223(f909(x38171,a899)),x38172),f230(f909(x38171,a899))))
% 168.50/168.37 [3819]E(f315(f315(f277(x38191,x38191,x38191),f295(x38191,x38192)),f295(x38191,f295(x38191,x38192))),f295(x38191,x38192))
% 168.50/168.37 [3820]E(f315(f315(f99(f909(x38201,a899)),f315(f252(x38201,x38201),x38202)),f315(f272(x38201,x38201),x38202)),f315(f269(x38201),x38202))
% 168.50/168.37 [3841]E(f301(x38411,x38412,f230(f909(x38411,a899)),f230(f909(x38412,a899))),f230(f909(f907(x38411,x38412),a899)))
% 168.50/168.37 [3891]P1(f315(f315(f223(a901),f38(a901,x38911,x38912)),x38911))
% 168.50/168.37 [3915]P1(f315(f315(f223(a1),f315(f72(a1),f315(f89(a1),x39151))),f315(f89(a1),x39152)))
% 168.50/168.37 [3939]P1(f315(f315(f317(f909(x39391,a899)),f177(f909(x39391,a899))),f315(f296(x39391),x39392)))
% 168.50/168.37 [3944]E(f295(x39441,f315(f315(f277(x39441,x39441,x39441),x39442),f295(x39441,x39442))),f295(x39441,x39442))
% 168.50/168.37 [3947]E(f315(f315(f277(x39471,x39471,x39471),f295(x39471,x39472)),x39472),f315(f315(f277(x39471,x39471,x39471),x39472),f295(x39471,x39472)))
% 168.50/168.37 [3949]E(f315(a93,f315(f315(f73(a1),f315(f315(f3(a1),x39491),x39492)),f71(a1))),f315(f28(a1),f291(a1,x39492,x39491)))
% 168.50/168.37 [3964]E(f315(f272(x39641,x39641),f315(f315(f277(x39641,x39641,x39641),x39642),f295(x39641,x39642))),f315(f272(x39641,x39641),x39642))
% 168.50/168.37 [3965]E(f315(f252(x39651,x39651),f315(f315(f277(x39651,x39651,x39651),x39652),f295(x39651,x39652))),f315(f252(x39651,x39651),x39652))
% 168.50/168.37 [3983]E(f315(f131(f902(x39831),f902(x39831),f123(x39831),f102(x39831)),f158(f902(x39831),x39832,f102(x39831))),f102(x39831))
% 168.50/168.37 [3992]P25(a901,a901,f315(f315(f9(a901,a901,a901),f73(a901)),x39921),x39922)
% 168.50/168.37 [3994]P13(a901,f315(f157(a901),f315(f315(f143(f902(x39941),a901),f178(f902(x39941))),f168(x39941,x39942))))
% 168.50/168.37 [4024]P53(x40241,f315(f315(f99(f909(f908(x40241,x40241),a899)),x40242),f315(f274(x40241,x40241),x40242)))
% 168.50/168.37 [4025]P53(x40251,f315(f315(f90(f909(f908(x40251,x40251),a899)),x40252),f315(f274(x40251,x40251),x40252)))
% 168.50/168.37 [4036]P1(f315(f315(f224(a1),f315(f72(a1),f315(f89(a1),f315(a101,x40361)))),f315(f89(a1),x40362)))
% 168.50/168.37 [4081]E(f315(f131(f902(x40811),x40811,f315(f9(x40811,f902(x40811),f902(x40811)),f140(x40811)),f102(x40811)),x40812),f315(f157(x40811),x40812))
% 168.50/168.37 [4129]P1(f315(f315(f223(f909(f908(f902(x41291),f902(x41291)),a899)),f147(x41291,x41292)),f295(f902(x41291),f146(x41291,x41292))))
% 168.50/168.37 [4158]P1(f315(f41(x41581,x41582),f315(f315(f240(a901,a901),f315(f315(f29(a901),x41581),x41582)),f38(a901,x41581,x41582))))
% 168.50/168.37 [4170]P1(f315(f315(f223(f909(f908(f902(x41701),f902(x41701)),a899)),f146(x41701,f295(x41701,x41702))),f295(f902(x41701),f146(x41701,x41702))))
% 168.50/168.37 [4386]E(f315(f315(f247(f908(a88,a88),a88,f908(a88,a88),f908(x43861,f908(a88,a88))),f255(f315(f154(a88),f315(f315(f143(f908(a88,x43861),a88),f239(a88,x43861)),x43862)))),f315(f315(f10(x43861,f909(f908(a88,a88),f908(x43861,f908(a88,a88))),a88),f240(x43861,f908(a88,a88))),f256(x43861,x43862))),f254(x43861,x43862))
% 168.50/168.37 [4463]E(f212(a901,f908(x44631,f903(x44631)),f2(a901),f315(f245(x44631,f903(x44631),a901),f315(f18(f909(f903(x44631),a901),x44631),f315(f315(f9(f903(x44631),a901,a901),f315(f315(f10(a901,f909(a901,a901),f903(x44631)),f73(a901)),f178(f903(x44631)))),f71(a901)))),f315(f124(x44631),x44632)),f315(f178(f903(x44631)),x44632))
% 168.50/168.37 [4569]E(f315(f245(f909(f908(x45691,x45691),a899),f909(f908(x45691,x45691),a899),f909(f909(x45692,x45691),f908(f909(f908(x45692,x45692),a899),f909(f908(x45692,x45692),a899)))),f315(f315(f9(f909(f908(x45691,x45691),a899),f909(f909(f908(x45691,x45691),a899),f909(f909(x45692,x45691),f909(f908(x45692,x45692),a899))),f909(f909(f908(x45691,x45691),a899),f909(f909(x45692,x45691),f908(f909(f908(x45692,x45692),a899),f909(f908(x45692,x45692),a899))))),f315(f315(f10(f909(f909(f909(x45692,x45691),f909(f908(x45692,x45692),a899)),f909(f909(x45692,x45691),f908(f909(f908(x45692,x45692),a899),f909(f908(x45692,x45692),a899)))),f909(f909(f909(f908(x45691,x45691),a899),f909(f909(x45692,x45691),f909(f908(x45692,x45692),a899))),f909(f909(f908(x45691,x45691),a899),f909(f909(x45692,x45691),f908(f909(f908(x45692,x45692),a899),f909(f908(x45692,x45692),a899))))),f909(f908(x45691,x45691),a899)),f10(f909(f909(x45692,x45691),f909(f908(x45692,x45692),a899)),f909(f909(x45692,x45691),f908(f909(f908(x45692,x45692),a899),f909(f908(x45692,x45692),a899))),f909(f908(x45691,x45691),a899))),f315(f315(f10(f909(f909(x45692,x45691),f909(f909(f908(x45692,x45692),a899),f908(f909(f908(x45692,x45692),a899),f909(f908(x45692,x45692),a899)))),f909(f909(f909(x45692,x45691),f909(f908(x45692,x45692),a899)),f909(f909(x45692,x45691),f908(f909(f908(x45692,x45692),a899),f909(f908(x45692,x45692),a899)))),f909(f908(x45691,x45691),a899)),f20(f909(x45692,x45691),f909(f908(x45692,x45692),a899),f908(f909(f908(x45692,x45692),a899),f909(f908(x45692,x45692),a899)))),f315(f315(f10(f909(f909(x45692,x45691),f909(f908(x45692,x45692),a899)),f909(f909(x45692,x45691),f909(f909(f908(x45692,x45692),a899),f908(f909(f908(x45692,x45692),a899),f909(f908(x45692,x45692),a899)))),f909(f908(x45691,x45691),a899)),f315(f10(f909(f908(x45692,x45692),a899),f909(f909(f908(x45692,x45692),a899),f908(f909(f908(x45692,x45692),a899),f909(f908(x45692,x45692),a899))),f909(x45692,x45691)),f240(f909(f908(x45692,x45692),a899),f909(f908(x45692,x45692),a899)))),f276(x45691,x45692))))),f276(x45691,x45692))),f67(x45691,x45692))
% 168.50/168.37 [4615]~E(f315(f296(x46151),x46152),f177(f909(f909(x46151,a899),a899)))
% 168.50/168.37 [4624]~P1(f315(f315(f161(x46241),f102(x46241)),x46242))
% 168.50/168.37 [4628]~P1(f315(f315(f317(x46281),x46282),f177(f909(x46281,a899))))
% 168.50/168.37 [4636]~P1(f315(f315(f224(f909(x46361,a899)),x46362),f177(f909(x46361,a899))))
% 168.50/168.37 [3505]E(f315(f315(f3(a901),x35051),f315(f315(f73(a901),x35051),x35052)),f2(a901))
% 168.50/168.37 [3508]E(f315(f315(f99(f909(x35081,a899)),x35082),x35082),x35082)
% 168.50/168.37 [3509]E(f315(f315(f90(f909(x35091,a899)),x35092),x35092),x35092)
% 168.50/168.37 [3537]E(f315(f315(f3(f909(x35371,a899)),x35372),x35372),f177(f909(x35371,a899)))
% 168.50/168.37 [3540]E(f315(f132(x35401,x35402),f2(a901)),f177(f909(f908(f902(x35401),f902(x35401)),a899)))
% 168.50/168.37 [3541]E(f315(f315(f73(a901),x35411),f315(a101,x35412)),f315(a101,f315(f315(f73(a901),x35411),x35412)))
% 168.50/168.37 [3552]E(f183(f315(f89(a1),x35521),f315(f89(a1),x35522)),f315(f89(a1),f315(f315(f3(a901),x35521),x35522)))
% 168.50/168.37 [3555]E(f315(f315(f29(a1),f315(f72(a1),x35551)),x35552),f315(f315(f29(a1),x35551),f315(f72(a1),x35552)))
% 168.50/168.37 [3559]E(f315(f28(a1),f315(f290(a1,x35591),x35592)),f315(a93,f315(f315(f3(a1),x35592),x35591)))
% 168.50/168.37 [3562]E(f315(f315(f73(a901),f315(a101,x35621)),x35622),f315(a101,f315(f315(f73(a901),x35621),x35622)))
% 168.50/168.37 [3565]E(f315(f72(f909(x35651,a899)),f315(f72(f909(x35651,a899)),x35652)),x35652)
% 168.50/168.37 [3577]E(f168(x35771,f315(f315(f140(f902(x35771)),f102(x35771)),x35772)),f168(x35771,x35772))
% 168.50/168.37 [3581]E(f315(f315(f73(a901),x35811),f315(f315(f74(a901),x35811),x35812)),f315(f315(f74(a901),x35811),f315(a101,x35812)))
% 168.50/168.37 [3588]E(f315(f315(a4,f315(a5,x35881)),f315(a5,x35882)),f315(a5,f315(f315(f3(a901),x35881),x35882)))
% 168.50/168.37 [3603]E(f315(f315(f74(a1),f315(f72(a1),x36031)),x36032),f315(f72(a1),f315(f315(f74(a1),x36031),x36032)))
% 168.50/168.37 [3605]E(f315(f315(f232(a1),f315(f89(a1),x36051)),x36052),f315(f89(a1),f315(f315(f232(a901),x36051),x36052)))
% 168.50/168.37 [3606]E(f315(f315(f74(a88),f315(a5,x36061)),f315(a5,x36062)),f315(a5,f315(f315(f74(a901),x36061),x36062)))
% 168.50/168.37 [3607]E(f315(f315(f73(a88),f315(a5,x36071)),f315(a5,x36072)),f315(a5,f315(f315(f73(a901),x36071),x36072)))
% 168.50/168.37 [3608]E(f315(f315(f221(a901),f315(a101,x36081)),f315(a101,x36082)),f315(a101,f315(f315(f221(a901),x36081),x36082)))
% 168.50/168.37 [3609]E(f315(f315(f222(a901),f315(a101,x36091)),f315(a101,x36092)),f315(a101,f315(f315(f222(a901),x36091),x36092)))
% 168.50/168.37 [3614]E(f315(f161(a901),f128(a901,f315(f290(a901,x36141),x36142))),f315(f290(a901,x36141),x36142))
% 168.50/168.37 [3615]E(f300(x36151,f315(f315(f297(x36151),x36152),f177(f909(x36151,a899)))),x36152)
% 168.50/168.37 [3619]E(f315(f272(x36191,x36192),f177(f909(f908(x36191,x36192),a899))),f177(f909(x36192,a899)))
% 168.50/168.37 [3620]E(f315(f252(x36201,x36202),f177(f909(f908(x36201,x36202),a899))),f177(f909(x36201,a899)))
% 168.50/168.37 [3624]E(f315(a93,f315(f315(f3(a1),x36241),x36242)),f315(f28(a1),f293(a1,x36242,x36241)))
% 168.50/168.37 [3629]E(f315(f315(f73(a901),x36291),f315(f315(f74(a901),x36292),x36291)),f315(f315(f74(a901),f315(a101,x36292)),x36291))
% 168.50/168.37 [3631]E(f315(f315(f53(x36311),f177(f909(x36311,a899))),x36312),f177(f909(f909(x36311,a899),a899)))
% 168.50/168.37 [3640]E(f315(f178(f902(a901)),f128(a901,f315(f290(a901,x36401),x36402))),f315(f315(f3(a901),x36402),x36401))
% 168.50/168.37 [3655]E(f315(f315(f99(f909(x36551,a899)),f177(f909(x36551,a899))),x36552),x36552)
% 168.50/168.37 [3656]E(f315(f315(f90(f909(x36561,a899)),f230(f909(x36561,a899))),x36562),x36562)
% 168.50/168.37 [3659]E(f315(f315(f73(a1),f315(f72(a1),x36591)),f315(f72(a1),x36592)),f315(f72(a1),f315(f315(f73(a1),x36591),x36592)))
% 168.50/168.37 [3661]E(f315(f315(f74(a1),f315(f92(a1),x36611)),f315(f92(a1),x36612)),f315(f92(a1),f315(f315(f74(a1),x36611),x36612)))
% 168.50/168.37 [3663]E(f315(f315(f74(a1),f315(f89(a1),x36631)),f315(f89(a1),x36632)),f315(f89(a1),f315(f315(f74(a901),x36631),x36632)))
% 168.50/168.37 [3664]E(f315(f315(f73(a1),f315(f92(a1),x36641)),f315(f92(a1),x36642)),f315(f92(a1),f315(f315(f73(a1),x36641),x36642)))
% 168.50/168.37 [3666]E(f315(f315(f73(a1),f315(f89(a1),x36661)),f315(f89(a1),x36662)),f315(f89(a1),f315(f315(f73(a901),x36661),x36662)))
% 168.50/168.37 [3667]E(f315(f315(f29(a1),f315(f89(a1),x36671)),f315(f89(a1),x36672)),f315(f89(a1),f315(f315(f29(a901),x36671),x36672)))
% 168.50/168.37 [3686]E(f315(f315(f8(x36861,a901),f315(f18(a901,x36861),f71(a901))),x36862),f315(f28(x36861),x36862))
% 168.50/168.37 [3691]E(f315(f72(a1),f38(a1,f315(f72(a1),x36911),x36912)),f38(a1,x36911,f315(f72(a1),x36912)))
% 168.50/168.37 [3693]E(f315(f161(a1),f167(x36931,f315(f315(f3(a1),x36932),f71(a1)))),f315(f290(a1,x36931),x36932))
% 168.50/168.37 [3698]P1(f315(f315(f223(a901),x36981),f315(f315(f73(a901),x36982),x36981)))
% 168.50/168.37 [3699]P1(f315(f315(f223(a901),x36991),f315(f315(f73(a901),x36991),x36992)))
% 168.50/168.37 [3701]E(f315(f315(f99(f909(x37011,a899)),f230(f909(x37011,a899))),x37012),f230(f909(x37011,a899)))
% 168.50/168.37 [3702]E(f315(f315(f3(f909(x37021,a899)),f177(f909(x37021,a899))),x37022),f177(f909(x37021,a899)))
% 168.50/168.37 [3703]E(f315(f315(f90(f909(x37031,a899)),f177(f909(x37031,a899))),x37032),f177(f909(x37031,a899)))
% 168.50/168.37 [3710]E(f315(f315(f240(a1,a1),x37101),f315(f72(a1),x37102)),f315(a44,f315(f315(f240(a1,a1),x37101),x37102)))
% 168.50/168.37 [3711]E(f315(f290(a1,f315(f315(f73(a1),x37111),f71(a1))),x37112),f294(a1,x37111,x37112))
% 168.50/168.37 [3722]E(f315(f315(f74(a901),x37221),f315(f315(f29(a901),x37222),x37221)),f315(f315(f3(a901),x37222),f38(a901,x37222,x37221)))
% 168.50/168.37 [3723]E(f315(f315(f74(a1),x37231),f315(f315(f29(a1),x37232),x37231)),f315(f315(f3(a1),x37232),f38(a1,x37232,x37231)))
% 168.50/168.37 [3726]E(f315(f161(a1),f167(f315(f315(f73(a1),x37261),f71(a1)),x37262)),f293(a1,x37261,x37262))
% 168.50/168.37 [3730]P1(f315(f315(f223(f909(x37301,a899)),x37302),x37302))
% 168.50/168.37 [3733]E(f315(f315(f99(f909(x37331,a899)),x37332),f315(f72(f909(x37331,a899)),x37332)),f230(f909(x37331,a899)))
% 168.50/168.37 [3734]E(f315(f315(f90(f909(x37341,a899)),x37342),f315(f72(f909(x37341,a899)),x37342)),f177(f909(x37341,a899)))
% 168.50/168.37 [3743]E(f315(f315(f3(a901),f315(f315(f3(a901),x37431),f71(a901))),x37432),f315(f315(f3(a901),x37431),f315(a101,x37432)))
% 168.50/168.37 [3749]E(f315(f315(f3(f909(x37491,a899)),f230(f909(x37491,a899))),x37492),f315(f72(f909(x37491,a899)),x37492))
% 168.50/168.37 [3750]E(f315(f315(f3(a1),f315(f92(a1),x37501)),f315(f92(a1),x37502)),f315(f92(a1),f315(f315(f73(a1),x37501),f315(f72(a1),x37502))))
% 168.50/168.37 [3763]E(f315(f161(a901),f128(a901,f315(f290(a901,x37631),f315(a101,x37632)))),f291(a901,x37631,x37632))
% 168.50/168.37 [3779]E(f315(f178(f902(f902(x37791))),f47(x37791,x37792)),f315(f315(f232(a901),f315(a101,f315(a101,f2(a901)))),f315(f178(f902(x37791)),x37792)))
% 168.50/168.37 [3798]E(f315(f315(f172(f908(x37981,x37981),a899),f2(a901)),x37982),f295(x37981,f177(f909(f908(x37981,x37981),a899))))
% 168.50/168.37 [3802]P1(f315(f126(a901),f128(a901,f315(f290(a901,x38021),x38022))))
% 168.50/168.37 [3818]E(f315(f298(a1,a901,a93),f291(a1,f315(f89(a1),x38181),f315(f89(a1),x38182))),f291(a901,x38181,x38182))
% 168.50/168.37 [3827]E(f174(a901,f2(a901),f7(a901),f315(f315(f3(a901),x38271),x38272)),f315(f315(f3(a901),x38271),f315(a101,x38272)))
% 168.50/168.37 [3828]E(f315(a93,f315(f315(f3(a1),x38281),f315(f315(f73(a1),x38282),f71(a1)))),f315(f28(a1),f294(a1,x38282,x38281)))
% 168.50/168.37 [3863]E(f315(f315(f143(a901,a901),a101),f128(a901,f315(f290(a901,x38631),x38632))),f128(a901,f315(f290(a901,f315(a101,x38631)),f315(a101,x38632))))
% 168.50/168.37 [3871]E(f315(f161(a1),f167(f315(f315(f73(a1),x38711),f71(a1)),f315(f315(f3(a1),x38712),f71(a1)))),f294(a1,x38711,x38712))
% 168.50/168.37 [3883]P1(f315(f315(f223(f909(x38831,a899)),f177(f909(x38831,a899))),x38832))
% 168.50/168.37 [3887]E(f78(x38871,f315(f315(f9(x38871,x38871,a899),a312),x38872)),x38872)
% 168.50/168.37 [3888]E(f83(x38881,f315(f315(f9(x38881,x38881,a899),a312),x38882)),x38882)
% 168.50/168.37 [3892]E(f315(f161(a901),f128(a901,f315(f290(a901,f315(a101,x38921)),f315(a101,x38922)))),f293(a901,x38921,x38922))
% 168.50/168.37 [3918]E(f315(f315(f242(x39181,x39182),f230(f909(x39181,a899))),f315(f18(f909(x39182,a899),x39181),f230(f909(x39182,a899)))),f230(f909(f908(x39181,x39182),a899)))
% 168.50/168.37 [3951]E(f315(f250(x39511),f315(f315(f10(a899,a899,x39511),a310),x39512)),f315(f72(f909(x39511,a899)),f315(f250(x39511),x39512)))
% 168.50/168.37 [3954]E(f315(f250(x39541),f315(f315(f9(x39541,x39541,a899),a312),x39542)),f315(f315(f297(x39541),x39542),f177(f909(x39541,a899))))
% 168.50/168.37 [3961]E(f315(f315(f73(a1),f315(f315(f3(a1),x39611),x39612)),f315(f315(f3(a1),x39611),x39612)),f315(f315(f3(a1),f315(f315(f73(a1),x39611),x39611)),f315(f315(f73(a1),x39612),x39612)))
% 168.50/168.37 [3962]E(f315(f315(f73(a1),f315(f315(f73(a1),x39621),x39621)),f315(f315(f73(a1),x39622),x39622)),f315(f315(f73(a1),f315(f315(f73(a1),x39621),x39622)),f315(f315(f73(a1),x39621),x39622)))
% 168.50/168.37 [3978]P1(f315(f315(f223(a901),f315(f28(x39781),f315(f161(x39781),x39782))),f315(f178(f902(x39781)),x39782)))
% 168.50/168.37 [3979]P1(f315(f315(f223(a901),f315(f178(f902(x39791)),f141(x39791,x39792))),f315(f178(f902(x39791)),x39792)))
% 168.50/168.37 [3989]E(f315(f250(x39891),f315(f315(f9(x39891,f909(x39891,a899),a899),f317(x39891)),x39892)),x39892)
% 168.50/168.37 [4003]E(f315(f315(f164(x40031),f315(f315(f3(a901),f315(f178(f902(x40031)),x40032)),f71(a901))),x40032),f103(x40031,x40032))
% 168.50/168.37 [4023]E(f174(a901,f2(a901),f315(f315(f10(a901,a901,a901),a101),f315(f221(a901),x40231)),x40232),f315(f315(f221(a901),f315(a101,x40231)),x40232))
% 168.50/168.37 [4028]E(f30(f909(x40281,a899),f315(f298(f909(f908(x40281,x40281),a899),f909(x40281,a899),f269(x40281)),x40282)),f315(f269(x40281),f30(f909(f908(x40281,x40281),a899),x40282)))
% 168.50/168.37 [4029]E(f174(a901,f315(a101,x40291),f315(f315(f10(a901,a901,a901),a101),f315(f222(a901),x40291)),x40292),f315(f315(f222(a901),f315(a101,x40291)),x40292))
% 168.50/168.37 [4031]E(f315(f315(f240(a1,a1),f315(f315(f29(a1),f315(f69(a1),x40311)),f315(f69(a1),x40312))),f38(a1,f315(f69(a1),x40311),f315(f69(a1),x40312))),f46(x40311,x40312))
% 168.50/168.37 [4054]P1(f315(f315(f223(f909(f909(x40541,a899),a899)),x40542),f315(f296(x40541),f30(f909(x40541,a899),x40542))))
% 168.50/168.37 [4086]E(f315(f315(f33(x40861,f909(x40861,a899)),x40862),f315(f315(f9(x40861,f909(x40861,a899),f909(x40861,a899)),f297(x40861)),f177(f909(x40861,a899)))),x40862)
% 168.50/168.37 [4087]E(f315(f315(f277(x40871,x40871,x40871),f315(f274(x40871,x40871),x40872)),f295(x40871,f315(f274(x40871,x40871),x40872))),f315(f274(x40871,x40871),f315(f315(f277(x40871,x40871,x40871),x40872),f295(x40871,x40872))))
% 168.50/168.37 [4150]E(f315(f161(x41501),f315(f131(f902(x41501),f902(x41501),f123(x41501),f102(x41501)),x41502)),f315(f315(f33(f902(x41501),f909(x41501,a899)),f315(f161(f902(x41501)),x41502)),f161(x41501)))
% 168.50/168.37 [4181]E(f315(f315(f99(f909(f908(x41811,x41811),a899)),f295(x41811,f177(f909(f908(x41811,x41811),a899)))),f315(f315(f277(x41811,x41811,x41811),f295(x41811,x41812)),x41812)),f295(x41811,x41812))
% 168.50/168.37 [4217]E(f315(f315(f170(x42171,x42171),x42172),x42172),f315(f315(f143(x42171,f908(x42171,x42171)),f315(f315(f20(x42171,x42171,f908(x42171,x42171)),f240(x42171,x42171)),f7(x42171))),x42172))
% 168.50/168.37 [4328]E(f315(f131(a901,f902(x43281),f315(f9(f902(x43281),a901,a901),f315(f315(f10(a901,f909(a901,a901),f902(x43281)),f222(a901)),f178(f902(x43281)))),f2(a901)),f315(f157(f902(x43281)),x43282)),f315(f178(f902(f902(x43281))),f168(x43281,x43282)))
% 168.50/168.37 [4400]E(f315(f315(f276(f908(a901,f902(x44001)),f902(x44001)),f307(a901,f902(x44001),a228,f134(x44001,x44002))),f315(f315(f20(f902(x44001),f902(x44001),f908(a901,f902(x44001))),f315(f315(f10(a901,f909(f902(x44001),f908(a901,f902(x44001))),f902(x44001)),f240(a901,f902(x44001))),f178(f902(x44001)))),f7(f902(x44001)))),f135(x44001,x44002))
% 168.50/168.37 [4527]E(f315(f250(x45271),f315(f315(f10(f909(f909(x45271,a899),a899),a899,x45271),f80(f909(x45271,a899))),f315(f315(f10(f909(f909(x45271,a899),a899),f909(f909(x45271,a899),a899),x45271),f315(f20(f909(x45271,a899),a899,a899),f315(f315(f10(a899,f909(a899,a899),f909(x45271,a899)),a313),f315(f315(f9(f909(x45271,a899),f909(f909(x45271,a899),a899),a899),f317(f909(x45271,a899))),x45272)))),f317(x45271)))),f30(f909(x45271,a899),x45272))
% 168.50/168.37 [4528]E(f315(f250(x45281),f315(f315(f10(f909(f909(x45281,a899),a899),a899,x45281),f81(f909(x45281,a899))),f315(f315(f10(f909(f909(x45281,a899),a899),f909(f909(x45281,a899),a899),x45281),f315(f20(f909(x45281,a899),a899,a899),f315(f315(f10(a899,f909(a899,a899),f909(x45281,a899)),a318),f315(f315(f9(f909(x45281,a899),f909(f909(x45281,a899),a899),a899),f317(f909(x45281,a899))),x45282)))),f317(x45281)))),f31(f909(x45281,a899),x45282))
% 168.50/168.37 [4637]~P1(f315(f315(f224(a1),f315(f89(a1),x46371)),f315(f72(a1),f315(f89(a1),x46372))))
% 168.50/168.37 [3627]E(f315(f315(f3(a901),f315(f315(f73(a901),x36271),x36272)),x36272),x36271)
% 168.50/168.37 [3628]E(f315(f315(f3(a901),f315(f315(f73(a901),x36281),x36282)),x36281),x36282)
% 168.50/168.37 [3692]E(f315(f315(f73(a901),f315(f315(f3(a901),x36921),x36922)),x36922),f315(f315(f222(a901),x36921),x36922))
% 168.50/168.37 [3805]E(f315(f315(f74(a901),f315(f315(f29(a901),x38051),x38052)),x38052),f315(f315(f3(a901),x38051),f38(a901,x38051,x38052)))
% 168.50/168.37 [3832]E(f315(f161(a901),f128(a901,f315(f290(a901,f315(a101,x38321)),x38322))),f294(a901,x38321,x38322))
% 168.50/168.37 [3840]E(f315(f89(a1),f205(f315(a93,f315(f69(a1),x38401)),f315(a93,f315(f69(a1),x38402)))),f315(f315(a206,x38401),x38402))
% 168.50/168.37 [3842]E(f315(f315(f99(f909(x38421,a899)),f315(f72(f909(x38421,a899)),x38422)),x38422),f230(f909(x38421,a899)))
% 168.50/168.37 [3843]E(f315(f315(f90(f909(x38431,a899)),f315(f72(f909(x38431,a899)),x38432)),x38432),f177(f909(x38431,a899)))
% 168.50/168.37 [3859]P1(f315(f315(f223(a901),f315(f315(f3(a901),x38591),x38592)),x38591))
% 168.50/168.37 [3860]P1(f315(f315(f223(a901),f315(f315(f29(a901),x38601),x38602)),x38601))
% 168.50/168.37 [3884]P1(f315(f315(f224(a901),x38841),f315(a101,f315(f315(f73(a901),x38842),x38841))))
% 168.50/168.37 [3885]P1(f315(f315(f224(a901),x38851),f315(a101,f315(f315(f73(a901),x38851),x38852))))
% 168.50/168.37 [3902]E(f315(f315(f74(a901),f315(a93,f315(f69(a1),x39021))),f315(a93,f315(f69(a1),x39022))),f315(a93,f315(f69(a1),f315(f315(f74(a1),x39021),x39022))))
% 168.50/168.37 [3914]P1(f315(f315(f223(a1),f2(a1)),f315(f315(f232(a1),f315(f69(a1),x39141)),x39142)))
% 168.50/168.37 [3982]E(f315(f273(f902(x39821),f902(x39821),f147(x39821,x39822)),f315(f315(f297(f902(x39821)),f102(x39821)),f177(f909(f902(x39821),a899)))),f315(f315(f297(f902(x39821)),f102(x39821)),f177(f909(f902(x39821),a899))))
% 168.50/168.37 [4001]E(f315(f315(f99(f909(f908(x40011,x40011),a899)),f295(x40011,x40012)),f295(x40011,f177(f909(f908(x40011,x40011),a899)))),f295(x40011,x40012))
% 168.50/168.37 [4013]E(f315(f315(f29(a1),f315(f92(a1),f315(f315(f73(a1),x40131),x40131))),f315(f92(a1),f315(f315(f73(a1),x40132),x40132))),f315(f315(f29(a1),f315(f92(a1),x40131)),f315(f92(a1),x40132)))
% 168.50/168.37 [4076]E(f315(f315(f232(a1),x40761),f315(f92(a901),f315(f315(f73(a1),x40762),x40762))),f315(f315(f79(a1,a1),f315(f315(f232(a1),x40761),f315(f92(a901),x40762))),f315(f315(f20(a1,a1,a1),f74(a1)),f7(a1))))
% 168.50/168.37 [4082]E(f315(f250(f909(x40821,a899)),f315(f315(f9(f909(x40821,a899),f909(x40821,a899),a899),f223(f909(x40821,a899))),x40822)),f315(f296(x40821),x40822))
% 168.50/168.37 [4098]E(f315(f315(f143(a1,a901),a93),f315(f315(f123(a1),f315(f315(f143(a901,a1),f89(a1)),x40981)),f315(f315(f143(a901,a1),f89(a1)),x40982))),f315(f315(f123(a901),x40981),x40982))
% 168.50/168.37 [4128]E(f315(f298(a1,a1,f315(f315(f9(a1,a1,a1),f73(a1)),x41281)),f315(f290(a1,f2(a1)),f315(f315(f3(a1),x41282),x41281))),f315(f290(a1,x41281),x41282))
% 168.50/168.37 [4130]P55(x41301,f315(f315(f3(f909(f908(x41301,x41301),a899)),x41302),f295(x41301,f177(f909(f908(x41301,x41301),a899)))))
% 168.50/168.37 [4148]E(f315(f178(f902(x41481)),f315(f131(f902(x41481),f902(x41481),f123(x41481),f102(x41481)),x41482)),f315(f154(a901),f315(f315(f143(f902(x41481),a901),f178(f902(x41481))),x41482)))
% 168.50/168.37 [4152]P54(x41521,f230(f909(x41521,a899)),f315(f315(f99(f909(f908(x41521,x41521),a899)),x41522),f295(x41521,f177(f909(f908(x41521,x41521),a899)))))
% 168.50/168.37 [4197]E(f174(a901,f2(a901),f315(f315(f10(a901,a901,a901),a101),f315(f315(f9(a901,a901,a901),f221(a901)),x41971)),x41972),f315(f315(f221(a901),x41972),f315(a101,x41971)))
% 168.50/168.37 [4200]E(f174(a901,f315(a101,x42001),f315(f315(f10(a901,a901,a901),a101),f315(f315(f9(a901,a901,a901),f222(a901)),x42001)),x42002),f315(f315(f222(a901),x42002),f315(a101,x42001)))
% 168.50/168.37 [4203]E(f315(f298(x42031,f902(x42031),f315(f315(f9(x42031,f902(x42031),f902(x42031)),f140(x42031)),f102(x42031))),x42032),f163(x42031,x42032,f315(f315(f297(f902(x42031)),f102(x42031)),f177(f909(f902(x42031),a899)))))
% 168.50/168.37 [4205]E(f315(f315(f99(f909(f908(x42051,x42051),a899)),f315(f315(f277(x42051,x42051,x42051),x42052),f295(x42051,x42052))),f295(x42051,f177(f909(f908(x42051,x42051),a899)))),f295(x42051,x42052))
% 168.50/168.37 [4212]P1(f315(f315(f223(f909(f908(x42121,x42121),a899)),f251(x42121,x42122)),f315(f315(f242(x42121,x42121),x42122),f315(f18(f909(x42121,a899),x42121),x42122))))
% 168.50/168.37 [4215]E(f315(f298(a1,a901,a93),f315(f315(f99(f909(a1,a899)),f315(f298(a901,a1,f89(a1)),x42151)),f315(f298(a901,a1,f89(a1)),x42152))),f315(f315(f99(f909(a901,a899)),x42151),x42152))
% 168.50/168.37 [4216]E(f315(f298(a1,a901,a93),f315(f315(f90(f909(a1,a899)),f315(f298(a901,a1,f89(a1)),x42161)),f315(f298(a901,a1,f89(a1)),x42162))),f315(f315(f90(f909(a901,a899)),x42161),x42162))
% 168.50/168.37 [4219]E(f315(f250(x42191),f315(f315(f10(a899,a899,x42191),a310),f315(f315(f9(x42191,f909(x42191,a899),a899),f317(x42191)),x42192))),f315(f72(f909(x42191,a899)),x42192))
% 168.50/168.37 [4246]E(f315(f131(f902(x42461),f902(x42461),f123(x42461),f102(x42461)),f315(f315(f143(f902(x42461),f902(x42461)),f157(x42461)),f315(f157(f902(x42461)),x42462))),f315(f157(x42461),f315(f131(f902(x42461),f902(x42461),f123(x42461),f102(x42461)),x42462)))
% 168.50/168.37 [4272]E(f315(f315(f33(a901,f909(f908(x42721,x42721),a899)),f230(f909(a901,a899))),f315(f315(f9(a901,f909(f908(x42721,x42721),a899),f909(f908(x42721,x42721),a899)),f172(f908(x42721,x42721),a899)),x42722)),f295(x42721,x42722))
% 168.50/168.37 [4290]E(f78(x42901,f315(f315(f10(f909(x42901,a899),a899,x42901),f315(a312,x42902)),f315(f315(f9(x42901,f909(x42901,a899),f909(x42901,a899)),f297(x42901)),f177(f909(x42901,a899))))),f300(x42901,x42902))
% 168.50/168.37 [4298]E(f315(f178(f902(x42981)),f141(x42981,f315(f131(f902(x42981),f902(x42981),f123(x42981),f102(x42981)),x42982))),f315(f28(x42981),f315(f315(f33(f902(x42981),f909(x42981,a899)),f315(f161(f902(x42981)),x42982)),f161(x42981))))
% 168.50/168.37 [4312]E(f315(f315(f99(f909(f908(x43121,x43121),a899)),x43122),f315(f315(f277(x43121,x43121,x43121),f315(f315(f277(x43121,x43121,x43121),x43122),f295(x43121,x43122))),x43122)),f315(f315(f277(x43121,x43121,x43121),x43122),f295(x43121,x43122)))
% 168.50/168.37 [4336]P1(f315(f315(f223(f909(f908(x43361,x43361),a899)),f315(f315(f277(x43361,x43361,x43361),x43362),f295(x43361,x43362))),f315(f315(f242(x43361,x43361),f315(f269(x43361),x43362)),f315(f18(f909(x43361,a899),x43361),f315(f269(x43361),x43362)))))
% 168.50/168.37 [4377]E(f315(f250(f902(x43771)),f315(f315(f9(f902(x43771),f909(x43771,a899),a899),f315(f315(f10(f909(x43771,a899),f909(f909(x43771,a899),a899),f902(x43771)),f223(f909(x43771,a899))),f161(x43771))),x43772)),f150(x43771,x43772))
% 168.50/168.37 [4388]E(f315(f145(f902(x43881),x43881,f102(x43881),f315(f315(f10(f902(x43881),f909(f902(x43881),f902(x43881)),x43881),f315(f9(f902(x43881),f902(x43881),f902(x43881)),f123(x43881))),f315(f315(f9(x43881,f902(x43881),f902(x43881)),f140(x43881)),f102(x43881)))),x43882),f315(f156(x43881),x43882))
% 168.50/168.37 [4428]P25(f909(x44281,x44282),f909(f908(x44281,x44282),a899),f315(f315(f10(f909(f908(x44281,x44282),a899),f909(f908(x44281,x44282),a899),f909(x44281,x44282)),f250(f908(x44281,x44282))),f315(f315(f10(f909(x44281,f909(x44282,a899)),f909(f908(x44281,x44282),a899),f909(x44281,x44282)),f245(x44281,x44282,a899)),f315(f10(x44282,f909(x44282,a899),x44281),f315(f9(x44282,x44282,a899),a312)))),f230(f909(f909(x44281,x44282),a899)))
% 168.50/168.37 [4433]E(f38(a1,f315(f92(a1),f315(f315(f73(a1),x44331),x44331)),f315(f92(a1),f315(f315(f73(a1),x44332),x44332))),f315(f315(f74(a1),f315(f92(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),f38(a1,f315(f92(a1),x44331),f315(f92(a1),x44332))))
% 168.50/168.37 [4477]E(f315(f315(f33(x44771,f909(f908(x44771,x44771),a899)),x44772),f315(f315(f9(x44771,f909(f908(x44771,x44771),a899),f909(f908(x44771,x44771),a899)),f315(f315(f10(f908(x44771,x44771),f909(f909(f908(x44771,x44771),a899),f909(f908(x44771,x44771),a899)),x44771),f297(f908(x44771,x44771))),f315(f315(f20(x44771,x44771,f908(x44771,x44771)),f240(x44771,x44771)),f7(x44771)))),f177(f909(f908(x44771,x44771),a899)))),f251(x44771,x44772))
% 168.50/168.37 [4485]E(f191(x44851,f315(f315(f240(a1,a1),f315(f72(a1),f315(f315(f66(f908(a1,a1),a1,x44851,f239(a1,a1)),f201(x44851)),x44852))),f315(f315(f66(f908(a1,a1),a1,x44851,f244(a1,a1)),f201(x44851)),x44852))),f216(x44851,x44852))
% 168.50/168.37 [4566]E(f315(f250(f909(x45661,a899)),f315(f315(f10(f909(f909(x45661,a899),a899),a899,f909(x45661,a899)),f80(f909(x45661,a899))),f315(f315(f9(f909(x45661,a899),f909(f909(x45661,a899),a899),f909(f909(x45661,a899),a899)),f315(f315(f10(f909(f909(x45661,a899),f909(a899,a899)),f909(f909(f909(x45661,a899),a899),f909(f909(x45661,a899),a899)),f909(x45661,a899)),f20(f909(x45661,a899),a899,a899)),f315(f315(f10(f909(f909(x45661,a899),a899),f909(f909(x45661,a899),f909(a899,a899)),f909(x45661,a899)),f315(f10(a899,f909(a899,a899),f909(x45661,a899)),a313)),f315(f315(f9(f909(x45661,a899),f909(f909(x45661,a899),f909(x45661,a899)),f909(f909(x45661,a899),a899)),f315(f315(f10(f909(f909(x45661,a899),a899),f909(f909(f909(x45661,a899),f909(x45661,a899)),f909(f909(x45661,a899),a899)),f909(x45661,a899)),f10(f909(x45661,a899),a899,f909(x45661,a899))),a312)),f72(f909(x45661,a899)))))),f315(f315(f10(f909(f909(x45661,a899),a899),a899,f909(x45661,a899)),f315(f317(f909(x45661,a899)),x45662)),f296(x45661))))),f315(f296(x45661),f315(f72(f909(x45661,a899)),x45662)))
% 168.50/168.37 [4635]~E(f315(f315(f73(a1),x46351),x46351),f315(f315(f3(a1),f315(f315(f73(a1),x46352),x46352)),a86))
% 168.50/168.37 [4639]~P1(f315(f315(f224(a901),f315(f315(f73(a901),x46391),x46392)),x46392))
% 168.50/168.37 [4640]~P1(f315(f315(f224(a901),f315(f315(f73(a901),x46401),x46402)),x46401))
% 168.50/168.37 [3919]E(f315(f315(f3(a901),x39191),f315(f315(f74(a901),f315(f315(f29(a901),x39191),x39192)),x39192)),f38(a901,x39191,x39192))
% 168.50/168.37 [3920]E(f315(f315(f3(a1),x39201),f315(f315(f74(a1),f315(f315(f29(a1),x39201),x39202)),x39202)),f38(a1,x39201,x39202))
% 168.50/168.37 [3952]E(f315(f315(f143(a901,x39521),f315(f153(x39521),x39522)),f128(a901,f315(f290(a901,f2(a901)),f315(f178(f902(x39521)),x39522)))),x39522)
% 168.50/168.37 [4009]E(f315(f273(x40091,x40091,f295(x40091,f177(f909(f908(x40091,x40091),a899)))),x40092),x40092)
% 168.50/168.37 [4133]E(f295(x41331,f315(f315(f99(f909(f908(x41331,x41331),a899)),x41332),f295(x41331,f177(f909(f908(x41331,x41331),a899))))),f295(x41331,x41332))
% 168.50/168.37 [4134]E(f295(x41341,f315(f315(f3(f909(f908(x41341,x41341),a899)),x41342),f295(x41341,f177(f909(f908(x41341,x41341),a899))))),f295(x41341,x41342))
% 168.50/168.37 [4184]E(f315(f315(f3(a1),f315(f315(f3(a1),f315(f315(f73(a1),x41841),x41841)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),x41842),x41842)),a86)),f315(f315(f73(a1),f315(f315(f3(a1),x41841),x41842)),f315(f315(f3(a1),x41841),x41842)))
% 168.50/168.37 [4224]E(f315(f315(f3(a1),f315(f315(f73(a1),f315(f315(f73(a1),x42241),x42242)),f315(f315(f73(a1),x42241),x42242))),a86),f315(f315(f73(a1),f315(f315(f73(a1),x42241),x42241)),f315(f315(f3(a1),f315(f315(f73(a1),x42242),x42242)),a86)))
% 168.50/168.37 [4249]E(f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),x42491),x42491)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),x42492),x42492)),a86)),f315(f315(f73(a1),f315(f315(f73(a1),x42491),f315(f315(f3(a1),x42492),a86))),f315(f315(f73(a1),x42491),f315(f315(f3(a1),x42492),a86))))
% 168.50/168.37 [4260]E(f315(f315(f3(a1),f315(f315(f73(a1),f315(f315(f3(a1),x42601),x42602)),f315(f315(f3(a1),x42601),x42602))),a86),f315(f315(f3(a1),f315(f315(f3(a1),f315(f315(f73(a1),x42601),x42601)),a86)),f315(f315(f73(a1),x42602),x42602)))
% 168.50/168.37 [4261]E(f315(f315(f3(a1),f315(f315(f73(a1),f315(f315(f73(a1),x42611),x42612)),f315(f315(f73(a1),x42611),x42612))),a86),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),x42611),x42611)),a86)),f315(f315(f73(a1),x42612),x42612)))
% 168.50/168.37 [4309]E(f315(f89(a1),f315(f315(f29(a901),f315(f315(f74(a901),f315(a93,f315(f69(a1),x43091))),f315(a93,f315(f69(a1),x43092)))),f205(f315(a93,f315(f69(a1),x43091)),f315(a93,f315(f69(a1),x43092))))),f207(x43091,x43092))
% 168.50/168.37 [4354]E(f315(f315(f247(f908(a88,a88),a88,f908(a88,a88),f908(x43541,f908(a88,a88))),f255(f315(a5,f315(f178(f902(x43541)),x43542)))),f315(f315(f10(x43541,f909(f908(a88,a88),f908(x43541,f908(a88,a88))),a88),f240(x43541,f908(a88,a88))),f315(f315(f10(a901,x43541,a88),f315(f153(x43541),x43542)),a22))),f263(x43541,x43542))
% 168.50/168.37 [4434]E(f315(f131(a901,f902(x44341),f315(f9(f902(x44341),a901,a901),f315(f315(f10(a901,f909(a901,a901),f902(x44341)),f222(a901)),f178(f902(x44341)))),f2(a901)),f315(f157(f902(x44341)),f168(x44341,x44342))),f315(f178(f902(f902(x44341))),f315(f125(f902(x44341),f315(f315(f10(a899,a899,f902(x44341)),a310),f315(f315(f9(f902(x44341),f902(x44341),a899),a312),f102(x44341)))),x44342)))
% 168.50/168.37 [4440]E(f315(f315(f33(a901,f909(x44401,a899)),f230(f909(a901,a899))),f315(f315(f9(a901,f909(a901,f909(x44401,a899)),f909(x44401,a899)),f315(f315(f10(f909(a901,a899),f909(f909(a901,f909(x44401,a899)),f909(x44401,a899)),a901),f33(a901,f909(x44401,a899))),f290(a901,f2(a901)))),x44402)),f315(f315(f33(a901,f909(x44401,a899)),f230(f909(a901,a899))),x44402))
% 168.50/168.37 [4462]P1(f315(f54(a901),f315(f250(a901),f315(f315(f20(a901,a899,a899),f315(f315(f10(a899,f909(a899,a899),a901),a313),x44621)),f315(f315(f9(a901,a901,a899),f224(a901)),x44622)))))
% 168.50/168.37 [4574]E(f315(f250(f908(f902(x45741),f902(x45741))),f315(f245(f902(x45741),f902(x45741),a899),f315(f315(f20(f902(x45741),f909(f902(x45741),a899),f909(f902(x45741),a899)),f315(f315(f10(f909(f902(x45741),f909(a899,a899)),f909(f909(f902(x45741),a899),f909(f902(x45741),a899)),f902(x45741)),f20(f902(x45741),a899,a899)),f315(f315(f10(f909(f902(x45741),a899),f909(f902(x45741),f909(a899,a899)),f902(x45741)),f315(f10(a899,f909(a899,a899),f902(x45741)),a314)),f315(f315(f9(f902(x45741),f909(f902(x45741),a901),f909(f902(x45741),a899)),f315(f315(f10(f909(a901,a899),f909(f909(f902(x45741),a901),f909(f902(x45741),a899)),f902(x45741)),f10(a901,a899,f902(x45741))),f315(f315(f10(a901,f909(a901,a899),f902(x45741)),f224(a901)),f178(f902(x45741))))),f178(f902(x45741)))))),f315(f315(f20(f902(x45741),f909(f902(x45741),a899),f909(f902(x45741),a899)),f315(f315(f10(f909(f902(x45741),f909(a899,a899)),f909(f909(f902(x45741),a899),f909(f902(x45741),a899)),f902(x45741)),f20(f902(x45741),a899,a899)),f315(f315(f10(f909(f902(x45741),a899),f909(f902(x45741),f909(a899,a899)),f902(x45741)),f315(f10(a899,f909(a899,a899),f902(x45741)),a313)),f315(f315(f9(f902(x45741),f909(f902(x45741),a901),f909(f902(x45741),a899)),f315(f315(f10(f909(a901,a899),f909(f909(f902(x45741),a901),f909(f902(x45741),a899)),f902(x45741)),f10(a901,a899,f902(x45741))),f315(f315(f10(a901,f909(a901,a899),f902(x45741)),a312),f178(f902(x45741))))),f178(f902(x45741)))))),f315(f315(f9(f902(x45741),f909(f908(f902(x45741),f902(x45741)),a899),f909(f902(x45741),a899)),f315(f315(f10(f909(f902(x45741),f909(f909(f908(f902(x45741),f902(x45741)),a899),a899)),f909(f909(f908(f902(x45741),f902(x45741)),a899),f909(f902(x45741),a899)),f902(x45741)),f9(f902(x45741),f909(f908(f902(x45741),f902(x45741)),a899),a899)),f315(f315(f10(f909(f902(x45741),f908(f902(x45741),f902(x45741))),f909(f902(x45741),f909(f909(f908(f902(x45741),f902(x45741)),a899),a899)),f902(x45741)),f315(f10(f908(f902(x45741),f902(x45741)),f909(f909(f908(f902(x45741),f902(x45741)),a899),a899),f902(x45741)),f317(f908(f902(x45741),f902(x45741))))),f240(f902(x45741),f902(x45741))))),f134(x45741,x45742)))))),f135(x45741,x45742))
% 168.50/168.37 [4252]E(f315(f315(f73(a1),f315(f315(f73(a1),f315(f315(f74(a1),x42521),x42522)),f315(f315(f74(a1),x42521),x42522))),x42522),f315(f315(f74(a1),f315(f315(f3(a1),f315(f315(f73(a1),x42521),x42521)),a86)),x42522))
% 168.50/168.37 [4353]E(f315(a93,f315(a82,f315(f273(f908(a901,a901),f908(a901,a901),a97),f315(f315(f297(f908(a901,a901)),f315(f315(f240(a901,a901),x43531),x43532)),f177(f909(f908(a901,a901),a899)))))),f315(f315(f3(a901),x43531),x43532))
% 168.50/168.37 [4357]E(f315(f315(f277(x43571,x43571,x43571),f315(f315(f99(f909(f908(x43571,x43571),a899)),x43572),f295(x43571,f177(f909(f908(x43571,x43571),a899))))),f295(x43571,f315(f315(f99(f909(f908(x43571,x43571),a899)),x43572),f295(x43571,f177(f909(f908(x43571,x43571),a899)))))),f295(x43571,x43572))
% 168.50/168.37 [4394]E(f256(x43941,f315(f125(f908(a88,x43941),f315(f245(a88,x43941,a899),f315(f315(f10(a899,f909(x43941,a899),a88),f18(a899,x43941)),f315(f224(a88),f2(a88))))),x43942)),f256(x43941,x43942))
% 168.50/168.37 [4395]E(f254(x43951,f315(f125(f908(a88,x43951),f315(f245(a88,x43951,a899),f315(f315(f10(a899,f909(x43951,a899),a88),f18(a899,x43951)),f315(f224(a88),f2(a88))))),x43952)),f254(x43951,x43952))
% 168.50/168.37 [4397]E(f315(f72(a1),f315(a82,f315(f273(f908(a901,a901),f908(a901,a901),a97),f315(f315(f297(f908(a901,a901)),f315(f315(f240(a901,a901),x43971),x43972)),f177(f909(f908(a901,a901),a899)))))),f315(a82,f315(f273(f908(a901,a901),f908(a901,a901),a97),f315(f315(f297(f908(a901,a901)),f315(f315(f240(a901,a901),x43972),x43971)),f177(f909(f908(a901,a901),a899))))))
% 168.50/168.37 [4453]E(f315(f315(f276(f902(a901),x44531),f134(a901,a228)),f315(f315(f9(x44531,f902(f909(x44531,a901)),f902(a901)),f315(f315(f10(f909(f909(x44531,a901),a901),f909(f902(f909(x44531,a901)),f902(a901)),x44531),f143(f909(x44531,a901),a901)),f315(f9(f909(x44531,a901),x44531,a901),f7(f909(x44531,a901))))),x44532)),f142(x44531,x44532))
% 168.50/168.37 [4474]E(f315(f315(f79(a1,a901),f315(f92(a1),f315(f315(f73(a1),x44741),a86))),f315(f315(f20(a1,a901,a901),f315(f315(f9(a1,a901,f909(a901,a901)),f315(f315(f10(a899,f909(a901,f909(a901,a901)),a1),f85(a901)),a182)),f2(a901))),f315(f315(f10(a901,a901,a1),a101),f315(f315(f10(a901,a901,a1),f315(f221(a901),x44742)),a93)))),f315(f315(f221(a901),f315(a101,x44742)),f315(f92(a901),x44741)))
% 168.50/168.37 [4475]E(f315(f315(f79(a1,a901),f315(f92(a1),f315(f315(f73(a1),x44751),a86))),f315(f315(f20(a1,a901,a901),f315(f315(f9(a1,a901,f909(a901,a901)),f315(f315(f10(a899,f909(a901,f909(a901,a901)),a1),f85(a901)),a182)),f315(a101,x44752))),f315(f315(f10(a901,a901,a1),a101),f315(f315(f10(a901,a901,a1),f315(f222(a901),x44752)),a93)))),f315(f315(f222(a901),f315(a101,x44752)),f315(f92(a901),x44751)))
% 168.50/168.37 [4495]E(f315(f131(f902(x44951),f902(x44951),f123(x44951),f102(x44951)),f315(f315(f143(f902(x44951),f902(x44951)),f145(f902(x44951),x44951,f102(x44951),f315(f315(f10(f902(x44951),f909(f902(x44951),f902(x44951)),x44951),f18(f902(x44951),f902(x44951))),f315(f315(f9(x44951,f902(x44951),f902(x44951)),f140(x44951)),f102(x44951))))),x44952)),f315(f315(f143(f902(x44951),x44951),f130(x44951)),f315(f125(f902(x44951),f315(f315(f10(a899,a899,f902(x44951)),a310),f315(f315(f9(f902(x44951),f902(x44951),a899),a312),f102(x44951)))),x44952)))
% 168.50/168.37 [4557]E(f315(f245(a1,a1,a899),f315(f315(f9(a1,f909(a1,a899),f909(a1,a899)),f315(f315(f10(f909(a1,f909(a899,a899)),f909(f909(a1,a899),f909(a1,a899)),a1),f20(a1,a899,a899)),f315(f315(f10(f909(a1,a899),f909(a1,f909(a899,a899)),a1),f315(f10(a899,f909(a899,a899),a1),a313)),f315(f315(f10(f909(a1,a1),f909(a1,a899),a1),f315(f10(a1,a899,a1),f315(a312,x45571))),f315(f315(f10(a1,f909(a1,a1),a1),f73(a1)),f315(f74(a1),x45572)))))),f315(f315(f20(a1,a899,a899),f315(f315(f10(a899,f909(a899,a899),a1),a313),f315(f315(f10(a899,a899,a1),f315(a318,f315(f315(f224(a1),f2(a1)),x45572))),f315(f315(f20(a1,a899,a899),f315(f315(f10(a899,f909(a899,a899),a1),a313),f315(f223(a1),f2(a1)))),f315(f315(f9(a1,a1,a899),f224(a1)),x45572))))),f315(f315(f10(a899,a899,a1),f315(a318,f315(a310,f315(f315(f224(a1),f2(a1)),x45572)))),f315(f315(f20(a1,a899,a899),f315(f315(f10(a899,f909(a899,a899),a1),a313),f315(f224(a1),x45572))),f315(f315(f9(a1,a1,a899),f223(a1)),f2(a1))))))),f42(x45571,x45572))
% 168.50/168.37 [4560]E(f315(f250(x45601),f315(f315(f10(f909(a901,a899),a899,x45601),f80(a901)),f315(f315(f9(x45601,f909(a901,a899),f909(a901,a899)),f315(f315(f10(f909(a901,f909(a899,a899)),f909(f909(a901,a899),f909(a901,a899)),x45601),f20(a901,a899,a899)),f315(f315(f10(f909(a901,a899),f909(a901,f909(a899,a899)),x45601),f315(f10(a899,f909(a899,a899),a901),a313)),f315(f315(f9(x45601,f909(a901,x45601),f909(a901,a899)),f315(f315(f10(f909(x45601,a899),f909(f909(a901,x45601),f909(a901,a899)),x45601),f10(x45601,a899,a901)),a312)),f315(f153(x45601),x45602))))),f315(f315(f9(a901,a901,a899),f224(a901)),f315(f178(f902(x45601)),x45602))))),f315(f161(x45601),x45602))
% 168.50/168.37 [4367]E(f315(f315(f3(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),x43671),a86)),x43672)),f315(f315(f3(a1),f315(f315(f73(a1),x43671),a86)),x43672))),a86),f315(f315(f3(a1),f315(f315(f73(a1),x43671),x43671)),f315(f315(f3(a1),f315(f315(f73(a1),x43672),x43672)),a86)))
% 168.50/168.37 [4490]E(f315(f131(f902(f902(x44901)),f902(f902(x44901)),f123(f902(x44901)),f102(f902(x44901))),f315(f315(f143(f902(x44901),f902(f902(x44901))),f145(f902(f902(x44901)),x44901,f102(f902(x44901)),f315(f18(f909(f902(x44901),f902(f902(x44901))),x44901),f315(f315(f9(f902(x44901),f902(f902(x44901)),f902(f902(x44901))),f140(f902(x44901))),f102(f902(x44901)))))),x44902)),f315(f315(f143(f902(x44901),f902(x44901)),f160(x44901)),f315(f125(f902(x44901),f315(f315(f10(a899,a899,f902(x44901)),a310),f315(f315(f9(f902(x44901),f902(x44901),a899),a312),f102(x44901)))),x44902)))
% 168.50/168.37 [4500]E(f315(f315(f79(a1,a901),f315(f92(a1),f315(f315(f73(a1),x45001),a86))),f315(f315(f20(a1,a901,a901),f315(f315(f9(a1,a901,f909(a901,a901)),f315(f315(f10(a899,f909(a901,f909(a901,a901)),a1),f85(a901)),a182)),f2(a901))),f315(f315(f10(a901,a901,a1),a101),f315(f315(f9(a1,a901,a901),f315(f315(f10(a901,f909(a901,a901),a1),f221(a901)),a93)),x45002)))),f315(f315(f221(a901),f315(f92(a901),x45001)),f315(a101,x45002)))
% 168.50/168.37 [4501]E(f315(f315(f79(a1,a901),f315(f92(a1),f315(f315(f73(a1),x45011),a86))),f315(f315(f20(a1,a901,a901),f315(f315(f9(a1,a901,f909(a901,a901)),f315(f315(f10(a899,f909(a901,f909(a901,a901)),a1),f85(a901)),a182)),f315(a101,x45012))),f315(f315(f10(a901,a901,a1),a101),f315(f315(f9(a1,a901,a901),f315(f315(f10(a901,f909(a901,a901),a1),f222(a901)),a93)),x45012)))),f315(f315(f222(a901),f315(f92(a901),x45011)),f315(a101,x45012)))
% 168.50/168.37 [4489]E(f315(f245(x44891,x44891,a899),f315(f315(f20(x44891,a899,f909(x44891,a899)),f315(f315(f10(f909(x44891,f909(a899,a899)),f909(a899,f909(x44891,a899)),x44891),f9(x44891,a899,a899)),f315(f315(f10(f909(x44891,a899),f909(x44891,f909(a899,a899)),x44891),f315(f10(a899,f909(a899,a899),x44891),a313)),a312))),x44892)),f251(x44891,x44892))
% 168.50/168.37 [4534]E(f315(f315(f29(a901),x45341),f315(f315(f73(a901),f315(f92(a901),f315(f315(f3(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))),a86))),x45342)),f315(f315(f29(a901),x45341),f315(a101,f315(a101,f315(a101,x45342)))))
% 168.50/168.37 [4535]E(f38(a901,x45351,f315(f315(f73(a901),f315(f92(a901),f315(f315(f3(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))),a86))),x45352)),f38(a901,x45351,f315(a101,f315(a101,f315(a101,x45352)))))
% 168.50/168.37 [4536]E(f38(a901,f315(f315(f73(a901),f315(f92(a901),f315(f315(f3(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))),a86))),x45361),x45362),f38(a901,f315(a101,f315(a101,f315(a101,x45361))),x45362))
% 168.50/168.37 [4548]E(f112(f315(x45481,f315(f315(f74(a88),f315(f92(a88),f315(f315(f3(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))),a86))),x45482))),f315(f189(x45481),x45482))
% 168.50/168.37 [4549]E(f315(f315(f29(a901),f315(f315(f73(a901),f315(f92(a901),f315(f315(f3(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))),a86))),x45491)),x45492),f315(f315(f29(a901),f315(a101,f315(a101,f315(a101,x45491)))),x45492))
% 168.50/168.37 [4602]~E(f115(x46021,x46022,x46023),f108(x46021))
% 168.50/168.37 [3355]E(f315(f181(x33551,x33552),x33553),f110(x33551,x33552))
% 168.50/168.37 [3374]E(f315(f188(x33741,x33742),x33743),f315(f118(x33741),x33742))
% 168.50/168.37 [3450]E(f315(f315(f143(x34501,x34502),x34503),f102(x34501)),f102(x34502))
% 168.50/168.37 [3489]E(f315(f173(x34891,x34892,x34893),f2(a901)),x34892)
% 168.50/168.37 [3491]E(f315(f315(f170(x34911,x34912),x34913),f102(x34912)),f102(f908(x34911,x34912)))
% 168.50/168.37 [3506]E(f315(f178(f902(x35061)),f158(x35061,x35062,x35063)),x35062)
% 168.50/168.37 [3525]E(f78(x35251,f55(x35251,x35252,x35253)),f315(f56(x35251,x35252),x35253))
% 168.50/168.37 [3529]E(f231(x35291,x35292,f231(x35292,x35291,x35293)),x35293)
% 168.50/168.37 [3549]E(f315(f157(x35491),f158(x35491,x35492,x35493)),f158(x35491,x35492,x35493))
% 168.50/168.37 [3574]E(f129(x35741,x35742,f141(x35741,x35743)),f141(x35741,f129(x35741,x35742,x35743)))
% 168.50/168.37 [3593]E(f315(f239(f902(x35931),f902(x35931)),f155(x35931,x35932,x35933)),f315(f125(x35931,x35932),x35933))
% 168.50/168.37 [3636]E(f315(f315(f140(x36361),x36362),f158(x36361,x36363,x36362)),f158(x36361,f315(a101,x36363),x36362))
% 168.50/168.37 [3668]E(f19(x36681,x36682,x36683,f2(a88)),x36682)
% 168.50/168.37 [3669]E(f174(x36691,x36692,x36693,f2(a901)),x36692)
% 168.50/168.37 [3670]E(f21(x36701,x36702,x36703,f2(a88)),x36702)
% 168.50/168.37 [3677]E(f152(x36771,x36772,x36773,f102(x36771)),f102(x36772))
% 168.50/168.37 [3678]E(f119(x36781,x36782,x36783,f108(x36781)),f108(x36782))
% 168.50/168.37 [3684]E(f315(f315(f153(x36841),f315(f315(f140(x36841),x36842),x36843)),f2(a901)),x36842)
% 168.50/168.37 [3712]E(f52(x37121,x37122,f102(x37121),x37123),f102(f908(x37121,x37122)))
% 168.50/168.37 [3732]P25(x37321,x37322,x37323,f177(f909(x37321,a899)))
% 168.50/168.37 [3836]E(f253(x38361,x38362,x38363),f315(f240(f909(a88,f909(a899,f905(f903(x38361)))),f908(a88,a88)),f34(x38361)))
% 168.50/168.37 [3893]E(f315(f66(x38931,x38932,x38931,x38933),f25(x38931)),x38933)
% 168.50/168.37 [4068]P1(f315(f315(f317(f908(x40681,x40681)),f315(f315(f240(x40681,x40681),x40682),x40682)),f295(x40681,x40683)))
% 168.50/168.37 [4644]~P1(f315(f315(f317(f908(f902(x46441),f902(x46441))),f315(f315(f240(f902(x46441),f902(x46441)),x46442),f102(x46441))),f134(x46441,x46443)))
% 168.50/168.37 [4645]~P1(f315(f315(f317(f908(f902(x46451),f902(x46451))),f315(f315(f240(f902(x46451),f902(x46451)),x46452),f102(x46451))),f136(x46451,x46453)))
% 168.50/168.37 [4646]~P1(f315(f315(f317(f908(f902(x46461),f902(x46461))),f315(f315(f240(f902(x46461),f902(x46461)),x46462),f102(x46461))),f146(x46461,x46463)))
% 168.50/168.37 [4647]~P1(f315(f315(f317(f908(f902(x46471),f902(x46471))),f315(f315(f240(f902(x46471),f902(x46471)),f102(x46471)),x46472)),f134(x46471,x46473)))
% 168.50/168.37 [4648]~P1(f315(f315(f317(f908(f902(x46481),f902(x46481))),f315(f315(f240(f902(x46481),f902(x46481)),f102(x46481)),x46482)),f146(x46481,x46483)))
% 168.50/168.37 [3425]E(f315(f315(f190(x34251),x34252),x34253),f191(x34251,f204(x34252,x34253)))
% 168.50/168.37 [3478]E(f315(f274(x34781,x34782),f315(f274(x34782,x34781),x34783)),x34783)
% 168.50/168.37 [3501]E(f315(f315(f170(x35011,x35012),f102(x35011)),x35013),f102(f908(x35011,x35012)))
% 168.50/168.37 [3504]E(f165(x35041,x35042,f315(f270(a901),x35043)),f315(f315(f164(x35041),x35043),x35042))
% 168.50/168.37 [3522]E(f141(x35221,f315(f125(x35221,x35222),x35223)),f315(f125(x35221,x35222),f141(x35221,x35223)))
% 168.50/168.37 [3523]E(f315(f272(x35231,x35232),f315(f274(x35232,x35231),x35233)),f315(f252(x35232,x35231),x35233))
% 168.50/168.37 [3524]E(f315(f252(x35241,x35242),f315(f274(x35242,x35241),x35243)),f315(f272(x35242,x35241),x35243))
% 168.50/168.37 [3542]E(f315(f125(x35421,x35422),f315(f157(x35421),x35423)),f315(f157(x35421),f315(f125(x35421,x35422),x35423)))
% 168.50/168.37 [3554]E(f315(f315(f127(x35541),x35542),f315(f160(x35541),x35543)),f315(f315(f127(x35541),f315(a101,x35542)),x35543))
% 168.50/168.37 [3570]E(f315(f273(x35701,x35702,x35703),f177(f909(x35701,a899))),f177(f909(x35702,a899)))
% 168.50/168.37 [3571]E(f315(f298(x35711,x35712,x35713),f177(f909(x35711,a899))),f177(f909(x35712,a899)))
% 168.50/168.37 [3572]E(f315(f299(x35721,x35722,x35723),f177(f909(x35722,a899))),f177(f909(x35721,a899)))
% 168.50/168.37 [3573]E(f315(f299(x35731,x35732,x35733),f230(f909(x35732,a899))),f230(f909(x35731,a899)))
% 168.50/168.37 [3599]E(f109(x35991,f115(f903(x35991),x35992,x35993)),f105(x35991,x35992,f109(x35991,x35993)))
% 168.50/168.37 [3601]E(f315(f315(f297(x36011),x36012),f315(f161(x36011),x36013)),f315(f161(x36011),f129(x36011,x36012,x36013)))
% 168.50/168.37 [3688]E(f315(f298(f908(x36881,x36882),x36882,f244(x36881,x36882)),x36883),f315(f272(x36881,x36882),x36883))
% 168.50/168.37 [3689]E(f315(f298(f908(x36891,x36892),x36891,f239(x36891,x36892)),x36893),f315(f252(x36891,x36892),x36893))
% 168.50/168.37 [3704]E(f315(f161(x37041),f158(x37041,f315(a101,x37042),x37043)),f315(f315(f297(x37041),x37043),f177(f909(x37041,a899))))
% 168.50/168.37 [3762]E(f315(f315(f240(x37621,x37622),f315(f239(x37621,x37622),x37623)),f315(f244(x37621,x37622),x37623)),x37623)
% 168.50/168.37 [3769]E(f315(f178(f903(x37691)),f115(x37691,x37692,x37693)),f315(f315(f73(a901),f315(f178(f903(x37691)),x37693)),f315(a101,f2(a901))))
% 168.50/168.37 [3771]E(f315(f315(f245(x37711,x37712,x37711),f18(x37711,x37712)),x37713),f315(f239(x37711,x37712),x37713))
% 168.50/168.37 [3898]E(f315(f66(x38981,x38981,x38982,f25(x38981)),x38983),x38983)
% 168.50/168.37 [3905]E(f315(f315(f123(x39051),f158(x39051,x39052,x39053)),f315(f315(f140(x39051),x39053),f102(x39051))),f315(f315(f140(x39051),x39053),f158(x39051,x39052,x39053)))
% 168.50/168.37 [4077]P1(f315(f315(f223(f909(x40771,a899)),f315(f161(x40771),f315(f125(x40771,x40772),x40773))),f315(f161(x40771),x40773)))
% 168.50/168.37 [4119]P1(f315(f315(f223(f909(x41191,a899)),f315(f161(x41191),f315(f315(f164(x41191),x41192),x41193))),f315(f161(x41191),x41193)))
% 168.50/168.37 [4120]P1(f315(f315(f223(f909(x41201,a899)),f315(f161(x41201),f315(f315(f127(x41201),x41202),x41203))),f315(f161(x41201),x41203)))
% 168.50/168.37 [4124]P1(f315(f315(f223(f909(x41241,a899)),f315(f161(x41241),f165(x41241,x41242,x41243))),f315(f161(x41241),x41242)))
% 168.50/168.37 [4125]P1(f315(f315(f223(f909(x41251,a899)),f315(f161(x41251),f159(x41251,x41252,x41253))),f315(f161(x41251),x41253)))
% 168.50/168.37 [4146]P25(f908(x41461,x41462),f908(x41462,x41461),f315(f245(x41461,x41462,f908(x41462,x41461)),f315(f9(x41462,x41461,f908(x41462,x41461)),f240(x41462,x41461))),x41463)
% 168.50/168.37 [4157]E(f315(f315(f315(f172(f902(x41571),f902(x41571)),f38(a901,x41572,f315(f178(f902(x41571)),x41573))),f156(x41571)),x41573),f315(f315(f315(f172(f902(x41571),f902(x41571)),x41572),f156(x41571)),x41573))
% 168.50/168.37 [4201]P1(f315(f315(f317(f908(f902(x42011),f902(x42011))),f315(f315(f240(f902(x42011),f902(x42011)),x42012),x42012)),f147(x42011,f295(x42011,x42013))))
% 168.50/168.37 [4340]E(f78(f908(x43401,x43402),f315(f315(f20(f908(x43401,x43402),x43402,a899),f315(f315(f10(x43401,f909(x43402,a899),f908(x43401,x43402)),x43403),f239(x43401,x43402))),f244(x43401,x43402))),f78(f908(x43401,x43402),f315(f245(x43401,x43402,a899),x43403)))
% 168.50/168.37 [4341]E(f83(f908(x43411,x43412),f315(f315(f20(f908(x43411,x43412),x43412,a899),f315(f315(f10(x43411,f909(x43412,a899),f908(x43411,x43412)),x43413),f239(x43411,x43412))),f244(x43411,x43412))),f83(f908(x43411,x43412),f315(f245(x43411,x43412,a899),x43413)))
% 168.50/168.37 [4374]E(f315(f315(f276(f908(a901,x43741),x43741),f307(a901,x43741,a228,x43742)),f315(f315(f20(x43741,x43741,f908(a901,x43741)),f315(f315(f10(a901,f909(x43741,f908(a901,x43741)),x43741),f240(a901,x43741)),x43743)),f7(x43741))),f309(x43741,x43743,x43742))
% 168.50/168.37 [4436]E(f315(f246(x44361,x44361,x44362,x44362,f7(x44361),f7(x44362)),x44363),x44363)
% 168.50/168.37 [4509]E(f315(f131(f902(f902(x45091)),f902(f902(x45091)),f123(f902(x45091)),f102(f902(x45091))),f315(f315(f143(f902(x45091),f902(f902(x45091))),f315(f315(f9(f902(x45091),f902(x45091),f902(f902(x45091))),f315(f315(f10(f909(x45091,f902(x45091)),f909(f902(x45091),f902(f902(x45091))),f902(x45091)),f143(x45091,f902(x45091))),f315(f9(x45091,f902(x45091),f902(x45091)),f140(x45091)))),x45092)),f48(x45091,x45093,x45092))),f48(x45091,f315(a101,x45093),x45092))
% 168.50/168.37 [4565]E(f212(a901,f908(x45651,f903(x45651)),f2(a901),f315(f245(x45651,f903(x45651),a901),f315(f315(f9(x45651,a901,f909(f903(x45651),a901)),f315(f315(f10(f909(f903(x45651),f909(a901,a901)),f909(a901,f909(f903(x45651),a901)),x45651),f9(f903(x45651),a901,a901)),f315(f315(f10(f909(f903(x45651),a901),f909(f903(x45651),f909(a901,a901)),x45651),f315(f10(a901,f909(a901,a901),f903(x45651)),f73(a901))),f315(f315(f9(x45651,f909(f903(x45651),a901),f909(f903(x45651),a901)),f315(f315(f10(f909(a901,a901),f909(f909(f903(x45651),a901),f909(f903(x45651),a901)),x45651),f10(a901,a901,f903(x45651))),f315(f315(f10(a901,f909(a901,a901),x45651),f73(a901)),x45652))),f114(x45651,x45652))))),f71(a901))),f315(f124(x45651),x45653)),f315(f114(x45651,x45652),x45653))
% 168.50/168.37 [4573]E(f315(f315(f79(a1,x45731),f207(f315(f315(f66(f908(a1,a1),a1,x45731,f244(a1,a1)),f201(x45731)),x45732),f315(f315(f66(f908(a1,a1),a1,x45731,f244(a1,a1)),f201(x45731)),x45733))),f315(f315(f20(a1,a1,x45731),f315(f315(f10(a1,f909(a1,x45731),a1),f190(x45731)),f315(f315(f20(a1,a1,a1),f315(f315(f10(a1,f909(a1,a1),a1),f73(a1)),f315(f315(f10(a1,a1,a1),f315(f74(a1),f315(f315(f66(f908(a1,a1),a1,x45731,f239(a1,a1)),f201(x45731)),x45732))),f315(f315(f9(a1,a1,a1),f29(a1)),f315(f315(f66(f908(a1,a1),a1,x45731,f244(a1,a1)),f201(x45731)),x45732))))),f315(f315(f10(a1,a1,a1),f315(f74(a1),f315(f315(f66(f908(a1,a1),a1,x45731,f239(a1,a1)),f201(x45731)),x45733))),f315(f315(f9(a1,a1,a1),f29(a1)),f315(f315(f66(f908(a1,a1),a1,x45731,f244(a1,a1)),f201(x45731)),x45733)))))),f7(a1))),f219(x45731,x45732,x45733))
% 168.50/168.37 [4597]~E(f315(f315(f140(x45971),x45972),x45973),x45973)
% 168.50/168.37 [4600]~E(f315(f315(f140(x46001),x46002),x46003),f102(x46001))
% 168.50/168.37 [4606]~E(f315(f315(f297(x46061),x46062),x46063),f177(f909(x46061,a899)))
% 168.50/168.37 [4626]~E(f315(f298(x46261,f909(x46261,a899),x46262),x46263),f315(f296(x46261),x46263))
% 168.50/168.37 [3483]E(f315(f315(f148(x34831,f102(x34831)),x34832),x34833),f102(x34831))
% 168.50/168.37 [3484]E(f315(f130(x34841),f315(f315(f140(x34841),x34842),x34843)),x34842)
% 168.50/168.37 [3485]E(f315(f160(x34851),f315(f315(f140(x34851),x34852),x34853)),x34853)
% 168.50/168.37 [3528]E(f315(f315(f127(x35281),f71(a901)),f315(f315(f140(x35281),x35282),x35283)),x35283)
% 168.50/168.37 [3561]E(f103(x35611,f315(f315(f127(x35611),x35612),x35613)),f315(f315(f127(x35611),x35612),f103(x35611,x35613)))
% 168.50/168.37 [3563]E(f315(f315(f148(x35631,x35632),x35633),f315(f315(f153(x35631),x35632),x35633)),x35632)
% 168.50/168.37 [3583]E(f315(f315(f297(x35831),x35832),f315(f315(f297(x35831),x35832),x35833)),f315(f315(f297(x35831),x35832),x35833))
% 168.50/168.37 [3596]E(f315(f315(f297(x35961),x35962),f315(f161(x35961),x35963)),f315(f161(x35961),f315(f315(f140(x35961),x35962),x35963)))
% 168.50/168.37 [3598]E(f315(f315(f127(x35981),x35982),f315(f160(x35981),x35983)),f315(f160(x35981),f315(f315(f127(x35981),x35982),x35983)))
% 168.50/168.37 [3610]E(f315(f315(f164(x36101),f71(a901)),f315(f315(f140(x36101),x36102),x36103)),f315(f315(f140(x36101),x36102),f102(x36101)))
% 168.50/168.37 [3653]E(f315(f56(x36531,x36532),f315(f315(f297(x36531),x36533),f177(f909(x36531,a899)))),x36533)
% 168.50/168.37 [3694]E(f315(f315(f73(a901),x36941),f315(f315(f73(a901),x36942),x36943)),f315(f315(f73(a901),x36942),f315(f315(f73(a901),x36941),x36943)))
% 168.50/168.37 [3695]E(f315(f315(f73(a1),x36951),f315(f315(f73(a1),x36952),x36953)),f315(f315(f73(a1),x36952),f315(f315(f73(a1),x36951),x36953)))
% 168.50/168.37 [3700]E(f315(f315(f242(x37001,x37002),f177(f909(x37001,a899))),x37003),f177(f909(f908(x37001,x37002),a899)))
% 168.50/168.37 [3724]E(f315(f315(f99(f909(x37241,a899)),x37242),x37243),f315(f315(f99(f909(x37241,a899)),x37243),x37242))
% 168.50/168.37 [3725]E(f315(f315(f90(f909(x37251,a899)),x37252),x37253),f315(f315(f90(f909(x37251,a899)),x37253),x37252))
% 168.50/168.37 [3727]E(f315(f315(f123(x37271),x37272),f315(f315(f140(x37271),x37273),f102(x37271))),f315(f156(x37271),f315(f315(f140(x37271),x37273),x37272)))
% 168.50/168.37 [3728]E(f315(f315(f123(x37281),f315(f157(x37281),x37282)),f315(f157(x37281),x37283)),f315(f157(x37281),f315(f315(f123(x37281),x37283),x37282)))
% 168.50/168.37 [3739]E(f315(f160(x37391),f315(f315(f164(x37391),f315(a101,x37392)),x37393)),f315(f315(f164(x37391),x37392),f315(f160(x37391),x37393)))
% 168.50/168.37 [3747]P1(f315(f315(f317(x37471),x37472),f315(f315(f297(x37471),x37472),x37473)))
% 168.50/168.37 [3751]E(f315(f315(f32(x37511,f909(x37512,a899)),f177(f909(x37511,a899))),x37513),f230(f909(x37512,a899)))
% 168.50/168.37 [3754]E(f315(f273(x37541,x37541,f251(x37541,x37542)),x37543),f315(f315(f90(f909(x37541,a899)),x37542),x37543))
% 168.50/168.37 [3768]E(f315(f178(f902(x37681)),f315(f315(f140(x37681),x37682),x37683)),f315(f315(f73(a901),f315(f178(f902(x37681)),x37683)),f315(a101,f2(a901))))
% 168.50/168.37 [3773]E(f103(x37731,f315(f315(f123(x37731),x37732),f315(f315(f140(x37731),x37733),f102(x37731)))),x37732)
% 168.50/168.37 [3774]E(f133(x37741,f315(f315(f123(x37741),x37742),f315(f315(f140(x37741),x37743),f102(x37741)))),x37743)
% 168.50/168.37 [3782]E(f315(f315(f123(x37821),f315(f315(f164(x37821),x37822),x37823)),f315(f315(f127(x37821),x37822),x37823)),x37823)
% 168.50/168.37 [3792]E(f315(f315(f3(a901),f315(f315(f73(a901),x37921),x37922)),f315(f315(f73(a901),x37923),x37922)),f315(f315(f3(a901),x37921),x37923))
% 168.50/168.37 [3793]E(f315(f315(f3(a901),f315(f315(f73(a901),x37931),x37932)),f315(f315(f73(a901),x37931),x37933)),f315(f315(f3(a901),x37932),x37933))
% 168.50/168.37 [3799]E(f315(f315(f123(x37991),f315(f157(x37991),x37992)),f315(f315(f140(x37991),x37993),f102(x37991))),f315(f157(x37991),f315(f315(f140(x37991),x37993),x37992)))
% 168.50/168.37 [3801]E(f315(f315(f73(a901),f315(f178(f902(x38011)),x38012)),f315(f178(f902(x38011)),x38013)),f315(f178(f902(x38011)),f315(f315(f123(x38011),x38012),x38013)))
% 168.50/168.37 [3804]E(f315(f315(f73(a901),f315(f178(f902(x38041)),x38042)),f315(f178(f902(x38041)),x38043)),f315(f178(f902(x38041)),f162(x38041,x38042,x38043)))
% 168.50/168.37 [3811]E(f315(f315(f99(f909(x38111,a899)),f315(f161(x38111),x38112)),f315(f161(x38111),x38113)),f315(f161(x38111),f315(f315(f123(x38111),x38112),x38113)))
% 168.50/168.37 [3812]E(f38(a901,f315(f315(f74(a901),x38121),x38122),f315(f315(f74(a901),x38121),x38123)),f315(f315(f74(a901),x38121),f38(a901,x38122,x38123)))
% 168.50/168.37 [3824]E(f315(f315(f164(x38241),f315(f315(f3(a901),x38242),f71(a901))),f315(f160(x38241),x38243)),f315(f160(x38241),f315(f315(f164(x38241),x38242),x38243)))
% 168.50/168.37 [3829]E(f315(f315(f90(f909(x38291,a899)),x38292),f315(f72(f909(x38291,a899)),x38293)),f315(f315(f3(f909(x38291,a899)),x38292),x38293))
% 168.50/168.37 [3830]E(f315(f315(f3(f909(x38301,a899)),x38302),f315(f72(f909(x38301,a899)),x38303)),f315(f315(f90(f909(x38301,a899)),x38302),x38303))
% 168.50/168.37 [3852]E(f315(f315(f242(x38521,x38522),x38523),f315(f18(f909(x38522,a899),x38521),f177(f909(x38522,a899)))),f177(f909(f908(x38521,x38522),a899)))
% 168.50/168.37 [3854]E(f315(f315(f3(a901),f315(f315(f74(a901),x38541),x38542)),f315(f315(f74(a901),x38541),x38543)),f315(f315(f74(a901),x38541),f315(f315(f3(a901),x38542),x38543)))
% 168.50/168.37 [3855]E(f315(f315(f73(a901),f315(f315(f74(a901),x38551),x38552)),f315(f315(f74(a901),x38551),x38553)),f315(f315(f74(a901),x38551),f315(f315(f73(a901),x38552),x38553)))
% 168.50/168.37 [3856]E(f315(f315(f3(a1),f315(f315(f74(a1),x38561),x38562)),f315(f315(f74(a1),x38561),x38563)),f315(f315(f74(a1),x38561),f315(f315(f3(a1),x38562),x38563)))
% 168.50/168.37 [3857]E(f315(f315(f73(a1),f315(f315(f74(a1),x38571),x38572)),f315(f315(f74(a1),x38571),x38573)),f315(f315(f74(a1),x38571),f315(f315(f73(a1),x38572),x38573)))
% 168.50/168.37 [3858]E(f315(f315(f74(a1),f315(f315(f232(a1),x38581),x38582)),f315(f315(f232(a1),x38581),x38583)),f315(f315(f232(a1),x38581),f315(f315(f73(a901),x38582),x38583)))
% 168.50/168.37 [3872]E(f315(f315(f33(x38721,f909(x38722,a899)),x38723),f315(f18(f909(x38722,a899),x38721),f177(f909(x38722,a899)))),f177(f909(x38722,a899)))
% 168.50/168.37 [3874]E(f38(a901,f315(f315(f74(a901),x38741),x38742),f315(f315(f74(a901),x38743),x38742)),f315(f315(f74(a901),f38(a901,x38741,x38743)),x38742))
% 168.50/168.37 [3879]E(f38(a1,f315(f315(f3(a1),x38791),f38(a1,x38792,x38793)),x38793),f38(a1,f315(f315(f3(a1),x38791),x38792),x38793))
% 168.50/168.37 [3880]E(f38(a1,f315(f315(f74(a1),x38801),f38(a1,x38802,x38803)),x38803),f38(a1,f315(f315(f74(a1),x38801),x38802),x38803))
% 168.50/168.37 [3881]P1(f315(f315(f223(f909(x38811,a899)),x38812),f315(f315(f297(x38811),x38813),x38812)))
% 168.50/168.37 [3956]E(f315(f315(f32(f909(x39561,a899),f909(x39561,a899)),x39562),f315(f99(f909(x39561,a899)),x39563)),f315(f315(f99(f909(x39561,a899)),x39563),f31(f909(x39561,a899),x39562)))
% 168.50/168.37 [3957]E(f315(f315(f33(f909(x39571,a899),f909(x39571,a899)),x39572),f315(f90(f909(x39571,a899)),x39573)),f315(f315(f90(f909(x39571,a899)),x39573),f30(f909(x39571,a899),x39572)))
% 168.50/168.37 [3969]E(f315(f161(x39691),f315(f315(f315(f172(f902(x39691),f902(x39691)),x39692),f156(x39691)),x39693)),f315(f161(x39691),x39693))
% 168.50/168.37 [3973]E(f315(f315(f164(x39731),f315(f178(f902(x39731)),f166(x39731,x39732,x39733))),x39733),f166(x39731,x39732,x39733))
% 168.50/168.37 [3977]E(f315(f178(f902(x39771)),f315(f315(f315(f172(f902(x39771),f902(x39771)),x39772),f156(x39771)),x39773)),f315(f178(f902(x39771)),x39773))
% 168.50/168.37 [3980]E(f315(f315(f245(x39801,x39802,x39802),f315(f18(f909(x39802,x39802),x39801),f7(x39802))),x39803),f315(f244(x39801,x39802),x39803))
% 168.50/168.37 [3986]E(f38(a1,f315(f315(f3(a1),f38(a1,x39861,x39862)),x39863),x39862),f38(a1,f315(f315(f3(a1),x39861),x39863),x39862))
% 168.50/168.37 [3987]E(f38(a1,f315(f315(f232(a1),f38(a1,x39871,x39872)),x39873),x39872),f38(a1,f315(f315(f232(a1),x39871),x39873),x39872))
% 168.50/168.37 [3990]E(f315(f315(f33(f909(f908(x39901,x39902),a899),f909(x39902,a899)),x39903),f272(x39901,x39902)),f315(f272(x39901,x39902),f30(f909(f908(x39901,x39902),a899),x39903)))
% 168.50/168.37 [3991]E(f315(f315(f33(f909(f908(x39911,x39912),a899),f909(x39911,a899)),x39913),f252(x39911,x39912)),f315(f252(x39911,x39912),f30(f909(f908(x39911,x39912),a899),x39913)))
% 168.50/168.37 [4014]E(f315(f66(x40141,x40141,x40141,x40142),f315(f315(f172(x40141,x40141),x40143),x40142)),f315(f315(f172(x40141,x40141),f315(a101,x40143)),x40142))
% 168.50/168.37 [4032]E(f315(f315(f127(x40321),f315(f315(f3(a901),f315(f178(f902(x40321)),x40322)),x40323)),f315(f157(x40321),x40322)),f315(f157(x40321),f315(f315(f164(x40321),x40323),x40322)))
% 168.50/168.37 [4033]E(f315(f315(f164(x40331),f315(f315(f3(a901),f315(f178(f902(x40331)),x40332)),x40333)),f315(f157(x40331),x40332)),f315(f157(x40331),f315(f315(f127(x40331),x40333),x40332)))
% 168.50/168.37 [4035]E(f315(f315(f73(a901),f315(f154(a901),f315(f315(f143(x40351,a901),x40352),x40353))),f315(f178(f902(x40351)),x40353)),f144(x40351,x40352,x40353))
% 168.50/168.37 [4055]E(f315(f156(x40551),f315(f315(f315(f172(f902(x40551),f902(x40551)),x40552),f156(x40551)),x40553)),f315(f315(f315(f172(f902(x40551),f902(x40551)),f315(a101,x40552)),f156(x40551)),x40553))
% 168.50/168.37 [4069]P1(f315(f315(f223(a901),f315(f178(f902(x40691)),f315(f125(x40691,x40692),x40693))),f315(f178(f902(x40691)),x40693)))
% 168.50/168.37 [4085]E(f315(f315(f99(f909(f909(x40851,a899),a899)),f315(f296(x40851),x40852)),f315(f298(f909(x40851,a899),f909(x40851,a899),f315(f297(x40851),x40853)),f315(f296(x40851),x40852))),f315(f296(x40851),f315(f315(f297(x40851),x40853),x40852)))
% 168.50/168.37 [4116]P1(f315(f315(f223(a901),f315(f178(f902(x41161)),f166(x41161,x41162,x41163))),f315(f178(f902(x41161)),x41163)))
% 168.50/168.37 [4123]E(f315(f252(x41231,x41232),f315(f250(f908(x41231,x41232)),f315(f245(x41231,x41232,a899),x41233))),f315(f250(x41231),f315(f315(f10(f909(x41232,a899),a899,x41231),f80(x41232)),x41233)))
% 168.50/168.37 [4135]E(f315(f298(a901,a901,f315(f315(f9(a901,a901,a901),f73(a901)),x41351)),f291(a901,x41352,x41353)),f291(a901,f315(f315(f73(a901),x41352),x41351),f315(f315(f73(a901),x41353),x41351)))
% 168.50/168.37 [4149]E(f315(f298(a901,a901,f315(f315(f9(a901,a901,a901),f73(a901)),x41491)),f315(f290(a901,x41492),x41493)),f315(f290(a901,f315(f315(f73(a901),x41492),x41491)),f315(f315(f73(a901),x41493),x41491)))
% 168.50/168.37 [4167]E(f315(f315(f170(x41671,x41672),f315(f315(f143(f908(x41671,x41672),x41671),f239(x41671,x41672)),x41673)),f315(f315(f143(f908(x41671,x41672),x41672),f244(x41671,x41672)),x41673)),x41673)
% 168.50/168.37 [4172]E(f315(f315(f73(a901),f315(f315(f74(a901),x41721),f38(a901,f315(f315(f29(a901),x41722),x41721),x41723))),f38(a901,x41722,x41721)),f38(a901,x41722,f315(f315(f74(a901),x41721),x41723)))
% 168.50/168.37 [4185]E(f315(f315(f123(x41851),x41852),f315(f131(f902(x41851),f902(x41851),f123(x41851),f102(x41851)),x41853)),f315(f131(f902(x41851),f902(x41851),f123(x41851),x41852),x41853))
% 168.50/168.37 [4206]P1(f315(f315(f317(f908(x42061,x42061)),f315(f315(f240(x42061,x42061),x42062),x42062)),f315(f315(f172(f908(x42061,x42061),a899),f2(a901)),x42063)))
% 168.50/168.37 [4211]E(f315(f250(x42111),f315(f315(f10(f909(x42112,a899),a899,x42111),f80(x42112)),f315(f9(x42112,x42111,a899),x42113))),f315(f272(x42112,x42111),f315(f250(f908(x42112,x42111)),f315(f245(x42112,x42111,a899),x42113))))
% 168.50/168.37 [4228]E(f315(f315(f99(f909(x42281,a899)),f315(f315(f33(a901,f909(x42281,a899)),f291(a901,f71(a901),x42282)),x42283)),f315(x42283,f2(a901))),f315(f315(f33(a901,f909(x42281,a899)),f315(f289(a901),x42282)),x42283))
% 168.50/168.37 [4243]E(f315(f131(f902(x42431),f902(x42431),f123(x42431),f102(x42431)),f315(f315(f143(f902(x42431),f902(x42431)),f125(x42431,x42432)),x42433)),f315(f125(x42431,x42432),f315(f131(f902(x42431),f902(x42431),f123(x42431),f102(x42431)),x42433)))
% 168.50/168.37 [4247]E(f315(f244(f902(x42471),f902(x42471)),f155(x42471,x42472,x42473)),f315(f125(x42471,f315(f66(a899,a899,x42471,a310),x42472)),x42473))
% 168.50/168.37 [4292]E(f315(f315(f73(a1),f315(f315(f73(a1),f315(f315(f74(a1),x42921),f315(f315(f29(a1),x42922),x42921))),f38(a1,x42922,x42921))),x42923),f315(f315(f73(a1),x42922),x42923))
% 168.50/168.37 [4329]E(f315(f315(f73(a1),f315(f315(f73(a1),f315(f315(f74(a1),f315(f315(f29(a1),x43291),x43292)),x43292)),f38(a1,x43291,x43292))),x43293),f315(f315(f73(a1),x43291),x43293))
% 168.50/168.37 [4355]E(f78(f908(x43551,x43552),f315(f245(x43551,x43552,a899),f315(f315(f10(f909(x43552,f908(x43551,x43552)),f909(x43552,a899),x43551),f315(f10(f908(x43551,x43552),a899,x43552),x43553)),f240(x43551,x43552)))),f78(f908(x43551,x43552),x43553))
% 168.50/168.37 [4356]E(f83(f908(x43561,x43562),f315(f245(x43561,x43562,a899),f315(f315(f10(f909(x43562,f908(x43561,x43562)),f909(x43562,a899),x43561),f315(f10(f908(x43561,x43562),a899,x43562),x43563)),f240(x43561,x43562)))),f83(f908(x43561,x43562),x43563))
% 168.50/168.37 [4383]P1(f315(f315(f223(f909(x43831,a899)),f30(f909(x43831,a899),f315(f315(f90(f909(f909(x43831,a899),a899)),x43832),x43833))),f315(f315(f90(f909(x43831,a899)),f30(f909(x43831,a899),x43832)),f30(f909(x43831,a899),x43833))))
% 168.50/168.37 [4384]E(f315(f157(x43841),f315(f315(f315(f172(f902(x43841),f902(x43841)),f315(f315(f3(a901),f315(f178(f902(x43841)),x43842)),f38(a901,x43843,f315(f178(f902(x43841)),x43842)))),f156(x43841)),x43842)),f315(f315(f315(f172(f902(x43841),f902(x43841)),x43843),f156(x43841)),f315(f157(x43841),x43842)))
% 168.50/168.37 [4421]P1(f315(f315(f223(a901),f315(f178(f902(x44211)),f315(f315(f127(x44211),f315(f178(f902(x44211)),f166(x44211,x44212,x44213))),x44213))),f315(f178(f902(x44211)),x44213)))
% 168.50/168.37 [4638]~P1(f315(f55(x46381,x46382,f177(f909(x46381,a899))),x46383))
% 168.50/168.37 [4643]~P1(f315(f315(f317(f908(x46431,x46431)),f315(f315(f240(x46431,x46431),x46432),x46433)),f142(x46431,f102(f909(x46431,a901)))))
% 168.50/168.37 [3740]E(f315(f178(f902(x37401)),f315(f315(f164(x37401),x37402),x37403)),f315(f315(f221(a901),f315(f178(f902(x37401)),x37403)),x37402))
% 168.50/168.37 [3741]E(f315(f178(f902(x37411)),f315(f315(f127(x37411),x37412),x37413)),f315(f315(f3(a901),f315(f178(f902(x37411)),x37413)),x37412))
% 168.50/168.37 [3767]E(f315(f178(f902(f902(x37671))),f48(x37671,x37672,x37673)),f315(f315(f232(a901),f315(f178(f902(x37671)),x37673)),x37672))
% 168.50/168.37 [3785]E(f315(f315(f29(a901),f315(f315(f29(a901),x37851),x37852)),x37853),f315(f315(f29(a901),x37851),f315(f315(f74(a901),x37852),x37853)))
% 168.50/168.37 [3786]E(f315(f315(f3(a901),f315(f315(f3(a901),x37861),x37862)),x37863),f315(f315(f3(a901),x37861),f315(f315(f73(a901),x37862),x37863)))
% 168.50/168.37 [3787]E(f315(f315(f74(a901),f315(f315(f74(a901),x37871),x37872)),x37873),f315(f315(f74(a901),x37871),f315(f315(f74(a901),x37872),x37873)))
% 168.50/168.37 [3788]E(f315(f315(f74(a1),f315(f315(f74(a1),x37881),x37882)),x37883),f315(f315(f74(a1),x37881),f315(f315(f74(a1),x37882),x37883)))
% 168.50/168.37 [3789]E(f315(f315(f73(a901),f315(f315(f73(a901),x37891),x37892)),x37893),f315(f315(f73(a901),x37891),f315(f315(f73(a901),x37892),x37893)))
% 168.50/168.37 [3790]E(f315(f315(f73(a1),f315(f315(f73(a1),x37901),x37902)),x37903),f315(f315(f73(a1),x37901),f315(f315(f73(a1),x37902),x37903)))
% 168.50/168.37 [3791]E(f315(f315(f232(a1),f315(f315(f232(a1),x37911),x37912)),x37913),f315(f315(f232(a1),x37911),f315(f315(f74(a901),x37912),x37913)))
% 168.50/168.37 [3810]E(f151(x38101,f315(f315(f140(f909(x38101,a899)),x38102),x38103)),f163(x38101,x38102,f151(x38101,x38103)))
% 168.50/168.37 [3853]E(f315(f315(f3(a901),f315(f315(f3(a901),x38531),x38532)),x38533),f315(f315(f3(a901),f315(f315(f3(a901),x38531),x38533)),x38532))
% 168.50/168.37 [3861]E(f315(f315(f90(f909(x38611,a899)),x38612),f315(f315(f3(f909(x38611,a899)),x38613),x38612)),f177(f909(x38611,a899)))
% 168.50/168.37 [3865]E(f315(f315(f143(a901,x38651),f315(f18(x38651,a901),x38652)),f128(a901,f315(f290(a901,f2(a901)),x38653))),f158(x38651,x38653,x38652))
% 168.50/168.37 [3903]E(f30(f909(x39031,a899),f315(f315(f297(f909(x39031,a899)),x39032),x39033)),f315(f315(f99(f909(x39031,a899)),x39032),f30(f909(x39031,a899),x39033)))
% 168.50/168.37 [3904]E(f31(f909(x39041,a899),f315(f315(f297(f909(x39041,a899)),x39042),x39043)),f315(f315(f90(f909(x39041,a899)),x39042),f31(f909(x39041,a899),x39043)))
% 168.50/168.37 [3906]E(f158(x39061,f315(f178(f902(x39061)),f315(f125(x39061,f315(a312,x39062)),x39063)),x39062),f315(f125(x39061,f315(a312,x39062)),x39063))
% 168.50/168.37 [3908]E(f315(f315(f3(a901),f315(f315(f74(a901),x39081),x39082)),f315(f315(f74(a901),x39083),x39082)),f315(f315(f74(a901),f315(f315(f3(a901),x39081),x39083)),x39082))
% 168.50/168.37 [3909]E(f315(f315(f73(a901),f315(f315(f74(a901),x39091),x39092)),f315(f315(f74(a901),x39093),x39092)),f315(f315(f74(a901),f315(f315(f73(a901),x39091),x39093)),x39092))
% 168.50/168.37 [3910]E(f315(f315(f3(a1),f315(f315(f74(a1),x39101),x39102)),f315(f315(f74(a1),x39103),x39102)),f315(f315(f74(a1),f315(f315(f3(a1),x39101),x39103)),x39102))
% 168.50/168.37 [3911]E(f315(f315(f73(a1),f315(f315(f74(a1),x39111),x39112)),f315(f315(f74(a1),x39113),x39112)),f315(f315(f74(a1),f315(f315(f73(a1),x39111),x39113)),x39112))
% 168.50/168.37 [3913]E(f315(f315(f221(a901),f315(f315(f3(a901),x39131),x39132)),f315(f315(f3(a901),x39133),x39132)),f315(f315(f3(a901),f315(f315(f221(a901),x39131),x39133)),x39132))
% 168.50/168.37 [3933]E(f315(f315(f90(f909(f902(x39331),a899)),f149(x39331,x39332)),f149(x39331,x39333)),f149(x39331,f315(f315(f90(f909(x39331,a899)),x39332),x39333)))
% 168.50/168.37 [3936]E(f315(f315(f99(f909(x39361,a899)),x39362),f315(f315(f99(f909(x39361,a899)),x39362),x39363)),f315(f315(f99(f909(x39361,a899)),x39362),x39363))
% 168.50/168.37 [3937]E(f315(f315(f99(f909(x39371,a899)),x39372),f315(f315(f3(f909(x39371,a899)),x39373),x39372)),f315(f315(f99(f909(x39371,a899)),x39372),x39373))
% 168.50/168.37 [3938]E(f315(f315(f90(f909(x39381,a899)),x39382),f315(f315(f90(f909(x39381,a899)),x39382),x39383)),f315(f315(f90(f909(x39381,a899)),x39382),x39383))
% 168.50/168.37 [3950]E(f315(f315(f277(x39501,x39502,x39502),x39503),f295(x39502,f177(f909(f908(x39502,x39502),a899)))),x39503)
% 168.50/168.37 [3953]E(f315(f315(f99(f909(x39531,a899)),f315(f315(f297(x39531),x39532),f177(f909(x39531,a899)))),x39533),f315(f315(f297(x39531),x39532),x39533))
% 168.50/168.37 [3972]E(f315(f315(f3(a901),f315(f315(f3(a901),f315(a101,x39721)),x39722)),f315(a101,x39723)),f315(f315(f3(a901),f315(f315(f3(a901),x39721),x39722)),x39723))
% 168.50/168.37 [3999]E(f315(f315(f90(f909(f909(x39991,a899),a899)),f315(f296(x39991),x39992)),f315(f296(x39991),x39993)),f315(f296(x39991),f315(f315(f90(f909(x39991,a899)),x39992),x39993)))
% 168.50/168.37 [4002]E(f315(f315(f99(f909(x40021,a899)),f315(f72(f909(x40021,a899)),x40022)),x40023),f315(f72(f909(x40021,a899)),f315(f315(f3(f909(x40021,a899)),x40022),x40023)))
% 168.50/168.37 [4011]E(f315(f315(f297(x40111),x40112),f315(f315(f3(f909(x40111,a899)),x40113),f315(f315(f297(x40111),x40112),f177(f909(x40111,a899))))),f315(f315(f297(x40111),x40112),x40113))
% 168.50/168.37 [4021]P1(f315(f315(f223(f909(x40211,a899)),x40212),f315(f315(f99(f909(x40211,a899)),x40213),x40212)))
% 168.50/168.37 [4022]P1(f315(f315(f223(f909(x40221,a899)),x40222),f315(f315(f99(f909(x40221,a899)),x40222),x40223)))
% 168.50/168.37 [4026]E(f315(f315(f90(f909(x40261,a899)),f315(f72(f909(x40261,a899)),x40262)),f315(f72(f909(x40261,a899)),x40263)),f315(f72(f909(x40261,a899)),f315(f315(f99(f909(x40261,a899)),x40262),x40263)))
% 168.50/168.37 [4027]E(f315(f315(f99(f909(x40271,a899)),f315(f72(f909(x40271,a899)),x40272)),f315(f72(f909(x40271,a899)),x40273)),f315(f72(f909(x40271,a899)),f315(f315(f90(f909(x40271,a899)),x40272),x40273)))
% 168.50/168.37 [4041]P1(f315(f315(f223(f909(x40411,a899)),f315(f161(x40411),x40412)),f315(f161(x40411),f315(f315(f140(x40411),x40413),x40412))))
% 168.50/168.37 [4053]E(f315(f315(f99(f909(x40531,a899)),f315(f315(f3(f909(x40531,a899)),x40532),x40533)),f315(f315(f90(f909(x40531,a899)),x40532),x40533)),x40532)
% 168.50/168.37 [4103]E(f315(f315(f8(x41031,a1),f315(f315(f10(a901,a1,x41031),f89(a1)),x41032)),x41033),f315(f89(a1),f315(f315(f8(x41031,a901),x41032),x41033)))
% 168.50/168.37 [4104]E(f315(f315(f11(x41041,a1),f315(f315(f10(a901,a1,x41041),f89(a1)),x41042)),x41043),f315(f89(a1),f315(f315(f11(x41041,a901),x41042),x41043)))
% 168.50/168.37 [4151]E(f315(f315(f123(x41511),f166(x41511,x41512,x41513)),f315(f315(f127(x41511),f315(f178(f902(x41511)),f166(x41511,x41512,x41513))),x41513)),x41513)
% 168.50/168.37 [4155]E(f315(f72(f909(f908(x41551,x41552),a899)),f315(f315(f242(x41551,x41552),x41553),f315(f18(f909(x41552,a899),x41551),f230(f909(x41552,a899))))),f315(f315(f242(x41551,x41552),f315(f72(f909(x41551,a899)),x41553)),f315(f18(f909(x41552,a899),x41551),f230(f909(x41552,a899)))))
% 168.50/168.37 [4156]E(f315(f72(f909(f908(x41561,x41562),a899)),f315(f315(f242(x41561,x41562),f230(f909(x41561,a899))),f315(f18(f909(x41562,a899),x41561),x41563))),f315(f315(f242(x41561,x41562),f230(f909(x41561,a899))),f315(f18(f909(x41562,a899),x41561),f315(f72(f909(x41562,a899)),x41563))))
% 168.50/168.37 [4207]E(f315(f315(f33(f909(x42071,a899),f909(x42071,a899)),x42072),f315(f315(f9(f909(x42071,a899),f909(x42071,a899),f909(x42071,a899)),f90(f909(x42071,a899))),x42073)),f315(f315(f90(f909(x42071,a899)),f30(f909(x42071,a899),x42072)),x42073))
% 168.50/168.37 [4213]E(f315(f131(f902(x42131),f902(x42131),f123(x42131),f102(x42131)),f315(f315(f140(f902(x42131)),x42132),x42133)),f315(f315(f123(x42131),x42132),f315(f131(f902(x42131),f902(x42131),f123(x42131),f102(x42131)),x42133)))
% 168.50/168.37 [4234]E(f315(f315(f297(f909(x42341,a899)),f315(f273(x42341,x42341,x42342),f315(f315(f297(x42341),x42343),f177(f909(x42341,a899))))),f177(f909(f909(x42341,a899),a899))),f315(f315(f53(x42341),f315(f315(f297(x42341),x42343),f177(f909(x42341,a899)))),x42342))
% 168.50/168.37 [4244]E(f315(f315(f73(a901),f315(f315(f74(a901),x42441),f315(f315(f29(a901),x42442),x42443))),f315(f315(f29(a901),f315(f315(f74(a901),x42441),f38(a901,x42442,x42443))),x42443)),f315(f315(f29(a901),f315(f315(f74(a901),x42441),x42442)),x42443))
% 168.50/168.37 [4245]E(f315(f315(f73(a1),f315(f315(f74(a1),x42451),f315(f315(f29(a1),x42452),x42453))),f315(f315(f29(a1),f315(f315(f74(a1),x42451),f38(a1,x42452,x42453))),x42453)),f315(f315(f29(a1),f315(f315(f74(a1),x42451),x42452)),x42453))
% 168.50/168.37 [4277]E(f315(f315(f3(f909(x42771,a899)),f315(f161(x42771),x42772)),f315(f315(f297(x42771),x42773),f177(f909(x42771,a899)))),f315(f161(x42771),f315(f125(x42771,f315(f315(f10(a899,a899,x42771),a310),f315(a312,x42773))),x42772)))
% 168.50/168.37 [4327]E(f315(f315(f123(x43271),f315(f131(f902(x43271),f902(x43271),f123(x43271),f102(x43271)),x43272)),f315(f131(f902(x43271),f902(x43271),f123(x43271),f102(x43271)),x43273)),f315(f131(f902(x43271),f902(x43271),f123(x43271),f102(x43271)),f315(f315(f123(f902(x43271)),x43272),x43273)))
% 168.50/168.37 [4330]E(f315(f315(f240(f902(x43301),f902(x43301)),f315(f125(x43301,x43302),x43303)),f315(f125(x43301,f315(f66(a899,a899,x43301,a310),x43302)),x43303)),f155(x43301,x43302,x43303))
% 168.50/168.37 [4333]E(f315(f315(f73(a901),f315(f315(f73(a901),f315(f315(f29(a901),x43331),x43332)),f315(f315(f29(a901),x43333),x43332))),f315(f315(f29(a901),f315(f315(f73(a901),f38(a901,x43331,x43332)),f38(a901,x43333,x43332))),x43332)),f315(f315(f29(a901),f315(f315(f73(a901),x43331),x43333)),x43332))
% 168.50/168.37 [4334]E(f315(f315(f73(a1),f315(f315(f73(a1),f315(f315(f29(a1),x43341),x43342)),f315(f315(f29(a1),x43343),x43342))),f315(f315(f29(a1),f315(f315(f73(a1),f38(a1,x43341,x43342)),f38(a1,x43343,x43342))),x43342)),f315(f315(f29(a1),f315(f315(f73(a1),x43341),x43343)),x43342))
% 168.50/168.37 [4387]E(f315(f315(f90(f909(f902(x43871),a899)),f315(f315(f9(f902(x43871),f909(f902(x43871),a899),a899),f317(f902(x43871))),f150(x43871,x43872))),f315(f315(f9(f902(x43871),f909(f902(x43871),a899),a899),f317(f902(x43871))),f150(x43871,x43873))),f149(x43871,f315(f315(f90(f909(x43871,a899)),f315(f315(f9(x43871,f909(x43871,a899),a899),f317(x43871)),x43872)),f315(f315(f9(x43871,f909(x43871,a899),a899),f317(x43871)),x43873))))
% 168.50/168.37 [4399]E(f315(f250(x43991),f315(f315(f20(x43991,a899,a899),f315(f315(f10(a899,f909(a899,a899),x43991),a314),f315(f315(f9(x43991,x43991,a899),a312),x43992))),f315(f315(f9(x43991,f909(x43991,a899),a899),f317(x43991)),x43993))),f315(f315(f297(x43991),x43992),x43993))
% 168.50/168.37 [4419]E(f315(f315(f79(f902(f902(x44191)),f902(f902(x44191))),f47(x44191,x44192)),f315(f315(f20(f902(f902(x44191)),f902(f902(x44191)),f902(f902(x44191))),f315(f315(f10(f902(f902(x44191)),f909(f902(f902(x44191)),f902(f902(x44191))),f902(f902(x44191))),f123(f902(x44191))),f315(f143(f902(x44191),f902(x44191)),f315(f140(x44191),x44193)))),f7(f902(f902(x44191))))),f47(x44191,f315(f315(f140(x44191),x44193),x44192)))
% 168.50/168.37 [4422]E(f315(f250(x44221),f315(f315(f20(x44221,a899,a899),f315(f315(f10(a899,f909(a899,a899),x44221),a314),f315(f315(f9(x44221,f909(x44221,a899),a899),f317(x44221)),x44222))),f315(f315(f9(x44221,f909(x44221,a899),a899),f317(x44221)),x44223))),f315(f315(f99(f909(x44221,a899)),x44222),x44223))
% 168.50/168.37 [4423]E(f315(f250(x44231),f315(f315(f20(x44231,a899,a899),f315(f315(f10(a899,f909(a899,a899),x44231),a313),f315(f315(f9(x44231,f909(x44231,a899),a899),f317(x44231)),x44232))),f315(f315(f9(x44231,f909(x44231,a899),a899),f317(x44231)),x44233))),f315(f315(f90(f909(x44231,a899)),x44232),x44233))
% 168.50/168.37 [4512]E(f315(f315(f33(x45121,f909(f909(x45121,a899),a899)),x45122),f315(f315(f9(x45121,f909(f909(x45121,a899),a899),f909(f909(x45121,a899),a899)),f315(f315(f10(f909(x45121,a899),f909(f909(f909(x45121,a899),a899),f909(f909(x45121,a899),a899)),x45121),f297(f909(x45121,a899))),f315(f315(f10(f909(x45121,a899),f909(x45121,a899),x45121),f273(x45121,x45121,x45123)),f315(f315(f9(x45121,f909(x45121,a899),f909(x45121,a899)),f297(x45121)),f177(f909(x45121,a899)))))),f177(f909(f909(x45121,a899),a899)))),f315(f315(f53(x45121),x45122),x45123))
% 168.50/168.37 [4514]E(f315(f315(f190(x45141),f315(f315(f74(a1),f315(f315(f66(f908(a1,a1),a1,x45141,f239(a1,a1)),f201(x45141)),x45142)),f315(f315(f66(f908(a1,a1),a1,x45141,f239(a1,a1)),f201(x45141)),x45143))),f315(f315(f74(a1),f315(f315(f66(f908(a1,a1),a1,x45141,f244(a1,a1)),f201(x45141)),x45142)),f315(f315(f66(f908(a1,a1),a1,x45141,f244(a1,a1)),f201(x45141)),x45143))),f217(x45141,x45142,x45143))
% 168.50/168.37 [4517]E(f315(f250(f902(x45171)),f315(f315(f20(f902(x45171),a899,a899),f315(f315(f10(a899,f909(a899,a899),f902(x45171)),a313),f315(f315(f9(f902(x45171),a901,a899),f315(f315(f10(a901,f909(a901,a899),f902(x45171)),a312),f178(f902(x45171)))),x45172))),f315(f315(f9(f902(x45171),f909(x45171,a899),a899),f315(f315(f10(f909(x45171,a899),f909(f909(x45171,a899),a899),f902(x45171)),f223(f909(x45171,a899))),f161(x45171))),f315(f161(x45171),x45173)))),f315(f161(f902(x45171)),f48(x45171,x45172,x45173)))
% 168.50/168.37 [3926]E(f38(a901,f315(f315(f73(a901),f315(f315(f74(a901),x39261),x39262)),x39263),x39262),f38(a901,x39263,x39262))
% 168.50/168.37 [3971]E(f128(a901,f315(f290(a901,f315(f315(f73(a901),x39711),x39712)),x39713)),f315(f315(f127(a901),x39712),f128(a901,f315(f290(a901,x39711),x39713))))
% 168.50/168.37 [4010]E(f315(f315(f73(a1),f315(f89(a1),x40101)),f315(f315(f73(a1),f315(f89(a1),x40102)),x40103)),f315(f315(f73(a1),f315(f89(a1),f315(f315(f73(a901),x40101),x40102))),x40103))
% 168.50/168.37 [4017]E(f315(f315(f99(f909(x40171,a899)),f315(f315(f3(f909(x40171,a899)),x40172),x40173)),x40173),f315(f315(f99(f909(x40171,a899)),x40172),x40173))
% 168.50/168.37 [4018]E(f315(f315(f3(f909(x40181,a899)),f315(f315(f3(f909(x40181,a899)),x40182),x40183)),x40183),f315(f315(f3(f909(x40181,a899)),x40182),x40183))
% 168.50/168.37 [4042]E(f315(f315(f277(x40421,x40421,x40422),f295(x40421,f177(f909(f908(x40421,x40421),a899)))),x40423),x40423)
% 168.50/168.37 [4050]E(f315(f315(f99(f909(x40501,a899)),f315(f269(x40501),x40502)),f315(f269(x40501),x40503)),f315(f269(x40501),f315(f315(f99(f909(f908(x40501,x40501),a899)),x40502),x40503)))
% 168.50/168.37 [4060]E(f254(x40601,f315(f315(f140(f908(a88,x40601)),f315(f315(f240(a88,x40601),f2(a88)),x40602)),x40603)),f254(x40601,x40603))
% 168.50/168.37 [4062]E(f315(f315(f99(f909(x40621,a899)),f30(f909(x40621,a899),x40622)),f30(f909(x40621,a899),x40623)),f30(f909(x40621,a899),f315(f315(f99(f909(f909(x40621,a899),a899)),x40622),x40623)))
% 168.50/168.37 [4063]E(f315(f315(f90(f909(x40631,a899)),f31(f909(x40631,a899),x40632)),f31(f909(x40631,a899),x40633)),f31(f909(x40631,a899),f315(f315(f99(f909(f909(x40631,a899),a899)),x40632),x40633)))
% 168.50/168.37 [4100]E(f315(f315(f277(x41001,x41001,x41001),f315(f315(f172(f908(x41001,x41001),a899),x41002),x41003)),x41003),f315(f315(f172(f908(x41001,x41001),a899),f315(a101,x41002)),x41003))
% 168.50/168.37 [4143]P1(f315(f315(f223(f909(x41431,a899)),f315(f315(f3(f909(x41431,a899)),x41432),x41433)),x41432))
% 168.50/168.37 [4144]P1(f315(f315(f223(f909(x41441,a899)),f315(f315(f90(f909(x41441,a899)),x41442),x41443)),x41443))
% 168.50/168.37 [4145]P1(f315(f315(f223(f909(x41451,a899)),f315(f315(f90(f909(x41451,a899)),x41452),x41453)),x41452))
% 168.50/168.37 [4169]E(f295(x41691,f315(f315(f99(f909(f908(x41691,x41691),a899)),f295(x41691,x41692)),f295(x41691,x41693))),f295(x41691,f315(f315(f99(f909(f908(x41691,x41691),a899)),x41692),x41693)))
% 168.50/168.37 [4173]E(f30(f909(x41731,a899),f315(f315(f297(f909(x41731,a899)),x41732),f315(f315(f297(f909(x41731,a899)),x41733),f177(f909(f909(x41731,a899),a899))))),f315(f315(f99(f909(x41731,a899)),x41732),x41733))
% 168.50/168.37 [4174]E(f31(f909(x41741,a899),f315(f315(f297(f909(x41741,a899)),x41742),f315(f315(f297(f909(x41741,a899)),x41743),f177(f909(f909(x41741,a899),a899))))),f315(f315(f90(f909(x41741,a899)),x41742),x41743))
% 168.50/168.37 [4179]E(f315(f315(f277(x41791,x41791,x41791),f315(f315(f172(f908(x41791,x41791),a899),x41792),x41793)),x41793),f315(f315(f277(x41791,x41791,x41791),x41793),f315(f315(f172(f908(x41791,x41791),a899),x41792),x41793)))
% 168.50/168.37 [4248]E(f315(f315(f99(f909(x42481,a899)),f315(f250(x42481),f315(f315(f9(x42481,x42481,a899),a312),x42482))),x42483),f315(f315(f297(x42481),x42482),x42483))
% 168.50/168.37 [4250]E(f315(a93,f315(f315(f8(x42501,a1),f315(f315(f10(a901,a1,x42501),f89(a1)),x42502)),x42503)),f315(f315(f8(x42501,a901),x42502),x42503))
% 168.50/168.37 [4251]E(f315(a93,f315(f315(f11(x42511,a1),f315(f315(f10(a901,a1,x42511),f89(a1)),x42512)),x42513)),f315(f315(f11(x42511,a901),x42512),x42513))
% 168.50/168.37 [4324]E(f315(f145(f902(x43241),x43241,f315(f160(x43241),x43242),f315(f18(f909(f902(x43241),f902(x43241)),x43241),f315(f315(f9(f902(x43241),f902(x43241),f902(x43241)),f123(x43241)),x43242))),x43243),f315(f160(x43241),f315(f315(f123(x43241),x43243),x43242)))
% 168.50/168.37 [4352]P1(f315(f315(f223(f909(f909(x43521,a899),a899)),f315(f315(f99(f909(f909(x43521,a899),a899)),f315(f296(x43521),x43522)),f315(f296(x43521),x43523))),f315(f296(x43521),f315(f315(f99(f909(x43521,a899)),x43522),x43523))))
% 168.50/168.37 [4441]E(f315(f250(x44411),f315(f315(f20(x44411,a899,a899),f315(f315(f10(a899,f909(a899,a899),x44411),a313),f315(f315(f9(x44411,f909(x44411,a899),a899),f317(x44411)),x44412))),f315(f315(f10(a899,a899,x44411),a310),f315(f315(f9(x44411,f909(x44411,a899),a899),f317(x44411)),x44413)))),f315(f315(f3(f909(x44411,a899)),x44412),x44413))
% 168.50/168.37 [4465]E(f315(f28(a901),f315(f250(a901),f315(f315(f20(a901,a899,a899),f315(f315(f10(a899,f909(a899,a899),a901),a313),f315(f315(f9(a901,a901,a899),f224(a901)),f315(f178(f902(x44651)),x44652)))),f315(f315(f10(x44651,a899,a901),x44653),f315(f153(x44651),x44652))))),f315(f178(f902(x44651)),f315(f125(x44651,x44653),x44652)))
% 168.50/168.37 [4467]E(f315(f178(f902(x44671)),f165(x44671,x44672,x44673)),f315(f28(a901),f315(f250(a901),f315(f315(f20(a901,a899,a899),f315(f315(f10(a899,f909(a899,a899),a901),a313),f315(f315(f9(a901,a901,a899),f224(a901)),f315(f178(f902(x44671)),x44672)))),f315(f315(f9(a901,f909(a901,a899),a899),f317(a901)),x44673)))))
% 168.50/168.37 [4563]E(f315(f315(f90(f909(f908(f902(x45631),f902(x45631)),a899)),f315(f298(f908(f908(x45631,f902(x45631)),f908(x45631,f902(x45631))),f908(f902(x45631),f902(x45631)),f246(f908(x45631,f902(x45631)),f902(x45631),f908(x45631,f902(x45631)),f902(x45631),f315(f245(x45631,f902(x45631),f902(x45631)),f140(x45631)),f315(f245(x45631,f902(x45631),f902(x45631)),f140(x45631)))),f307(x45631,f902(x45631),x45632,f315(f132(x45631,x45632),x45633)))),f315(f250(f908(f902(x45631),f902(x45631))),f315(f245(f902(x45631),f902(x45631),a899),f315(f315(f9(f902(x45631),f909(f902(x45631),a899),f909(f902(x45631),a899)),f315(f315(f10(f909(a899,a899),f909(f909(f902(x45631),a899),f909(f902(x45631),a899)),f902(x45631)),f10(a899,a899,f902(x45631))),f315(f315(f10(a899,f909(a899,a899),f902(x45631)),a313),f315(f315(f9(f902(x45631),a901,a899),f315(f315(f10(a901,f909(a901,a899),f902(x45631)),a312),f178(f902(x45631)))),f315(a101,x45633))))),f315(f315(f9(f902(x45631),a901,a899),f315(f315(f10(a901,f909(a901,a899),f902(x45631)),a312),f178(f902(x45631)))),f315(a101,x45633)))))),f315(f132(x45631,x45632),f315(a101,x45633)))
% 168.50/168.37 [4064]E(f38(a901,f315(a101,f315(f315(f73(a901),f315(f315(f74(a901),x40641),x40642)),x40643)),x40642),f38(a901,f315(a101,x40643),x40642))
% 168.50/168.37 [4310]E(f315(f250(x43101),f315(f315(f20(x43101,a899,a899),f315(f315(f10(a899,f909(a899,a899),x43101),a313),x43102)),x43103)),f315(f315(f90(f909(x43101,a899)),f315(f250(x43101),x43102)),f315(f250(x43101),x43103)))
% 168.50/168.37 [4311]E(f315(f250(x43111),f315(f315(f20(x43111,a899,a899),f315(f315(f10(a899,f909(a899,a899),x43111),a314),x43112)),x43113)),f315(f315(f99(f909(x43111,a899)),f315(f250(x43111),x43112)),f315(f250(x43111),x43113)))
% 168.50/168.37 [4313]E(f315(f315(f123(x43131),f315(f315(f127(x43131),f38(a901,x43132,f315(f178(f902(x43131)),x43133))),x43133)),f315(f315(f164(x43131),f38(a901,x43132,f315(f178(f902(x43131)),x43133))),x43133)),f315(f315(f315(f172(f902(x43131),f902(x43131)),x43132),f156(x43131)),x43133))
% 168.50/168.37 [4319]E(f315(f250(x43191),f315(f315(f20(x43191,a899,a899),f315(f315(f10(a899,f909(a899,a899),x43191),a318),x43192)),x43193)),f315(f315(f99(f909(x43191,a899)),f315(f72(f909(x43191,a899)),f315(f250(x43191),x43192))),f315(f250(x43191),x43193)))
% 168.50/168.37 [4335]E(f315(f315(f73(a901),f315(f178(f902(x43351)),f315(f125(x43351,x43352),x43353))),f315(f178(f902(x43351)),f315(f125(x43351,f315(f315(f10(a899,a899,x43351),a310),x43352)),x43353))),f315(f178(f902(x43351)),x43353))
% 168.50/168.37 [4358]P1(f315(f315(f223(f909(x43581,a899)),f315(f315(f99(f909(x43581,a899)),f31(f909(x43581,a899),x43582)),f31(f909(x43581,a899),x43583))),f31(f909(x43581,a899),f315(f315(f90(f909(f909(x43581,a899),a899)),x43582),x43583))))
% 168.50/168.37 [4372]E(f315(f161(x43721),f315(f125(x43721,f315(f315(f10(a899,a899,x43721),a310),f315(f315(f9(x43721,x43721,a899),a312),x43722))),x43723)),f315(f315(f3(f909(x43721,a899)),f315(f161(x43721),x43723)),f315(f315(f297(x43721),x43722),f177(f909(x43721,a899)))))
% 168.50/168.37 [4381]P1(f315(f315(f223(f909(f908(x43811,x43811),a899)),f315(f315(f99(f909(f908(x43811,x43811),a899)),f295(x43811,x43812)),f295(x43811,x43813))),f295(x43811,f315(f315(f99(f909(f908(x43811,x43811),a899)),x43812),x43813))))
% 168.50/168.37 [4404]E(f315(f315(f74(a901),f315(a101,f315(a101,f2(a901)))),f315(f315(f8(a901,a901),f315(f315(f10(a901,a901,a901),f315(f73(a901),x44041)),f315(f315(f9(a901,a901,a901),f74(a901)),x44042))),f315(f270(a901),x44043))),f315(f315(f74(a901),x44043),f315(f315(f73(a901),x44041),f315(f315(f73(a901),x44041),f315(f315(f74(a901),f315(f315(f3(a901),x44043),f71(a901))),x44042)))))
% 168.50/168.37 [4414]E(f315(f250(x44141),f315(f315(f20(x44141,a899,a899),f315(f315(f10(a899,f909(a899,a899),x44141),a313),f315(f315(f9(x44141,f909(x44141,a899),a899),f317(x44141)),f315(f161(x44141),x44142)))),x44143)),f315(f161(x44141),f315(f125(x44141,x44143),x44142)))
% 168.50/168.37 [4562]E(f315(f250(x45621),f315(f315(f10(f909(a901,a899),a899,x45621),f80(a901)),f315(f315(f9(x45621,f909(a901,a899),f909(a901,a899)),f315(f315(f10(f909(a901,f909(a899,a899)),f909(f909(a901,a899),f909(a901,a899)),x45621),f20(a901,a899,a899)),f315(f315(f10(f909(a901,a899),f909(a901,f909(a899,a899)),x45621),f315(f10(a899,f909(a899,a899),a901),a313)),f315(f315(f9(x45621,f909(a901,x45621),f909(a901,a899)),f315(f315(f10(f909(x45621,a899),f909(f909(a901,x45621),f909(a901,a899)),x45621),f10(x45621,a899,a901)),a312)),f315(f153(x45621),x45622))))),f315(f315(f20(a901,a899,a899),f315(f315(f10(a899,f909(a899,a899),a901),a313),f315(f315(f9(a901,a901,a899),f224(a901)),f315(f178(f902(x45621)),x45622)))),f315(f315(f9(a901,f909(a901,a899),a899),f317(a901)),x45623))))),f315(f161(x45621),f165(x45621,x45622,x45623)))
% 168.50/168.37 [4454]E(f315(f250(x44541),f315(f315(f20(x44541,a899,a899),f315(f315(f10(a899,f909(a899,a899),x44541),a318),f315(f315(f10(a899,a899,x44541),a310),f315(f315(f9(x44541,x44541,a899),a312),x44542)))),x44543)),f315(f315(f297(x44541),x44542),f315(f250(x44541),x44543)))
% 168.50/168.37 [4486]E(f315(f315(f143(f908(x44861,a901),x44861),f239(x44861,a901)),f315(f125(f908(x44861,a901),f315(f315(f9(f908(x44861,a901),f909(a901,a899),a899),f315(f315(f10(a901,f909(f909(a901,a899),a899),f908(x44861,a901)),f317(a901)),f244(x44861,a901))),x44862)),f315(f315(f170(x44861,a901),x44863),f128(a901,f315(f290(a901,f2(a901)),f315(f178(f902(x44861)),x44863)))))),f165(x44861,x44863,x44862))
% 168.50/168.37 [4513]E(f315(f315(f74(a1),f315(f92(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),f315(f315(f8(a901,a1),f315(f315(f10(a1,a1,a901),f315(f73(a1),x45131)),f315(f315(f9(a901,a1,a1),f315(f315(f10(a1,f909(a1,a1),a901),f74(a1)),f89(a1))),x45132))),f315(f270(a901),x45133))),f315(f315(f74(a1),f315(f89(a1),x45133)),f315(f315(f73(a1),x45131),f315(f315(f73(a1),x45131),f315(f315(f74(a1),f315(f89(a1),f315(f315(f3(a901),x45133),f71(a901)))),x45132)))))
% 168.50/168.37 [4555]E(f315(f250(f908(x45551,x45552)),f315(f245(x45551,x45552,a899),f315(f315(f9(x45551,f909(f908(x45552,x45551),a899),f909(x45552,a899)),f315(f315(f10(f909(x45552,f909(f909(f908(x45552,x45551),a899),a899)),f909(f909(f908(x45552,x45551),a899),f909(x45552,a899)),x45551),f9(x45552,f909(f908(x45552,x45551),a899),a899)),f315(f315(f10(f909(x45552,f908(x45552,x45551)),f909(x45552,f909(f909(f908(x45552,x45551),a899),a899)),x45551),f315(f10(f908(x45552,x45551),f909(f909(f908(x45552,x45551),a899),a899),x45552),f317(f908(x45552,x45551)))),f315(f9(x45552,x45551,f908(x45552,x45551)),f240(x45552,x45551))))),x45553))),f315(f274(x45552,x45551),x45553))
% 168.50/168.37 [4575]E(f315(f250(f902(x45751)),f315(f315(f10(f909(x45751,a899),a899,f902(x45751)),f80(x45751)),f315(f315(f10(f909(x45751,f909(f902(x45751),a899)),f909(x45751,a899),f902(x45751)),f315(f10(f909(f902(x45751),a899),a899,x45751),f80(f902(x45751)))),f315(f315(f9(f902(x45751),f909(x45751,f909(f902(x45751),a899)),f909(x45751,f909(f902(x45751),a899))),f315(f315(f10(f909(x45751,f909(f909(f902(x45751),a899),f909(f902(x45751),a899))),f909(f909(x45751,f909(f902(x45751),a899)),f909(x45751,f909(f902(x45751),a899))),f902(x45751)),f20(x45751,f909(f902(x45751),a899),f909(f902(x45751),a899))),f315(f315(f10(f909(x45751,f909(f902(x45751),f909(a899,a899))),f909(x45751,f909(f909(f902(x45751),a899),f909(f902(x45751),a899))),f902(x45751)),f315(f10(f909(f902(x45751),f909(a899,a899)),f909(f909(f902(x45751),a899),f909(f902(x45751),a899)),x45751),f20(f902(x45751),a899,a899))),f315(f315(f10(f909(x45751,f909(f902(x45751),a899)),f909(x45751,f909(f902(x45751),f909(a899,a899))),f902(x45751)),f315(f10(f909(f902(x45751),a899),f909(f902(x45751),f909(a899,a899)),x45751),f315(f10(a899,f909(a899,a899),f902(x45751)),a313))),f315(f315(f9(f902(x45751),f909(x45751,f909(f902(x45751),f902(x45751))),f909(x45751,f909(f902(x45751),a899))),f315(f315(f10(f909(f909(f902(x45751),f902(x45751)),f909(f902(x45751),a899)),f909(f909(x45751,f909(f902(x45751),f902(x45751))),f909(x45751,f909(f902(x45751),a899))),f902(x45751)),f10(f909(f902(x45751),f902(x45751)),f909(f902(x45751),a899),x45751)),f315(f315(f10(f909(f902(x45751),a899),f909(f909(f902(x45751),f902(x45751)),f909(f902(x45751),a899)),f902(x45751)),f10(f902(x45751),a899,f902(x45751))),a312))),f140(x45751)))))),f315(f315(f9(x45751,f909(f902(x45751),a899),f909(f902(x45751),a899)),f315(f315(f10(f909(a899,a899),f909(f909(f902(x45751),a899),f909(f902(x45751),a899)),x45751),f10(a899,a899,f902(x45751))),f315(f315(f10(a899,f909(a899,a899),x45751),a313),f315(f315(f9(x45751,f909(x45751,a899),a899),f317(x45751)),x45752)))),f315(f315(f9(f902(x45751),f909(f902(x45751),a899),a899),f317(f902(x45751))),x45753)))))),f163(x45751,x45752,x45753))
% 168.50/168.37 [4572]E(f315(f315(f79(a1,f908(a1,a1)),f315(f315(f3(a1),x45721),x45722)),f315(f315(f9(a1,f908(a1,a1),f908(a1,a1)),f315(f315(f20(a1,f908(a1,a1),f909(f908(a1,a1),f908(a1,a1))),f315(f315(f10(a899,f909(f908(a1,a1),f909(f908(a1,a1),f908(a1,a1))),a1),f85(f908(a1,a1))),f315(f223(a1),f2(a1)))),f315(f240(a1,a1),f315(f315(f73(a1),f315(f315(f74(a1),f315(f92(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),x45723)),f71(a1))))),f315(f315(f240(a1,a1),f315(f315(f74(a1),f315(f92(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),x45723)),x45721))),f315(f36(x45722),f315(f315(f240(a1,a1),x45723),x45721)))
% 168.50/168.37 [3626]E(f105(x36261,f315(x36262,x36263),f315(x36264,x36263)),f315(f192(x36261,x36262,x36264),x36263))
% 168.50/168.37 [3679]E(f315(f315(f233(x36791,x36792,x36793),x36794),f2(a901)),x36792)
% 168.50/168.37 [3717]E(f174(x37171,x37172,x37173,f315(a101,x37174)),f315(x37173,x37174))
% 168.50/168.37 [3759]E(f159(x37591,x37592,f159(x37591,x37593,x37594)),f159(x37591,x37593,f159(x37591,x37592,x37594)))
% 168.50/168.37 [3760]E(f115(x37601,x37602,f105(x37601,x37603,x37604)),f105(x37601,f115(x37601,x37602,x37603),x37604))
% 168.50/168.37 [3894]E(f315(f145(x38941,x38942,x38943,x38944),f102(x38942)),x38943)
% 168.50/168.37 [3895]E(f315(f131(x38951,x38952,x38953,x38954),f102(x38952)),x38954)
% 168.50/168.37 [3932]E(f315(f178(f906(x39321,x39322)),f209(x39321,x39322,x39323,x39324)),f2(a901))
% 168.50/168.37 [3955]E(f315(f245(x39551,x39552,x39553),f243(x39551,x39552,x39553,x39554)),x39554)
% 168.50/168.37 [3998]E(f315(f315(f123(x39981),f158(x39981,x39982,x39983)),f158(x39981,x39984,x39983)),f315(f315(f123(x39981),f158(x39981,x39984,x39983)),f158(x39981,x39982,x39983)))
% 168.50/168.37 [4083]E(f315(f315(f247(x40831,x40832,x40833,f908(x40832,x40833)),x40834),f240(x40832,x40833)),x40834)
% 168.50/168.37 [4093]E(f116(x40931,x40932,x40933,x40934,f108(x40932)),x40933)
% 168.50/168.37 [4099]E(f68(x40991,x40992,x40993,x40994,f315(x40993,x40994)),x40993)
% 168.50/168.37 [4365]P44(x43651,x43652,x43653,x43654,f177(f909(x43651,a899)),x43654)
% 168.50/168.37 [3431]E(f315(f315(f18(x34311,x34312),x34313),x34314),x34313)
% 168.50/168.37 [3707]E(f159(x37071,x37072,f315(f125(x37071,x37073),x37074)),f315(f125(x37071,x37073),f159(x37071,x37072,x37074)))
% 168.50/168.37 [3742]E(f315(f315(f57(x37421,x37422,x37423),x37424),f177(f909(x37421,a899))),x37424)
% 168.50/168.37 [3766]E(f315(f315(f153(x37661),f315(f315(f140(x37661),x37662),x37663)),f315(a101,x37664)),f315(f315(f153(x37661),x37663),x37664))
% 168.50/168.37 [3834]E(f315(f315(x38341,x38342),f315(f173(x38343,x38344,x38341),x38342)),f315(f173(x38343,x38344,x38341),f315(a101,x38342)))
% 168.50/168.37 [3875]E(f243(x38751,x38752,x38753,f315(f245(x38751,x38752,x38753),x38754)),x38754)
% 168.50/168.37 [3930]E(f315(f315(f148(x39301,f315(f315(f140(x39301),x39302),x39303)),f2(a901)),x39304),f315(f315(f140(x39301),x39304),x39303))
% 168.50/168.37 [3940]E(f315(f315(f33(f909(x39401,a899),f909(x39402,a899)),x39403),f298(x39401,x39402,x39404)),f315(f298(x39401,x39402,x39404),f30(f909(x39401,a899),x39403)))
% 168.50/168.37 [3941]E(f315(f315(f33(f909(x39411,a899),f909(x39412,a899)),x39413),f299(x39412,x39411,x39414)),f315(f299(x39412,x39411,x39414),f30(f909(x39411,a899),x39413)))
% 168.50/168.37 [3966]E(f109(x39661,f119(x39662,f903(x39661),x39663,x39664)),f315(f107(x39662,x39661,x39664),x39663))
% 168.50/168.37 [4038]E(f315(f114(x40381,x40382),f115(x40381,x40383,x40384)),f315(f315(f73(a901),f315(f315(f73(a901),f315(x40382,x40383)),f315(f114(x40381,x40382),x40384))),f315(a101,f2(a901))))
% 168.50/168.37 [4059]E(f315(f131(x40591,x40592,f315(f9(x40592,x40591,x40591),x40593),x40594),f315(f157(x40592),f102(x40592))),x40594)
% 168.50/168.37 [4163]E(f212(x41631,f908(x41632,f903(x41632)),x41633,f315(f245(x41632,f903(x41632),x41631),x41634),f315(f124(x41632),f108(x41632))),x41633)
% 168.50/168.37 [4295]E(f315(f245(x42951,x42952,x42953),f315(f315(f10(f909(x42952,f908(x42951,x42952)),f909(x42952,x42953),x42951),f315(f10(f908(x42951,x42952),x42953,x42952),x42954)),f240(x42951,x42952))),x42954)
% 168.50/168.37 [3617]E(f315(f244(x36171,x36172),f315(f315(f240(x36171,x36172),x36173),x36174)),x36174)
% 168.50/168.37 [3618]E(f315(f239(x36181,x36182),f315(f315(f240(x36181,x36182),x36183),x36184)),x36183)
% 168.50/168.37 [3651]E(f315(f178(f902(x36511)),f315(f315(f148(x36511,x36512),x36513),x36514)),f315(f178(f902(x36511)),x36512))
% 168.50/168.37 [3652]E(f315(f178(f902(x36521)),f315(f315(f143(x36522,x36521),x36523),x36524)),f315(f178(f902(x36522)),x36524))
% 168.50/168.37 [3673]E(f315(f315(f127(x36731),f315(a101,x36732)),f315(f315(f140(x36731),x36733),x36734)),f315(f315(f127(x36731),x36732),x36734))
% 168.50/168.37 [3737]E(f315(f315(f164(x37371),x37372),f158(x37371,x37373,x37374)),f158(x37371,f315(f315(f221(a901),x37372),x37373),x37374))
% 168.50/168.37 [3738]E(f315(f315(f127(x37381),x37382),f158(x37381,x37383,x37384)),f158(x37381,f315(f315(f3(a901),x37383),x37382),x37384))
% 168.50/168.37 [3744]E(f315(f315(f297(x37441),x37442),f315(f315(f297(x37441),x37443),x37444)),f315(f315(f297(x37441),x37443),f315(f315(f297(x37441),x37442),x37444)))
% 168.50/168.37 [3748]E(f315(f315(f143(x37481,x37482),x37483),f103(x37481,x37484)),f103(x37482,f315(f315(f143(x37481,x37482),x37483),x37484)))
% 168.50/168.37 [3764]E(f315(f157(x37641),f315(f315(f143(x37642,x37641),x37643),x37644)),f315(f315(f143(x37642,x37641),x37643),f315(f157(x37642),x37644)))
% 168.50/168.37 [3765]E(f315(f315(f143(x37651,x37652),x37653),f315(f160(x37651),x37654)),f315(f160(x37652),f315(f315(f143(x37651,x37652),x37653),x37654)))
% 168.50/168.37 [3780]E(f315(f315(f164(x37801),f315(a101,x37802)),f315(f315(f140(x37801),x37803),x37804)),f315(f315(f140(x37801),x37803),f315(f315(f164(x37801),x37802),x37804)))
% 168.50/168.37 [3784]E(f315(f161(x37841),f315(f315(f143(x37842,x37841),x37843),x37844)),f315(f298(x37842,x37841,x37843),f315(f161(x37842),x37844)))
% 168.50/168.37 [3797]E(f315(f315(f143(x37971,x37972),f315(f18(x37972,x37971),x37973)),x37974),f158(x37972,f315(f178(f902(x37971)),x37974),x37973))
% 168.50/168.37 [3833]E(f19(x38331,x38332,x38333,f315(a5,f315(a101,f315(a22,x38334)))),f315(x38333,x38334))
% 168.50/168.37 [3837]E(f315(f315(f123(x38371),f315(f125(x38371,x38372),x38373)),f315(f125(x38371,x38372),x38374)),f315(f125(x38371,x38372),f315(f315(f123(x38371),x38373),x38374)))
% 168.50/168.37 [3849]E(f141(x38491,f315(f315(f143(x38492,x38491),x38493),f141(x38492,x38494))),f141(x38491,f315(f315(f143(x38492,x38491),x38493),x38494)))
% 168.50/168.37 [3864]E(f315(f274(x38641,x38641),f315(f315(f276(x38642,x38641),x38643),x38644)),f315(f315(f276(x38642,x38641),f315(f274(x38642,x38642),x38643)),x38644))
% 168.50/168.37 [3876]E(f315(f315(f277(x38761,x38762,x38763),x38764),f177(f909(f908(x38762,x38763),a899))),f177(f909(f908(x38761,x38763),a899)))
% 168.50/168.37 [3877]E(f315(f315(f164(x38771),f315(f315(f3(a901),x38772),x38773)),f315(f315(f127(x38771),x38773),x38774)),f315(f315(f127(x38771),x38773),f315(f315(f164(x38771),x38772),x38774)))
% 168.50/168.37 [3896]E(f315(f315(f123(x38961),f158(x38961,x38962,x38963)),f158(x38961,x38964,x38963)),f158(x38961,f315(f315(f73(a901),x38962),x38964),x38963))
% 168.50/168.37 [3897]E(f315(f315(f315(f266(x38971),x38972),x38973),x38974),f315(f240(f909(a88,f909(a899,f905(f903(x38971)))),f908(a88,a88)),f315(f35(x38971),x38972)))
% 168.50/168.37 [3923]E(f30(f909(x39231,a899),f315(f298(x39232,f909(x39231,a899),x39233),x39234)),f315(f315(f33(x39232,f909(x39231,a899)),x39234),x39233))
% 168.50/168.37 [3924]E(f31(f909(x39241,a899),f315(f298(x39242,f909(x39241,a899),x39243),x39244)),f315(f315(f32(x39242,f909(x39241,a899)),x39244),x39243))
% 168.50/168.37 [3925]E(f315(f178(f902(f908(x39251,x39252))),f315(f315(f170(x39251,x39252),x39253),x39254)),f315(f315(f221(a901),f315(f178(f902(x39251)),x39253)),f315(f178(f902(x39252)),x39254)))
% 168.50/168.37 [3927]E(f315(f299(x39271,x39272,x39273),f315(f72(f909(x39272,a899)),x39274)),f315(f72(f909(x39271,a899)),f315(f299(x39271,x39272,x39273),x39274)))
% 168.50/168.37 [3976]E(f315(f299(x39761,x39762,x39763),f315(f250(x39762),x39764)),f315(f250(x39761),f315(f315(f10(x39762,a899,x39761),x39764),x39763)))
% 168.50/168.37 [3993]E(f315(f315(f153(x39931),f315(f315(f123(x39931),x39932),f315(f315(f140(x39931),x39933),x39934))),f315(f178(f902(x39931)),x39932)),x39933)
% 168.50/168.37 [4015]E(f315(f298(x40151,x40152,x40153),f315(f299(x40151,x40152,x40153),x40154)),f315(f315(f90(f909(x40152,a899)),x40154),f315(f298(x40151,x40152,x40153),f230(f909(x40151,a899)))))
% 168.50/168.37 [4034]P1(f315(f315(f317(x40341),f315(x40342,x40343)),f315(f298(x40344,x40341,x40342),f230(f909(x40344,a899)))))
% 168.50/168.37 [4043]E(f21(x40431,x40432,x40433,f315(a5,f315(a101,f315(a22,x40434)))),f315(f315(x40433,x40434),f21(x40431,x40432,x40433,x40434)))
% 168.50/168.37 [4047]E(f315(f315(f123(x40471),f158(x40471,x40472,x40473)),f315(f315(f140(x40471),x40473),x40474)),f315(f315(f140(x40471),x40473),f315(f315(f123(x40471),f158(x40471,x40472,x40473)),x40474)))
% 168.50/168.37 [4049]E(f315(f315(f242(x40491,x40492),f315(f161(x40491),x40493)),f315(f18(f909(x40492,a899),x40491),f315(f161(x40492),x40494))),f315(f161(f908(x40491,x40492)),f52(x40491,x40492,x40493,x40494)))
% 168.50/168.37 [4061]E(f144(x40611,x40612,f315(f315(f140(x40611),x40613),x40614)),f315(f315(f73(a901),f315(f315(f73(a901),f315(x40612,x40613)),f144(x40611,x40612,x40614))),f315(a101,f2(a901))))
% 168.50/168.37 [4074]E(f174(f902(x40741),f315(f315(f140(x40741),x40742),x40743),f315(f315(f9(a901,f902(x40741),f902(x40741)),f127(x40741)),x40743),x40744),f315(f315(f127(x40741),x40744),f315(f315(f140(x40741),x40742),x40743)))
% 168.50/168.38 [4075]P25(x40751,f908(x40752,x40751),f319(x40753,x40754,x40752,x40751),f315(f315(f33(x40752,f909(x40751,a899)),x40754),x40753))
% 168.50/168.38 [4084]E(f315(f315(f3(f909(x40841,a899)),f315(f315(f3(f909(x40841,a899)),x40842),x40843)),f315(f315(f297(x40841),x40844),f177(f909(x40841,a899)))),f315(f315(f3(f909(x40841,a899)),x40842),f315(f315(f297(x40841),x40844),x40843)))
% 168.50/168.38 [4097]E(f315(f315(f172(f909(x40971,x40972),f909(x40971,x40972)),x40973),f66(x40972,x40972,x40971,x40974)),f66(x40972,x40972,x40971,f315(f315(f172(x40972,x40972),x40973),x40974)))
% 168.50/168.38 [4168]E(f315(f315(f315(f172(f902(x41681),f902(x41681)),x41682),f156(x41681)),f315(f315(f315(f172(f902(x41681),f902(x41681)),x41683),f156(x41681)),x41684)),f315(f315(f315(f172(f902(x41681),f902(x41681)),f315(f315(f73(a901),x41682),x41683)),f156(x41681)),x41684))
% 168.50/168.38 [4253]P1(f315(f315(f223(f909(x42531,a899)),f315(f161(x42531),f315(f315(f148(x42531,x42532),x42533),x42534))),f315(f315(f297(x42531),x42534),f315(f161(x42531),x42532))))
% 168.50/168.38 [4285]E(f315(f315(f33(f909(x42851,a899),f909(f908(x42851,x42852),a899)),x42853),f315(f315(f9(f909(x42851,a899),f909(x42851,f909(x42852,a899)),f909(f908(x42851,x42852),a899)),f242(x42851,x42852)),x42854)),f315(f315(f242(x42851,x42852),f30(f909(x42851,a899),x42853)),x42854))
% 168.50/168.38 [4323]E(f198(x43231,x43232,x43233,f315(f66(x43232,f909(a88,f909(a88,f909(f908(a88,a88),f909(a88,f903(x43232))))),x43231,f197(x43232)),x43234)),f199(x43231,x43232,x43234,x43233))
% 168.50/168.38 [4338]E(f194(x43381,x43382,x43383,f315(f66(x43382,f909(a88,f909(a88,f909(f908(a88,a88),f909(a88,f903(f905(x43382)))))),x43381,f193(x43382)),x43384)),f195(x43381,x43382,x43384,x43383))
% 168.50/168.38 [4343]P1(f315(f59(x43431,x43432,x43433,x43434,f177(f909(x43431,a899))),x43434))
% 168.50/168.38 [4382]E(f315(f315(f33(x43821,f909(x43822,a899)),x43823),f315(f315(f9(x43821,f909(x43822,a899),f909(x43822,a899)),f315(f315(f10(x43822,f909(f909(x43822,a899),f909(x43822,a899)),x43821),f297(x43822)),x43824)),f177(f909(x43822,a899)))),f315(f298(x43821,x43822,x43824),x43823))
% 168.50/168.38 [4389]P1(f315(f315(f223(f909(x43891,a899)),f315(f272(x43892,x43891),f315(f315(f90(f909(f908(x43892,x43891),a899)),x43893),x43894))),f315(f315(f90(f909(x43891,a899)),f315(f272(x43892,x43891),x43893)),f315(f272(x43892,x43891),x43894))))
% 168.50/168.38 [4390]P1(f315(f315(f223(f909(x43901,a899)),f315(f252(x43901,x43902),f315(f315(f90(f909(f908(x43901,x43902),a899)),x43903),x43904))),f315(f315(f90(f909(x43901,a899)),f315(f252(x43901,x43902),x43903)),f315(f252(x43901,x43902),x43904))))
% 168.50/168.38 [4450]P1(f315(f315(f223(f909(f908(x44501,x44502),a899)),f315(f298(x44502,f908(x44501,x44502),f319(x44503,x44504,x44501,x44502)),f315(f315(f33(x44501,f909(x44502,a899)),x44504),x44503))),f315(f315(f242(x44501,x44502),x44504),x44503)))
% 168.50/168.38 [4451]E(f315(f107(x44511,f908(x44511,x44512),x44513),f315(f315(f10(f909(x44512,f903(f908(x44511,x44512))),f903(f908(x44511,x44512)),x44511),f107(x44512,f908(x44511,x44512),x44514)),f315(f315(f10(f909(x44512,f908(x44511,x44512)),f909(x44512,f903(f908(x44511,x44512))),x44511),f315(f10(f908(x44511,x44512),f903(f908(x44511,x44512)),x44512),f118(f908(x44511,x44512)))),f240(x44511,x44512)))),f120(x44511,x44512,x44513,x44514))
% 168.50/168.38 [4452]E(f264(x44521,x44522,x44523,f315(f66(x44522,f909(a88,f909(a88,f909(f908(a88,a88),f908(f909(a88,f909(a899,f905(f903(x44522)))),f908(a88,a88))))),x44521,f266(x44522)),x44524)),f267(x44521,x44522,x44524,x44523))
% 168.50/168.38 [4492]E(f78(f908(x44921,x44922),f315(f245(x44921,x44922,a899),f315(f315(f9(x44921,f909(x44922,a899),f909(x44922,a899)),f315(f315(f10(f909(a899,a899),f909(f909(x44922,a899),f909(x44922,a899)),x44921),f10(a899,a899,x44922)),f315(f315(f10(a899,f909(a899,a899),x44921),a313),f315(a312,x44923)))),f315(a312,x44924)))),f315(f315(f240(x44921,x44922),x44923),x44924))
% 168.50/168.38 [4493]E(f83(f908(x44931,x44932),f315(f245(x44931,x44932,a899),f315(f315(f9(x44931,f909(x44932,a899),f909(x44932,a899)),f315(f315(f10(f909(a899,a899),f909(f909(x44932,a899),f909(x44932,a899)),x44931),f10(a899,a899,x44932)),f315(f315(f10(a899,f909(a899,a899),x44931),a313),f315(a312,x44933)))),f315(a312,x44934)))),f315(f315(f240(x44931,x44932),x44933),x44934))
% 168.50/168.38 [4564]E(f315(f315(f245(f902(x45641),f902(x45641),f908(f902(x45641),f902(x45641))),f315(f315(f20(f902(x45641),f909(f902(x45641),f908(f902(x45641),f902(x45641))),f909(f902(x45641),f908(f902(x45641),f902(x45641)))),f315(f315(f10(f909(f902(x45641),f909(f908(f902(x45641),f902(x45641)),f908(f902(x45641),f902(x45641)))),f909(f909(f902(x45641),f908(f902(x45641),f902(x45641))),f909(f902(x45641),f908(f902(x45641),f902(x45641)))),f902(x45641)),f20(f902(x45641),f908(f902(x45641),f902(x45641)),f908(f902(x45641),f902(x45641)))),f315(f315(f10(f909(f902(x45641),f908(f902(x45641),f902(x45641))),f909(f902(x45641),f909(f908(f902(x45641),f902(x45641)),f908(f902(x45641),f902(x45641)))),f902(x45641)),f315(f10(f908(f902(x45641),f902(x45641)),f909(f908(f902(x45641),f902(x45641)),f908(f902(x45641),f902(x45641))),f902(x45641)),f315(f85(f908(f902(x45641),f902(x45641))),f315(x45642,x45643)))),f315(f315(f10(f902(x45641),f909(f902(x45641),f908(f902(x45641),f902(x45641))),f902(x45641)),f240(f902(x45641),f902(x45641))),f315(f140(x45641),x45643))))),f315(f315(f9(f902(x45641),f909(f902(x45641),f902(x45641)),f909(f902(x45641),f908(f902(x45641),f902(x45641)))),f315(f315(f10(f909(f902(x45641),f908(f902(x45641),f902(x45641))),f909(f909(f902(x45641),f902(x45641)),f909(f902(x45641),f908(f902(x45641),f902(x45641)))),f902(x45641)),f10(f902(x45641),f908(f902(x45641),f902(x45641)),f902(x45641))),f240(f902(x45641),f902(x45641)))),f315(f140(x45641),x45643)))),f155(x45641,x45642,x45644)),f155(x45641,x45642,f315(f315(f140(x45641),x45643),x45644)))
% 168.50/168.38 [3813]E(f315(f315(f164(x38131),x38132),f315(f315(f164(x38131),x38133),x38134)),f315(f315(f164(x38131),f315(f315(f221(a901),x38132),x38133)),x38134))
% 168.50/168.38 [3814]E(f315(f315(f127(x38141),x38142),f315(f315(f127(x38141),x38143),x38144)),f315(f315(f127(x38141),f315(f315(f73(a901),x38142),x38143)),x38144))
% 168.50/168.38 [3825]E(f315(f315(f123(x38251),f315(f315(f140(x38251),x38252),x38253)),x38254),f315(f315(f140(x38251),x38252),f315(f315(f123(x38251),x38253),x38254)))
% 168.50/168.38 [3826]E(f315(f315(f123(x38261),f315(f315(f123(x38261),x38262),x38263)),x38264),f315(f315(f123(x38261),x38262),f315(f315(f123(x38261),x38263),x38264)))
% 168.50/168.38 [3907]E(f315(f315(f153(x39071),f315(f315(f140(x39071),x39072),x39073)),x39074),f174(x39071,x39072,f315(f153(x39071),x39073),x39074))
% 168.50/168.38 [3916]E(f315(f315(f172(x39161,x39161),x39162),f315(f315(f172(x39161,x39161),x39163),x39164)),f315(f315(f172(x39161,x39161),f315(f315(f74(a901),x39163),x39162)),x39164))
% 168.50/168.38 [3943]E(f315(f315(f99(f909(x39431,a899)),x39432),f315(f315(f297(x39431),x39433),x39434)),f315(f315(f297(x39431),x39433),f315(f315(f99(f909(x39431,a899)),x39432),x39434)))
% 168.50/168.38 [3958]E(f315(f315(f315(f172(x39581,x39581),x39582),x39583),f315(x39583,x39584)),f315(x39583,f315(f315(f315(f172(x39581,x39581),x39582),x39583),x39584)))
% 168.50/168.38 [3967]E(f315(f315(f277(x39671,x39672,x39673),f177(f909(f908(x39671,x39672),a899))),x39674),f177(f909(f908(x39671,x39673),a899)))
% 168.50/168.38 [3981]E(f315(f315(f99(f909(x39811,a899)),f315(f315(f297(x39811),x39812),x39813)),x39814),f315(f315(f297(x39811),x39812),f315(f315(f99(f909(x39811,a899)),x39813),x39814)))
% 168.50/168.38 [4000]E(f315(f28(f908(x40001,x40002)),f315(f315(f242(x40001,x40002),x40003),f315(f18(f909(x40002,a899),x40001),x40004))),f315(f315(f74(a901),f315(f28(x40001),x40003)),f315(f28(x40002),x40004)))
% 168.50/168.38 [4006]E(f315(f315(f90(f909(x40061,a899)),f315(f315(f297(x40061),x40062),x40063)),f315(f315(f297(x40061),x40062),x40064)),f315(f315(f297(x40061),x40062),f315(f315(f90(f909(x40061,a899)),x40063),x40064)))
% 168.50/168.38 [4019]E(f315(f315(f99(f909(x40191,a899)),x40192),f315(f315(f99(f909(x40191,a899)),x40193),x40194)),f315(f315(f99(f909(x40191,a899)),x40193),f315(f315(f99(f909(x40191,a899)),x40192),x40194)))
% 168.50/168.38 [4020]E(f315(f315(f90(f909(x40201,a899)),x40202),f315(f315(f90(f909(x40201,a899)),x40203),x40204)),f315(f315(f90(f909(x40201,a899)),x40203),f315(f315(f90(f909(x40201,a899)),x40202),x40204)))
% 168.50/168.38 [4030]E(f57(x40301,x40302,f315(f315(f10(x40302,f909(x40302,x40302),x40301),x40303),x40304)),f315(f58(x40302,x40301,x40303),x40304))
% 168.50/168.38 [4039]E(f168(x40391,f315(f315(f143(f902(x40392),f902(x40391)),f315(f143(x40392,x40391),x40393)),x40394)),f315(f315(f143(f902(x40392),f902(x40391)),f315(f143(x40392,x40391),x40393)),f168(x40392,x40394)))
% 168.50/168.38 [4058]E(f315(f131(f902(x40581),f902(x40581),f123(x40581),f102(x40581)),f315(f315(f143(x40582,f902(x40581)),x40583),x40584)),f152(x40582,x40581,x40583,x40584))
% 168.50/168.38 [4115]E(f315(f66(x41151,x41151,x41151,f315(f315(f172(x41151,x41151),x41152),x41153)),f315(f315(f172(x41151,x41151),x41154),x41153)),f315(f315(f172(x41151,x41151),f315(f315(f73(a901),x41152),x41154)),x41153))
% 168.50/168.38 [4138]E(f315(f315(f90(f909(x41381,a899)),f315(f315(f99(f909(x41381,a899)),x41382),x41383)),f315(f315(f99(f909(x41381,a899)),x41382),x41384)),f315(f315(f99(f909(x41381,a899)),x41382),f315(f315(f90(f909(x41381,a899)),x41383),x41384)))
% 168.50/168.38 [4139]E(f315(f315(f90(f909(x41391,a899)),f315(f315(f3(f909(x41391,a899)),x41392),x41393)),f315(f315(f3(f909(x41391,a899)),x41392),x41394)),f315(f315(f3(f909(x41391,a899)),x41392),f315(f315(f99(f909(x41391,a899)),x41393),x41394)))
% 168.50/168.38 [4140]E(f315(f315(f99(f909(x41401,a899)),f315(f315(f3(f909(x41401,a899)),x41402),x41403)),f315(f315(f3(f909(x41401,a899)),x41402),x41404)),f315(f315(f3(f909(x41401,a899)),x41402),f315(f315(f90(f909(x41401,a899)),x41403),x41404)))
% 168.50/168.38 [4141]E(f315(f315(f99(f909(x41411,a899)),f315(f315(f90(f909(x41411,a899)),x41412),x41413)),f315(f315(f90(f909(x41411,a899)),x41412),x41414)),f315(f315(f90(f909(x41411,a899)),x41412),f315(f315(f99(f909(x41411,a899)),x41413),x41414)))
% 168.50/168.38 [4142]E(f315(f315(f3(f909(x41421,a899)),f315(f315(f90(f909(x41421,a899)),x41422),x41423)),f315(f315(f90(f909(x41421,a899)),x41422),x41424)),f315(f315(f90(f909(x41421,a899)),x41422),f315(f315(f3(f909(x41421,a899)),x41423),x41424)))
% 168.50/168.38 [4147]E(f315(f28(f908(x41471,x41472)),f315(f315(f242(x41471,x41472),f315(f315(f297(x41471),x41473),f177(f909(x41471,a899)))),f315(f18(f909(x41472,a899),x41471),x41474))),f315(f28(x41472),x41474))
% 168.50/168.38 [4182]E(f315(f315(f33(x41821,f909(x41822,a899)),x41823),f315(f315(f10(f909(x41822,a899),f909(x41822,a899),x41821),f72(f909(x41822,a899))),x41824)),f315(f72(f909(x41822,a899)),f315(f315(f32(x41821,f909(x41822,a899)),x41823),x41824)))
% 168.50/168.38 [4183]E(f315(f315(f32(x41831,f909(x41832,a899)),x41833),f315(f315(f10(f909(x41832,a899),f909(x41832,a899),x41831),f72(f909(x41832,a899))),x41834)),f315(f72(f909(x41832,a899)),f315(f315(f33(x41831,f909(x41832,a899)),x41833),x41834)))
% 168.50/168.38 [4199]E(f315(f315(f277(x41991,x41991,x41991),f315(f315(f172(f908(x41991,x41991),a899),x41992),x41993)),f315(f315(f172(f908(x41991,x41991),a899),x41994),x41993)),f315(f315(f172(f908(x41991,x41991),a899),f315(f315(f73(a901),x41992),x41994)),x41993))
% 168.50/168.38 [4229]E(f315(f315(f32(x42291,f909(f909(x42292,a899),a899)),x42293),f315(f315(f10(f909(x42292,a899),f909(f909(x42292,a899),a899),x42291),f296(x42292)),x42294)),f315(f296(x42292),f315(f315(f32(x42291,f909(x42292,a899)),x42293),x42294)))
% 168.50/168.38 [4258]E(f315(f315(f32(f909(x42581,a899),f909(x42582,a899)),x42583),f315(f315(f9(f909(x42581,a899),f909(x42581,f909(x42582,a899)),f909(x42582,a899)),f32(x42581,f909(x42582,a899))),x42584)),f315(f315(f32(x42581,f909(x42582,a899)),f30(f909(x42581,a899),x42583)),x42584))
% 168.50/168.38 [4259]E(f315(f315(f33(f909(x42591,a899),f909(x42592,a899)),x42593),f315(f315(f9(f909(x42591,a899),f909(x42591,f909(x42592,a899)),f909(x42592,a899)),f33(x42591,f909(x42592,a899))),x42594)),f315(f315(f33(x42591,f909(x42592,a899)),f30(f909(x42591,a899),x42593)),x42594))
% 168.50/168.38 [4264]E(f315(f315(f143(x42641,x42642),x42643),f315(f131(f902(x42641),f902(x42641),f123(x42641),f102(x42641)),x42644)),f315(f131(f902(x42642),f902(x42642),f123(x42642),f102(x42642)),f315(f315(f143(f902(x42641),f902(x42642)),f315(f143(x42641,x42642),x42643)),x42644)))
% 168.50/168.38 [4266]E(f174(f902(x42661),f102(x42661),f315(f315(f10(f902(x42661),f902(x42661),a901),f315(f140(x42661),x42662)),f315(f315(f9(a901,f902(x42661),f902(x42661)),f164(x42661)),x42663)),x42664),f315(f315(f164(x42661),x42664),f315(f315(f140(x42661),x42662),x42663)))
% 168.50/168.38 [4304]P1(f315(f315(f223(f909(x43041,a899)),f315(f298(x43042,x43041,x43043),f315(f299(x43042,x43041,x43043),x43044))),x43044))
% 168.50/168.38 [4306]E(f315(f298(f908(x43061,x43062),f908(x43062,x43061),f315(f245(x43061,x43062,f908(x43062,x43061)),f315(f9(x43062,x43061,f908(x43062,x43061)),f240(x43062,x43061)))),f315(f315(f242(x43061,x43062),x43063),f315(f18(f909(x43062,a899),x43061),x43064))),f315(f315(f242(x43062,x43061),x43064),f315(f18(f909(x43061,a899),x43062),x43063)))
% 168.50/168.38 [4315]E(f315(f315(f33(x43151,f909(x43152,a899)),x43153),f315(f315(f10(f909(x43151,a899),f909(x43152,a899),x43151),f273(x43151,x43152,x43154)),f315(f315(f9(x43151,f909(x43151,a899),f909(x43151,a899)),f297(x43151)),f177(f909(x43151,a899))))),f315(f273(x43151,x43152,x43154),x43153))
% 168.50/168.38 [4316]E(f315(f315(f33(x43161,f909(x43162,a899)),x43163),f315(f315(f10(f909(x43161,a899),f909(x43162,a899),x43161),f299(x43162,x43161,x43164)),f315(f315(f9(x43161,f909(x43161,a899),f909(x43161,a899)),f297(x43161)),f177(f909(x43161,a899))))),f315(f299(x43162,x43161,x43164),x43163))
% 168.50/168.38 [4403]E(f315(f315(f99(f909(x44031,a899)),f315(f315(f99(f909(x44031,a899)),f315(f315(f90(f909(x44031,a899)),x44032),x44033)),f315(f315(f90(f909(x44031,a899)),x44033),x44034))),f315(f315(f90(f909(x44031,a899)),x44034),x44032)),f315(f315(f90(f909(x44031,a899)),f315(f315(f90(f909(x44031,a899)),f315(f315(f99(f909(x44031,a899)),x44032),x44033)),f315(f315(f99(f909(x44031,a899)),x44033),x44034))),f315(f315(f99(f909(x44031,a899)),x44034),x44032)))
% 168.50/168.38 [4466]E(f315(f131(f902(x44661),f902(x44661),f123(x44661),f102(x44661)),f315(f315(f143(x44662,f902(x44661)),f315(f315(f9(x44662,f902(x44661),f902(x44661)),f315(f315(f10(x44661,f909(f902(x44661),f902(x44661)),x44662),f140(x44661)),x44663)),f102(x44661))),x44664)),f315(f315(f143(x44662,x44661),x44663),x44664))
% 168.50/168.38 [4476]E(f315(f315(f79(a1,x44761),f315(f92(a1),f315(f315(f73(a1),x44762),a86))),f315(f315(f20(a1,x44761,x44761),f315(f315(f9(a1,x44761,f909(x44761,x44761)),f315(f315(f10(a899,f909(x44761,f909(x44761,x44761)),a1),f85(x44761)),a182)),x44763)),f315(f315(f10(a901,x44761,a1),x44764),a93))),f174(x44761,x44763,x44764,f315(f92(a901),x44762)))
% 168.50/168.38 [4507]E(f315(f250(x45071),f315(f315(f10(f909(x45072,a899),a899,x45071),f80(x45072)),f315(f315(f10(f909(x45072,a899),f909(x45072,a899),x45071),f315(f20(x45072,a899,a899),f315(f315(f10(a899,f909(a899,a899),x45072),a313),f315(f315(f9(x45072,f909(x45072,a899),a899),f317(x45072)),x45073)))),f315(f9(x45072,x45071,a899),x45074)))),f315(f273(x45072,x45071,f315(f250(f908(x45072,x45071)),f315(f245(x45072,x45071,a899),x45074))),x45073))
% 168.50/168.38 [4642]~P1(f315(f315(f177(f909(x46421,f909(x46422,a899))),x46423),x46424))
% 168.50/168.38 [3970]E(f315(f315(f153(x39701),f315(f315(f123(x39701),x39702),x39703)),f315(f315(f73(a901),f315(f178(f902(x39701)),x39702)),x39704)),f315(f315(f153(x39701),x39703),x39704))
% 168.50/168.38 [3975]E(f315(f315(f127(x39751),x39752),f315(f315(f164(x39751),f315(f315(f73(a901),x39753),x39752)),x39754)),f315(f315(f164(x39751),x39753),f315(f315(f127(x39751),x39752),x39754)))
% 168.50/168.38 [4072]E(f315(f315(f99(f909(x40721,a899)),f315(f272(x40722,x40721),x40723)),f315(f272(x40722,x40721),x40724)),f315(f272(x40722,x40721),f315(f315(f99(f909(f908(x40722,x40721),a899)),x40723),x40724)))
% 168.50/168.38 [4073]E(f315(f315(f99(f909(x40731,a899)),f315(f252(x40731,x40732),x40733)),f315(f252(x40731,x40732),x40734)),f315(f252(x40731,x40732),f315(f315(f99(f909(f908(x40731,x40732),a899)),x40733),x40734)))
% 168.50/168.38 [4078]E(f315(f315(f99(f909(x40781,a899)),f315(f315(f99(f909(x40781,a899)),x40782),x40783)),x40784),f315(f315(f99(f909(x40781,a899)),x40782),f315(f315(f99(f909(x40781,a899)),x40783),x40784)))
% 168.50/168.38 [4079]E(f315(f315(f3(f909(x40791,a899)),f315(f315(f90(f909(x40791,a899)),x40792),x40793)),x40794),f315(f315(f90(f909(x40791,a899)),x40792),f315(f315(f3(f909(x40791,a899)),x40793),x40794)))
% 168.50/168.38 [4080]E(f315(f315(f90(f909(x40801,a899)),f315(f315(f90(f909(x40801,a899)),x40802),x40803)),x40804),f315(f315(f90(f909(x40801,a899)),x40802),f315(f315(f90(f909(x40801,a899)),x40803),x40804)))
% 168.50/168.38 [4117]E(f315(f315(f99(f909(f908(x41171,x41172),a899)),f315(f274(x41172,x41171),x41173)),f315(f274(x41172,x41171),x41174)),f315(f274(x41172,x41171),f315(f315(f99(f909(f908(x41172,x41171),a899)),x41173),x41174)))
% 168.50/168.38 [4118]E(f315(f315(f90(f909(f908(x41181,x41182),a899)),f315(f274(x41182,x41181),x41183)),f315(f274(x41182,x41181),x41184)),f315(f274(x41182,x41181),f315(f315(f90(f909(f908(x41182,x41181),a899)),x41183),x41184)))
% 168.50/168.38 [4131]E(f315(f315(f99(f909(x41311,f909(x41312,a899))),f231(x41312,x41311,x41313)),f231(x41312,x41311,x41314)),f231(x41312,x41311,f315(f315(f99(f909(x41312,f909(x41311,a899))),x41313),x41314)))
% 168.50/168.38 [4132]E(f315(f315(f90(f909(x41321,f909(x41322,a899))),f231(x41322,x41321,x41323)),f231(x41322,x41321,x41324)),f231(x41322,x41321,f315(f315(f90(f909(x41322,f909(x41321,a899))),x41323),x41324)))
% 168.50/168.38 [4186]E(f315(f315(f90(f909(x41861,a899)),f315(f315(f99(f909(x41861,a899)),x41862),x41863)),f315(f315(f99(f909(x41861,a899)),x41864),x41863)),f315(f315(f99(f909(x41861,a899)),f315(f315(f90(f909(x41861,a899)),x41862),x41864)),x41863))
% 168.50/168.38 [4187]E(f315(f315(f99(f909(x41871,a899)),f315(f315(f3(f909(x41871,a899)),x41872),x41873)),f315(f315(f3(f909(x41871,a899)),x41874),x41873)),f315(f315(f3(f909(x41871,a899)),f315(f315(f99(f909(x41871,a899)),x41872),x41874)),x41873))
% 168.50/168.38 [4188]E(f315(f315(f99(f909(x41881,a899)),f315(f315(f90(f909(x41881,a899)),x41882),x41883)),f315(f315(f90(f909(x41881,a899)),x41884),x41883)),f315(f315(f90(f909(x41881,a899)),f315(f315(f99(f909(x41881,a899)),x41882),x41884)),x41883))
% 168.50/168.38 [4189]E(f315(f315(f3(f909(x41891,a899)),f315(f315(f90(f909(x41891,a899)),x41892),x41893)),f315(f315(f90(f909(x41891,a899)),x41894),x41893)),f315(f315(f90(f909(x41891,a899)),f315(f315(f3(f909(x41891,a899)),x41892),x41894)),x41893))
% 168.50/168.38 [4190]E(f315(f315(f3(f909(x41901,a899)),f315(f315(f90(f909(x41901,a899)),x41902),x41903)),f315(f315(f90(f909(x41901,a899)),x41904),x41903)),f315(f315(f3(f909(x41901,a899)),f315(f315(f90(f909(x41901,a899)),x41902),x41903)),x41904))
% 168.50/168.38 [4202]E(f315(f315(f3(f909(x42021,a899)),f315(f315(f3(f909(x42021,a899)),x42022),f315(f315(f297(x42021),x42023),f177(f909(x42021,a899))))),x42024),f315(f315(f3(f909(x42021,a899)),x42022),f315(f315(f297(x42021),x42023),x42024)))
% 168.50/168.38 [4255]E(f315(f315(f99(f909(x42551,a899)),f315(f315(f297(x42551),x42552),f315(f315(f297(x42551),x42553),f177(f909(x42551,a899))))),f315(f269(x42551),x42554)),f315(f269(x42551),f315(f315(f297(f908(x42551,x42551)),f315(f315(f240(x42551,x42551),x42552),x42553)),x42554)))
% 168.50/168.38 [4280]E(f315(f315(f33(a901,f909(x42801,a899)),f315(f289(a901),x42802)),f315(f315(f10(a901,f909(x42801,a899),a901),x42803),f315(f315(f9(a901,a901,a901),f73(a901)),x42804))),f315(f315(f33(a901,f909(x42801,a899)),f291(a901,x42804,f315(f315(f73(a901),x42802),x42804))),x42803))
% 168.50/168.38 [4281]E(f163(x42811,f315(f273(x42811,x42811,x42812),f315(f315(f297(x42811),x42813),f177(f909(x42811,a899)))),f315(f273(f902(x42811),f902(x42811),f147(x42811,x42812)),f315(f315(f297(f902(x42811)),x42814),f177(f909(f902(x42811),a899))))),f315(f273(f902(x42811),f902(x42811),f147(x42811,x42812)),f315(f315(f297(f902(x42811)),f315(f315(f140(x42811),x42813),x42814)),f177(f909(f902(x42811),a899)))))
% 168.50/168.38 [4345]E(f315(f250(x43451),f315(f315(f9(x43451,f909(x43452,a899),a899),f315(f315(f10(x43452,f909(f909(x43452,a899),a899),x43451),f317(x43452)),x43453)),x43454)),f315(f299(x43451,x43452,x43453),x43454))
% 168.50/168.38 [4435]E(f315(f250(x44351),f315(f315(f9(x44351,f909(f908(x44352,x44351),a899),a899),f315(f315(f10(f908(x44352,x44351),f909(f909(f908(x44352,x44351),a899),a899),x44351),f317(f908(x44352,x44351))),f315(f240(x44352,x44351),x44353))),x44354)),f315(f273(x44352,x44351,x44354),f315(f315(f297(x44352),x44353),f177(f909(x44352,a899)))))
% 168.50/168.38 [4449]E(f315(f315(f143(f908(x44491,a901),x44491),f239(x44491,a901)),f315(f125(f908(x44491,a901),f315(f315(f10(a901,a899,f908(x44491,a901)),x44492),f315(f315(f10(a901,a901,f908(x44491,a901)),a101),f244(x44491,a901)))),f315(f315(f170(x44491,a901),x44493),x44494))),f315(f315(f143(f908(x44491,a901),x44491),f239(x44491,a901)),f315(f125(f908(x44491,a901),f315(f315(f10(a901,a899,f908(x44491,a901)),x44492),f244(x44491,a901))),f315(f315(f170(x44491,a901),x44493),f315(f315(f143(a901,a901),a101),x44494)))))
% 168.50/168.38 [4458]P1(f315(f315(f223(f909(f909(x44581,a899),a899)),f315(f315(f33(x44582,f909(f909(x44581,a899),a899)),x44583),f315(f315(f10(f909(x44581,a899),f909(f909(x44581,a899),a899),x44582),f296(x44581)),x44584))),f315(f296(x44581),f315(f315(f33(x44582,f909(x44581,a899)),x44583),x44584))))
% 168.50/168.38 [4499]E(f315(f315(f79(a1,x44991),f315(f92(a1),f315(f315(f73(a1),x44992),a86))),f315(f315(f20(a1,x44991,x44991),f315(f315(f9(a1,x44991,f909(x44991,x44991)),f315(f315(f10(a899,f909(x44991,f909(x44991,x44991)),a1),f85(x44991)),a182)),x44993)),f315(f315(f20(a1,x44991,x44991),f315(f315(f10(a901,f909(x44991,x44991),a1),x44994),a93)),f315(f315(f10(a901,x44991,a1),f173(x44991,x44993,x44994)),a93)))),f315(f173(x44991,x44993,x44994),f315(f92(a901),x44992)))
% 168.50/168.38 [4523]E(f315(f250(f908(x45231,x45232)),f315(f245(x45231,x45232,a899),f315(f315(f9(x45231,f909(x45232,a899),f909(x45232,a899)),f315(f315(f10(f909(a899,a899),f909(f909(x45232,a899),f909(x45232,a899)),x45231),f10(a899,a899,x45232)),f315(f315(f10(a899,f909(a899,a899),x45231),a313),f315(f315(f9(x45231,f909(x45231,a899),a899),f317(x45231)),x45233)))),f315(f315(f9(x45232,f909(x45232,a899),a899),f317(x45232)),x45234)))),f218(x45231,x45232,x45233,x45234))
% 168.50/168.38 [4559]E(f315(f315(f33(x45591,f909(f908(x45591,x45592),a899)),x45593),f315(f315(f20(x45591,f909(x45592,f909(f908(x45591,x45592),a899)),f909(f908(x45591,x45592),a899)),f315(f315(f10(f909(x45592,a899),f909(f909(x45592,f909(f908(x45591,x45592),a899)),f909(f908(x45591,x45592),a899)),x45591),f33(x45592,f909(f908(x45591,x45592),a899))),x45594)),f315(f315(f9(x45591,f909(f908(x45591,x45592),a899),f909(x45592,f909(f908(x45591,x45592),a899))),f315(f315(f10(f909(x45592,f909(f909(f908(x45591,x45592),a899),f909(f908(x45591,x45592),a899))),f909(f909(f908(x45591,x45592),a899),f909(x45592,f909(f908(x45591,x45592),a899))),x45591),f9(x45592,f909(f908(x45591,x45592),a899),f909(f908(x45591,x45592),a899))),f315(f315(f10(f909(x45592,f908(x45591,x45592)),f909(x45592,f909(f909(f908(x45591,x45592),a899),f909(f908(x45591,x45592),a899))),x45591),f315(f10(f908(x45591,x45592),f909(f909(f908(x45591,x45592),a899),f909(f908(x45591,x45592),a899)),x45592),f297(f908(x45591,x45592)))),f240(x45591,x45592)))),f177(f909(f908(x45591,x45592),a899))))),f315(f315(f242(x45591,x45592),x45593),x45594))
% 168.50/168.38 [4126]E(f315(f315(f123(x41261),f315(f315(f164(x41261),x41262),x41263)),f315(f315(f164(x41261),f315(f315(f3(a901),x41262),f315(f178(f902(x41261)),x41263))),x41264)),f315(f315(f164(x41261),x41262),f315(f315(f123(x41261),x41263),x41264)))
% 168.50/168.38 [4127]E(f315(f315(f123(x41271),f315(f315(f127(x41271),x41272),x41273)),f315(f315(f127(x41271),f315(f315(f3(a901),x41272),f315(f178(f902(x41271)),x41273))),x41274)),f315(f315(f127(x41271),x41272),f315(f315(f123(x41271),x41273),x41274)))
% 168.50/168.38 [4176]E(f315(f315(f73(a901),f315(f315(f74(a901),x41761),x41762)),f315(f315(f73(a901),f315(f315(f74(a901),x41763),x41762)),x41764)),f315(f315(f73(a901),f315(f315(f74(a901),f315(f315(f73(a901),x41761),x41763)),x41762)),x41764))
% 168.50/168.38 [4321]E(f83(x43211,f315(f315(f9(x43211,x43212,a899),f315(f315(f10(x43212,f909(x43212,a899),x43211),a312),x43213)),x43214)),f315(f84(x43211,x43212,f230(f909(x43211,a899)),x43213),x43214))
% 168.50/168.38 [4369]P1(f315(f315(f223(f909(x43691,a899)),f315(f315(f3(f909(x43691,a899)),f315(f272(x43692,x43691),x43693)),f315(f272(x43692,x43691),x43694))),f315(f272(x43692,x43691),f315(f315(f3(f909(f908(x43692,x43691),a899)),x43693),x43694))))
% 168.50/168.38 [4370]P1(f315(f315(f223(f909(x43701,a899)),f315(f315(f3(f909(x43701,a899)),f315(f252(x43701,x43702),x43703)),f315(f252(x43701,x43702),x43704))),f315(f252(x43701,x43702),f315(f315(f3(f909(f908(x43701,x43702),a899)),x43703),x43704))))
% 168.50/168.38 [4478]E(f315(f315(f73(a1),f315(a82,f315(f273(f908(a901,a901),f908(a901,a901),a97),f315(f315(f297(f908(a901,a901)),f315(f315(f240(a901,a901),x44781),x44782)),f177(f909(f908(a901,a901),a899)))))),f315(a82,f315(f273(f908(a901,a901),f908(a901,a901),a97),f315(f315(f297(f908(a901,a901)),f315(f315(f240(a901,a901),x44783),x44784)),f177(f909(f908(a901,a901),a899)))))),f315(a82,f315(f273(f908(a901,a901),f908(a901,a901),a97),f315(f315(f297(f908(a901,a901)),f315(f315(f240(a901,a901),f315(f315(f73(a901),x44781),x44783)),f315(f315(f73(a901),x44782),x44784))),f177(f909(f908(a901,a901),a899))))))
% 168.50/168.38 [4518]E(f315(f315(f74(a1),f315(a82,f315(f273(f908(a901,a901),f908(a901,a901),a97),f315(f315(f297(f908(a901,a901)),f315(f315(f240(a901,a901),x45181),x45182)),f177(f909(f908(a901,a901),a899)))))),f315(a82,f315(f273(f908(a901,a901),f908(a901,a901),a97),f315(f315(f297(f908(a901,a901)),f315(f315(f240(a901,a901),x45183),x45184)),f177(f909(f908(a901,a901),a899)))))),f315(a82,f315(f273(f908(a901,a901),f908(a901,a901),a97),f315(f315(f297(f908(a901,a901)),f315(f315(f240(a901,a901),f315(f315(f73(a901),f315(f315(f74(a901),x45181),x45183)),f315(f315(f74(a901),x45182),x45184))),f315(f315(f73(a901),f315(f315(f74(a901),x45181),x45184)),f315(f315(f74(a901),x45182),x45183)))),f177(f909(f908(a901,a901),a899))))))
% 168.50/168.38 [4539]E(f315(f250(x45391),f315(f315(f10(f909(x45392,a899),a899,x45391),f81(x45392)),f315(f315(f10(f909(x45392,a899),f909(x45392,a899),x45391),f315(f20(x45392,a899,a899),f315(f315(f10(a899,f909(a899,a899),x45392),a318),f315(f315(f9(x45392,f909(x45392,a899),a899),f317(x45392)),x45393)))),f315(f315(f9(x45391,f909(x45392,f909(x45391,a899)),f909(x45392,a899)),f315(f315(f10(f909(f909(x45391,a899),a899),f909(f909(x45392,f909(x45391,a899)),f909(x45392,a899)),x45391),f10(f909(x45391,a899),a899,x45392)),f317(x45391))),x45394)))),f315(f315(f32(x45392,f909(x45391,a899)),x45393),x45394))
% 168.50/168.38 [4571]E(f315(f315(f277(x45711,x45711,x45711),f315(f315(f297(f908(x45711,x45711)),f315(f315(f240(x45711,x45711),x45712),x45713)),x45714)),f295(x45711,f315(f315(f297(f908(x45711,x45711)),f315(f315(f240(x45711,x45711),x45712),x45713)),x45714))),f315(f315(f99(f909(f908(x45711,x45711),a899)),f315(f315(f277(x45711,x45711,x45711),x45714),f295(x45711,x45714))),f315(f250(f908(x45711,x45711)),f315(f245(x45711,x45711,a899),f315(f315(f9(x45711,f909(x45711,a899),f909(x45711,a899)),f315(f315(f10(f909(a899,a899),f909(f909(x45711,a899),f909(x45711,a899)),x45711),f10(a899,a899,x45711)),f315(f315(f10(a899,f909(a899,a899),x45711),a313),f315(f315(f9(x45711,f909(f908(x45711,x45711),a899),a899),f315(f315(f10(f908(x45711,x45711),f909(f909(f908(x45711,x45711),a899),a899),x45711),f317(f908(x45711,x45711))),f315(f315(f9(x45711,x45711,f908(x45711,x45711)),f240(x45711,x45711)),x45712))),f295(x45711,x45714))))),f315(f315(f9(x45711,f909(f908(x45711,x45711),a899),a899),f315(f315(f10(f908(x45711,x45711),f909(f909(f908(x45711,x45711),a899),a899),x45711),f317(f908(x45711,x45711))),f315(f240(x45711,x45711),x45713))),f295(x45711,x45714)))))))
% 168.50/168.38 [4371]E(f315(f125(x43711,f315(f315(f20(x43711,a899,a899),f315(f315(f10(a899,f909(a899,a899),x43711),a313),x43712)),x43713)),x43714),f315(f125(x43711,x43713),f315(f125(x43711,x43712),x43714)))
% 168.50/168.38 [4472]E(f315(f315(f123(x44721),f315(f315(f315(f85(f902(x44721)),f315(f315(f317(a901),f2(a901)),x44722)),f315(f315(f140(x44721),x44723),f102(x44721))),f102(x44721))),f165(x44721,x44724,f315(f250(a901),f315(f315(f9(a901,f909(a901,a899),a899),f315(f315(f10(a901,f909(f909(a901,a899),a899),a901),f317(a901)),a101)),x44722)))),f165(x44721,f315(f315(f140(x44721),x44723),x44724),x44722))
% 168.50/168.38 [4567]E(f315(f250(f908(x45671,x45672)),f315(f315(f10(f909(a901,a899),a899,f908(x45671,x45672)),f80(a901)),f315(f315(f9(f908(x45671,x45672),f909(a901,a899),f909(a901,a899)),f315(f315(f10(f909(a901,f909(a899,a899)),f909(f909(a901,a899),f909(a901,a899)),f908(x45671,x45672)),f20(a901,a899,a899)),f315(f315(f10(f909(a901,a899),f909(a901,f909(a899,a899)),f908(x45671,x45672)),f315(f10(a899,f909(a899,a899),a901),a313)),f315(f315(f9(f908(x45671,x45672),f909(a901,f908(x45671,x45672)),f909(a901,a899)),f315(f315(f10(f909(f908(x45671,x45672),a899),f909(f909(a901,f908(x45671,x45672)),f909(a901,a899)),f908(x45671,x45672)),f10(f908(x45671,x45672),a899,a901)),a312)),f315(f315(f20(a901,x45672,f908(x45671,x45672)),f315(f315(f10(x45671,f909(x45672,f908(x45671,x45672)),a901),f240(x45671,x45672)),f315(f153(x45671),x45673))),f315(f153(x45672),x45674)))))),f315(f315(f9(a901,a901,a899),f224(a901)),f315(f315(f221(a901),f315(f178(f902(x45671)),x45673)),f315(f178(f902(x45672)),x45674)))))),f315(f161(f908(x45671,x45672)),f315(f315(f170(x45671,x45672),x45673),x45674)))
% 168.50/168.38 [4491]E(f315(f250(f908(x44911,x44912)),f315(f245(x44911,x44912,a899),f315(f315(f9(x44911,f909(x44912,a899),f909(x44912,a899)),f315(f315(f10(f909(a899,a899),f909(f909(x44912,a899),f909(x44912,a899)),x44911),f10(a899,a899,x44912)),f315(f315(f10(a899,f909(a899,a899),x44911),a313),x44913))),x44914))),f315(f315(f242(x44911,x44912),f315(f250(x44911),x44913)),f315(f18(f909(x44912,a899),x44911),f315(f250(x44912),x44914))))
% 168.50/168.38 [4494]E(f315(f250(f908(x44941,x44942)),f315(f245(x44941,x44942,a899),f315(f315(f20(x44941,f909(x44942,a899),f909(x44942,a899)),f315(f315(f10(f909(a899,a899),f909(f909(x44942,a899),f909(x44942,a899)),x44941),f10(a899,a899,x44942)),f315(f315(f10(a899,f909(a899,a899),x44941),a313),x44943))),x44944))),f315(f315(f242(x44941,x44942),f315(f250(x44941),x44943)),f315(f315(f10(f909(x44942,a899),f909(x44942,a899),x44941),f250(x44942)),x44944)))
% 168.50/168.38 [4506]E(f315(f250(x45061),f315(f315(f10(f909(x45062,a899),a899,x45061),f81(x45062)),f315(f315(f10(f909(x45062,a899),f909(x45062,a899),x45061),f315(f20(x45062,a899,a899),f315(f315(f10(a899,f909(a899,a899),x45062),a318),f315(f315(f9(x45062,f909(x45062,a899),a899),f317(x45062)),x45063)))),x45064))),f315(f315(f32(x45062,f909(x45061,a899)),x45063),f315(f315(f10(f909(x45061,a899),f909(x45061,a899),x45062),f250(x45061)),f315(f9(x45061,x45062,a899),x45064))))
% 168.50/168.38 [4551]E(f315(f315(f143(f908(x45511,a901),x45511),f239(x45511,a901)),f315(f125(f908(x45511,a901),f315(f315(f9(f908(x45511,a901),f909(a901,a899),a899),f315(f315(f10(a901,f909(f909(a901,a899),a899),f908(x45511,a901)),f317(a901)),f244(x45511,a901))),x45512)),f315(f315(f170(x45511,a901),x45513),f128(a901,f315(f290(a901,x45514),f315(f315(f73(a901),x45514),f315(f178(f902(x45511)),x45513))))))),f315(f315(f143(f908(x45511,a901),x45511),f239(x45511,a901)),f315(f125(f908(x45511,a901),f315(f315(f9(f908(x45511,a901),f909(a901,a899),a899),f315(f315(f10(a901,f909(f909(a901,a899),a899),f908(x45511,a901)),f317(a901)),f315(f315(f9(f908(x45511,a901),a901,a901),f315(f315(f10(a901,f909(a901,a901),f908(x45511,a901)),f73(a901)),f244(x45511,a901))),x45514))),x45512)),f315(f315(f170(x45511,a901),x45513),f128(a901,f315(f290(a901,f2(a901)),f315(f178(f902(x45511)),x45513)))))))
% 168.50/168.38 [4552]E(f315(a101,f315(f315(f222(a901),f315(f178(f902(x45521)),x45522)),f315(f131(a901,f902(x45523),f315(f9(f902(x45523),a901,a901),f315(f315(f10(a901,f909(a901,a901),f902(x45523)),f222(a901)),f315(f315(f9(f902(x45523),a901,a901),f315(f315(f10(a901,f909(a901,a901),f902(x45523)),f3(a901)),f178(f902(x45523)))),f315(a101,f2(a901))))),f2(a901)),f315(f157(f902(x45523)),f315(f125(f902(x45523),f315(f315(f10(a899,a899,f902(x45523)),a310),f315(f315(f9(f902(x45523),f902(x45523),a899),a312),f102(x45523)))),x45524))))),f315(f315(f222(a901),f315(a101,f315(f178(f902(x45521)),x45522))),f315(f131(a901,f902(x45523),f315(f9(f902(x45523),a901,a901),f315(f315(f10(a901,f909(a901,a901),f902(x45523)),f222(a901)),f178(f902(x45523)))),f2(a901)),f315(f157(f902(x45523)),x45524))))
% 168.50/168.38 [4505]E(f315(f315(f123(x45051),f165(x45051,x45052,x45053)),f165(x45051,x45054,f315(f250(a901),f315(f315(f9(a901,f909(a901,a899),a899),f315(f315(f10(a901,f909(f909(a901,a899),a899),a901),f317(a901)),f315(f315(f9(a901,a901,a901),f73(a901)),f315(f178(f902(x45051)),x45052)))),x45053)))),f165(x45051,f315(f315(f123(x45051),x45052),x45054),x45053))
% 168.50/168.38 [4553]E(f31(f909(x45531,a899),f315(f250(f909(x45531,a899)),f315(f315(f10(f909(x45532,a899),a899,f909(x45531,a899)),f80(x45532)),f315(f315(f10(f909(x45532,a899),f909(x45532,a899),f909(x45531,a899)),f315(f20(x45532,a899,a899),f315(f315(f10(a899,f909(a899,a899),x45532),a313),f315(f315(f9(x45532,f909(x45532,a899),a899),f317(x45532)),x45533)))),f315(f315(f9(f909(x45531,a899),f909(x45532,f909(x45531,a899)),f909(x45532,a899)),f315(f315(f10(f909(f909(x45531,a899),a899),f909(f909(x45532,f909(x45531,a899)),f909(x45532,a899)),f909(x45531,a899)),f10(f909(x45531,a899),a899,x45532)),a312)),x45534))))),f315(f315(f32(x45532,f909(x45531,a899)),x45533),x45534))
% 168.50/168.38 [4554]E(f30(f909(x45541,a899),f315(f250(f909(x45541,a899)),f315(f315(f10(f909(x45542,a899),a899,f909(x45541,a899)),f80(x45542)),f315(f315(f10(f909(x45542,a899),f909(x45542,a899),f909(x45541,a899)),f315(f20(x45542,a899,a899),f315(f315(f10(a899,f909(a899,a899),x45542),a313),f315(f315(f9(x45542,f909(x45542,a899),a899),f317(x45542)),x45543)))),f315(f315(f9(f909(x45541,a899),f909(x45542,f909(x45541,a899)),f909(x45542,a899)),f315(f315(f10(f909(f909(x45541,a899),a899),f909(f909(x45542,f909(x45541,a899)),f909(x45542,a899)),f909(x45541,a899)),f10(f909(x45541,a899),a899,x45542)),a312)),x45544))))),f315(f315(f33(x45542,f909(x45541,a899)),x45543),x45544))
% 168.50/168.38 [4561]E(f315(f315(f140(f902(x45611)),f315(f315(f140(x45611),x45612),f315(f131(f902(x45611),f902(x45611),f123(x45611),f102(x45611)),f315(f315(f143(f902(x45611),f902(x45611)),f145(f902(x45611),x45611,f102(x45611),f315(f315(f10(f902(x45611),f909(f902(x45611),f902(x45611)),x45611),f18(f902(x45611),f902(x45611))),f315(f315(f9(x45611,f902(x45611),f902(x45611)),f140(x45611)),f102(x45611))))),x45613)))),f168(x45611,f315(f315(f140(f902(x45611)),x45614),f315(f131(f902(f902(x45611)),f902(f902(x45611)),f123(f902(x45611)),f102(f902(x45611))),f315(f315(f143(f902(x45611),f902(f902(x45611))),f145(f902(f902(x45611)),x45611,f102(f902(x45611)),f315(f18(f909(f902(x45611),f902(f902(x45611))),x45611),f315(f315(f9(f902(x45611),f902(f902(x45611)),f902(f902(x45611))),f140(f902(x45611))),f102(f902(x45611)))))),x45613))))),f168(x45611,f315(f315(f140(f902(x45611)),f315(f315(f140(x45611),x45612),x45614)),x45613)))
% 168.50/168.38 [4568]E(f315(f250(f908(x45681,x45681)),f315(f245(x45681,x45681,a899),f315(f315(f9(x45681,f909(f908(x45682,x45682),a899),f909(x45681,a899)),f315(f315(f10(f909(x45681,f909(f909(f908(x45682,x45682),a899),a899)),f909(f909(f908(x45682,x45682),a899),f909(x45681,a899)),x45681),f9(x45681,f909(f908(x45682,x45682),a899),a899)),f315(f315(f10(f909(x45681,f908(x45682,x45682)),f909(x45681,f909(f909(f908(x45682,x45682),a899),a899)),x45681),f315(f10(f908(x45682,x45682),f909(f909(f908(x45682,x45682),a899),a899),x45681),f317(f908(x45682,x45682)))),f315(f315(f9(x45681,f909(x45681,x45682),f909(x45681,f908(x45682,x45682))),f315(f315(f10(f909(x45682,f908(x45682,x45682)),f909(f909(x45681,x45682),f909(x45681,f908(x45682,x45682))),x45681),f10(x45682,f908(x45682,x45682),x45681)),f315(f315(f10(x45682,f909(x45682,f908(x45682,x45682)),x45681),f240(x45682,x45682)),x45683))),x45683)))),x45684))),f315(f315(f276(x45682,x45681),x45684),x45683))
% 168.50/168.38 [3708]E(f315(f315(f143(x37081,x37082),x37083),f158(x37081,x37084,x37085)),f158(x37082,x37084,f315(x37083,x37085)))
% 168.50/168.38 [4040]E(f119(x40401,x40402,x40403,f115(x40401,x40404,x40405)),f115(x40402,f315(x40403,x40404),f119(x40401,x40402,x40403,x40405)))
% 168.50/168.38 [4270]E(f315(f68(x42701,x42702,x42703,x42704,x42705),x42704),x42705)
% 168.50/168.38 [4322]E(f241(x43221,x43222,x43223,f231(x43222,x43221,x43224),f231(x43223,x43222,x43225)),f231(x43223,x43221,f241(x43223,x43222,x43221,x43225,x43224)))
% 168.50/168.38 [3901]E(f315(f315(f245(x39011,x39012,x39013),x39014),x39015),f315(f315(x39014,f315(f239(x39011,x39012),x39015)),f315(f244(x39011,x39012),x39015)))
% 168.50/168.38 [3935]E(f315(f315(f315(f58(x39351,x39352,x39353),x39354),x39355),f177(f909(x39352,a899))),x39355)
% 168.50/168.38 [4210]E(f315(f66(f902(x42101),f902(x42102),f902(x42103),f315(f143(x42101,x42102),x42104)),f315(f143(x42103,x42101),x42105)),f315(f143(x42103,x42102),f315(f66(x42101,x42102,x42103,x42104),x42105)))
% 168.50/168.38 [4284]E(f78(x42841,f59(x42842,x42841,x42843,x42844,x42845)),f315(f315(f57(x42842,x42841,x42843),x42844),x42845))
% 168.50/168.38 [4318]E(f315(f315(f73(a901),f315(f315(f73(a901),f315(x43181,f315(f239(x43182,x43183),x43184))),f315(x43185,f315(f244(x43182,x43183),x43184)))),f315(a101,f2(a901))),f249(x43182,x43183,x43181,x43185,x43184))
% 168.50/168.38 [3838]E(f315(f315(f164(x38381),x38382),f315(f315(f143(x38383,x38381),x38384),x38385)),f315(f315(f143(x38383,x38381),x38384),f315(f315(f164(x38383),x38382),x38385)))
% 168.50/168.38 [3839]E(f315(f315(f127(x38391),x38392),f315(f315(f143(x38393,x38391),x38394),x38395)),f315(f315(f143(x38393,x38391),x38394),f315(f315(f127(x38393),x38392),x38395)))
% 168.50/168.38 [3870]E(f315(f315(f143(x38701,x38702),x38703),f315(f315(f140(x38701),x38704),x38705)),f315(f315(f140(x38702),f315(x38703,x38704)),f315(f315(f143(x38701,x38702),x38703),x38705)))
% 168.50/168.38 [3931]E(f315(f298(x39311,x39312,x39313),f315(f315(f297(x39311),x39314),x39315)),f315(f315(f297(x39312),f315(x39313,x39314)),f315(f298(x39311,x39312,x39313),x39315)))
% 168.50/168.38 [3959]E(f162(x39591,f315(f315(f140(x39591),x39592),x39593),f315(f315(f140(x39591),x39594),x39595)),f315(f315(f140(x39591),x39592),f315(f315(f140(x39591),x39594),f162(x39591,x39593,x39595))))
% 168.50/168.38 [3995]E(f315(f315(f170(x39951,x39952),f315(f315(f164(x39951),x39953),x39954)),f315(f315(f164(x39952),x39953),x39955)),f315(f315(f164(f908(x39951,x39952)),x39953),f315(f315(f170(x39951,x39952),x39954),x39955)))
% 168.50/168.38 [3996]E(f315(f315(f170(x39961,x39962),f315(f315(f127(x39961),x39963),x39964)),f315(f315(f127(x39962),x39963),x39965)),f315(f315(f127(f908(x39961,x39962)),x39963),f315(f315(f170(x39961,x39962),x39964),x39965)))
% 168.50/168.38 [4005]E(f315(f315(f148(x40051,f315(f315(f140(x40051),x40052),x40053)),f315(a101,x40054)),x40055),f315(f315(f140(x40051),x40052),f315(f315(f148(x40051,x40053),x40054),x40055)))
% 168.50/168.38 [4008]E(f315(f315(f123(x40081),f315(f315(f143(x40082,x40081),x40083),x40084)),f315(f315(f143(x40082,x40081),x40083),x40085)),f315(f315(f143(x40082,x40081),x40083),f315(f315(f123(x40082),x40084),x40085)))
% 168.50/168.38 [4012]E(f315(f315(x40121,x40122),f315(f315(f233(x40123,x40124,x40121),x40122),x40125)),f315(f315(f233(x40123,x40124,x40121),x40122),f315(a101,x40125)))
% 168.50/168.38 [4044]E(f152(x40441,x40442,x40443,f315(f315(f140(x40441),x40444),x40445)),f315(f315(f123(x40442),f315(x40443,x40444)),f152(x40441,x40442,x40443,x40445)))
% 168.50/168.38 [4056]E(f315(f315(f277(x40561,x40562,x40563),f315(f274(x40562,x40561),x40564)),f315(f274(x40563,x40562),x40565)),f315(f274(x40563,x40561),f315(f315(f277(x40563,x40562,x40561),x40565),x40564)))
% 168.50/168.38 [4088]E(f315(f315(f315(f172(f902(x40881),f902(x40881)),x40882),f156(x40881)),f315(f315(f143(x40883,x40881),x40884),x40885)),f315(f315(f143(x40883,x40881),x40884),f315(f315(f315(f172(f902(x40883),f902(x40883)),x40882),f156(x40883)),x40885)))
% 168.50/168.38 [4089]E(f315(f315(f247(x40891,x40892,x40891,x40893),f315(f240(x40892,x40891),x40894)),x40895),f315(x40895,x40894))
% 168.50/168.38 [4112]E(f144(x41121,x41122,f315(f315(f143(x41123,x41121),x41124),x41125)),f144(x41123,f315(f66(x41121,a901,x41123,x41122),x41124),x41125))
% 168.50/168.38 [4175]E(f166(f908(x41751,x41752),f315(f66(x41752,a899,f908(x41751,x41752),x41753),f244(x41751,x41752)),f315(f315(f170(x41751,x41752),x41754),x41755)),f315(f315(f170(x41751,x41752),x41754),f166(x41752,x41753,x41755)))
% 168.50/168.38 [4180]E(f315(f298(x41801,x41802,f315(f315(f10(x41803,x41802,x41801),x41804),x41805)),f230(f909(x41801,a899))),f315(f298(x41803,x41802,x41804),f315(f298(x41801,x41803,x41805),f230(f909(x41801,a899)))))
% 168.50/168.38 [4193]E(f166(f908(x41931,x41932),f315(f66(x41931,a899,f908(x41931,x41932),x41933),f239(x41931,x41932)),f315(f315(f170(x41931,x41932),x41934),x41935)),f315(f315(f170(x41931,x41932),f166(x41931,x41933,x41934)),x41935))
% 168.50/168.38 [4214]E(f315(f315(f99(f909(x42141,a899)),f315(f299(x42141,x42142,x42143),f315(f315(f297(x42142),x42144),f177(f909(x42142,a899))))),f315(f299(x42141,x42142,x42143),x42145)),f315(f299(x42141,x42142,x42143),f315(f315(f297(x42142),x42144),x42145)))
% 168.50/168.38 [4269]E(f315(f315(f123(f908(x42691,x42692)),f315(f315(f143(x42692,f908(x42691,x42692)),f315(f240(x42691,x42692),x42693)),x42694)),f52(x42691,x42692,x42695,x42694)),f52(x42691,x42692,f315(f315(f140(x42691),x42693),x42695),x42694))
% 168.50/168.38 [4271]E(f315(f315(f143(x42711,x42712),x42713),f166(x42711,f315(f66(x42712,a899,x42711,x42714),x42713),x42715)),f166(x42712,x42714,f315(f315(f143(x42711,x42712),x42713),x42715)))
% 168.50/168.38 [4276]E(f315(f131(x42761,x42762,f315(f9(x42762,x42761,x42761),f315(f9(x42761,x42762,x42761),x42763)),x42764),f315(f157(x42762),f315(f157(x42762),x42765))),f315(f131(x42761,x42762,x42763,x42764),x42765))
% 168.50/168.38 [4379]P1(f315(f315(f223(f909(x43791,a899)),f315(f273(x43792,x43791,x43793),f315(f315(f90(f909(x43792,a899)),x43794),x43795))),f315(f315(f90(f909(x43791,a899)),f315(f273(x43792,x43791,x43793),x43794)),f315(f273(x43792,x43791,x43793),x43795))))
% 168.50/168.38 [4380]P1(f315(f315(f223(f909(x43801,a899)),f315(f298(x43802,x43801,x43803),f315(f315(f90(f909(x43802,a899)),x43804),x43805))),f315(f315(f90(f909(x43801,a899)),f315(f298(x43802,x43801,x43803),x43804)),f315(f298(x43802,x43801,x43803),x43805))))
% 168.50/168.38 [4479]E(f315(f244(x44791,x44792),f315(f246(x44793,x44791,x44792,x44792,x44794,f25(x44792)),x44795)),f315(f244(x44793,x44792),x44795))
% 168.50/168.38 [4480]E(f315(f239(x44801,x44802),f315(f246(x44801,x44801,x44803,x44802,f25(x44801),x44804),x44805)),f315(f239(x44801,x44803),x44805))
% 168.50/168.38 [3680]E(f315(f315(f315(f315(f193(x36801),x36802),x36803),x36804),x36805),f181(x36801,x36802))
% 168.50/168.38 [3681]E(f315(f315(f315(f315(f197(x36811),x36812),x36813),x36814),x36815),f188(x36811,x36812))
% 168.50/168.38 [4045]E(f315(f315(f32(x40451,f909(x40452,a899)),f315(f315(f297(x40451),x40453),x40454)),x40455),f315(f315(f90(f909(x40452,a899)),f315(x40455,x40453)),f315(f315(f32(x40451,f909(x40452,a899)),x40454),x40455)))
% 168.50/168.38 [4046]E(f315(f315(f33(x40461,f909(x40462,a899)),f315(f315(f297(x40461),x40463),x40464)),x40465),f315(f315(f99(f909(x40462,a899)),f315(x40465,x40463)),f315(f315(f33(x40461,f909(x40462,a899)),x40464),x40465)))
% 168.50/168.38 [4096]E(f315(f107(x40961,x40962,f315(x40963,x40964)),f315(f315(f9(x40961,a88,f903(x40962)),x40965),x40964)),f315(f186(x40961,x40962,x40963,x40965),x40964))
% 168.50/168.38 [4106]E(f315(f315(f99(f909(x41061,a899)),f315(f273(x41062,x41061,x41063),x41064)),f315(f273(x41062,x41061,x41063),x41065)),f315(f273(x41062,x41061,x41063),f315(f315(f99(f909(x41062,a899)),x41064),x41065)))
% 168.50/168.38 [4107]E(f315(f315(f99(f909(x41071,a899)),f315(f298(x41072,x41071,x41073),x41074)),f315(f298(x41072,x41071,x41073),x41075)),f315(f298(x41072,x41071,x41073),f315(f315(f99(f909(x41072,a899)),x41074),x41075)))
% 168.50/168.38 [4108]E(f315(f315(f99(f909(x41081,a899)),f315(f299(x41081,x41082,x41083),x41084)),f315(f299(x41081,x41082,x41083),x41085)),f315(f299(x41081,x41082,x41083),f315(f315(f99(f909(x41082,a899)),x41084),x41085)))
% 168.50/168.38 [4109]E(f315(f315(f3(f909(x41091,a899)),f315(f299(x41091,x41092,x41093),x41094)),f315(f299(x41091,x41092,x41093),x41095)),f315(f299(x41091,x41092,x41093),f315(f315(f3(f909(x41092,a899)),x41094),x41095)))
% 168.50/168.38 [4110]E(f315(f315(f90(f909(x41101,a899)),f315(f299(x41101,x41102,x41103),x41104)),f315(f299(x41101,x41102,x41103),x41105)),f315(f299(x41101,x41102,x41103),f315(f315(f90(f909(x41102,a899)),x41104),x41105)))
% 168.50/168.38 [4171]E(f315(f315(f148(x41711,f315(f315(f123(x41711),x41712),f315(f315(f140(x41711),x41713),x41714))),f315(f178(f902(x41711)),x41712)),x41715),f315(f315(f123(x41711),x41712),f315(f315(f140(x41711),x41715),x41714)))
% 168.50/168.38 [4178]E(f315(f315(f32(x41781,f909(x41782,a899)),x41783),f315(f315(f10(f909(x41782,a899),f909(x41782,a899),x41781),f315(f297(x41782),x41784)),x41785)),f315(f315(f297(x41782),x41784),f315(f315(f32(x41781,f909(x41782,a899)),x41783),x41785)))
% 168.50/168.38 [4331]E(f315(f315(f143(x43311,x43312),x43313),f315(f125(x43311,f315(f66(x43312,a899,x43311,x43314),x43313)),x43315)),f315(f125(x43312,x43314),f315(f315(f143(x43311,x43312),x43313),x43315)))
% 168.50/168.38 [4337]E(f315(f178(f902(x43371)),f315(f125(x43371,x43372),f315(f315(f143(x43373,x43371),x43374),x43375))),f315(f178(f902(x43373)),f315(f125(x43373,f315(f66(x43371,a899,x43373,x43372),x43374)),x43375)))
% 168.50/168.38 [4544]E(f315(f145(f902(f908(x45441,x45442)),x45442,f102(f908(x45441,x45442)),f315(f315(f9(x45442,f909(f902(x45442),f902(f908(x45441,x45442))),f909(f902(x45442),f902(f908(x45441,x45442)))),f315(f315(f10(f909(f902(f908(x45441,x45442)),f902(f908(x45441,x45442))),f909(f909(f902(x45442),f902(f908(x45441,x45442))),f909(f902(x45442),f902(f908(x45441,x45442)))),x45442),f10(f902(f908(x45441,x45442)),f902(f908(x45441,x45442)),f902(x45442))),f315(f315(f10(f908(x45441,x45442),f909(f902(f908(x45441,x45442)),f902(f908(x45441,x45442))),x45442),f140(f908(x45441,x45442))),f315(f240(x45441,x45442),x45443)))),f315(f170(x45441,x45442),x45444))),x45445),f315(f315(f170(x45441,x45442),f315(f315(f140(x45441),x45443),x45444)),x45445))
% 168.50/168.38 [4037]E(f315(f315(f148(x40371,f315(f315(f148(x40371,x40372),x40373),x40374)),x40373),x40375),f315(f315(f148(x40371,x40372),x40373),x40375))
% 168.50/168.38 [4090]E(f315(f272(x40901,x40902),f315(f315(f297(f908(x40901,x40902)),f315(f315(f240(x40901,x40902),x40903),x40904)),x40905)),f315(f315(f297(x40902),x40904),f315(f272(x40901,x40902),x40905)))
% 168.50/168.38 [4091]E(f315(f252(x40911,x40912),f315(f315(f297(f908(x40911,x40912)),f315(f315(f240(x40911,x40912),x40913),x40914)),x40915)),f315(f315(f297(x40911),x40913),f315(f252(x40911,x40912),x40915)))
% 168.50/168.38 [4136]E(f111(x41361,x41362,f315(x41363,x41364),f315(f315(f9(x41361,a88,f903(f905(x41362))),x41365),x41364)),f315(f184(x41361,x41362,x41363,x41365),x41364))
% 168.50/168.38 [4164]E(f315(f315(f99(f909(f908(x41641,x41642),a899)),f315(f315(f242(x41641,x41642),x41643),x41644)),f315(f315(f242(x41641,x41642),x41645),x41644)),f315(f315(f242(x41641,x41642),f315(f315(f99(f909(x41641,a899)),x41643),x41645)),x41644))
% 168.50/168.38 [4165]E(f315(f315(f3(f909(f908(x41651,x41652),a899)),f315(f315(f242(x41651,x41652),x41653),x41654)),f315(f315(f242(x41651,x41652),x41655),x41654)),f315(f315(f242(x41651,x41652),f315(f315(f3(f909(x41651,a899)),x41653),x41655)),x41654))
% 168.50/168.38 [4166]E(f315(f315(f90(f909(f908(x41661,x41662),a899)),f315(f315(f242(x41661,x41662),x41663),x41664)),f315(f315(f242(x41661,x41662),x41665),x41664)),f315(f315(f242(x41661,x41662),f315(f315(f90(f909(x41661,a899)),x41663),x41665)),x41664))
% 168.50/168.38 [4225]E(f315(f315(f90(f909(x42251,a899)),f315(f315(f32(x42252,f909(x42251,a899)),x42253),x42254)),f315(f315(f32(x42252,f909(x42251,a899)),x42255),x42254)),f315(f315(f32(x42252,f909(x42251,a899)),f315(f315(f99(f909(x42252,a899)),x42253),x42255)),x42254))
% 168.50/168.38 [4226]E(f315(f315(f99(f909(x42261,a899)),f315(f315(f33(x42262,f909(x42261,a899)),x42263),x42264)),f315(f315(f33(x42262,f909(x42261,a899)),x42265),x42264)),f315(f315(f33(x42262,f909(x42261,a899)),f315(f315(f99(f909(x42262,a899)),x42263),x42265)),x42264))
% 168.50/168.38 [4240]E(f315(f315(f32(x42401,f909(x42402,a899)),x42403),f315(f315(f10(f909(x42402,a899),f909(x42402,a899),x42401),f315(f99(f909(x42402,a899)),x42404)),x42405)),f315(f315(f99(f909(x42402,a899)),x42404),f315(f315(f32(x42401,f909(x42402,a899)),x42403),x42405)))
% 168.50/168.38 [4241]E(f315(f315(f33(x42411,f909(x42412,a899)),x42413),f315(f315(f10(f909(x42412,a899),f909(x42412,a899),x42411),f315(f3(f909(x42412,a899)),x42414)),x42415)),f315(f315(f3(f909(x42412,a899)),x42414),f315(f315(f32(x42411,f909(x42412,a899)),x42413),x42415)))
% 168.50/168.38 [4242]E(f315(f315(f33(x42421,f909(x42422,a899)),x42423),f315(f315(f10(f909(x42422,a899),f909(x42422,a899),x42421),f315(f90(f909(x42422,a899)),x42424)),x42425)),f315(f315(f90(f909(x42422,a899)),x42424),f315(f315(f33(x42421,f909(x42422,a899)),x42423),x42425)))
% 168.50/168.38 [4296]E(f174(f902(x42961),f315(f315(f140(x42961),x42962),x42963),f315(f315(f10(f902(x42961),f902(x42961),a901),f315(f140(x42961),x42964)),f315(f315(f9(a901,x42961,f902(x42961)),f148(x42961,x42963)),x42962)),x42965),f315(f315(f148(x42961,f315(f315(f140(x42961),x42964),x42963)),x42965),x42962))
% 168.50/168.38 [4300]E(f315(f315(f32(x43001,f909(f908(x43002,x43003),a899)),x43004),f315(f315(f10(f909(f908(x43003,x43002),a899),f909(f908(x43002,x43003),a899),x43001),f274(x43003,x43002)),x43005)),f315(f274(x43003,x43002),f315(f315(f32(x43001,f909(f908(x43003,x43002),a899)),x43004),x43005)))
% 168.50/168.38 [4301]E(f315(f315(f33(x43011,f909(f908(x43012,x43013),a899)),x43014),f315(f315(f10(f909(f908(x43013,x43012),a899),f909(f908(x43012,x43013),a899),x43011),f274(x43013,x43012)),x43015)),f315(f274(x43013,x43012),f315(f315(f33(x43011,f909(f908(x43013,x43012),a899)),x43014),x43015)))
% 168.50/168.38 [4402]P1(f315(f315(f223(f909(x44021,a899)),f315(f315(f3(f909(x44021,a899)),f315(f298(x44022,x44021,x44023),x44024)),f315(f298(x44022,x44021,x44023),x44025))),f315(f298(x44022,x44021,x44023),f315(f315(f3(f909(x44022,a899)),x44024),x44025))))
% 168.50/168.38 [4547]E(f315(f145(f902(f908(x45471,x45472)),x45471,f102(f908(x45471,x45472)),f315(f315(f9(x45471,f909(f902(x45471),f902(f908(x45471,x45472))),f909(f902(x45471),f902(f908(x45471,x45472)))),f315(f315(f10(f909(f902(f908(x45471,x45472)),f902(f908(x45471,x45472))),f909(f909(f902(x45471),f902(f908(x45471,x45472))),f909(f902(x45471),f902(f908(x45471,x45472)))),x45471),f10(f902(f908(x45471,x45472)),f902(f908(x45471,x45472)),f902(x45471))),f315(f315(f10(f908(x45471,x45472),f909(f902(f908(x45471,x45472)),f902(f908(x45471,x45472))),x45471),f140(f908(x45471,x45472))),f315(f315(f9(x45471,x45472,f908(x45471,x45472)),f240(x45471,x45472)),x45473)))),f315(f315(f9(f902(x45471),f902(x45472),f902(f908(x45471,x45472))),f170(x45471,x45472)),x45474))),x45475),f315(f315(f170(x45471,x45472),x45475),f315(f315(f140(x45472),x45473),x45474)))
% 168.50/168.38 [4265]E(f315(f315(f99(f909(x42651,a899)),f315(f273(x42652,x42651,x42653),x42654)),f315(f273(x42652,x42651,x42655),x42654)),f315(f273(x42652,x42651,f315(f315(f99(f909(f908(x42652,x42651),a899)),x42653),x42655)),x42654))
% 168.50/168.38 [4302]E(f315(f315(f123(f908(x43021,x43022)),f315(f315(f170(x43021,x43022),x43023),f315(f315(f164(x43022),f315(f178(f902(x43021)),x43023)),x43024))),f315(f315(f170(x43021,x43022),x43025),f315(f315(f127(x43022),f315(f178(f902(x43021)),x43023)),x43024))),f315(f315(f170(x43021,x43022),f315(f315(f123(x43021),x43023),x43025)),x43024))
% 168.50/168.38 [4405]E(f315(f315(f242(x44051,x44052),x44053),f315(f315(f20(x44051,f909(x44052,a899),f909(x44052,a899)),f315(f315(f10(f909(x44052,a899),f909(f909(x44052,a899),f909(x44052,a899)),x44051),f99(f909(x44052,a899))),x44054)),x44055)),f315(f315(f99(f909(f908(x44051,x44052),a899)),f315(f315(f242(x44051,x44052),x44053),x44054)),f315(f315(f242(x44051,x44052),x44053),x44055)))
% 168.50/168.38 [4406]E(f315(f315(f242(x44061,x44062),x44063),f315(f315(f20(x44061,f909(x44062,a899),f909(x44062,a899)),f315(f315(f10(f909(x44062,a899),f909(f909(x44062,a899),f909(x44062,a899)),x44061),f3(f909(x44062,a899))),x44064)),x44065)),f315(f315(f3(f909(f908(x44061,x44062),a899)),f315(f315(f242(x44061,x44062),x44063),x44064)),f315(f315(f242(x44061,x44062),x44063),x44065)))
% 168.50/168.38 [4407]E(f315(f315(f242(x44071,x44072),x44073),f315(f315(f20(x44071,f909(x44072,a899),f909(x44072,a899)),f315(f315(f10(f909(x44072,a899),f909(f909(x44072,a899),f909(x44072,a899)),x44071),f90(f909(x44072,a899))),x44074)),x44075)),f315(f315(f90(f909(f908(x44071,x44072),a899)),f315(f315(f242(x44071,x44072),x44073),x44074)),f315(f315(f242(x44071,x44072),x44073),x44075)))
% 168.50/168.38 [4411]E(f315(f315(f32(x44111,f909(x44112,a899)),x44113),f315(f315(f9(x44111,f909(x44112,a899),f909(x44112,a899)),f315(f315(f10(f909(x44112,a899),f909(f909(x44112,a899),f909(x44112,a899)),x44111),f99(f909(x44112,a899))),x44114)),x44115)),f315(f315(f99(f909(x44112,a899)),f315(f315(f32(x44111,f909(x44112,a899)),x44113),x44114)),x44115))
% 168.50/168.38 [4412]E(f315(f315(f33(x44121,f909(x44122,a899)),x44123),f315(f315(f9(x44121,f909(x44122,a899),f909(x44122,a899)),f315(f315(f10(f909(x44122,a899),f909(f909(x44122,a899),f909(x44122,a899)),x44121),f3(f909(x44122,a899))),x44124)),x44125)),f315(f315(f3(f909(x44122,a899)),f315(f315(f33(x44121,f909(x44122,a899)),x44123),x44124)),x44125))
% 168.50/168.38 [4413]E(f315(f315(f33(x44131,f909(x44132,a899)),x44133),f315(f315(f9(x44131,f909(x44132,a899),f909(x44132,a899)),f315(f315(f10(f909(x44132,a899),f909(f909(x44132,a899),f909(x44132,a899)),x44131),f90(f909(x44132,a899))),x44134)),x44135)),f315(f315(f90(f909(x44132,a899)),f315(f315(f33(x44131,f909(x44132,a899)),x44133),x44134)),x44135))
% 168.50/168.38 [4417]E(f315(f315(f32(x44171,f909(x44172,a899)),x44173),f315(f315(f20(x44171,f909(x44172,a899),f909(x44172,a899)),f315(f315(f10(f909(x44172,a899),f909(f909(x44172,a899),f909(x44172,a899)),x44171),f90(f909(x44172,a899))),x44174)),x44175)),f315(f315(f90(f909(x44172,a899)),f315(f315(f32(x44171,f909(x44172,a899)),x44173),x44174)),f315(f315(f32(x44171,f909(x44172,a899)),x44173),x44175)))
% 168.50/168.38 [4418]E(f315(f315(f33(x44181,f909(x44182,a899)),x44183),f315(f315(f20(x44181,f909(x44182,a899),f909(x44182,a899)),f315(f315(f10(f909(x44182,a899),f909(f909(x44182,a899),f909(x44182,a899)),x44181),f99(f909(x44182,a899))),x44184)),x44185)),f315(f315(f99(f909(x44182,a899)),f315(f315(f33(x44181,f909(x44182,a899)),x44183),x44184)),f315(f315(f33(x44181,f909(x44182,a899)),x44183),x44185)))
% 168.50/168.38 [4431]E(f315(f315(f32(x44311,f909(x44312,a899)),x44313),f315(f315(f20(x44311,f909(x44312,a899),f909(x44312,a899)),f315(f315(f10(f909(x44312,a899),f909(f909(x44312,a899),f909(x44312,a899)),x44311),f90(f909(x44312,a899))),x44314)),x44315)),f315(f315(f90(f909(x44312,a899)),f31(f909(x44312,a899),f315(f298(x44311,f909(x44312,a899),x44314),x44313))),f31(f909(x44312,a899),f315(f298(x44311,f909(x44312,a899),x44315),x44313))))
% 168.50/168.38 [4432]E(f315(f315(f33(x44321,f909(x44322,a899)),x44323),f315(f315(f20(x44321,f909(x44322,a899),f909(x44322,a899)),f315(f315(f10(f909(x44322,a899),f909(f909(x44322,a899),f909(x44322,a899)),x44321),f99(f909(x44322,a899))),x44324)),x44325)),f315(f315(f99(f909(x44322,a899)),f30(f909(x44322,a899),f315(f298(x44321,f909(x44322,a899),x44324),x44323))),f30(f909(x44322,a899),f315(f298(x44321,f909(x44322,a899),x44325),x44323))))
% 168.50/168.38 [4468]E(f315(f315(f127(x44681),f315(f178(f902(x44681)),f166(x44681,x44682,f315(f315(f143(x44683,x44681),x44684),x44685)))),f315(f315(f143(x44683,x44681),x44684),x44685)),f315(f315(f143(x44683,x44681),x44684),f315(f315(f127(x44683),f315(f178(f902(x44683)),f166(x44683,f315(f66(x44681,a899,x44683,x44682),x44684),x44685))),x44685)))
% 168.50/168.38 [4344]E(f315(f315(f123(f908(x43441,x43442)),f315(f315(f170(x43441,x43442),f315(f315(f164(x43441),f315(f178(f902(x43442)),x43443)),x43444)),x43443)),f315(f315(f170(x43441,x43442),f315(f315(f127(x43441),f315(f178(f902(x43442)),x43443)),x43444)),x43445)),f315(f315(f170(x43441,x43442),x43444),f315(f315(f123(x43442),x43443),x43445)))
% 168.50/168.38 [4459]E(f78(x44591,f315(f315(f20(x44591,a899,a899),f315(f315(f10(a899,f909(a899,a899),x44591),a313),f315(f315(f9(x44591,f909(x44591,a899),a899),f317(x44591)),x44592))),f315(f315(f9(x44591,x44593,a899),f315(f315(f10(x44593,f909(x44593,a899),x44591),a312),x44594)),x44595))),f315(f70(x44591,x44593,x44592,x44594),x44595))
% 168.50/168.38 [4460]E(f83(x44601,f315(f315(f20(x44601,a899,a899),f315(f315(f10(a899,f909(a899,a899),x44601),a313),f315(f315(f9(x44601,f909(x44601,a899),a899),f317(x44601)),x44602))),f315(f315(f9(x44601,x44603,a899),f315(f315(f10(x44603,f909(x44603,a899),x44601),a312),x44604)),x44605))),f315(f84(x44601,x44603,x44602,x44604),x44605))
% 168.50/168.38 [4508]E(f315(f315(f79(a1,x45081),f315(f92(a1),f315(f315(f73(a1),x45082),a86))),f315(f315(f20(a1,x45081,x45081),f315(f315(f9(a1,x45081,f909(x45081,x45081)),f315(f315(f10(a899,f909(x45081,f909(x45081,x45081)),a1),f85(x45081)),a182)),f174(x45081,x45083,x45084,x45085))),f315(f315(f10(a901,x45081,a1),x45084),f315(f315(f9(a1,a901,a901),f315(f315(f10(a901,f909(a901,a901),a1),f73(a901)),a93)),x45085)))),f174(x45081,x45083,x45084,f315(f315(f73(a901),f315(f92(a901),x45082)),x45085)))
% 168.50/168.38 [4543]E(f315(f315(f79(a1,x45431),f315(f92(a1),f315(f315(f73(a1),x45432),a86))),f315(f315(f20(a1,x45431,x45431),f315(f315(f9(a1,x45431,f909(x45431,x45431)),f315(f315(f10(a899,f909(x45431,f909(x45431,x45431)),a1),f85(x45431)),a182)),f315(f173(x45431,x45433,x45434),x45435))),f315(f315(f20(a1,x45431,x45431),f315(f315(f10(a901,f909(x45431,x45431),a1),x45434),f315(f315(f9(a1,a901,a901),f315(f315(f10(a901,f909(a901,a901),a1),f73(a901)),a93)),x45435))),f315(f315(f10(a901,x45431,a1),f173(x45431,x45433,x45434)),f315(f315(f9(a1,a901,a901),f315(f315(f10(a901,f909(a901,a901),a1),f73(a901)),a93)),x45435))))),f315(f173(x45431,x45433,x45434),f315(f315(f73(a901),f315(f92(a901),x45432)),x45435)))
% 168.50/168.38 [4576]E(f315(f250(f908(x45761,x45762)),f315(f245(x45761,x45762,a899),f315(f315(f10(f909(x45762,f909(x45763,a899)),f909(x45762,a899),x45761),f315(f10(f909(x45763,a899),a899,x45762),f80(x45763))),f315(f315(f9(x45761,f909(x45762,f909(x45763,a899)),f909(x45762,f909(x45763,a899))),f315(f315(f10(f909(f909(x45763,a899),f909(x45763,a899)),f909(f909(x45762,f909(x45763,a899)),f909(x45762,f909(x45763,a899))),x45761),f10(f909(x45763,a899),f909(x45763,a899),x45762)),f315(f315(f10(f909(x45763,f909(a899,a899)),f909(f909(x45763,a899),f909(x45763,a899)),x45761),f20(x45763,a899,a899)),f315(f315(f10(f909(x45763,a899),f909(x45763,f909(a899,a899)),x45761),f315(f10(a899,f909(a899,a899),x45763),a313)),f315(f315(f9(x45761,f909(f908(x45761,x45763),a899),f909(x45763,a899)),f315(f315(f10(f909(x45763,f909(f909(f908(x45761,x45763),a899),a899)),f909(f909(f908(x45761,x45763),a899),f909(x45763,a899)),x45761),f9(x45763,f909(f908(x45761,x45763),a899),a899)),f315(f315(f10(f909(x45763,f908(x45761,x45763)),f909(x45763,f909(f909(f908(x45761,x45763),a899),a899)),x45761),f315(f10(f908(x45761,x45763),f909(f909(f908(x45761,x45763),a899),a899),x45763),f317(f908(x45761,x45763)))),f240(x45761,x45763)))),x45764))))),f315(f315(f9(x45762,f909(f908(x45763,x45762),a899),f909(x45763,a899)),f315(f315(f10(f909(x45763,f909(f909(f908(x45763,x45762),a899),a899)),f909(f909(f908(x45763,x45762),a899),f909(x45763,a899)),x45762),f9(x45763,f909(f908(x45763,x45762),a899),a899)),f315(f315(f10(f909(x45763,f908(x45763,x45762)),f909(x45763,f909(f909(f908(x45763,x45762),a899),a899)),x45762),f315(f10(f908(x45763,x45762),f909(f909(f908(x45763,x45762),a899),a899),x45763),f317(f908(x45763,x45762)))),f315(f9(x45763,x45762,f908(x45763,x45762)),f240(x45763,x45762))))),x45765))))),f315(f315(f277(x45761,x45763,x45762),x45764),x45765))
% 168.50/168.38 [4194]E(f213(x41941,x41942,x41943,x41944,f209(x41941,x41942,x41945,x41946)),f315(f315(x41944,x41945),x41946))
% 168.50/168.38 [4195]E(f214(x41951,x41952,x41953,x41954,f209(x41951,x41952,x41955,x41956)),f315(f315(x41954,x41955),x41956))
% 168.50/168.38 [4320]E(f116(x43201,x43202,x43203,x43204,f115(x43202,x43205,x43206)),f315(f315(f315(x43204,x43205),x43206),f116(x43201,x43202,x43203,x43204,x43206)))
% 168.50/168.38 [4339]E(f68(x43391,x43392,f68(x43391,x43392,x43393,x43394,x43395),x43394,x43396),f68(x43391,x43392,x43393,x43394,x43396))
% 168.50/168.38 [4447]E(f315(f66(f908(x44471,x44472),x44472,f908(x44473,x44474),f244(x44471,x44472)),f246(x44473,x44471,x44474,x44472,x44475,x44476)),f315(f66(x44474,x44472,f908(x44473,x44474),x44476),f244(x44473,x44474)))
% 168.50/168.38 [4448]E(f315(f66(f908(x44481,x44482),x44481,f908(x44483,x44484),f239(x44481,x44482)),f246(x44483,x44481,x44484,x44482,x44485,x44486)),f315(f66(x44483,x44481,f908(x44483,x44484),x44485),f239(x44483,x44484)))
% 168.50/168.38 [4066]E(f315(f315(f66(x40661,x40662,x40663,x40664),x40665),x40666),f315(x40664,f315(x40665,x40666)))
% 168.50/168.38 [4204]E(f212(x42041,f908(x42042,f903(x42042)),x42043,f315(f245(x42042,f903(x42042),x42041),x42044),f315(f124(x42042),f115(x42042,x42045,x42046))),f315(f315(x42044,x42045),x42046))
% 168.50/168.38 [4254]E(f215(x42541,x42542,x42543,x42544,f209(x42541,x42542,x42545,x42546)),f315(f315(f73(a901),f315(f315(f73(a901),f315(x42543,x42545)),f315(x42544,x42546))),f315(a101,f2(a901))))
% 168.50/168.38 [3868]E(f315(f315(f245(x38681,x38682,x38683),x38684),f315(f315(f240(x38681,x38682),x38685),x38686)),f315(f315(x38684,x38685),x38686))
% 168.50/168.38 [3928]E(f315(f315(f315(f10(x39281,x39282,x39283),x39284),x39285),x39286),f315(x39284,f315(x39285,x39286)))
% 168.50/168.38 [3929]E(f315(f315(f315(f9(x39291,x39292,x39293),x39294),x39295),x39296),f315(f315(x39294,x39296),x39295))
% 168.50/168.38 [3945]E(f315(f315(f315(f20(x39451,x39452,x39453),x39454),x39455),x39456),f315(f315(x39454,x39456),f315(x39455,x39456)))
% 168.50/168.38 [3968]E(f315(f145(x39681,x39682,x39683,x39684),f315(f315(f140(x39682),x39685),x39686)),f315(f315(x39684,x39685),x39686))
% 168.50/168.38 [4004]E(f158(f908(x40041,x40042),f315(f315(f221(a901),x40043),x40044),f315(f315(f240(x40041,x40042),x40045),x40046)),f315(f315(f170(x40041,x40042),f158(x40041,x40043,x40045)),f158(x40042,x40044,x40046)))
% 168.50/168.38 [4070]E(f315(f315(f140(f908(x40701,x40702)),f315(f315(f240(x40701,x40702),x40703),x40704)),f315(f315(f170(x40701,x40702),x40705),x40706)),f315(f315(f170(x40701,x40702),f315(f315(f140(x40701),x40703),x40705)),f315(f315(f140(x40702),x40704),x40706)))
% 168.50/168.38 [4071]E(f315(f315(f143(x40711,x40712),x40713),f315(f315(f148(x40711,x40714),x40715),x40716)),f315(f315(f148(x40712,f315(f315(f143(x40711,x40712),x40713),x40714)),x40715),f315(x40713,x40716)))
% 168.50/168.38 [4095]E(f315(f315(f243(x40951,x40952,x40953,x40954),x40955),x40956),f315(x40954,f315(f315(f240(x40951,x40952),x40955),x40956)))
% 168.50/168.38 [4111]E(f315(f131(x41111,x41112,x41113,x41114),f315(f315(f140(x41112),x41115),x41116)),f315(f131(x41111,x41112,x41113,f315(f315(x41113,x41114),x41115)),x41116))
% 168.50/168.38 [4137]E(f248(x41371,x41372,x41373,x41374,f315(f315(f240(x41371,x41372),x41375),x41376)),f315(f315(x41374,x41375),x41376))
% 168.50/168.38 [4218]E(f315(f315(f33(x42181,f909(x42182,a899)),x42183),f315(f66(x42184,f909(x42182,a899),x42181,x42185),x42186)),f315(f315(f33(x42184,f909(x42182,a899)),f315(f298(x42181,x42184,x42186),x42183)),x42185))
% 168.50/168.38 [4268]E(f315(f315(f143(x42681,x42682),x42683),f315(f315(f143(x42684,x42681),x42685),x42686)),f315(f315(f143(x42684,x42682),f315(f66(x42681,x42682,x42684,x42683),x42685)),x42686))
% 168.50/168.38 [4274]E(f315(f298(x42741,x42742,f315(f66(x42743,x42742,x42741,x42744),x42745)),x42746),f315(f298(x42743,x42742,x42744),f315(f298(x42741,x42743,x42745),x42746)))
% 168.50/168.38 [4275]E(f315(f299(x42751,x42752,f315(f66(x42753,x42752,x42751,x42754),x42755)),x42756),f315(f299(x42751,x42753,x42755),f315(f299(x42753,x42752,x42754),x42756)))
% 168.50/168.38 [4303]E(f315(f131(x43031,x43032,x43033,f315(f131(x43031,x43032,x43033,x43034),x43035)),x43036),f315(f131(x43031,x43032,x43033,x43034),f315(f315(f123(x43032),x43035),x43036)))
% 168.50/168.38 [4437]E(f315(f246(x44371,x44371,x44372,x44373,f25(x44371),x44374),f315(f315(f240(x44371,x44372),x44375),x44376)),f315(f315(f240(x44371,x44373),x44375),f315(x44374,x44376)))
% 168.50/168.38 [4438]E(f315(f246(x44381,x44382,x44383,x44383,x44384,f25(x44383)),f315(f315(f240(x44381,x44383),x44385),x44386)),f315(f315(f240(x44382,x44383),f315(x44384,x44385)),x44386))
% 168.50/168.38 [4526]E(f315(f315(f143(f908(x45261,x45262),f908(x45261,x45263)),f315(f245(x45261,x45262,f908(x45261,x45263)),f315(f315(f9(x45261,f909(x45262,x45263),f909(x45262,f908(x45261,x45263))),f315(f315(f10(f909(x45263,f908(x45261,x45263)),f909(f909(x45262,x45263),f909(x45262,f908(x45261,x45263))),x45261),f10(x45263,f908(x45261,x45263),x45262)),f240(x45261,x45263))),x45264))),f315(f315(f170(x45261,x45262),x45265),x45266)),f315(f315(f170(x45261,x45263),x45265),f315(f315(f143(x45262,x45263),x45264),x45266)))
% 168.50/168.38 [4121]E(f315(f315(f66(x41211,x41212,x41213,f315(f18(x41212,x41211),x41214)),x41215),x41216),x41214)
% 168.50/168.38 [4153]E(f315(f298(x41531,x41532,x41533),f315(f298(x41534,x41531,x41535),x41536)),f315(f298(x41534,x41532,f315(f315(f10(x41531,x41532,x41534),x41533),x41535)),x41536))
% 168.50/168.38 [4159]E(f315(f315(f32(x41591,f909(x41592,a899)),f315(f298(x41593,x41591,x41594),x41595)),x41596),f315(f315(f32(x41593,f909(x41592,a899)),x41595),f315(f315(f10(x41591,f909(x41592,a899),x41593),x41596),x41594)))
% 168.50/168.38 [4160]E(f315(f315(f33(x41601,f909(x41602,a899)),f315(f298(x41603,x41601,x41604),x41605)),x41606),f315(f315(f33(x41603,f909(x41602,a899)),x41605),f315(f315(f10(x41601,f909(x41602,a899),x41603),x41606),x41604)))
% 168.50/168.38 [4161]E(f315(f315(f32(x41611,f909(x41612,a899)),x41613),f315(f315(f10(x41614,f909(x41612,a899),x41611),x41615),x41616)),f315(f315(f32(x41614,f909(x41612,a899)),f315(f298(x41611,x41614,x41616),x41613)),x41615))
% 168.50/168.38 [4162]E(f315(f315(f33(x41621,f909(x41622,a899)),x41623),f315(f315(f10(x41624,f909(x41622,a899),x41621),x41625),x41626)),f315(f315(f33(x41624,f909(x41622,a899)),f315(f298(x41621,x41624,x41626),x41623)),x41625))
% 168.50/168.38 [4220]E(f315(f315(f33(x42201,f909(x42202,a899)),x42203),f315(f315(f10(f909(x42204,a899),f909(x42202,a899),x42201),f273(x42204,x42202,x42205)),x42206)),f315(f273(x42204,x42202,x42205),f315(f315(f33(x42201,f909(x42204,a899)),x42203),x42206)))
% 168.50/168.38 [4221]E(f315(f315(f33(x42211,f909(x42212,a899)),x42213),f315(f315(f10(f909(x42214,a899),f909(x42212,a899),x42211),f298(x42214,x42212,x42215)),x42216)),f315(f298(x42214,x42212,x42215),f315(f315(f33(x42211,f909(x42214,a899)),x42213),x42216)))
% 168.50/168.38 [4222]E(f315(f315(f32(x42221,f909(x42222,a899)),x42223),f315(f315(f10(f909(x42224,a899),f909(x42222,a899),x42221),f299(x42222,x42224,x42225)),x42226)),f315(f299(x42222,x42224,x42225),f315(f315(f32(x42221,f909(x42224,a899)),x42223),x42226)))
% 168.50/168.38 [4223]E(f315(f315(f33(x42231,f909(x42232,a899)),x42233),f315(f315(f10(f909(x42234,a899),f909(x42232,a899),x42231),f299(x42232,x42234,x42235)),x42236)),f315(f299(x42232,x42234,x42235),f315(f315(f33(x42231,f909(x42234,a899)),x42233),x42236)))
% 168.50/168.38 [4308]E(f315(f131(x43081,x43082,f315(f9(x43082,x43081,x43081),x43083),x43084),f315(f157(x43082),f315(f315(f140(x43082),x43085),x43086))),f315(f315(x43083,x43085),f315(f131(x43081,x43082,f315(f9(x43082,x43081,x43081),x43083),x43084),f315(f157(x43082),x43086))))
% 168.50/168.38 [4366]E(f315(f315(f20(f908(x43661,x43662),x43662,x43663),f315(f315(f10(x43664,f909(x43662,x43663),f908(x43661,x43662)),x43665),f315(f315(f10(x43661,x43664,f908(x43661,x43662)),x43666),f239(x43661,x43662)))),f244(x43661,x43662)),f315(f245(x43661,x43662,x43663),f315(f315(f10(x43664,f909(x43662,x43663),x43661),x43665),x43666)))
% 168.50/168.38 [4373]E(f315(f131(x43731,x43732,f315(f9(x43732,x43731,x43731),x43733),f315(f131(x43731,x43732,f315(f9(x43732,x43731,x43731),x43733),x43734),f315(f157(x43732),x43735))),f315(f157(x43732),x43736)),f315(f131(x43731,x43732,f315(f9(x43732,x43731,x43731),x43733),x43734),f315(f157(x43732),f315(f315(f123(x43732),x43736),x43735))))
% 168.50/168.38 [4375]E(f315(f315(f143(f908(x43751,x43752),f908(x43753,x43752)),f315(f245(x43751,x43752,f908(x43753,x43752)),f315(f315(f10(x43753,f909(x43752,f908(x43753,x43752)),x43751),f240(x43753,x43752)),x43754))),f315(f315(f170(x43751,x43752),x43755),x43756)),f315(f315(f170(x43753,x43752),f315(f315(f143(x43751,x43753),x43754),x43755)),x43756))
% 168.50/168.38 [4420]P1(f315(f315(f223(f909(x44201,a899)),f315(f273(x44202,x44201,x44203),f315(f315(f32(x44204,f909(x44202,a899)),x44205),x44206))),f315(f315(f32(x44204,f909(x44201,a899)),x44205),f315(f315(f10(f909(x44202,a899),f909(x44201,a899),x44204),f273(x44202,x44201,x44203)),x44206))))
% 168.50/168.38 [4233]E(f315(f315(f170(x42331,x42332),f315(f315(f148(x42331,x42333),x42334),f315(f239(x42331,x42332),x42335))),f315(f315(f148(x42332,x42336),x42334),f315(f244(x42331,x42332),x42335))),f315(f315(f148(f908(x42331,x42332),f315(f315(f170(x42331,x42332),x42333),x42336)),x42334),x42335))
% 168.50/168.38 [4291]E(f315(f315(f99(f909(f908(x42911,x42912),a899)),f315(f315(f277(x42911,x42913,x42912),x42914),x42915)),f315(f315(f277(x42911,x42913,x42912),x42914),x42916)),f315(f315(f277(x42911,x42913,x42912),x42914),f315(f315(f99(f909(f908(x42913,x42912),a899)),x42915),x42916)))
% 168.50/168.38 [4385]E(f315(f315(f297(f908(x43851,x43852)),f315(f315(f240(x43851,x43852),x43853),x43854)),f315(f315(f99(f909(f908(x43851,x43852),a899)),f315(f315(f242(x43851,x43852),x43855),f315(f18(f909(x43852,a899),x43851),f315(f315(f297(x43852),x43854),x43856)))),f315(f315(f242(x43851,x43852),f315(f315(f297(x43851),x43853),x43855)),f315(f18(f909(x43852,a899),x43851),x43856)))),f315(f315(f242(x43851,x43852),f315(f315(f297(x43851),x43853),x43855)),f315(f18(f909(x43852,a899),x43851),f315(f315(f297(x43852),x43854),x43856))))
% 168.50/168.38 [4464]E(f315(f315(f90(f909(x44641,a899)),f315(f299(x44641,x44642,f315(f66(f908(x44642,x44643),x44642,x44641,f239(x44642,x44643)),x44644)),x44645)),f315(f299(x44641,x44643,f315(f66(f908(x44642,x44643),x44643,x44641,f244(x44642,x44643)),x44644)),x44646)),f315(f299(x44641,f908(x44642,x44643),x44644),f315(f315(f242(x44642,x44643),x44645),f315(f18(f909(x44643,a899),x44642),x44646))))
% 168.50/168.38 [4314]E(f315(f315(f99(f909(f908(x43141,x43142),a899)),f315(f315(f277(x43141,x43143,x43142),x43144),x43145)),f315(f315(f277(x43141,x43143,x43142),x43146),x43145)),f315(f315(f277(x43141,x43143,x43142),f315(f315(f99(f909(f908(x43141,x43143),a899)),x43144),x43146)),x43145))
% 168.50/168.38 [4445]E(f315(f315(f32(x44451,f909(x44452,a899)),x44453),f315(f315(f9(x44451,f909(x44454,f909(x44452,a899)),f909(x44452,a899)),f315(f315(f10(f909(x44454,a899),f909(f909(x44454,f909(x44452,a899)),f909(x44452,a899)),x44451),f32(x44454,f909(x44452,a899))),x44455)),x44456)),f315(f315(f32(x44454,f909(x44452,a899)),f315(f315(f33(x44451,f909(x44454,a899)),x44453),x44455)),x44456))
% 168.50/168.38 [4446]E(f315(f315(f33(x44461,f909(x44462,a899)),x44463),f315(f315(f9(x44461,f909(x44464,f909(x44462,a899)),f909(x44462,a899)),f315(f315(f10(f909(x44464,a899),f909(f909(x44464,f909(x44462,a899)),f909(x44462,a899)),x44461),f33(x44464,f909(x44462,a899))),x44465)),x44466)),f315(f315(f33(x44464,f909(x44462,a899)),f315(f315(f33(x44461,f909(x44464,a899)),x44463),x44465)),x44466))
% 168.50/168.38 [4498]E(f315(f245(x44981,x44982,f908(x44983,x44984)),f315(f315(f9(x44981,f909(x44982,x44984),f909(x44982,f908(x44983,x44984))),f315(f315(f10(f909(x44984,f908(x44983,x44984)),f909(f909(x44982,x44984),f909(x44982,f908(x44983,x44984))),x44981),f10(x44984,f908(x44983,x44984),x44982)),f315(f315(f10(x44983,f909(x44984,f908(x44983,x44984)),x44981),f240(x44983,x44984)),x44985))),x44986)),f246(x44981,x44983,x44982,x44984,x44985,x44986))
% 168.50/168.38 [4521]E(f315(f298(x45211,x45212,f315(f315(f20(x45211,x45212,x45212),f315(f315(f20(x45211,x45212,f909(x45212,x45212)),f315(f315(f10(a899,f909(x45212,f909(x45212,x45212)),x45211),f85(x45212)),x45213)),x45214)),x45215)),x45216),f315(f315(f99(f909(x45212,a899)),f315(f298(x45211,x45212,x45214),f315(f315(f90(f909(x45211,a899)),x45216),f315(f250(x45211),x45213)))),f315(f298(x45211,x45212,x45215),f315(f315(f90(f909(x45211,a899)),x45216),f315(f250(x45211),f315(f315(f10(a899,a899,x45211),a310),x45213))))))
% 168.50/168.38 [4533]E(f315(f298(x45331,f908(x45332,x45333),f315(f315(f20(x45331,x45333,f908(x45332,x45333)),f315(f315(f10(x45332,f909(x45333,f908(x45332,x45333)),x45331),f240(x45332,x45333)),x45334)),x45335)),x45336),f315(f315(f242(x45332,x45333),f315(f298(x45331,x45332,x45334),x45336)),f315(f315(f10(f909(x45331,a899),f909(x45333,a899),x45332),f298(x45331,x45333,x45335)),f315(f315(f9(x45332,f909(x45331,a899),f909(x45331,a899)),f315(f315(f10(f909(x45331,a899),f909(f909(x45331,a899),f909(x45331,a899)),x45332),f90(f909(x45331,a899))),f315(f315(f10(f909(x45332,a899),f909(x45331,a899),x45332),f299(x45331,x45332,x45334)),f315(f315(f9(x45332,f909(x45332,a899),f909(x45332,a899)),f297(x45332)),f177(f909(x45332,a899)))))),x45336))))
% 168.50/168.38 [4558]E(f234(x45581,x45582,x45583,x45584,x45585,x45586),f315(x45584,f315(f250(x45581),f315(f315(f10(f909(f909(x45583,x45581),a899),a899,x45581),f80(f909(x45583,x45581))),f315(f315(f10(f909(f909(x45583,x45581),a899),f909(f909(x45583,x45581),a899),x45581),f315(f20(f909(x45583,x45581),a899,a899),f315(f315(f10(a899,f909(a899,a899),f909(x45583,x45581)),a313),f315(f315(f9(f909(x45583,x45581),f909(f909(x45583,x45581),a899),a899),f317(f909(x45583,x45581))),x45585)))),f315(f315(f9(x45581,f909(f909(x45583,x45581),x45581),f909(f909(x45583,x45581),a899)),f315(f315(f10(f909(x45581,a899),f909(f909(f909(x45583,x45581),x45581),f909(f909(x45583,x45581),a899)),x45581),f10(x45581,a899,f909(x45583,x45581))),a312)),f315(f315(f9(f909(x45583,x45581),x45583,x45581),f7(f909(x45583,x45581))),x45586)))))))
% 168.50/168.38 [4347]E(f315(f66(x43471,x43472,x43473,x43474),f68(x43473,x43471,x43475,x43476,x43477)),f68(x43473,x43472,f315(f66(x43471,x43472,x43473,x43474),x43475),x43476,f315(x43474,x43477)))
% 168.50/168.38 [4481]E(f315(f244(x44811,x44812),f315(f246(x44813,x44811,x44814,x44812,x44815,x44816),x44817)),f315(x44816,f315(f244(x44813,x44814),x44817)))
% 168.50/168.38 [4482]E(f315(f239(x44821,x44822),f315(f246(x44823,x44821,x44824,x44822,x44825,x44826),x44827)),f315(x44825,f315(f239(x44823,x44824),x44827)))
% 168.50/168.38 [4196]E(f315(f315(f170(x41961,x41962),f315(f315(f148(x41961,x41963),x41964),x41965)),f315(f315(f148(x41962,x41966),x41964),x41967)),f315(f315(f148(f908(x41961,x41962),f315(f315(f170(x41961,x41962),x41963),x41966)),x41964),f315(f315(f240(x41961,x41962),x41965),x41967)))
% 168.50/168.38 [4263]E(f315(f315(f315(f247(x42631,x42632,x42633,x42634),x42635),x42636),x42637),f315(f315(f245(x42632,x42633,x42634),x42636),f315(x42635,x42637)))
% 168.50/168.38 [4273]E(f315(f315(f315(f247(x42731,x42732,x42733,x42734),x42735),x42736),x42737),f315(f315(x42736,f315(f239(x42732,x42733),f315(x42735,x42737))),f315(f244(x42732,x42733),f315(x42735,x42737))))
% 168.50/168.38 [4325]E(f315(f66(x43251,x43252,x43253,x43254),f315(f66(x43255,x43251,x43253,x43256),x43257)),f315(f66(x43255,x43252,x43253,f315(f66(x43251,x43252,x43255,x43254),x43256)),x43257))
% 168.50/168.38 [4502]E(f315(f246(x45021,x45022,x45023,x45023,x45024,f25(x45023)),f315(f246(x45021,x45021,x45025,x45023,f25(x45021),x45026),x45027)),f315(f315(f240(x45022,x45023),f315(x45024,f315(f239(x45021,x45025),x45027))),f315(x45026,f315(f244(x45021,x45025),x45027))))
% 168.50/168.38 [4503]E(f315(f246(x45031,x45031,x45032,x45033,f25(x45031),x45034),f315(f246(x45035,x45031,x45032,x45032,x45036,f25(x45032)),x45037)),f315(f315(f240(x45031,x45033),f315(x45036,f315(f239(x45035,x45032),x45037))),f315(x45034,f315(f244(x45035,x45032),x45037))))
% 168.50/168.38 [4519]E(f315(f246(x45191,x45192,x45193,x45193,x45194,f25(x45193)),f315(f246(x45195,x45191,x45193,x45193,x45196,f25(x45193)),x45197)),f315(f246(x45195,x45192,x45193,x45193,f315(f66(x45191,x45192,x45195,x45194),x45196),f25(x45193)),x45197))
% 168.50/168.38 [4520]E(f315(f246(x45201,x45201,x45202,x45203,f25(x45201),x45204),f315(f246(x45201,x45201,x45205,x45202,f25(x45201),x45206),x45207)),f315(f246(x45201,x45201,x45205,x45203,f25(x45201),f315(f66(x45202,x45203,x45205,x45204),x45206)),x45207))
% 168.50/168.38 [4530]E(f315(f246(x45301,x45302,x45303,x45303,x45304,f25(x45303)),f315(f246(x45301,x45301,x45305,x45303,f25(x45301),x45306),x45307)),f315(f246(x45302,x45302,x45305,x45303,f25(x45302),x45306),f315(f246(x45301,x45302,x45305,x45305,x45304,f25(x45305)),x45307)))
% 168.50/168.38 [4230]E(f315(f315(f277(x42301,x42302,x42303),f315(f315(f277(x42301,x42304,x42302),x42305),x42306)),x42307),f315(f315(f277(x42301,x42304,x42303),x42305),f315(f315(f277(x42304,x42302,x42303),x42306),x42307)))
% 168.50/168.38 [4297]E(f315(f315(f245(x42971,x42972,x42973),f315(f66(x42974,f909(x42972,x42973),x42971,x42975),x42976)),x42977),f315(f315(x42975,f315(x42976,f315(f239(x42971,x42972),x42977))),f315(f244(x42971,x42972),x42977)))
% 168.50/168.38 [4378]E(f315(f131(x43781,x43782,f315(f9(x43782,x43781,x43781),x43783),x43784),f315(f157(x43782),f315(f315(f143(x43785,x43782),x43786),x43787))),f315(f131(x43781,x43785,f315(f9(x43785,x43781,x43781),f315(f66(x43782,f909(x43781,x43781),x43785,x43783),x43786)),x43784),f315(f157(x43785),x43787)))
% 168.50/168.38 [4326]E(f315(f315(f33(x43261,f909(f908(x43262,x43263),a899)),x43264),f315(f315(f10(f909(f908(x43265,x43263),a899),f909(f908(x43262,x43263),a899),x43261),f315(f277(x43262,x43265,x43263),x43266)),x43267)),f315(f315(f277(x43262,x43265,x43263),x43266),f315(f315(f33(x43261,f909(f908(x43265,x43263),a899)),x43264),x43267)))
% 168.50/168.38 [4469]E(f315(f315(f33(x44691,f909(f908(x44692,x44693),a899)),x44694),f315(f315(f9(x44691,f909(f908(x44695,x44693),a899),f909(f908(x44692,x44693),a899)),f315(f315(f10(f909(f908(x44692,x44695),a899),f909(f909(f908(x44695,x44693),a899),f909(f908(x44692,x44693),a899)),x44691),f277(x44692,x44695,x44693)),x44696)),x44697)),f315(f315(f277(x44692,x44695,x44693),f315(f315(f33(x44691,f909(f908(x44692,x44695),a899)),x44694),x44696)),x44697))
% 168.50/168.38 [4470]E(f315(f131(x44701,x44702,f315(f315(f9(x44701,f909(x44702,x44703),f909(x44702,x44701)),f315(f315(f10(f909(x44703,x44701),f909(f909(x44702,x44703),f909(x44702,x44701)),x44701),f10(x44703,x44701,x44702)),x44704)),x44705),x44706),x44707),f315(f131(x44701,x44703,x44704,x44706),f315(f315(f143(x44702,x44703),x44705),x44707)))
% 168.50/168.38 [4531]E(f315(f315(f32(x45311,f909(x45312,a899)),x45313),f315(f315(f10(f909(x45314,f909(x45312,a899)),f909(x45312,a899),x45311),f315(f32(x45314,f909(x45312,a899)),x45315)),f315(f315(f9(x45311,f909(x45314,f909(x45312,a899)),f909(x45314,f909(x45312,a899))),f315(f315(f10(f909(f909(x45312,a899),f909(x45312,a899)),f909(f909(x45314,f909(x45312,a899)),f909(x45314,f909(x45312,a899))),x45311),f10(f909(x45312,a899),f909(x45312,a899),x45314)),f315(f315(f10(f909(x45312,a899),f909(f909(x45312,a899),f909(x45312,a899)),x45311),f99(f909(x45312,a899))),x45316))),x45317))),f315(f315(f99(f909(x45312,a899)),f315(f315(f32(x45311,f909(x45312,a899)),x45313),x45316)),f315(f315(f32(x45314,f909(x45312,a899)),x45315),x45317)))
% 168.50/168.38 [4532]E(f315(f315(f33(x45321,f909(x45322,a899)),x45323),f315(f315(f10(f909(x45324,f909(x45322,a899)),f909(x45322,a899),x45321),f315(f33(x45324,f909(x45322,a899)),x45325)),f315(f315(f9(x45321,f909(x45324,f909(x45322,a899)),f909(x45324,f909(x45322,a899))),f315(f315(f10(f909(f909(x45322,a899),f909(x45322,a899)),f909(f909(x45324,f909(x45322,a899)),f909(x45324,f909(x45322,a899))),x45321),f10(f909(x45322,a899),f909(x45322,a899),x45324)),f315(f315(f10(f909(x45322,a899),f909(f909(x45322,a899),f909(x45322,a899)),x45321),f90(f909(x45322,a899))),x45326))),x45327))),f315(f315(f90(f909(x45322,a899)),f315(f315(f33(x45321,f909(x45322,a899)),x45323),x45326)),f315(f315(f33(x45324,f909(x45322,a899)),x45325),x45327)))
% 168.50/168.38 [4524]E(f186(x45241,x45242,f315(f315(f315(x45243,x45244),x45245),x45246),f315(f315(f9(x45241,f908(a88,a88),f909(a88,f903(x45242))),f315(f315(f9(x45241,a88,f909(f908(a88,a88),f909(a88,f903(x45242)))),f315(f315(f9(x45241,a88,f909(a88,f909(f908(a88,a88),f909(a88,f903(x45242))))),x45247),x45244)),x45245)),x45246)),f315(f315(f315(f198(x45241,x45242,x45243,x45247),x45244),x45245),x45246))
% 168.50/168.38 [4538]E(f187(x45381,x45382,f315(f315(f315(x45383,x45384),x45385),x45386),f315(f315(f9(x45381,f908(a88,a88),f909(a88,f903(x45382))),f315(f315(f9(x45381,a88,f909(f908(a88,a88),f909(a88,f903(x45382)))),f315(f315(f9(x45381,a88,f909(a88,f909(f908(a88,a88),f909(a88,f903(x45382))))),x45387),x45384)),x45385)),x45386)),f200(x45381,x45382,x45383,x45387,x45384,x45385,x45386))
% 168.50/168.38 [4529]E(f184(x45291,x45292,f315(f315(f315(x45293,x45294),x45295),x45296),f315(f315(f9(x45291,f908(a88,a88),f909(a88,f903(f905(x45292)))),f315(f315(f9(x45291,a88,f909(f908(a88,a88),f909(a88,f903(f905(x45292))))),f315(f315(f9(x45291,a88,f909(a88,f909(f908(a88,a88),f909(a88,f903(f905(x45292)))))),x45297),x45294)),x45295)),x45296)),f315(f315(f315(f194(x45291,x45292,x45293,x45297),x45294),x45295),x45296))
% 168.50/168.38 [4540]E(f185(x45401,x45402,f315(f315(f315(x45403,x45404),x45405),x45406),f315(f315(f9(x45401,f908(a88,a88),f909(a88,f903(f905(x45402)))),f315(f315(f9(x45401,a88,f909(f908(a88,a88),f909(a88,f903(f905(x45402))))),f315(f315(f9(x45401,a88,f909(a88,f909(f908(a88,a88),f909(a88,f903(f905(x45402)))))),x45407),x45404)),x45405)),x45406)),f196(x45401,x45402,x45403,x45407,x45404,x45405,x45406))
% 168.50/168.38 [4439]E(f315(f246(x44391,x44392,x44393,x44394,x44395,x44396),f315(f315(f240(x44391,x44393),x44397),x44398)),f315(f315(f240(x44392,x44394),f315(x44395,x44397)),f315(x44396,x44398)))
% 168.50/168.38 [4542]E(f315(f315(f143(f908(x45421,x45422),f908(x45423,x45424)),f315(f245(x45421,x45422,f908(x45423,x45424)),f315(f315(f9(x45421,f909(x45422,x45424),f909(x45422,f908(x45423,x45424))),f315(f315(f10(f909(x45424,f908(x45423,x45424)),f909(f909(x45422,x45424),f909(x45422,f908(x45423,x45424))),x45421),f10(x45424,f908(x45423,x45424),x45422)),f315(f315(f10(x45423,f909(x45424,f908(x45423,x45424)),x45421),f240(x45423,x45424)),x45425))),x45426))),f315(f315(f170(x45421,x45422),x45427),x45428)),f315(f315(f170(x45423,x45424),f315(f315(f143(x45421,x45423),x45425),x45427)),f315(f315(f143(x45422,x45424),x45426),x45428)))
% 168.50/168.38 [4545]E(f315(f315(f143(f908(x45451,x45452),x45453),f315(f245(x45451,x45452,x45453),f315(f315(f10(f909(x45452,f908(x45451,x45454)),f909(x45452,x45453),x45451),f315(f10(f908(x45451,x45454),x45453,x45452),x45455)),f315(f315(f9(x45451,f909(x45452,x45454),f909(x45452,f908(x45451,x45454))),f315(f315(f10(f909(x45454,f908(x45451,x45454)),f909(f909(x45452,x45454),f909(x45452,f908(x45451,x45454))),x45451),f10(x45454,f908(x45451,x45454),x45452)),f240(x45451,x45454))),x45456)))),f315(f315(f170(x45451,x45452),x45457),x45458)),f315(f315(f143(f908(x45451,x45454),x45453),x45455),f315(f315(f170(x45451,x45454),x45457),f315(f315(f143(x45452,x45454),x45456),x45458))))
% 168.50/168.38 [4473]E(f315(f315(f143(f908(x44731,x44732),x44733),f315(f245(x44731,x44732,x44733),f315(f315(f10(f909(x44732,f908(x44734,x44732)),f909(x44732,x44733),x44731),f315(f10(f908(x44734,x44732),x44733,x44732),x44735)),f315(f315(f10(x44734,f909(x44732,f908(x44734,x44732)),x44731),f240(x44734,x44732)),x44736)))),f315(f315(f170(x44731,x44732),x44737),x44738)),f315(f315(f143(f908(x44734,x44732),x44733),x44735),f315(f315(f170(x44734,x44732),f315(f315(f143(x44731,x44734),x44736),x44737)),x44738)))
% 168.50/168.38 [4430]E(f315(f315(f245(x44301,x44302,x44303),f315(f315(f10(f909(x44302,f908(x44304,x44305)),f909(x44302,x44303),x44301),f315(f10(f908(x44304,x44305),x44303,x44302),f315(f245(x44304,x44305,x44303),x44306))),x44307)),x44308),f315(f315(f245(x44304,x44305,x44303),x44306),f315(f315(f245(x44301,x44302,f908(x44304,x44305)),x44307),x44308)))
% 168.50/168.38 [4546]E(f315(f315(f33(f908(x45461,x45462),f909(f908(x45463,x45464),a899)),f315(f315(f242(x45461,x45462),x45465),f315(f18(f909(x45462,a899),x45461),x45466))),f315(f245(x45461,x45462,f909(f908(x45463,x45464),a899)),f315(f315(f9(x45461,f909(x45462,f909(x45463,f909(x45464,a899))),f909(x45462,f909(f908(x45463,x45464),a899))),f315(f315(f10(f909(f909(x45463,f909(x45464,a899)),f909(f908(x45463,x45464),a899)),f909(f909(x45462,f909(x45463,f909(x45464,a899))),f909(x45462,f909(f908(x45463,x45464),a899))),x45461),f10(f909(x45463,f909(x45464,a899)),f909(f908(x45463,x45464),a899),x45462)),f315(f315(f10(f909(x45463,a899),f909(f909(x45463,f909(x45464,a899)),f909(f908(x45463,x45464),a899)),x45461),f242(x45463,x45464)),x45467))),f315(f315(f10(f909(x45464,a899),f909(x45463,f909(x45464,a899)),x45462),f18(f909(x45464,a899),x45463)),x45468)))),f315(f315(f242(x45463,x45464),f315(f315(f33(x45461,f909(x45463,a899)),x45465),x45467)),f315(f18(f909(x45464,a899),x45463),f315(f315(f33(x45462,f909(x45464,a899)),x45466),x45468))))
% 168.50/168.38 [4487]E(f315(f315(f247(x44871,x44872,x44873,x44874),f315(f315(f247(x44871,x44875,x44876,f908(x44872,x44873)),x44877),x44878)),x44879),f315(f315(f247(x44871,x44875,x44876,x44874),x44877),f315(f315(f9(x44875,f909(x44872,f909(x44873,x44874)),f909(x44876,x44874)),f315(f315(f10(f909(x44876,f908(x44872,x44873)),f909(f909(x44872,f909(x44873,x44874)),f909(x44876,x44874)),x44875),f247(x44876,x44872,x44873,x44874)),x44878)),x44879)))
% 168.50/168.38 [4516]E(f315(f66(f908(x45161,x45162),f908(x45163,x45164),f908(x45165,x45166),f246(x45161,x45163,x45162,x45164,x45167,x45168)),f246(x45165,x45161,x45166,x45162,x45169,x451610)),f246(x45165,x45163,x45166,x45164,f315(f66(x45161,x45163,x45165,x45167),x45169),f315(f66(x45162,x45164,x45166,x45168),x451610)))
% 168.50/168.38 [4522]E(f315(f246(x45221,x45222,x45223,x45224,x45225,x45226),f315(f246(x45227,x45221,x45228,x45223,x45229,x452210),x452211)),f315(f246(x45227,x45222,x45228,x45224,f315(f66(x45221,x45222,x45227,x45225),x45229),f315(f66(x45223,x45224,x45228,x45226),x452210)),x452211))
% 168.50/168.38 [4649]~P4(x46491)+P4(f905(x46491))
% 168.50/168.38 [4650]~P64(x46501)+P64(f905(x46501))
% 168.50/168.38 [4651]~P106(x46511)+P106(f902(x46511))
% 168.50/168.38 [4654]~P146(x46541)+~E(f71(x46541),f2(x46541))
% 168.50/168.38 [4656]~E(x46561,f2(a88))+E(f315(a24,x46561),f2(a1))
% 168.50/168.38 [4657]~E(x46571,f2(a1))+E(f75(a1,x46571),f2(a1))
% 168.50/168.38 [4663]~P147(x46631)+P30(x46631,f2(x46631))
% 168.50/168.38 [4665]~P110(x46651)+P13(x46651,f102(x46651))
% 168.50/168.38 [4674]P1(x46741)+P1(f315(a310,x46741))
% 168.50/168.38 [4728]~P147(x47281)+~P30(x47281,f71(x47281))
% 168.50/168.38 [4765]~P1(x47651)+~P1(f315(a310,x47651))
% 168.50/168.38 [4786]E(f315(a93,x47861),f2(a901))+~P1(f315(a182,x47861))
% 168.50/168.38 [4852]~P70(x48521)+P17(x48521,x48521,f74(x48521))
% 168.50/168.38 [4853]~P103(x48531)+P15(x48531,x48531,f99(x48531))
% 168.50/168.38 [4854]~P99(x48541)+P15(x48541,x48541,f74(x48541))
% 168.50/168.38 [4855]~P104(x48551)+P15(x48551,x48551,f90(x48551))
% 168.50/168.38 [4856]~P110(x48561)+P15(x48561,x48561,f221(x48561))
% 168.50/168.38 [4857]~P110(x48571)+P15(x48571,x48571,f222(x48571))
% 168.50/168.38 [4660]~E(x46601,f2(a901))+E(f315(f89(a1),x46601),f2(a1))
% 168.50/168.38 [4667]~P97(x46671)+E(f315(f92(x46671),a76),f2(x46671))
% 168.50/168.38 [4670]~E(f562(x46701),f2(a901))+E(f315(f154(a901),x46701),f2(a901))
% 168.50/168.38 [4671]~P109(x46711)+E(f225(x46711,f223(x46711)),f221(x46711))
% 168.50/168.38 [4672]~P109(x46721)+E(f226(x46721,f223(x46721)),f222(x46721))
% 168.50/168.38 [4673]~P93(x46731)+E(f75(x46731,f2(x46731)),f2(x46731))
% 168.50/168.38 [4682]~P147(x46821)+E(f315(f89(x46821),f71(a901)),f71(x46821))
% 168.50/168.38 [4683]~P147(x46831)+E(f315(f89(x46831),f2(a901)),f2(x46831))
% 168.50/168.38 [4684]~P143(x46841)+E(f315(f91(x46841),f71(a1)),f71(x46841))
% 168.50/168.38 [4685]~P143(x46851)+E(f315(f91(x46851),f2(a1)),f2(x46851))
% 168.50/168.38 [4686]E(x46861,f2(a901))+~E(f315(f89(a1),x46861),f2(a1))
% 168.50/168.38 [4722]~P114(x47221)+E(f315(f69(x47221),f71(x47221)),f71(x47221))
% 168.50/168.38 [4723]~P89(x47231)+E(f315(f69(x47231),f2(x47231)),f2(x47231))
% 168.50/168.38 [4724]~P98(x47241)+E(f315(f72(x47241),f177(x47241)),f230(x47241))
% 168.50/168.38 [4725]~P76(x47251)+E(f315(f72(x47251),f2(x47251)),f2(x47251))
% 168.50/168.38 [4726]~P98(x47261)+E(f315(f72(x47261),f230(x47261)),f177(x47261))
% 168.50/168.38 [4727]~P85(x47271)+E(f315(f154(x47271),f102(x47271)),f2(x47271))
% 168.50/168.38 [4745]~P38(x47451)+P42(f315(f161(a1),x47451))
% 168.50/168.38 [4770]~P97(x47701)+E(f315(f72(x47701),f71(x47701)),f315(f92(x47701),a86))
% 168.50/168.38 [4785]~P97(x47851)+P30(x47851,f315(f92(x47851),a76))
% 168.50/168.38 [4811]P38(x48111)+~P42(f315(f161(a1),x48111))
% 168.50/168.38 [4858]E(f315(f89(a1),f315(a93,x48581)),x48581)+P1(f315(a182,x48581))
% 168.50/168.38 [4928]~P117(x49281)+E(f233(x49281,f71(x49281),f74(x49281)),f232(x49281))
% 168.50/168.38 [4961]~P97(x49611)+~P30(x49611,f315(f92(x49611),a86))
% 168.50/168.38 [5114]E(f315(f69(a1),x51141),x51141)+P1(f315(f315(f224(a1),x51141),f2(a1)))
% 168.50/168.38 [5132]~E(f315(a93,x51321),f2(a901))+P1(f315(f315(f223(a1),x51321),f2(a1)))
% 168.50/168.38 [5198]~P1(f315(a182,x51981))+P1(f315(f315(f224(a1),x51981),f2(a1)))
% 168.50/168.38 [5238]~P143(x52381)+P1(f315(f315(f317(x52381),f71(x52381)),f98(x52381)))
% 168.50/168.38 [5239]~P147(x52391)+P1(f315(f315(f317(x52391),f71(x52391)),f175(x52391)))
% 168.50/168.38 [5240]~P143(x52401)+P1(f315(f315(f317(x52401),f2(x52401)),f98(x52401)))
% 168.50/168.38 [5241]~P147(x52411)+P1(f315(f315(f317(x52411),f2(x52411)),f175(x52411)))
% 168.50/168.38 [5242]~P128(x52421)+P1(f315(f315(f223(x52421),f2(x52421)),f71(x52421)))
% 168.50/168.38 [5243]~P128(x52431)+P1(f315(f315(f224(x52431),f2(x52431)),f71(x52431)))
% 168.50/168.38 [5296]E(x52961,f71(a901))+~P1(f315(f315(f275(a901),x52961),f71(a901)))
% 168.50/168.38 [5297]E(x52971,f2(a901))+~P1(f315(f315(f223(a901),x52971),f2(a901)))
% 168.50/168.38 [5339]E(f315(a93,x53391),f2(a901))+~P1(f315(f315(f223(a1),x53391),f2(a1)))
% 168.50/168.38 [5397]P1(f315(a182,x53971))+~P1(f315(f315(f224(a1),x53971),f2(a1)))
% 168.50/168.38 [5404]~P110(x54041)+P17(x54041,f902(x54041),f137(x54041,x54041,f7(x54041)))
% 168.50/168.38 [5422]P42(x54221)+~P1(f315(f315(f223(a1),f2(a1)),f392(x54221)))
% 168.50/168.38 [5427]E(f315(f69(a1),x54271),f315(f72(a1),x54271))+~P1(f315(f315(f224(a1),x54271),f2(a1)))
% 168.50/168.38 [5600]~P128(x56001)+~P1(f315(f315(f223(x56001),f71(x56001)),f2(x56001)))
% 168.50/168.38 [5601]~P128(x56011)+~P1(f315(f315(f224(x56011),f71(x56011)),f2(x56011)))
% 168.50/168.38 [5617]~E(x56171,f2(a901))+P1(f315(f315(f223(a1),f315(f89(a1),x56171)),f2(a1)))
% 168.50/168.38 [5618]~E(x56181,f2(a1))+P1(f315(f315(f224(a1),f315(f69(a1),x56181)),f71(a1)))
% 168.50/168.38 [5742]~P85(x57421)+E(f131(x57421,x57421,f73(x57421),f2(x57421)),f154(x57421))
% 168.50/168.38 [5925]~P105(x59251)+P25(a901,x59251,f89(x59251),f230(f909(a901,a899)))
% 168.50/168.38 [6132]E(x61321,f2(a901))+~P1(f315(f315(f223(a1),f315(f89(a1),x61321)),f2(a1)))
% 168.50/168.38 [6133]E(x61331,f2(a1))+~P1(f315(f315(f224(a1),f315(f69(a1),x61331)),f71(a1)))
% 168.50/168.38 [6957]~P1(f315(f315(f224(a1),x69571),f2(a1)))+P1(f315(f315(f224(a1),f315(f315(f73(a1),x69571),x69571)),f2(a1)))
% 168.50/168.38 [7522]P1(f315(f315(f224(a1),x75221),f2(a1)))+~P1(f315(f315(f224(a1),f315(f315(f73(a1),x75221),x75221)),f2(a1)))
% 168.50/168.38 [8072]E(x80721,f315(a5,f2(a901)))+P1(f315(f315(f224(a901),f315(f315(f3(a901),f315(a22,x80721)),f315(a101,f2(a901)))),f315(a22,x80721)))
% 168.50/168.38 [8840]~P1(f315(f315(f224(a1),x88401),f2(a1)))+P1(f315(f315(f224(a1),f315(f315(f3(a1),f315(f315(f73(a1),x88401),x88401)),a86)),f2(a1)))
% 168.50/168.38 [8937]~P1(f315(f315(f224(a1),x89371),f2(a1)))+P1(f315(f315(f224(a1),f315(f315(f73(a1),f315(f315(f73(a1),f71(a1)),x89371)),x89371)),f2(a1)))
% 168.50/168.38 [9256]P1(f315(f315(f224(a1),x92561),f2(a1)))+~P1(f315(f315(f224(a1),f315(f315(f3(a1),f315(f315(f73(a1),x92561),x92561)),a86)),f2(a1)))
% 168.50/168.38 [9318]P1(f315(f315(f224(a1),x93181),f2(a1)))+~P1(f315(f315(f224(a1),f315(f315(f73(a1),f315(f315(f73(a1),f71(a1)),x93181)),x93181)),f2(a1)))
% 168.50/168.38 [4759]~E(a76,x47591)+E(f315(f315(f73(a1),x47591),x47591),a76)
% 168.50/168.38 [4760]~E(x47601,a76)+E(f315(f315(f73(a1),x47601),x47601),a76)
% 168.50/168.38 [4771]E(x47711,f2(a1))+E(f315(f315(f29(a1),x47711),x47711),f71(a1))
% 168.50/168.38 [4905]E(x49051,a76)+~E(f315(f315(f73(a1),x49051),x49051),a76)
% 168.50/168.38 [4906]E(a76,x49061)+~E(f315(f315(f73(a1),x49061),x49061),a76)
% 168.50/168.38 [4918]~P5(x49181)+E(f30(x49181,f177(f909(x49181,a899))),f177(x49181))
% 168.50/168.38 [4919]~P5(x49191)+E(f30(x49191,f230(f909(x49191,a899))),f230(x49191))
% 168.50/168.38 [4920]~P5(x49201)+E(f31(x49201,f177(f909(x49201,a899))),f230(x49201))
% 168.50/168.38 [4921]~P5(x49211)+E(f31(x49211,f230(f909(x49211,a899))),f177(x49211))
% 168.50/168.38 [4922]~P110(x49221)+E(f128(x49221,f177(f909(x49221,a899))),f102(x49221))
% 168.50/168.38 [5069]E(x50691,f2(a901))+P1(f315(f315(f224(a901),f2(a901)),x50691))
% 168.50/168.38 [5089]~P6(x50891)+P1(f315(f315(f223(a1),f2(a1)),x50891))
% 168.50/168.38 [5123]~E(f315(f92(a901),x51231),f2(a901))+P1(f315(f315(f223(a1),x51231),a76))
% 168.50/168.38 [5128]P42(x51281)+P1(f315(f315(f317(a1),f392(x51281)),x51281))
% 168.50/168.38 [5129]E(x51291,f315(a5,f2(a901)))+P1(f315(f315(f223(a88),f71(a88)),x51291))
% 168.50/168.38 [5170]P1(f315(a182,x51701))+P1(f315(f315(f223(a1),f2(a1)),x51701))
% 168.50/168.38 [5220]E(f315(f89(a1),f315(a93,x52201)),f2(a1))+P1(f315(f315(f223(a1),f2(a1)),x52201))
% 168.50/168.38 [5277]E(f315(f89(a1),f315(f92(a901),x52771)),f315(f92(a1),x52771))+P1(f315(a182,f315(f92(a1),x52771)))
% 168.50/168.38 [5303]E(f315(f92(a901),x53031),f2(a901))+~P1(f315(a182,f315(f92(a1),x53031)))
% 168.50/168.38 [5304]E(f315(f92(a901),x53041),f2(a901))+~P1(f315(f315(f223(a1),x53041),a76))
% 168.50/168.38 [5336]P6(x53361)+~P1(f315(f315(f223(a1),f2(a1)),x53361))
% 168.50/168.38 [5407]E(f315(a101,f655(x54071)),x54071)+~P1(f315(f315(f224(a901),f2(a901)),x54071))
% 168.50/168.38 [5416]E(f315(a101,f315(f92(a901),x54161)),f71(a901))+~P1(f315(a182,f315(f92(a1),x54161)))
% 168.50/168.38 [5423]E(f315(f89(a1),f328(x54231)),x54231)+~P1(f315(f315(f224(a1),f2(a1)),x54231))
% 168.50/168.38 [5430]~E(x54301,f315(a5,f2(a901)))+~P1(f315(f315(f223(a88),f71(a88)),x54301))
% 168.50/168.38 [5437]E(f315(f89(a1),f315(f92(a901),x54371)),f2(a1))+~P1(f315(a182,f315(f92(a1),x54371)))
% 168.50/168.38 [5463]E(f315(f154(a901),x54631),f2(a901))+P1(f315(f315(f317(a901),f562(x54631)),f315(f161(a901),x54631)))
% 168.50/168.38 [5484]E(f315(f89(a1),f315(a93,x54841)),x54841)+~P1(f315(f315(f223(a1),f2(a1)),x54841))
% 168.50/168.38 [5492]~P1(f315(a182,x54921))+~P1(f315(f315(f223(a1),f2(a1)),x54921))
% 168.50/168.38 [5593]E(f315(f315(f73(a901),f71(a901)),f315(f92(a901),x55931)),f71(a901))+~P1(f315(f315(f224(a1),x55931),a76))
% 168.50/168.38 [5660]E(x56601,f2(a901))+~P1(f315(f315(f224(a901),x56601),f315(a101,f2(a901))))
% 168.50/168.38 [5683]E(x56831,f315(a101,f2(a901)))+~P1(f315(f315(f275(a901),x56831),f315(a101,f2(a901))))
% 168.50/168.38 [5701]E(f315(f315(f3(a901),f315(f92(a901),x57011)),f71(a901)),f2(a901))+~P1(f315(f315(f223(a1),x57011),a76))
% 168.50/168.38 [5702]E(f315(f315(f73(a901),f315(f92(a901),x57021)),f71(a901)),f71(a901))+~P1(f315(f315(f224(a1),x57021),a76))
% 168.50/168.38 [5714]~P42(x57141)+E(f315(f28(a901),f315(f298(a1,a901,a93),x57141)),f315(f28(a1),x57141))
% 168.50/168.38 [5743]~P110(x57431)+E(f225(x57431,f315(f9(x57431,x57431,a899),f223(x57431))),f222(x57431))
% 168.50/168.38 [5744]~P110(x57441)+E(f226(x57441,f315(f9(x57441,x57441,a899),f223(x57441))),f221(x57441))
% 168.50/168.38 [5754]E(f38(a901,f315(a101,f2(a901)),f315(f92(a901),x57541)),f315(a101,f2(a901)))+~P1(f315(a182,f315(f92(a1),x57541)))
% 168.50/168.38 [5763]~P1(f315(f315(f224(a1),f2(a1)),x57631))+P1(f315(f315(f223(a1),f71(a1)),x57631))
% 168.50/168.38 [5764]P1(f315(f315(f224(a1),f2(a1)),x57641))+~P1(f315(f315(f223(a1),f71(a1)),x57641))
% 168.50/168.38 [5775]E(f315(a101,f315(f315(f3(a901),x57751),f71(a901))),x57751)+~P1(f315(f315(f224(a901),f2(a901)),x57751))
% 168.50/168.38 [5831]P1(f315(f315(f224(a901),f2(a901)),f328(x58311)))+~P1(f315(f315(f224(a1),f2(a1)),x58311))
% 168.50/168.38 [5892]E(f38(a1,f315(f92(a1),a86),x58921),f315(f315(f3(a1),x58921),f71(a1)))+~P1(f315(f315(f224(a1),f2(a1)),x58921))
% 168.50/168.38 [5938]~P1(f315(f315(f224(a1),a76),x59381))+P1(f315(f315(f224(a901),f2(a901)),f315(f92(a901),x59381)))
% 168.50/168.38 [5943]E(f315(a22,f790(x59431)),x59431)+~P1(f315(f315(f317(a901),x59431),f230(f909(a901,a899))))
% 168.50/168.38 [5996]P1(f315(f315(f224(a901),f2(a901)),f315(a93,x59961)))+~P1(f315(f315(f224(a1),f2(a1)),x59961))
% 168.50/168.38 [6046]~P1(f315(f315(f224(a901),f2(a901)),x60461))+P1(f315(f315(f224(a1),f2(a1)),f315(f89(a1),x60461)))
% 168.50/168.38 [6082]~P1(f315(f315(f224(a901),f2(a901)),f315(a93,x60821)))+P1(f315(f315(f224(a1),f2(a1)),x60821))
% 168.50/168.38 [6098]~P42(x60981)+E(f315(f298(a901,a1,f89(a1)),f315(f298(a1,a901,a93),x60981)),x60981)
% 168.50/168.38 [6111]P1(f315(f315(f224(a1),a76),x61111))+~P1(f315(f315(f224(a901),f2(a901)),f315(f92(a901),x61111)))
% 168.50/168.38 [6170]P1(f315(f315(f224(a901),f2(a901)),x61701))+~P1(f315(f315(f224(a1),f2(a1)),f315(f89(a1),x61701)))
% 168.50/168.38 [6290]E(f315(f298(a901,a1,f89(a1)),f315(f270(a901),f315(a93,x62901))),f315(f290(a1,f2(a1)),x62901))+~P1(f315(f315(f223(a1),f2(a1)),x62901))
% 168.50/168.38 [6306]~P128(x63061)+P1(f315(f315(f224(x63061),f2(x63061)),f315(f315(f73(x63061),f71(x63061)),f71(x63061))))
% 168.50/168.38 [6356]P1(f315(f315(f224(a901),f315(a101,f2(a901))),f315(a93,x63561)))+~P1(f315(f315(f224(a1),f71(a1)),x63561))
% 168.50/168.38 [6458]E(x64581,f2(a1))+P1(f315(f42(f2(a1),x64581),f315(f315(f240(a1,a1),f2(a1)),f2(a1))))
% 168.50/168.38 [6633]~P1(f315(f315(f224(a901),f315(a101,f2(a901))),f315(a93,x66331)))+P1(f315(f315(f224(a1),f71(a1)),x66331))
% 168.50/168.38 [7073]~P119(x70731)+P39(x70731,f315(f250(f908(x70731,x70731)),f315(f245(x70731,x70731,a899),f224(x70731))))
% 168.50/168.38 [5647]E(f315(f92(a901),f315(f315(f3(a1),x56471),a86)),f315(a101,f315(f92(a901),x56471)))+P1(f315(a182,f315(f92(a1),x56471)))
% 168.50/168.38 [5663]~P38(x56631)+E(f315(f315(f143(a901,a1),f89(a1)),f315(f315(f143(a1,a901),a93),x56631)),x56631)
% 168.50/168.38 [5677]P28(a898,a801,x56771)+~P1(f315(f315(f317(f900(a898)),x56771),a910))
% 168.50/168.38 [5781]E(f315(f72(a1),f315(f89(a1),f315(a101,f352(x57811)))),x57811)+~P1(f315(f315(f224(a1),x57811),f2(a1)))
% 168.50/168.38 [5791]E(f315(f315(f73(a901),f71(a901)),f315(f92(a901),x57911)),f315(f92(a901),f315(f315(f3(a1),x57911),a86)))+P1(f315(f315(f224(a1),x57911),a76))
% 168.50/168.38 [5833]E(f315(f315(f29(a1),f315(f92(a1),a86)),x58331),f315(f92(a1),a86))+~P1(f315(f315(f224(a1),f2(a1)),x58331))
% 168.50/168.38 [5934]E(f315(f315(f3(a901),f315(f92(a901),x59341)),f71(a901)),f315(f92(a901),f315(f315(f73(a1),x59341),a86)))+P1(f315(f315(f223(a1),x59341),a76))
% 168.50/168.38 [5935]E(f315(f315(f73(a901),f315(f92(a901),x59351)),f71(a901)),f315(f92(a901),f315(f315(f3(a1),x59351),a86)))+P1(f315(f315(f224(a1),x59351),a76))
% 168.50/168.38 [5981]E(f315(a93,f315(f315(f73(a1),f71(a1)),x59811)),f315(a101,f315(a93,x59811)))+~P1(f315(f315(f223(a1),f2(a1)),x59811))
% 168.50/168.38 [6017]E(f315(a101,f315(f315(f3(a901),x60171),f315(a101,f2(a901)))),x60171)+~P1(f315(f315(f224(a901),f2(a901)),x60171))
% 168.50/168.38 [6238]E(f38(a901,f315(a101,f2(a901)),f315(f92(a901),x62381)),f315(a93,f38(a1,f71(a1),f315(f92(a1),x62381))))+P1(f315(a182,f315(f92(a1),x62381)))
% 168.50/168.38 [6283]~P1(f315(f315(f223(a1),a76),x62831))+P1(f315(f315(f223(a1),a76),f315(f315(f73(a1),x62831),x62831)))
% 168.50/168.38 [6284]~P1(f315(f315(f224(a1),a86),x62841))+P1(f315(f315(f223(a1),a86),f315(f315(f73(a1),x62841),x62841)))
% 168.50/168.38 [6285]~P1(f315(f315(f224(a1),a76),x62851))+P1(f315(f315(f224(a1),a76),f315(f315(f73(a1),x62851),x62851)))
% 168.50/168.38 [6286]~P1(f315(f315(f224(a1),a86),x62861))+P1(f315(f315(f224(a1),a86),f315(f315(f73(a1),x62861),x62861)))
% 168.50/168.38 [6472]~P1(f315(f54(x64721),f230(f909(x64721,a899))))+P1(f315(f54(f905(x64721)),f230(f909(f905(x64721),a899))))
% 168.50/168.38 [6561]~P1(f315(f315(f223(a1),f2(a1)),x65611))+P1(f315(f315(f224(a1),f2(a1)),f315(f315(f73(a1),f71(a1)),x65611)))
% 168.50/168.38 [6568]E(f315(f239(a1,a1),f40(f71(a1),f315(f92(a1),x65681))),f315(f315(f29(a1),f71(a1)),f315(f92(a1),x65681)))+~P1(f315(f315(f223(a1),f2(a1)),f315(f92(a1),x65681)))
% 168.50/168.38 [6592]E(f315(f244(a1,a1),f40(f71(a1),f315(f92(a1),x65921))),f38(a1,f71(a1),f315(f92(a1),x65921)))+~P1(f315(f315(f223(a1),f2(a1)),f315(f92(a1),x65921)))
% 168.50/168.38 [6604]P1(f315(f54(x66041),f230(f909(x66041,a899))))+~P1(f315(f54(f905(x66041)),f230(f909(f905(x66041),a899))))
% 168.50/168.38 [6634]P1(f315(f315(f223(a1),a76),x66341))+~P1(f315(f315(f223(a1),a76),f315(f315(f73(a1),x66341),x66341)))
% 168.50/168.38 [6635]P1(f315(f315(f224(a1),a76),x66351))+~P1(f315(f315(f224(a1),a76),f315(f315(f73(a1),x66351),x66351)))
% 168.50/168.38 [6636]P1(f315(f315(f224(a1),a86),x66361))+~P1(f315(f315(f223(a1),a86),f315(f315(f73(a1),x66361),x66361)))
% 168.50/168.38 [6637]P1(f315(f315(f224(a1),a86),x66371))+~P1(f315(f315(f224(a1),a86),f315(f315(f73(a1),x66371),x66371)))
% 168.50/168.38 [6961]~P1(f315(f54(x69611),f230(f909(x69611,a899))))+P1(f315(f315(f224(a901),f2(a901)),f315(f28(x69611),f230(f909(x69611,a899)))))
% 168.50/168.38 [7560]P1(f315(f54(a901),x75601))+~P1(f315(f54(a1),f315(f298(a901,a1,f89(a1)),x75601)))
% 168.50/168.38 [5568]~E(a86,x55681)+E(f315(f315(f3(a1),f315(f315(f73(a1),x55681),x55681)),a86),a86)
% 168.50/168.38 [5569]~E(x55691,a86)+E(f315(f315(f3(a1),f315(f315(f73(a1),x55691),x55691)),a86),a86)
% 168.50/168.38 [6106]E(x61061,a86)+~E(f315(f315(f3(a1),f315(f315(f73(a1),x61061),x61061)),a86),a86)
% 168.50/168.38 [6107]E(a86,x61071)+~E(f315(f315(f3(a1),f315(f315(f73(a1),x61071),x61071)),a86),a86)
% 168.50/168.38 [6529]~E(f315(f92(a901),x65291),f2(a901))+P1(f315(a182,f315(f92(a1),f315(f315(f73(a1),x65291),a86))))
% 168.50/168.38 [6891]~P1(f315(a182,f315(f92(a1),x68911)))+P1(f315(a182,f315(f92(a1),f315(f315(f73(a1),x68911),x68911))))
% 168.50/168.38 [6892]~P1(f315(f315(f223(a1),x68921),a76))+P1(f315(f315(f223(a1),f315(f315(f73(a1),x68921),x68921)),a76))
% 168.50/168.38 [6893]~P1(f315(f315(f223(a1),x68931),a86))+P1(f315(f315(f223(a1),f315(f315(f73(a1),x68931),x68931)),a86))
% 168.50/168.38 [6894]~P1(f315(f315(f224(a1),x68941),a76))+P1(f315(f315(f224(a1),f315(f315(f73(a1),x68941),x68941)),a76))
% 168.50/168.38 [6895]~P1(f315(f315(f223(a1),x68951),a86))+P1(f315(f315(f224(a1),f315(f315(f73(a1),x68951),x68951)),a86))
% 168.50/168.38 [7221]E(f315(f92(a901),x72211),f2(a901))+~P1(f315(a182,f315(f92(a1),f315(f315(f73(a1),x72211),a86))))
% 168.50/168.38 [7475]~P1(f315(f315(f223(a1),f2(a1)),f315(f92(a1),x74751)))+P1(f315(f315(f223(a1),f2(a1)),f315(f92(a1),f315(f315(f73(a1),x74751),x74751))))
% 168.50/168.38 [7476]P1(f315(a182,f315(f92(a1),x74761)))+~P1(f315(a182,f315(f92(a1),f315(f315(f73(a1),x74761),x74761))))
% 168.50/168.38 [7477]P1(f315(f315(f223(a1),x74771),a76))+~P1(f315(f315(f223(a1),f315(f315(f73(a1),x74771),x74771)),a76))
% 168.50/168.38 [7478]P1(f315(f315(f223(a1),x74781),a86))+~P1(f315(f315(f223(a1),f315(f315(f73(a1),x74781),x74781)),a86))
% 168.50/168.38 [7479]P1(f315(f315(f223(a1),x74791),a86))+~P1(f315(f315(f224(a1),f315(f315(f73(a1),x74791),x74791)),a86))
% 168.50/168.38 [7480]P1(f315(f315(f224(a1),x74801),a76))+~P1(f315(f315(f224(a1),f315(f315(f73(a1),x74801),x74801)),a76))
% 168.50/168.38 [7842]E(f315(a95,f500(x78421)),x78421)+~P1(f315(f315(f317(f909(f908(a901,a901),a899)),x78421),a87))
% 168.50/168.38 [6445]~P97(x64451)+E(f315(f92(x64451),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f71(x64451))
% 168.50/168.38 [6941]~P1(f315(a182,f315(f92(a1),x69411)))+E(f315(f92(a901),f315(f315(f3(a1),f315(f315(f73(a1),x69411),x69411)),a86)),f2(a901))
% 168.50/168.38 [8017]~P1(f315(f315(f224(a1),f315(f92(a1),x80171)),f2(a1)))+E(f315(f239(a1,a1),f315(a44,f43(f315(f72(a1),f71(a1)),f315(f72(a1),f315(f92(a1),x80171))))),f315(f315(f29(a1),f71(a1)),f315(f92(a1),x80171)))
% 168.50/168.38 [8030]~P1(f315(f315(f224(a1),f315(f92(a1),x80301)),f2(a1)))+E(f315(f244(a1,a1),f315(a44,f43(f315(f72(a1),f71(a1)),f315(f72(a1),f315(f92(a1),x80301))))),f38(a1,f71(a1),f315(f92(a1),x80301)))
% 168.50/168.38 [8079]~P1(f315(f315(f223(a1),a76),x80791))+P1(f315(f315(f223(a1),a76),f315(f315(f3(a1),f315(f315(f73(a1),x80791),x80791)),a86)))
% 168.50/168.38 [8080]~P1(f315(f315(f223(a1),a86),x80801))+P1(f315(f315(f223(a1),a86),f315(f315(f3(a1),f315(f315(f73(a1),x80801),x80801)),a86)))
% 168.50/168.38 [8081]~P1(f315(f315(f223(a1),a76),x80811))+P1(f315(f315(f224(a1),a76),f315(f315(f3(a1),f315(f315(f73(a1),x80811),x80811)),a86)))
% 168.50/168.38 [8082]~P1(f315(f315(f224(a1),a86),x80821))+P1(f315(f315(f224(a1),a86),f315(f315(f3(a1),f315(f315(f73(a1),x80821),x80821)),a86)))
% 168.50/168.38 [8382]~P97(x83821)+~P30(x83821,f315(f92(x83821),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))
% 168.50/168.38 [8565]P1(f315(f315(f223(a1),a76),x85651))+~P1(f315(f315(f223(a1),a76),f315(f315(f3(a1),f315(f315(f73(a1),x85651),x85651)),a86)))
% 168.50/168.38 [8566]P1(f315(f315(f223(a1),a76),x85661))+~P1(f315(f315(f224(a1),a76),f315(f315(f3(a1),f315(f315(f73(a1),x85661),x85661)),a86)))
% 168.50/168.38 [8567]P1(f315(f315(f223(a1),a86),x85671))+~P1(f315(f315(f223(a1),a86),f315(f315(f3(a1),f315(f315(f73(a1),x85671),x85671)),a86)))
% 168.50/168.38 [8568]P1(f315(f315(f224(a1),a86),x85681))+~P1(f315(f315(f224(a1),a86),f315(f315(f3(a1),f315(f315(f73(a1),x85681),x85681)),a86)))
% 168.50/168.38 [8887]E(f315(f92(a901),f315(f315(f3(a1),f315(f315(f73(a1),x88871),x88871)),a86)),f315(f315(f79(a901,a901),f315(f92(a901),x88871)),f315(f315(f10(a901,a901,a901),a101),f315(f315(f20(a901,a901,a901),f73(a901)),f7(a901)))))+P1(f315(a182,f315(f92(a1),x88871)))
% 168.50/168.38 [9754]E(x97541,f177(f909(f908(a901,a901),a899)))+P1(f315(f315(f317(f908(f909(f908(a901,a901),a899),f909(f908(a901,a901),a899))),f315(f315(f240(f909(f908(a901,a901),a899),f909(f908(a901,a901),a899)),x97541),f177(f909(f908(a901,a901),a899)))),a62))
% 168.50/168.38 [8814]~P1(f315(a182,f315(f92(a1),x88141)))+P1(f315(a182,f315(f92(a1),f315(f315(f3(a1),f315(f315(f73(a1),x88141),x88141)),a86))))
% 168.50/168.38 [8815]~P1(f315(f315(f224(a1),x88151),a76))+P1(f315(f315(f223(a1),f315(f315(f3(a1),f315(f315(f73(a1),x88151),x88151)),a86)),a76))
% 168.50/168.38 [8816]~P1(f315(f315(f223(a1),x88161),a86))+P1(f315(f315(f223(a1),f315(f315(f3(a1),f315(f315(f73(a1),x88161),x88161)),a86)),a86))
% 168.50/168.38 [8817]~P1(f315(f315(f224(a1),x88171),a76))+P1(f315(f315(f224(a1),f315(f315(f3(a1),f315(f315(f73(a1),x88171),x88171)),a86)),a76))
% 168.50/168.38 [8818]~P1(f315(f315(f224(a1),x88181),a86))+P1(f315(f315(f224(a1),f315(f315(f3(a1),f315(f315(f73(a1),x88181),x88181)),a86)),a86))
% 168.50/168.38 [8928]~P1(f315(f315(f223(a1),f2(a1)),f315(f92(a1),x89281)))+P1(f315(f315(f223(a1),f2(a1)),f315(f92(a1),f315(f315(f3(a1),f315(f315(f73(a1),x89281),x89281)),a86))))
% 168.50/168.38 [9087]~P97(x90871)+E(f315(f315(f73(x90871),f71(x90871)),f71(x90871)),f315(f92(x90871),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))))
% 168.50/168.38 [9240]P1(f315(a182,f315(f92(a1),x92401)))+~P1(f315(a182,f315(f92(a1),f315(f315(f3(a1),f315(f315(f73(a1),x92401),x92401)),a86))))
% 168.50/168.38 [9241]P1(f315(f315(f223(a1),x92411),a86))+~P1(f315(f315(f223(a1),f315(f315(f3(a1),f315(f315(f73(a1),x92411),x92411)),a86)),a86))
% 168.50/168.38 [9242]P1(f315(f315(f224(a1),x92421),a76))+~P1(f315(f315(f223(a1),f315(f315(f3(a1),f315(f315(f73(a1),x92421),x92421)),a86)),a76))
% 168.50/168.38 [9243]P1(f315(f315(f224(a1),x92431),a76))+~P1(f315(f315(f224(a1),f315(f315(f3(a1),f315(f315(f73(a1),x92431),x92431)),a86)),a76))
% 168.50/168.38 [9244]P1(f315(f315(f224(a1),x92441),a86))+~P1(f315(f315(f224(a1),f315(f315(f3(a1),f315(f315(f73(a1),x92441),x92441)),a86)),a86))
% 168.50/168.38 [9799]~P1(f315(f54(f908(a901,a901)),x97991))+P1(f315(f315(f317(f908(f909(f908(a901,a901),a899),f909(f908(a901,a901),a899))),f315(f315(f240(f909(f908(a901,a901),a899),f909(f908(a901,a901),a899)),f177(f909(f908(a901,a901),a899))),x97991)),a63))
% 168.50/168.38 [9576]~P147(x95761)+E(f315(f315(f232(x95761),f71(x95761)),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),f71(x95761))
% 168.50/168.38 [9577]~P147(x95771)+E(f315(f315(f232(x95771),f2(x95771)),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),f2(x95771))
% 168.50/168.38 [10022]~P1(f315(f315(f224(a901),f71(a901)),x100221))+P1(f315(f315(f224(a901),f2(a901)),f315(f315(f29(a901),x100221),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))))))
% 168.50/168.38 [10028]~P1(f315(f315(f224(a901),f2(a901)),x100281))+P1(f315(f315(f224(a901),f2(a901)),f315(f315(f29(a901),f315(f315(f73(a901),x100281),f71(a901))),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))))))
% 168.50/168.38 [10066]~E(f38(a901,x100661,f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),f71(a901))+P1(f315(f315(f224(a901),f2(a901)),f38(a901,x100661,f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))))))
% 168.50/168.38 [10096]E(f38(a901,x100961,f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),f71(a901))+~P1(f315(f315(f224(a901),f2(a901)),f38(a901,x100961,f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))))))
% 168.50/168.38 [4691]~P7(x46911,x46912)+P45(x46911,x46912)
% 168.50/168.38 [4692]~P39(x46921,x46922)+P59(x46921,x46922)
% 168.50/168.38 [4693]~P46(x46931,x46932)+P59(x46931,x46932)
% 168.50/168.38 [4695]~P7(x46951,x46952)+P51(x46951,x46952)
% 168.50/168.38 [4697]~P16(x46971,x46972)+P51(x46971,x46972)
% 168.50/168.38 [4699]~P7(x46991,x46992)+P52(x46991,x46992)
% 168.50/168.38 [4701]~P16(x47011,x47012)+P52(x47011,x47012)
% 168.50/168.38 [4702]~P7(x47021,x47022)+P16(x47021,x47022)
% 168.50/168.38 [4652]~E(x46521,x46522)+E(f257(x46521,x46522),f71(a88))
% 168.50/168.38 [4655]E(f205(x46551,x46552),x46551)+~E(x46552,f2(a901))
% 168.50/168.38 [4662]~E(x46622,f102(x46621))+E(f141(x46621,x46622),f102(x46621))
% 168.50/168.38 [4681]~E(f141(x46812,x46811),f102(x46812))+E(x46811,f102(x46812))
% 168.50/168.38 [4706]~P2(x47062)+P2(f909(x47061,x47062))
% 168.50/168.38 [4707]~P108(x47072)+P108(f909(x47071,x47072))
% 168.50/168.38 [4708]~P109(x47082)+P109(f909(x47081,x47082))
% 168.50/168.38 [4709]~P111(x47092)+P111(f909(x47091,x47092))
% 168.50/168.38 [4710]~P3(x47102)+P3(f909(x47101,x47102))
% 168.50/168.38 [4711]~P80(x47112)+P80(f909(x47111,x47112))
% 168.50/168.38 [4712]~P100(x47122)+P81(f909(x47121,x47122))
% 168.50/168.38 [4713]~P80(x47132)+P103(f909(x47131,x47132))
% 168.50/168.38 [4714]~P80(x47142)+P104(f909(x47141,x47142))
% 168.50/168.38 [4715]~P101(x47152)+P101(f909(x47151,x47152))
% 168.50/168.38 [4716]~P5(x47162)+P5(f909(x47161,x47162))
% 168.50/168.38 [4717]~P98(x47172)+P98(f909(x47171,x47172))
% 168.50/168.38 [4718]~P92(x47182)+P92(f909(x47181,x47182))
% 168.50/168.38 [4719]~P118(x47192)+P118(f909(x47191,x47192))
% 168.50/168.38 [4720]~P100(x47202)+P102(f909(x47201,x47202))
% 168.50/168.38 [4721]~P100(x47212)+P100(f909(x47211,x47212))
% 168.50/168.38 [4734]E(x47341,x47342)+~E(f315(a101,x47341),f315(a101,x47342))
% 168.50/168.38 [4735]E(x47351,x47352)+~E(f315(a95,x47351),f315(a95,x47352))
% 168.50/168.38 [4736]E(x47361,x47362)+~E(f315(a5,x47361),f315(a5,x47362))
% 168.50/168.38 [4738]E(x47381,x47382)+~E(f315(a22,x47381),f315(a22,x47382))
% 168.50/168.38 [4787]P41(x47871,x47872)+~E(f688(x47872,x47871),f689(x47872,x47871))
% 168.50/168.38 [4817]~P59(x48171,x48172)+P41(x48171,f295(x48171,x48172))
% 168.50/168.38 [4818]~P53(x48181,x48182)+P53(x48181,f295(x48181,x48182))
% 168.50/168.38 [4831]~P62(x48311)+E(f38(x48311,x48312,x48312),f2(x48311))
% 168.50/168.38 [4865]~P39(x48651,x48652)+P39(f902(x48651),f135(x48651,x48652))
% 168.50/168.38 [4866]~P39(x48661,x48662)+P39(f902(x48661),f134(x48661,x48662))
% 168.50/168.38 [4867]~P40(x48671,x48672)+P40(f902(x48671),f136(x48671,x48672))
% 168.50/168.38 [4868]~P40(x48681,x48682)+P40(f902(x48681),f147(x48681,x48682))
% 168.50/168.38 [4869]~P53(x48691,x48692)+P53(f902(x48691),f147(x48691,x48692))
% 168.50/168.38 [4966]~P39(x49661,x49662)+P39(f909(x49661,a899),f308(x49661,x49662))
% 168.50/168.38 [4967]~P39(x49671,x49672)+P39(f909(x49671,a899),f306(x49671,x49672))
% 168.50/168.38 [5098]~P6(x50981)+P42(f291(a1,x50981,x50982))
% 168.50/168.38 [5201]~P39(x52011,x52012)+P61(x52011,f60(x52011,x52011,x52012))
% 168.50/168.38 [5708]~P82(x57081)+P25(x57081,x57081,f72(x57081),x57082)
% 168.50/168.38 [4676]~E(x46762,f102(x46761))+E(f315(f156(x46761),x46762),f102(x46761))
% 168.50/168.38 [4677]~E(x46772,f102(x46771))+E(f315(f157(x46771),x46772),f102(x46771))
% 168.50/168.38 [4740]E(x47401,f315(a93,x47402))+~E(f315(f89(a1),x47401),x47402)
% 168.50/168.38 [4743]E(x47431,f102(x47432))+~E(f315(f156(x47432),x47431),f102(x47432))
% 168.50/168.38 [4744]E(x47441,f102(x47442))+~E(f315(f157(x47442),x47441),f102(x47442))
% 168.50/168.38 [4756]~P97(x47561)+E(f315(f92(x47561),x47562),f315(f91(x47561),x47562))
% 168.50/168.38 [4764]~P4(x47641)+P1(f315(f54(x47641),x47642))
% 168.50/168.38 [4772]~E(f647(x47722,x47721),f102(x47721))+E(f168(x47721,x47722),f102(f902(x47721)))
% 168.50/168.38 [4781]~E(x47812,f102(x47811))+E(f315(f161(x47811),x47812),f177(f909(x47811,a899)))
% 168.50/168.38 [4782]~E(x47822,f102(x47821))+E(f177(f909(x47821,a899)),f315(f161(x47821),x47822))
% 168.50/168.38 [4784]E(x47841,x47842)+~E(f315(f89(a1),x47841),f315(f89(a1),x47842))
% 168.50/168.38 [4788]E(f203(x47881,x47882),f2(a901))+P1(f315(f54(x47881),x47882))
% 168.50/168.38 [4806]~P114(x48061)+E(f75(x48061,f75(x48061,x48062)),f75(x48061,x48062))
% 168.50/168.38 [4820]~P84(x48201)+E(f315(f315(f232(x48201),x48202),f71(a901)),x48202)
% 168.50/168.38 [4821]~P121(x48211)+E(f315(f315(f232(x48211),x48212),f71(a901)),x48212)
% 168.50/168.38 [4822]~P53(x48221,x48222)+E(f315(f274(x48221,x48221),x48222),x48222)
% 168.50/168.38 [4826]E(x48261,x48262)+E(f257(x48261,x48262),f315(f315(f73(a88),x48262),f71(a88)))
% 168.50/168.38 [4829]E(f315(f28(x48291),x48292),f2(a901))+P1(f315(f54(x48291),x48292))
% 168.50/168.38 [4832]~E(f141(x48321,x48322),x48322)+P1(f315(f126(x48321),x48322))
% 168.50/168.38 [4835]~P81(x48351)+E(f315(f315(f99(x48351),x48352),f177(x48351)),x48352)
% 168.50/168.38 [4836]~P76(x48361)+E(f315(f315(f3(x48361),x48362),f2(x48361)),x48362)
% 168.50/168.38 [4837]~P77(x48371)+E(f315(f315(f74(x48371),x48372),f71(x48371)),x48372)
% 168.50/168.38 [4838]~P84(x48381)+E(f315(f315(f74(x48381),x48382),f71(x48381)),x48382)
% 168.50/168.38 [4839]~P121(x48391)+E(f315(f315(f74(x48391),x48392),f71(x48391)),x48392)
% 168.50/168.38 [4840]~P102(x48401)+E(f315(f315(f90(x48401),x48402),f230(x48401)),x48402)
% 168.50/168.38 [4841]~P72(x48411)+E(f315(f315(f73(x48411),x48412),f2(x48411)),x48412)
% 168.50/168.38 [4842]~P121(x48421)+E(f315(f315(f73(x48421),x48422),f2(x48421)),x48422)
% 168.50/168.38 [4843]~P85(x48431)+E(f315(f315(f73(x48431),x48432),f2(x48431)),x48432)
% 168.50/168.38 [4844]~P125(x48441)+E(f315(f315(f279(x48441),x48442),f71(x48441)),x48442)
% 168.50/168.38 [4845]~P62(x48451)+E(f315(f315(f29(x48451),x48452),f71(x48451)),x48452)
% 168.50/168.38 [4846]~P121(x48461)+E(f315(f315(f232(x48461),x48462),f2(a901)),f71(x48461))
% 168.50/168.38 [4847]~P117(x48471)+E(f315(f315(f232(x48471),x48472),f2(a901)),f71(x48471))
% 168.50/168.38 [4848]~E(x48482,f177(f909(x48481,a899)))+E(f315(f28(x48481),x48482),f2(a901))
% 168.50/168.38 [4859]~P62(x48591)+E(f38(x48591,x48592,f2(x48591)),x48592)
% 168.50/168.38 [4870]~P102(x48701)+E(f315(f315(f99(x48701),x48702),f230(x48701)),f230(x48701))
% 168.50/168.38 [4871]~P121(x48711)+E(f315(f315(f74(x48711),x48712),f2(x48711)),f2(x48711))
% 168.50/168.38 [4872]~P135(x48721)+E(f315(f315(f74(x48721),x48722),f2(x48721)),f2(x48721))
% 168.50/168.38 [4873]~P81(x48731)+E(f315(f315(f90(x48731),x48732),f177(x48731)),f177(x48731))
% 168.50/168.38 [4874]~P126(x48741)+E(f315(f315(f279(x48741),x48742),f2(x48741)),f2(x48741))
% 168.50/168.38 [4875]~P62(x48751)+E(f315(f315(f29(x48751),x48752),f2(x48751)),f2(x48751))
% 168.50/168.38 [4877]~P62(x48771)+E(f38(x48771,x48772,f71(x48771)),f2(x48771))
% 168.50/168.38 [4878]~P62(x48781)+E(f38(x48781,f2(x48781),x48782),f2(x48781))
% 168.50/168.38 [4907]E(x49071,f2(a901))+E(f48(x49072,x49071,f102(x49072)),f102(f902(x49072)))
% 168.50/168.38 [4930]P53(x49301,x49302)+~E(f315(f274(x49301,x49301),x49302),x49302)
% 168.50/168.38 [4931]P39(x49311,x49312)+~E(f563(x49312,x49311),f177(f909(x49311,a899)))
% 168.50/168.38 [4932]E(x49321,f102(x49322))+~E(f315(f161(x49322),x49321),f177(f909(x49322,a899)))
% 168.50/168.38 [4933]E(x49331,f102(x49332))+~E(f177(f909(x49332,a899)),f315(f161(x49332),x49331))
% 168.50/168.38 [4936]~E(x49361,x49362)+P1(f315(f315(a312,x49361),x49362))
% 168.50/168.38 [4946]P1(x49461)+P1(f315(f315(a318,x49461),x49462))
% 168.50/168.38 [4947]E(x49471,f102(x49472))+E(f315(f315(f153(x49472),x49471),f2(a901)),f315(f130(x49472),x49471))
% 168.50/168.38 [4950]E(f141(x49501,x49502),x49502)+~P1(f315(f126(x49501),x49502))
% 168.50/168.38 [4957]~P1(x49572)+P1(f315(f315(a318,x49571),x49572))
% 168.50/168.38 [4958]~P1(x49582)+P1(f315(f315(a314,x49581),x49582))
% 168.50/168.38 [4959]~P1(x49591)+P1(f315(f315(a314,x49591),x49592))
% 168.50/168.38 [4969]~E(f648(x49692,x49691),f654(x49692,x49691))+P1(f315(f126(x49691),x49692))
% 168.50/168.38 [4976]E(f315(f250(x49761),x49762),f177(f909(x49761,a899)))+P1(f315(x49762,f525(x49762)))
% 168.50/168.38 [4977]E(f177(f909(x49771,a899)),f315(f250(x49771),x49772))+P1(f315(x49772,f537(x49772)))
% 168.50/168.38 [5050]~P114(x50501)+E(f315(f315(f74(x50501),x50502),f75(x50501,x50502)),f315(f69(x50501),x50502))
% 168.50/168.38 [5062]~E(x50621,f2(a1))+E(f39(x50621,x50622),f315(f315(f240(a1,a1),f2(a1)),f2(a1)))
% 168.50/168.38 [5094]~P59(x50941,x50942)+P59(x50941,f315(f274(x50941,x50941),x50942))
% 168.50/168.38 [5095]~P40(x50951,x50952)+P40(x50951,f315(f274(x50951,x50951),x50952))
% 168.50/168.38 [5096]~P41(x50961,x50962)+P41(x50961,f315(f274(x50961,x50961),x50962))
% 168.50/168.38 [5097]~P53(x50971,x50972)+P53(x50971,f315(f274(x50971,x50971),x50972))
% 168.50/168.38 [5119]E(x51191,x51192)+~P1(f315(f315(a312,x51191),x51192))
% 168.50/168.38 [5130]P1(x51301)+~P1(f315(f315(a313,x51302),x51301))
% 168.50/168.38 [5131]P1(x51311)+~P1(f315(f315(a313,x51311),x51312))
% 168.50/168.38 [5136]~P118(x51361)+P1(f315(f315(f223(x51361),x51362),f230(x51361)))
% 168.50/168.38 [5137]~P121(x51371)+P1(f315(f315(f275(x51371),x51372),f2(x51371)))
% 168.50/168.38 [5141]E(x51411,x51412)+~E(f315(x51411,f393(x51412,x51411)),f315(x51412,f393(x51412,x51411)))
% 168.50/168.38 [5172]E(x51721,f2(a901))+E(f205(x51721,f38(a901,x51722,x51721)),f205(x51722,x51721))
% 168.50/168.38 [5177]~P110(x51771)+P13(x51771,f315(f315(f140(x51771),x51772),f102(x51771)))
% 168.50/168.38 [5179]E(x51791,f2(a1))+P1(f315(f42(x51792,x51791),f39(x51792,x51791)))
% 168.50/168.38 [5196]~P16(x51962,x51961)+P1(f315(f315(x51961,f782(x51961)),f782(x51961)))
% 168.50/168.38 [5199]~E(x51991,x51992)+P1(f315(f315(f224(a901),x51991),f315(a101,x51992)))
% 168.50/168.38 [5209]~E(x52091,f2(a901))+P1(f315(f315(f224(a901),x52091),f315(a101,x52092)))
% 168.50/168.38 [5219]P1(f315(x52191,x52192))+P1(f315(f315(f223(a1),f2(a1)),f342(x52191)))
% 168.50/168.38 [5282]E(f315(f315(f297(x52822),f346(x52822,x52821)),f394(x52822,x52821)),x52821)+E(x52821,f177(f909(x52822,a899)))
% 168.50/168.38 [5283]P59(x52831,x52832)+~P59(x52831,f315(f274(x52831,x52831),x52832))
% 168.50/168.38 [5284]P40(x52841,x52842)+~P40(x52841,f315(f274(x52841,x52841),x52842))
% 168.50/168.38 [5285]P41(x52851,x52852)+~P41(x52851,f315(f274(x52851,x52851),x52852))
% 168.50/168.38 [5286]P53(x52861,x52862)+~P53(x52861,f315(f274(x52861,x52861),x52862))
% 168.50/168.38 [5289]~E(f38(a901,x52892,x52891),f2(a901))+E(f315(f315(f74(a901),x52891),f347(x52891,x52892)),x52892)
% 168.50/168.38 [5290]~E(f38(a1,x52902,x52901),f2(a1))+E(f315(f315(f74(a1),x52901),f322(x52901,x52902)),x52902)
% 168.50/168.38 [5317]~P1(f315(x53171,x53172))+P1(f315(f315(f223(a1),f2(a1)),f321(x53171)))
% 168.50/168.38 [5328]E(f315(f315(f3(a901),f315(a93,x53281)),f315(a93,x53282)),f315(a93,x53281))+~P1(f315(a182,x53282))
% 168.50/168.38 [5351]E(f260(x53511,x53512),f71(a88))+~P1(f315(f315(f223(a88),x53511),f71(a88)))
% 168.50/168.38 [5449]E(f315(f315(f153(x54491),x54492),f648(x54492,x54491)),f315(f315(f153(x54491),x54492),f654(x54492,x54491)))+P1(f315(f126(x54491),x54492))
% 168.50/168.38 [5493]~P1(f315(x54931,f83(x54932,x54931)))+P1(f315(x54931,f564(x54932,x54931)))
% 168.50/168.38 [5558]P61(x55581,x55582)+~P1(f315(f303(x55581,x55582),f538(x55582,x55581)))
% 168.50/168.38 [5705]~P16(x57052,x57051)+P1(f315(f315(x57051,f783(x57051,x57052)),f783(x57051,x57052)))
% 168.50/168.38 [5706]~P16(x57062,x57061)+P1(f315(f315(x57061,f787(x57061,x57062)),f787(x57061,x57062)))
% 168.50/168.38 [5715]~E(f315(a101,f38(a901,x57151,x57152)),x57152)+E(f38(a901,f315(a101,x57151),x57152),f2(a901))
% 168.50/168.38 [5770]P39(x57701,x57702)+P1(f315(f315(f317(x57701),f580(x57702,x57701)),f581(x57702,x57701)))
% 168.50/168.38 [5777]~P97(x57771)+P1(f315(f315(f317(x57771),f315(f92(x57771),x57772)),f98(x57771)))
% 168.50/168.38 [5778]~P143(x57781)+P1(f315(f315(f317(x57781),f315(f89(x57781),x57782)),f98(x57781)))
% 168.50/168.38 [5779]~P147(x57791)+P1(f315(f315(f317(x57791),f315(f89(x57791),x57792)),f175(x57791)))
% 168.50/168.38 [5780]~P143(x57801)+P1(f315(f315(f317(x57801),f315(f91(x57801),x57802)),f98(x57801)))
% 168.50/168.38 [5923]~P40(x59231,x59232)+E(f315(f315(f277(x59231,x59231,x59231),x59232),f295(x59231,x59232)),x59232)
% 168.50/168.38 [5937]E(f315(a101,f38(a901,x59371,x59372)),x59372)+E(f38(a901,f315(a101,x59371),x59372),f315(a101,f38(a901,x59371,x59372)))
% 168.50/168.38 [6369]P39(x63691,x63692)+~P1(f315(f315(f317(x63691),f539(x63692,x63691)),f304(x63691,x63692)))
% 168.50/168.38 [6407]~P128(x64071)+~P1(f315(f315(f224(x64071),f315(f89(x64071),x64072)),f2(x64071)))
% 168.50/168.38 [6408]~P89(x64081)+~P1(f315(f315(f224(x64081),f315(f69(x64081),x64082)),f2(x64081)))
% 168.50/168.38 [6441]E(x64411,f177(f909(x64412,a899)))+~P1(f315(f315(f317(x64412),f346(x64412,x64411)),f394(x64412,x64411)))
% 168.50/168.38 [6499]P1(f315(f315(f224(a1),x64991),f38(a1,x64992,x64991)))+~P1(f315(f315(f224(a1),x64991),f2(a1)))
% 168.50/168.38 [6606]E(f315(f315(f297(a901),f315(a101,x66061)),f291(a901,x66062,x66061)),f291(a901,x66062,f315(a101,x66061)))+~P1(f315(f315(f223(a901),x66062),f315(a101,x66061)))
% 168.50/168.38 [6698]~P110(x66981)+P13(x66981,f139(x66981,x66981,f7(x66981),x66982))
% 168.50/168.38 [6830]E(f315(f156(x68301),x68302),x68302)+~P1(f315(f315(f223(a901),f315(f178(f902(x68301)),x68302)),f71(a901)))
% 168.50/168.38 [6852]~P89(x68521)+P1(f315(f315(f223(x68521),f315(f72(x68521),f315(f69(x68521),x68522))),f2(x68521)))
% 168.50/168.38 [6887]~P39(x68871,x68872)+P39(x68871,f315(f315(f277(x68871,x68871,x68871),x68872),f295(x68871,x68872)))
% 168.50/168.38 [6888]~P53(x68881,x68882)+P53(x68881,f315(f315(f277(x68881,x68881,x68881),x68882),f295(x68881,x68882)))
% 168.50/168.38 [7114]~P1(f315(f315(f224(a1),x71142),f2(a1)))+P1(f315(f315(f223(a1),f38(a1,x71141,x71142)),f2(a1)))
% 168.50/168.38 [7517]~P147(x75171)+E(f179(x75171,f315(f315(f9(x75171,x75171,x75171),f73(x75171)),f71(x75171)),x75172,f2(x75171)),f315(f89(x75171),x75172))
% 168.50/168.38 [7546]~P129(x75461)+~P1(f315(f315(f224(x75461),f315(f315(f74(x75461),x75462),x75462)),f2(x75461)))
% 168.50/168.38 [10187]~P114(x101871)+~P1(f315(f315(f224(x101871),f315(f315(f232(x101871),x101872),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))))),f2(x101871)))
% 168.50/168.38 [4741]~E(x47412,f102(x47411))+E(f315(f178(f902(x47411)),x47412),f2(a901))
% 168.50/168.38 [4773]~E(x47731,f2(a901))+E(f315(f315(f73(a901),x47731),x47732),x47732)
% 168.50/168.38 [4774]~E(x47742,f2(a901))+E(f315(f315(f74(a901),x47741),x47742),f2(a901))
% 168.50/168.38 [4776]~E(x47761,f2(a901))+E(f315(f315(f74(a901),x47761),x47762),f2(a901))
% 168.50/168.38 [4777]~E(x47772,f2(a1))+E(f315(f315(f29(a1),x47771),x47772),f2(a1))
% 168.50/168.38 [4778]~E(x47782,f2(a901))+E(f315(f315(f232(a901),x47781),x47782),f71(a901))
% 168.50/168.38 [4789]E(x47891,f102(x47892))+~E(f315(f178(f902(x47892)),x47891),f2(a901))
% 168.50/168.38 [4790]~P80(x47901)+E(f315(f315(f99(x47901),x47902),x47902),x47902)
% 168.50/168.38 [4792]~P103(x47921)+E(f315(f315(f99(x47921),x47922),x47922),x47922)
% 168.50/168.38 [4794]~P99(x47941)+E(f315(f315(f74(x47941),x47942),x47942),x47942)
% 168.50/168.38 [4795]~P80(x47951)+E(f315(f315(f90(x47951),x47952),x47952),x47952)
% 168.50/168.38 [4797]~P104(x47971)+E(f315(f315(f90(x47971),x47972),x47972),x47972)
% 168.50/168.38 [4799]~P110(x47991)+E(f315(f315(f221(x47991),x47992),x47992),x47992)
% 168.50/168.38 [4801]~P110(x48011)+E(f315(f315(f222(x48011),x48012),x48012),x48012)
% 168.50/168.38 [4819]~P76(x48191)+E(f315(f315(f3(x48191),x48192),x48192),f2(x48191))
% 168.50/168.38 [4833]~P76(x48331)+E(f315(f72(x48331),f315(f72(x48331),x48332)),x48332)
% 168.50/168.38 [4834]~P98(x48341)+E(f315(f72(x48341),f315(f72(x48341),x48342)),x48342)
% 168.50/168.38 [4851]~E(x48512,f2(a901))+E(f315(f315(f232(a901),x48511),x48512),f315(a101,f2(a901)))
% 168.50/168.38 [4886]~P81(x48861)+E(f315(f315(f99(x48861),f177(x48861)),x48862),x48862)
% 168.50/168.38 [4887]~P77(x48871)+E(f315(f315(f74(x48871),f71(x48871)),x48872),x48872)
% 168.50/168.38 [4888]~P84(x48881)+E(f315(f315(f74(x48881),f71(x48881)),x48882),x48882)
% 168.50/168.38 [4889]~P121(x48891)+E(f315(f315(f74(x48891),f71(x48891)),x48892),x48892)
% 168.50/168.38 [4890]~P102(x48901)+E(f315(f315(f90(x48901),f230(x48901)),x48902),x48902)
% 168.50/168.38 [4891]~P72(x48911)+E(f315(f315(f73(x48911),f2(x48911)),x48912),x48912)
% 168.50/168.38 [4892]~P121(x48921)+E(f315(f315(f73(x48921),f2(x48921)),x48922),x48922)
% 168.50/168.38 [4893]~P85(x48931)+E(f315(f315(f73(x48931),f2(x48931)),x48932),x48932)
% 168.50/168.38 [4911]~P102(x49111)+E(f315(f315(f99(x49111),f230(x49111)),x49112),f230(x49111))
% 168.50/168.38 [4912]~P121(x49121)+E(f315(f315(f74(x49121),f2(x49121)),x49122),f2(x49121))
% 168.50/168.38 [4913]~P135(x49131)+E(f315(f315(f74(x49131),f2(x49131)),x49132),f2(x49131))
% 168.50/168.38 [4914]~P81(x49141)+E(f315(f315(f90(x49141),f177(x49141)),x49142),f177(x49141))
% 168.50/168.38 [4915]~P125(x49151)+E(f315(f315(f279(x49151),f2(x49151)),x49152),f2(x49151))
% 168.50/168.38 [4916]~P62(x49161)+E(f315(f315(f29(x49161),f2(x49161)),x49162),f2(x49161))
% 168.50/168.38 [4917]~P84(x49171)+E(f315(f315(f232(x49171),f71(x49171)),x49172),f71(x49171))
% 168.50/168.38 [4925]E(x49251,f102(x49252))+E(f133(x49252,f315(f157(x49252),x49251)),f315(f130(x49252),x49251))
% 168.50/168.38 [4926]E(x49261,f102(x49262))+E(f315(f130(x49262),f315(f157(x49262),x49261)),f133(x49262,x49261))
% 168.50/168.38 [4927]E(x49271,f2(a901))+~E(f315(f315(f73(a901),x49272),x49271),x49272)
% 168.50/168.38 [4934]~P97(x49341)+E(f315(f91(x49341),f315(f92(a1),x49342)),f315(f92(x49341),x49342))
% 168.50/168.38 [4935]~P143(x49351)+E(f315(f91(x49351),f315(f89(a1),x49352)),f315(f89(x49351),x49352))
% 168.50/168.38 [4942]E(x49421,f71(a901))+~E(f315(f315(f74(a901),x49422),x49421),f71(a901))
% 168.50/168.38 [4943]E(x49431,f71(a901))+~E(f315(f315(f74(a901),x49431),x49432),f71(a901))
% 168.50/168.38 [4944]E(x49441,f2(a901))+~E(f315(f315(f73(a901),x49442),x49441),f2(a901))
% 168.50/168.38 [4945]E(x49451,f2(a901))+~E(f315(f315(f73(a901),x49451),x49452),f2(a901))
% 168.50/168.38 [4962]~P114(x49621)+E(f315(f69(x49621),f315(f89(x49621),x49622)),f315(f89(x49621),x49622))
% 168.50/168.38 [4963]~P89(x49631)+E(f315(f69(x49631),f315(f69(x49631),x49632)),f315(f69(x49631),x49632))
% 168.50/168.38 [4964]~P89(x49641)+E(f315(f69(x49641),f315(f72(x49641),x49642)),f315(f69(x49641),x49642))
% 168.50/168.38 [4965]~P72(x49651)+E(f315(f154(x49651),f315(f157(x49651),x49652)),f315(f154(x49651),x49652))
% 168.50/168.38 [4970]~E(x49701,f315(a101,f2(a901)))+E(f315(f315(f232(a901),x49701),x49702),f315(a101,f2(a901)))
% 168.50/168.38 [4979]~P76(x49791)+E(f315(f315(f3(x49791),f2(x49791)),x49792),f315(f72(x49791),x49792))
% 168.50/168.38 [4980]~E(x49802,f2(a901))+E(f128(a901,f315(f290(a901,x49801),x49802)),f102(a901))
% 168.50/168.38 [4989]~P97(x49891)+E(f315(f315(f73(x49891),x49892),f315(f92(x49891),a76)),x49892)
% 168.50/168.38 [4990]E(x49901,f2(a1))+E(f40(f315(f69(a1),x49902),f315(f69(a1),x49901)),f46(x49902,x49901))
% 168.50/168.38 [5006]~E(x50061,x50062)+P1(f315(f315(f223(a901),x50061),x50062))
% 168.50/168.38 [5010]~E(x50101,x50102)+P1(f315(f315(f275(a901),x50101),x50102))
% 168.50/168.38 [5017]~E(x50171,f2(a88))+E(f315(f315(f73(a901),f315(a22,x50171)),x50172),x50172)
% 168.50/168.38 [5031]~P6(x50311)+P6(f315(f315(f232(a1),x50311),x50312))
% 168.50/168.38 [5032]~P98(x50321)+E(f315(f315(f99(x50321),x50322),f315(f72(x50321),x50322)),f230(x50321))
% 168.50/168.38 [5033]~P98(x50331)+E(f315(f315(f90(x50331),x50332),f315(f72(x50331),x50332)),f177(x50331))
% 168.50/168.38 [5034]~P76(x50341)+E(f315(f315(f73(x50341),x50342),f315(f72(x50341),x50342)),f2(x50341))
% 168.50/168.38 [5059]E(x50591,f2(a901))+~E(f315(f72(a1),f315(f89(a1),x50592)),f315(f89(a1),x50591))
% 168.50/168.38 [5060]E(x50601,f2(a901))+~E(f315(f72(a1),f315(f89(a1),x50601)),f315(f89(a1),x50602))
% 168.50/168.38 [5070]E(f183(x50701,x50702),f2(a1))+P1(f315(f315(f223(a1),x50702),x50701))
% 168.50/168.38 [5071]E(f167(x50711,x50712),f102(a1))+P1(f315(f315(f223(a1),x50711),x50712))
% 168.50/168.38 [5072]E(f229(x50721,x50722),f2(a88))+P1(f315(f315(f224(a88),x50721),x50722))
% 168.50/168.38 [5085]E(x50851,f315(a101,f2(a901)))+~E(f315(f315(f74(a901),x50852),x50851),f315(a101,f2(a901)))
% 168.50/168.38 [5086]E(x50861,f315(a101,f2(a901)))+~E(f315(f315(f74(a901),x50861),x50862),f315(a101,f2(a901)))
% 168.50/168.38 [5087]~P108(x50871)+P1(f315(f315(f223(x50871),x50872),x50872))
% 168.50/168.38 [5088]~P121(x50881)+P1(f315(f315(f275(x50881),x50882),x50882))
% 168.50/168.38 [5091]~P97(x50911)+E(f315(f315(f74(x50911),x50912),f315(f92(x50911),a86)),f315(f72(x50911),x50912))
% 168.50/168.38 [5111]~P97(x51111)+E(f315(f72(x51111),f315(f92(x51111),x51112)),f315(f92(x51111),f315(f72(a1),x51112)))
% 168.50/168.38 [5112]~P143(x51121)+E(f315(f72(x51121),f315(f91(x51121),x51122)),f315(f91(x51121),f315(f72(a1),x51122)))
% 168.50/168.38 [5142]~E(x51421,f315(a101,x51422))+P1(f315(f315(f224(a901),f2(a901)),x51421))
% 168.50/168.38 [5160]~P110(x51601)+E(f315(f72(f909(x51601,a899)),f315(f270(x51601),x51602)),f315(f271(x51601),x51602))
% 168.50/168.38 [5161]~P110(x51611)+E(f315(f72(f909(x51611,a899)),f315(f289(x51611),x51612)),f315(f292(x51611),x51612))
% 168.50/168.38 [5162]~P110(x51621)+E(f315(f72(f909(x51621,a899)),f315(f271(x51621),x51622)),f315(f270(x51621),x51622))
% 168.50/168.38 [5163]~P110(x51631)+E(f315(f72(f909(x51631,a899)),f315(f292(x51631),x51632)),f315(f289(x51631),x51632))
% 168.50/168.38 [5171]~E(f315(f89(a1),x51712),x51711)+P1(f315(f315(f223(a1),f2(a1)),x51711))
% 168.50/168.38 [5178]~E(x51782,f2(a1))+E(f46(x51781,x51782),f315(f315(f240(a1,a1),f2(a1)),f315(f69(a1),x51781)))
% 168.50/168.38 [5180]~P2(x51801)+P1(f315(f315(f223(x51801),f177(x51801)),x51802))
% 168.50/168.38 [5181]~P121(x51811)+P1(f315(f315(f275(x51811),f71(x51811)),x51812))
% 168.50/168.38 [5214]E(x52141,x52142)+~E(f315(f315(f73(a1),x52141),x52141),f315(f315(f73(a1),x52142),x52142))
% 168.50/168.38 [5218]~P1(f315(x52181,x52182))+P1(f315(x52181,f315(a93,f321(x52181))))
% 168.50/168.38 [5244]~P114(x52441)+E(f315(f315(f74(x52441),f75(x52441,x52442)),f315(f69(x52441),x52442)),x52442)
% 168.50/168.38 [5251]~E(x52512,f2(a901))+E(f78(f908(a901,a901),f41(x52511,x52512)),f315(f315(f240(a901,a901),f2(a901)),x52511))
% 168.50/168.38 [5256]~E(x52561,x52562)+~P1(f315(f315(f224(a901),x52561),x52562))
% 168.50/168.38 [5257]~E(x52571,x52572)+~P1(f315(f315(f224(a1),x52571),x52572))
% 168.50/168.38 [5260]~P147(x52601)+E(f315(f315(f73(x52601),f71(x52601)),f315(f89(x52601),x52602)),f315(f89(x52601),f315(a101,x52602)))
% 168.50/168.38 [5264]~E(x52641,f2(a901))+~P1(f315(f315(f224(a901),x52642),x52641))
% 168.50/168.38 [5278]E(f141(x52781,x52782),x52782)+~E(f315(f178(f902(x52781)),f141(x52781,x52782)),f315(f178(f902(x52781)),x52782))
% 168.50/168.38 [5279]E(f315(f28(x52791),f315(f161(x52791),x52792)),f315(f178(f902(x52791)),x52792))+~P1(f315(f126(x52791),x52792))
% 168.50/168.38 [5294]~P1(f315(x52941,f323(x52941)))+P1(f315(x52941,f315(f89(a1),x52942)))
% 168.50/168.38 [5305]E(f229(x53051,x53052),x53052)+~P1(f315(f315(f224(a88),x53051),x53052))
% 168.50/168.38 [5307]E(f260(x53071,x53072),f71(a88))+~P1(f315(f315(f224(a88),x53072),x53071))
% 168.50/168.38 [5308]E(f167(x53081,x53082),f102(a1))+~P1(f315(f315(f224(a1),x53082),x53081))
% 168.50/168.38 [5309]E(f117(x53091,x53092),f104(a1))+~P1(f315(f315(f224(a1),x53091),x53092))
% 168.50/168.38 [5311]~P111(x53111)+E(f291(x53111,x53112,x53112),f315(f315(f297(x53111),x53112),f177(f909(x53111,a899))))
% 168.50/168.38 [5331]~E(f315(f315(f3(a901),x53311),x53312),f2(a901))+P1(f315(f315(f223(a901),x53311),x53312))
% 168.50/168.38 [5348]~E(x53482,f2(a901))+E(f48(x53481,x53482,f102(x53481)),f315(f315(f140(f902(x53481)),f102(x53481)),f102(f902(x53481))))
% 168.50/168.38 [5352]~P108(x53521)+~P1(f315(f315(f224(x53521),x53522),x53522))
% 168.50/168.38 [5354]~E(f38(a1,x53541,x53542),f2(a1))+E(f38(a1,x53541,f315(f72(a1),x53542)),f2(a1))
% 168.50/168.38 [5356]~E(f38(a1,x53561,x53562),f2(a1))+E(f38(a1,f315(f72(a1),x53561),x53562),f2(a1))
% 168.50/168.38 [5365]E(f315(f290(a901,x53651),f315(a101,x53652)),f177(f909(a901,a899)))+P1(f315(f315(f223(a901),x53651),x53652))
% 168.50/168.38 [5389]E(f128(a901,f315(f290(a901,x53891),x53892)),f102(a901))+P1(f315(f315(f224(a901),x53891),x53892))
% 168.50/168.38 [5394]~E(f315(f28(x53941),f315(f161(x53941),x53942)),f315(f178(f902(x53941)),x53942))+P1(f315(f126(x53941),x53942))
% 168.50/168.38 [5398]~P1(f315(f126(x53981),x53982))+P1(f315(f126(x53981),f315(f156(x53981),x53982)))
% 168.50/168.38 [5399]~P1(f315(f126(x53991),x53992))+P1(f315(f126(x53991),f315(f160(x53991),x53992)))
% 168.50/168.38 [5400]~P1(f315(f126(x54001),x54002))+P1(f315(f126(x54001),f315(f157(x54001),x54002)))
% 168.50/168.38 [5408]P1(f315(x54081,x54082))+~P1(f315(x54081,f315(a93,f342(x54081))))
% 168.50/168.38 [5409]P1(f315(f315(f223(a901),x54092),x54091))+P1(f315(f315(f223(a901),x54091),x54092))
% 168.50/168.38 [5410]P1(f315(f315(f223(a1),x54102),x54101))+P1(f315(f315(f223(a1),x54101),x54102))
% 168.50/168.38 [5414]~P89(x54141)+P1(f315(f315(f223(x54141),x54142),f315(f69(x54141),x54142)))
% 168.50/168.38 [5417]P1(f315(x54171,f324(x54171)))+~P1(f315(x54171,f315(f89(a1),x54172)))
% 168.50/168.38 [5441]E(f315(f315(f3(a901),x54411),x54412),f2(a901))+~P1(f315(f315(f223(a901),x54411),x54412))
% 168.50/168.38 [5442]E(f315(f315(f29(a901),x54421),x54422),f2(a901))+~P1(f315(f315(f224(a901),x54421),x54422))
% 168.50/168.38 [5461]E(f38(a901,x54611,x54612),x54611)+~P1(f315(f315(f224(a901),x54611),x54612))
% 168.50/168.38 [5469]E(f38(a1,x54691,f315(f72(a1),x54692)),f280(x54691,x54692))+P1(f315(f315(f223(a1),f2(a1)),x54692))
% 168.50/168.38 [5482]E(f315(f315(f3(a1),x54821),x54822),f183(x54821,x54822))+~P1(f315(f315(f223(a1),x54822),x54821))
% 168.50/168.38 [5502]P1(f315(f315(f223(a1),f2(a1)),f323(x55021)))+P1(f315(x55021,f315(f89(a1),x55022)))
% 168.50/168.38 [5515]~P128(x55151)+P1(f315(f315(f223(x55151),f2(x55151)),f315(f89(x55151),x55152)))
% 168.50/168.38 [5516]~P89(x55161)+P1(f315(f315(f223(x55161),f2(x55161)),f315(f69(x55161),x55162)))
% 168.50/168.38 [5544]E(f315(f315(f73(a901),x55441),f579(x55442,x55441)),x55442)+~P1(f315(f315(f223(a901),x55441),x55442))
% 168.50/168.38 [5559]E(f291(a1,x55591,x55592),f177(f909(a1,a899)))+~P1(f315(f315(f224(a1),x55592),x55591))
% 168.50/168.38 [5561]~P114(x55611)+E(f315(f315(f74(x55611),f315(f69(x55611),x55612)),f315(f69(x55611),x55612)),f315(f315(f74(x55611),x55612),x55612))
% 168.50/168.38 [5567]E(f128(a901,f315(f290(a901,x55671),f315(a101,x55672))),f102(a901))+P1(f315(f315(f223(a901),x55671),x55672))
% 168.50/168.38 [5571]E(f315(f315(f29(a1),x55711),x55712),f281(x55711,x55712))+~P1(f315(f315(f223(a1),f2(a1)),x55712))
% 168.50/168.38 [5591]P1(f315(f126(x55911),x55912))+~P1(f315(f126(x55911),f315(f156(x55911),x55912)))
% 168.50/168.38 [5592]P1(f315(f126(x55921),x55922))+~P1(f315(f126(x55921),f315(f157(x55921),x55922)))
% 168.50/168.38 [5619]P1(f315(f54(a901),x56191))+P1(f315(f315(f317(a901),f395(x56191,x56192)),x56191))
% 168.50/168.38 [5620]P1(f315(f54(a901),x56201))+P1(f315(f315(f317(a901),f397(x56201,x56202)),x56201))
% 168.50/168.38 [5623]P1(f315(f315(f224(a901),x56232),f315(a101,x56231)))+P1(f315(f315(f224(a901),x56231),x56232))
% 168.50/168.38 [5624]E(f38(a1,x56241,x56242),f280(x56241,x56242))+~P1(f315(f315(f223(a1),f2(a1)),x56242))
% 168.50/168.38 [5628]E(f128(a901,f315(f290(a901,x56281),x56282)),f102(a901))+~P1(f315(f315(f223(a901),x56282),x56281))
% 168.50/168.38 [5629]~P82(x56291)+E(f315(f298(x56291,x56291,f72(x56291)),f315(f270(x56291),x56292)),f315(f292(x56291),f315(f72(x56291),x56292)))
% 168.50/168.38 [5630]~P82(x56301)+E(f315(f298(x56301,x56301,f72(x56301)),f315(f289(x56301),x56302)),f315(f271(x56301),f315(f72(x56301),x56302)))
% 168.50/168.38 [5631]~P82(x56311)+E(f315(f298(x56311,x56311,f72(x56311)),f315(f271(x56311),x56312)),f315(f289(x56311),f315(f72(x56311),x56312)))
% 168.50/168.38 [5632]~P82(x56321)+E(f315(f298(x56321,x56321,f72(x56321)),f315(f292(x56321),x56322)),f315(f270(x56321),f315(f72(x56321),x56322)))
% 168.50/168.38 [5643]E(x56431,f177(f909(x56432,a899)))+P1(f315(f315(f317(x56432),f351(x56431,x56432)),x56431))
% 168.50/168.38 [5644]E(x56441,f177(f909(x56442,a899)))+P1(f315(f315(f317(x56442),f366(x56441,x56442)),x56441))
% 168.50/168.38 [5655]~P1(f315(f315(f224(a901),x56551),x56552))+P1(f315(f315(f223(a901),x56551),x56552))
% 168.50/168.38 [5656]~P1(f315(f315(f224(a1),x56561),x56562))+P1(f315(f315(f223(a1),x56561),x56562))
% 168.50/168.38 [5672]E(f40(x56721,x56722),f315(f315(f240(a1,a1),f2(a1)),x56721))+~P1(f315(f315(f224(a1),x56721),x56722))
% 168.50/168.38 [5674]E(f204(f315(f72(a1),x56741),f315(f72(a1),x56742)),f204(x56741,x56742))+~P1(f315(f315(f224(a1),x56742),f2(a1)))
% 168.50/168.38 [5687]E(x56871,x56872)+~E(f315(a5,f315(a101,f315(a22,x56871))),f315(a5,f315(a101,f315(a22,x56872))))
% 168.50/168.38 [5692]E(f40(x56921,x56922),f315(f315(f240(a1,a1),f2(a1)),x56921))+~P1(f315(f315(f223(a1),x56922),f2(a1)))
% 168.50/168.38 [5721]E(f38(a901,f315(f92(a901),x57211),f315(f92(a901),x57212)),f2(a901))+~P1(f315(a182,f315(f92(a1),x57211)))
% 168.50/168.38 [5735]P1(f315(f315(f223(a1),f2(a1)),f324(x57351)))+~P1(f315(x57351,f315(f89(a1),x57352)))
% 168.50/168.38 [5768]P42(f291(a1,x57681,x57682))+~P1(f315(f315(f223(a1),f2(a1)),x57681))
% 168.50/168.38 [5773]~P1(f315(f54(x57731),x57732))+P1(f315(f54(f909(x57731,a899)),f315(f296(x57731),x57732)))
% 168.50/168.38 [5786]E(f315(f315(f73(a1),x57861),f315(f89(a1),f329(x57862,x57861))),x57862)+~P1(f315(f315(f223(a1),x57861),x57862))
% 168.50/168.38 [5794]P1(f315(f315(f223(a901),x57941),x57942))+P1(f315(f315(f223(a901),f315(a101,x57942)),x57941))
% 168.50/168.38 [5838]E(f315(f315(f29(a901),f315(f92(a901),x58381)),f315(f92(a901),x58382)),f2(a901))+~P1(f315(a182,f315(f92(a1),x58381)))
% 168.50/168.38 [5839]E(f315(f315(f74(a901),f315(f92(a901),x58391)),f315(f92(a901),x58392)),f2(a901))+~P1(f315(f315(f224(a1),x58391),a76))
% 168.50/168.38 [5841]P1(f315(f315(f223(a901),x58411),f315(a101,x58412)))+~P1(f315(f315(f223(a901),x58411),x58412))
% 168.50/168.38 [5843]P1(f315(f315(f224(a901),x58431),f315(a101,x58432)))+~P1(f315(f315(f223(a901),x58431),x58432))
% 168.50/168.38 [5845]P1(f315(f315(f224(a901),x58451),f315(a101,x58452)))+~P1(f315(f315(f224(a901),x58451),x58452))
% 168.50/168.38 [5848]~E(x58481,x58482)+P1(f315(f315(f224(a1),x58481),f315(f315(f73(a1),x58482),f71(a1))))
% 168.50/168.38 [5851]E(f38(a1,x58511,x58512),f2(a1))+E(f315(f315(f3(a1),x58512),f38(a1,x58511,x58512)),f38(a1,f315(f72(a1),x58511),x58512))
% 168.50/168.38 [5860]E(x58601,f102(x58602))+P1(f315(f315(f317(x58602),f133(x58602,x58601)),f315(f161(x58602),x58601)))
% 168.50/168.38 [5872]E(f78(f908(a901,a901),f41(x58721,x58722)),f315(f315(f240(a901,a901),f2(a901)),x58721))+~P1(f315(f315(f224(a901),x58721),x58722))
% 168.50/168.38 [5916]E(f315(f315(f3(a901),f315(f92(a901),x59161)),f315(f92(a901),x59162)),f315(f92(a901),x59161))+~P1(f315(f315(f224(a1),x59162),a76))
% 168.50/168.38 [5917]E(f315(f315(f73(a901),f315(f92(a901),x59171)),f315(f92(a901),x59172)),f315(f92(a901),x59172))+~P1(f315(f315(f224(a1),x59171),a76))
% 168.50/168.38 [5924]E(f315(a101,f315(f315(f73(a901),x59241),f604(x59242,x59241))),x59242)+~P1(f315(f315(f224(a901),x59241),x59242))
% 168.50/168.38 [5948]P1(f315(x59481,x59482))+~P1(f315(x59481,f315(a82,f559(x59482,x59481))))
% 168.50/168.38 [5949]P1(f315(x59491,x59492))+~P1(f315(x59491,f315(a5,f799(x59492,x59491))))
% 168.50/168.38 [5958]~P1(f315(f315(f224(a901),x59581),f315(a101,x59582)))+P1(f315(f315(f223(a901),x59581),x59582))
% 168.50/168.38 [6008]E(f315(f315(f297(a901),x60081),f315(f290(a901,x60082),x60081)),f315(f290(a901,x60082),f315(a101,x60081)))+~P1(f315(f315(f223(a901),x60082),x60081))
% 168.50/168.38 [6010]E(x60101,f102(x60102))+E(f315(f315(f123(x60102),f103(x60102,x60101)),f315(f315(f140(x60102),f133(x60102,x60101)),f102(x60102))),x60101)
% 168.50/168.38 [6027]P1(f315(f54(x60271),x60272))+~P1(f315(f315(f224(a901),f2(a901)),f315(f28(x60271),x60272)))
% 168.50/168.38 [6031]~E(x60311,f177(f909(x60312,a899)))+~P1(f315(f315(f224(a901),f2(a901)),f315(f28(x60312),x60311)))
% 168.50/168.38 [6043]~P1(f315(f315(f224(a901),x60431),x60432))+P1(f315(f315(f223(a901),f315(a101,x60431)),x60432))
% 168.50/168.38 [6047]~P110(x60471)+E(f139(x60471,x60471,f7(x60471),f141(x60471,x60472)),f128(x60471,f315(f161(x60471),x60472)))
% 168.50/168.38 [6050]E(x60501,f102(x60502))+P1(f315(f315(f317(x60502),f315(f130(x60502),x60501)),f315(f161(x60502),x60501)))
% 168.50/168.38 [6056]~P128(x60561)+P1(f315(f315(f224(x60561),x60562),f315(f315(f73(x60561),x60562),f71(x60561))))
% 168.50/168.38 [6058]~P89(x60581)+P1(f315(f315(f223(x60581),f315(f72(x60581),x60582)),f315(f69(x60581),x60582)))
% 168.50/168.38 [6072]~E(x60721,x60722)+E(f278(a901,f275(a901),x60721,x60722),f315(f315(f297(a901),x60721),f177(f909(a901,a899))))
% 168.50/168.38 [6090]P1(f315(f54(a901),x60901))+~P1(f315(f315(f223(a901),f397(x60901,x60902)),x60902))
% 168.50/168.38 [6091]P1(f315(f54(a901),x60911))+~P1(f315(f315(f224(a901),f395(x60911,x60912)),x60912))
% 168.50/168.38 [6095]~P1(f315(f54(f908(x60951,x60951)),x60952))+P1(f315(f54(x60951),f315(f269(x60951),x60952)))
% 168.50/168.38 [6151]E(f278(a901,f275(a901),x61511,x61512),f177(f909(a901,a899)))+P1(f315(f315(f275(a901),x61511),x61512))
% 168.50/168.38 [6154]~P1(f315(f315(f224(a901),x61542),f315(a101,x61541)))+~P1(f315(f315(f224(a901),x61541),x61542))
% 168.50/168.38 [6155]~P111(x61551)+E(f315(f315(f90(f909(x61551,a899)),f315(f289(x61551),x61552)),f315(f271(x61551),x61552)),f315(f315(f297(x61551),x61552),f177(f909(x61551,a899))))
% 168.50/168.38 [6167]P1(f315(f54(x61671),x61672))+~P1(f315(f54(f909(x61671,a899)),f315(f296(x61671),x61672)))
% 168.50/168.38 [6190]P1(f315(f315(f223(a901),f315(a101,x61901)),f315(a101,x61902)))+~P1(f315(f315(f223(a901),x61901),x61902))
% 168.50/168.38 [6191]P1(f315(f315(f223(a901),f315(a22,x61911)),f315(a22,x61912)))+~P1(f315(f315(f223(a88),x61911),x61912))
% 168.50/168.38 [6192]P1(f315(f315(f223(a88),f315(a5,x61921)),f315(a5,x61922)))+~P1(f315(f315(f223(a901),x61921),x61922))
% 168.50/168.38 [6194]P1(f315(f315(f224(a901),f315(a101,x61941)),f315(a101,x61942)))+~P1(f315(f315(f224(a901),x61941),x61942))
% 168.50/168.38 [6195]P1(f315(f315(f224(a901),f315(a22,x61951)),f315(a22,x61952)))+~P1(f315(f315(f224(a88),x61951),x61952))
% 168.50/168.38 [6196]P1(f315(f315(f224(a88),f315(a5,x61961)),f315(a5,x61962)))+~P1(f315(f315(f224(a901),x61961),x61962))
% 168.50/168.38 [6201]E(x62011,x62012)+~E(f315(f298(a901,a1,f89(a1)),x62011),f315(f298(a901,a1,f89(a1)),x62012))
% 168.50/168.38 [6217]P1(f315(f315(f223(a901),x62171),x62172))+~P1(f315(f315(f223(a901),f315(a101,x62171)),x62172))
% 168.50/168.38 [6220]P1(f315(f315(f224(a901),x62201),x62202))+~P1(f315(f315(f223(a901),f315(a101,x62201)),x62202))
% 168.50/168.38 [6221]P1(f315(f315(f224(a901),x62211),x62212))+~P1(f315(f315(f224(a901),f315(a101,x62211)),x62212))
% 168.50/168.38 [6241]E(f38(a1,x62411,x62412),f2(a1))+E(f315(f315(f3(a1),f38(a1,x62411,x62412)),x62412),f38(a1,x62411,f315(f72(a1),x62412)))
% 168.50/168.38 [6309]E(f315(f28(f909(x63091,a899)),f315(f296(x63091),x63092)),f315(f315(f232(a901),f315(a101,f315(a101,f2(a901)))),f315(f28(x63091),x63092)))+~P1(f315(f54(x63091),x63092))
% 168.50/168.38 [6312]E(x63121,f102(x63122))+E(f315(f315(f153(x63122),x63121),f315(f315(f3(a901),f315(f178(f902(x63122)),x63121)),f71(a901))),f133(x63122,x63121))
% 168.50/168.38 [6334]E(x63341,f102(x63342))+E(f315(f315(f123(x63342),f315(f160(x63342),x63341)),f315(f315(f140(x63342),f315(f130(x63342),x63341)),f102(x63342))),f315(f156(x63342),x63341))
% 168.50/168.38 [6366]~P1(f315(f54(x63661),f30(f909(x63661,a899),x63662)))+P1(f315(f54(f909(x63661,a899)),x63662))
% 168.50/168.38 [6388]P1(f315(f315(f223(a901),f315(f92(a901),x63881)),f315(f92(a901),x63882)))+~P1(f315(f315(f223(a1),x63881),a76))
% 168.50/168.38 [6411]~P1(f315(f315(f224(a1),x64111),x64112))+P1(f315(f315(f223(a1),x64111),f315(f315(f3(a1),x64112),f71(a1))))
% 168.50/168.38 [6412]~P1(f315(f315(f223(a1),x64121),x64122))+P1(f315(f315(f224(a1),x64121),f315(f315(f73(a1),x64122),f71(a1))))
% 168.50/168.38 [6413]~P1(f315(f315(f224(a1),x64131),x64132))+P1(f315(f315(f224(a1),x64131),f315(f315(f73(a1),x64132),f71(a1))))
% 168.50/168.38 [6415]~P1(f315(f315(f223(a1),x64151),x64152))+P1(f315(f315(f223(a901),f315(f92(a901),x64151)),f315(f92(a901),x64152)))
% 168.50/168.38 [6416]~P1(f315(f315(f223(a1),x64161),x64162))+P1(f315(f315(f223(a1),f315(f92(a1),x64161)),f315(f92(a1),x64162)))
% 168.50/168.38 [6418]~P1(f315(f315(f223(a901),x64181),x64182))+P1(f315(f315(f223(a1),f315(f89(a1),x64181)),f315(f89(a1),x64182)))
% 168.50/168.38 [6419]~P1(f315(f315(f224(a1),x64191),x64192))+P1(f315(f315(f224(a1),f315(f92(a1),x64191)),f315(f92(a1),x64192)))
% 168.50/168.38 [6421]~P1(f315(f315(f224(a901),x64211),x64212))+P1(f315(f315(f224(a1),f315(f89(a1),x64211)),f315(f89(a1),x64212)))
% 168.50/168.38 [6442]~P1(f315(f315(f223(a901),x64421),x64422))+~P1(f315(f315(f223(a901),f315(a101,x64422)),x64421))
% 168.50/168.38 [6485]~P1(f315(f315(f223(a901),f315(a101,x64851)),f315(a101,x64852)))+P1(f315(f315(f223(a901),x64851),x64852))
% 168.50/168.38 [6486]~P1(f315(f315(f223(a88),f315(a5,x64861)),f315(a5,x64862)))+P1(f315(f315(f223(a901),x64861),x64862))
% 168.50/168.38 [6487]~P1(f315(f315(f223(a901),f315(a22,x64871)),f315(a22,x64872)))+P1(f315(f315(f223(a88),x64871),x64872))
% 168.50/168.38 [6489]~P1(f315(f315(f224(a901),f315(a101,x64891)),f315(a101,x64892)))+P1(f315(f315(f224(a901),x64891),x64892))
% 168.50/168.38 [6490]~P1(f315(f315(f224(a88),f315(a5,x64901)),f315(a5,x64902)))+P1(f315(f315(f224(a901),x64901),x64902))
% 168.50/168.38 [6491]~P1(f315(f315(f224(a901),f315(a93,x64911)),f315(a93,x64912)))+P1(f315(f315(f224(a1),x64911),x64912))
% 168.50/168.38 [6492]~P1(f315(f315(f224(a901),f315(a22,x64921)),f315(a22,x64922)))+P1(f315(f315(f224(a88),x64921),x64922))
% 168.50/168.38 [6535]~P1(f315(f315(f224(a901),f315(a93,x65352)),f315(a93,x65351)))+P1(f315(f315(f224(a1),f2(a1)),x65351))
% 168.50/168.38 [6567]P1(f315(f315(f223(a1),f2(a1)),f38(a1,x65671,x65672)))+~P1(f315(f315(f224(a1),f2(a1)),x65672))
% 168.50/168.38 [6732]P39(x67321,x67322)+~E(f315(f315(f277(x67321,x67321,x67321),x67322),x67322),f177(f909(f908(x67321,x67321),a899)))
% 168.50/168.38 [6748]~P39(x67481,x67482)+P39(x67481,f315(f315(f277(x67481,x67481,x67481),x67482),x67482))
% 168.50/168.38 [6759]P1(f315(f315(f223(a1),x67591),x67592))+~P1(f315(f315(f224(a1),x67591),f315(f315(f73(a1),x67592),f71(a1))))
% 168.50/168.38 [6760]P1(f315(f315(f224(a1),x67601),x67602))+~P1(f315(f315(f223(a1),x67601),f315(f315(f3(a1),x67602),f71(a1))))
% 168.50/168.38 [6763]P1(f315(f315(f223(a901),x67631),x67632))+~P1(f315(f315(f223(a1),f315(f89(a1),x67631)),f315(f89(a1),x67632)))
% 168.50/168.38 [6764]P1(f315(f315(f223(a1),x67641),x67642))+~P1(f315(f315(f223(a1),f315(f92(a1),x67641)),f315(f92(a1),x67642)))
% 168.50/168.38 [6766]P1(f315(f315(f224(a901),x67661),x67662))+~P1(f315(f315(f224(a1),f315(f89(a1),x67661)),f315(f89(a1),x67662)))
% 168.50/168.38 [6767]P1(f315(f315(f224(a1),x67671),x67672))+~P1(f315(f315(f224(a901),f315(f92(a901),x67671)),f315(f92(a901),x67672)))
% 168.50/168.38 [6768]P1(f315(f315(f224(a1),x67681),x67682))+~P1(f315(f315(f224(a1),f315(f92(a1),x67681)),f315(f92(a1),x67682)))
% 168.50/168.38 [6841]~E(f278(a901,f275(a901),x68411,x68412),f177(f909(a901,a899)))+~P1(f315(f315(f275(a901),x68411),x68412))
% 168.50/168.38 [6868]~E(f678(x68682,x68681),f102(x68681))+E(f315(f131(f902(x68681),f902(x68681),f123(x68681),f102(x68681)),x68682),f102(x68681))
% 168.50/168.38 [6869]~E(f679(x68692,x68691),f102(x68691))+E(f315(f131(f902(x68691),f902(x68691),f123(x68691),f102(x68691)),x68692),f102(x68691))
% 168.50/168.38 [6874]~P5(x68741)+E(f315(f131(x68741,x68741,f99(x68741),f177(x68741)),x68742),f30(x68741,f315(f161(x68741),x68742)))
% 168.50/168.38 [6875]~P5(x68751)+E(f315(f131(x68751,x68751,f90(x68751),f230(x68751)),x68752),f31(x68751,f315(f161(x68751),x68752)))
% 168.50/168.38 [6889]E(x68891,f2(a88))+E(f315(f315(f73(a901),f315(a22,f315(f315(f3(a88),x68891),f71(a88)))),f315(a101,x68892)),f315(f315(f73(a901),f315(a22,x68891)),x68892))
% 168.50/168.38 [6938]P1(f315(f315(f224(a1),f315(f315(f3(a1),x69381),x69382)),f2(a1)))+~P1(f315(f315(f224(a1),x69381),x69382))
% 168.50/168.38 [6963]~P110(x69631)+E(f315(f315(f99(f909(x69631,a899)),f315(f315(f297(x69631),x69632),f177(f909(x69631,a899)))),f315(f292(x69631),x69632)),f315(f271(x69631),x69632))
% 168.50/168.38 [7041]~P61(x70411,x70412)+P39(x70411,f315(f250(f908(x70411,x70411)),f315(f245(x70411,x70411,a899),x70412)))
% 168.50/168.38 [7042]~P61(x70421,x70422)+P59(x70421,f315(f250(f908(x70421,x70421)),f315(f245(x70421,x70421,a899),x70422)))
% 168.50/168.38 [7043]~P51(x70431,x70432)+P40(x70431,f315(f250(f908(x70431,x70431)),f315(f245(x70431,x70431,a899),x70432)))
% 168.50/168.38 [7044]~P52(x70441,x70442)+P53(x70441,f315(f250(f908(x70441,x70441)),f315(f245(x70441,x70441,a899),x70442)))
% 168.50/168.38 [7045]E(x70451,f177(f909(x70452,a899)))+~P1(f315(f315(f223(f909(x70452,a899)),x70451),f177(f909(x70452,a899))))
% 168.50/168.38 [7130]~P1(f315(f315(f224(a901),f2(a901)),x71302))+P1(f315(f315(f223(a901),f38(a901,x71301,x71302)),x71302))
% 168.50/168.38 [7131]~P1(f315(f315(f223(a1),f2(a1)),x71311))+P1(f315(f315(f223(a1),f38(a1,x71311,x71312)),x71311))
% 168.50/168.38 [7132]~P1(f315(f315(f224(a901),f2(a901)),x71322))+P1(f315(f315(f224(a901),f38(a901,x71321,x71322)),x71322))
% 168.50/168.38 [7134]~P1(f315(f315(f224(a1),f2(a1)),x71342))+P1(f315(f315(f224(a1),f38(a1,x71341,x71342)),x71342))
% 168.50/168.38 [7211]~P111(x72111)+E(f315(f315(f3(f909(x72111,a899)),f315(f315(f297(x72111),x72112),f177(f909(x72111,a899)))),f315(f270(x72111),x72112)),f315(f315(f297(x72111),x72112),f177(f909(x72111,a899))))
% 168.50/168.38 [7286]~P45(x72861,x72862)+P54(x72861,f230(f909(x72861,a899)),f315(f250(f908(x72861,x72861)),f315(f245(x72861,x72861,a899),x72862)))
% 168.50/168.38 [7287]P1(f315(x72871,x72872))+P1(f315(f315(f317(f909(f908(a901,a901),a899)),f559(x72872,x72871)),a87))
% 168.50/168.38 [7332]E(f315(f315(f123(a901),f128(a901,f315(f290(a901,x73321),x73322))),f315(f315(f140(a901),x73322),f102(a901))),f128(a901,f315(f290(a901,x73321),f315(a101,x73322))))+~P1(f315(f315(f223(a901),x73321),x73322))
% 168.50/168.38 [7484]E(x74841,f2(a901))+~E(f315(f131(a901,a901,f73(a901),x74841),x74842),f2(a901))
% 168.50/168.38 [7509]~P1(f315(f315(f224(a1),f315(f315(f3(a1),x75091),x75092)),f2(a1)))+P1(f315(f315(f224(a1),x75091),x75092))
% 168.50/168.38 [7538]P39(x75381,x75382)+~P39(x75381,f315(f315(f277(x75381,x75381,x75381),x75382),x75382))
% 168.50/168.38 [7563]~P1(f315(f315(f223(a901),f315(a101,x75631)),x75632))+P1(f174(a899,a227,f315(f223(a901),x75631),x75632))
% 168.50/168.38 [7718]P25(a901,a901,f315(f315(f9(a901,a901,a901),f3(a901)),x77181),x77182)+P1(f315(f315(f317(a901),f566(x77181,x77182)),x77182))
% 168.50/168.38 [7776]E(f315(f315(f315(f58(a901,x77761,f73(a901)),f315(f18(a901,x77761),f71(a901))),f2(a901)),x77762),f315(f28(x77761),x77762))+~P1(f315(f54(x77761),x77762))
% 168.50/168.38 [7818]P25(a901,a901,f315(f315(f9(a901,a901,a901),f3(a901)),x78181),x78182)+~P1(f315(f315(f223(a901),x78181),f566(x78181,x78182)))
% 168.50/168.38 [7874]P39(x78741,x78742)+P1(f315(f315(f223(f909(x78741,a899)),f563(x78742,x78741)),f315(f273(x78741,x78741,x78742),f563(x78742,x78741))))
% 168.50/168.38 [7879]P61(x78791,x78792)+~P39(x78791,f315(f250(f908(x78791,x78791)),f315(f245(x78791,x78791,a899),x78792)))
% 168.50/168.38 [7880]P51(x78801,x78802)+~P40(x78801,f315(f250(f908(x78801,x78801)),f315(f245(x78801,x78801,a899),x78802)))
% 168.50/168.38 [7881]P52(x78811,x78812)+~P53(x78811,f315(f250(f908(x78811,x78811)),f315(f245(x78811,x78811,a899),x78812)))
% 168.50/168.38 [7948]P1(f315(f315(f223(a901),f315(a101,x79481)),x79482))+~P1(f174(a899,a227,f315(f223(a901),x79481),x79482))
% 168.50/168.38 [8005]P1(f315(f315(f317(f908(a901,a901)),f315(f315(f240(a901,a901),x80051),x80052)),f295(a901,a305)))+~P1(f315(f315(f223(a901),x80051),x80052))
% 168.50/168.38 [8102]P45(x81021,x81022)+~P54(x81021,f230(f909(x81021,a899)),f315(f250(f908(x81021,x81021)),f315(f245(x81021,x81021,a899),x81022)))
% 168.50/168.38 [8157]~P1(f315(f126(x81571),x81572))+P1(f315(f126(f909(x81571,a899)),f315(f315(f143(f902(x81571),f909(x81571,a899)),f161(x81571)),f47(x81571,x81572))))
% 168.50/168.38 [8360]~P39(x83601,f315(f274(x83601,x83601),x83602))+P39(x83601,f315(f274(x83601,x83601),f315(f315(f277(x83601,x83601,x83601),x83602),f295(x83601,x83602))))
% 168.50/168.38 [8458]P26(x84581,a901,f804(x84582,x84581),x84582,f315(f290(a901,f2(a901)),f315(f28(x84581),x84582)))+~P1(f315(f54(x84581),x84582))
% 168.50/168.38 [8459]P26(a901,x84591,f805(x84592,x84591),f315(f290(a901,f2(a901)),f315(f28(x84591),x84592)),x84592)+~P1(f315(f54(x84591),x84592))
% 168.50/168.38 [8476]P26(a901,x84761,f806(x84762,x84761),f291(a901,f71(a901),f315(f28(x84761),x84762)),x84762)+~P1(f315(f54(x84761),x84762))
% 168.50/168.38 [8486]P1(f315(f54(f908(x84861,x84861)),f315(f315(f277(x84861,x84861,x84861),x84862),f295(x84861,x84862))))+~P1(f315(f54(f908(x84861,x84861)),x84862))
% 168.50/168.38 [8513]E(x85131,f2(a1))+P1(f315(f42(x85132,x85131),f315(f315(f240(a1,a1),f315(f315(f29(a1),x85132),x85131)),f38(a1,x85132,x85131))))
% 168.50/168.38 [8526]~P1(f315(f315(f317(f908(a901,a901)),f315(f315(f240(a901,a901),x85261),x85262)),f295(a901,a305)))+P1(f315(f315(f223(a901),x85261),x85262))
% 168.50/168.38 [8543]~P85(x85431)+E(f315(f131(x85431,x85431,f315(f9(x85431,x85431,x85431),f73(x85431)),f2(x85431)),f315(f157(x85431),x85432)),f315(f131(x85431,x85431,f73(x85431),f2(x85431)),x85432))
% 168.50/168.38 [8714]~P110(x87141)+E(f315(f131(f902(x87141),x87141,f315(f9(x87141,f902(x87141),f902(x87141)),f137(x87141,x87141,f7(x87141))),f102(x87141)),x87142),f139(x87141,x87141,f7(x87141),x87142))
% 168.50/168.38 [8825]~P59(x88251,f315(f250(f908(x88251,x88251)),f315(f245(x88251,x88251,a899),x88252)))+P59(x88251,f315(f250(f908(x88251,x88251)),f315(f245(x88251,x88251,a899),f231(x88251,x88251,x88252))))
% 168.50/168.38 [8839]P1(f315(f315(f317(f908(a901,a901)),f315(f315(f240(a901,a901),x88391),x88392)),f315(f315(f277(a901,a901,a901),a305),f295(a901,a305))))+~P1(f315(f315(f224(a901),x88391),x88392))
% 168.50/168.38 [8885]~P1(f315(f54(f908(x88851,x88851)),f315(f315(f277(x88851,x88851,x88851),x88852),f295(x88851,x88852))))+P1(f315(f54(f908(x88851,x88851)),x88852))
% 168.50/168.38 [8943]~P59(x89431,f315(f250(f908(x89431,x89431)),f315(f245(x89431,x89431,a899),f231(x89431,x89431,x89432))))+P59(x89431,f315(f250(f908(x89431,x89431)),f315(f245(x89431,x89431,a899),x89432)))
% 168.50/168.38 [9141]P59(x91411,x91412)+P1(f315(f315(f317(f908(x91411,x91411)),f315(f315(f240(x91411,x91411),f595(x91412,x91411)),f595(x91412,x91411))),f315(f315(f277(x91411,x91411,x91411),x91412),f295(x91411,x91412))))
% 168.50/168.38 [9142]P59(x91421,x91422)+P1(f315(f315(f317(f908(x91421,x91421)),f315(f315(f240(x91421,x91421),f596(x91422,x91421)),f596(x91422,x91421))),f315(f315(f277(x91421,x91421,x91421),x91422),f295(x91421,x91422))))
% 168.50/168.38 [9259]~P1(f315(f315(f317(f908(a901,a901)),f315(f315(f240(a901,a901),x92591),x92592)),f315(f315(f277(a901,a901,a901),a305),f295(a901,a305))))+P1(f315(f315(f224(a901),x92591),x92592))
% 168.50/168.38 [5156]~P97(x51561)+E(f315(f315(f73(x51561),f315(f92(x51561),a76)),x51562),x51562)
% 168.50/168.38 [5186]~P98(x51861)+E(f315(f315(f99(x51861),f315(f72(x51861),x51862)),x51862),f230(x51861))
% 168.50/168.38 [5187]~P98(x51871)+E(f315(f315(f90(x51871),f315(f72(x51871),x51872)),x51872),f177(x51871))
% 168.50/168.38 [5188]~P69(x51881)+E(f315(f315(f73(x51881),f315(f72(x51881),x51882)),x51882),f2(x51881))
% 168.50/168.38 [5189]~P76(x51891)+E(f315(f315(f73(x51891),f315(f72(x51891),x51892)),x51892),f2(x51891))
% 168.50/168.38 [5222]~P97(x52221)+E(f315(f315(f74(x52221),f315(f92(x52221),a86)),x52222),f315(f72(x52221),x52222))
% 168.50/168.38 [5381]~P116(x53811)+E(f315(f315(f74(x53811),f315(f72(x53811),f71(x53811))),x53812),f315(f72(x53811),x53812))
% 168.50/168.38 [5426]E(f315(f69(a1),x54261),f71(a1))+~E(f315(f69(a1),f315(f315(f74(a1),x54261),x54262)),f71(a1))
% 168.50/168.38 [5518]~P97(x55181)+E(f315(f315(f73(x55181),f71(x55181)),f315(f92(x55181),x55182)),f315(f92(x55181),f315(f315(f3(a1),x55182),a86)))
% 168.50/168.38 [5572]~P80(x55721)+E(f12(x55721,f315(f315(f297(x55721),x55722),f177(f909(x55721,a899)))),x55722)
% 168.50/168.38 [5573]~P80(x55731)+E(f13(x55731,f315(f315(f297(x55731),x55732),f177(f909(x55731,a899)))),x55732)
% 168.50/168.38 [5574]~P5(x55741)+E(f30(x55741,f315(f315(f297(x55741),x55742),f177(f909(x55741,a899)))),x55742)
% 168.50/168.38 [5575]~P110(x55751)+E(f16(x55751,f315(f315(f297(x55751),x55752),f177(f909(x55751,a899)))),x55752)
% 168.50/168.38 [5576]~P5(x55761)+E(f31(x55761,f315(f315(f297(x55761),x55762),f177(f909(x55761,a899)))),x55762)
% 168.50/168.38 [5577]~P110(x55771)+E(f17(x55771,f315(f315(f297(x55771),x55772),f177(f909(x55771,a899)))),x55772)
% 168.50/168.38 [5599]E(f315(f315(f73(a901),x55991),f315(f315(f3(a901),x55992),x55991)),x55992)+P1(f315(f315(f224(a901),x55992),x55991))
% 168.50/168.38 [5638]E(x56381,f102(x56382))+P1(f315(f315(f224(a901),f2(a901)),f315(f178(f902(x56382)),x56381)))
% 168.50/168.38 [5765]~P110(x57651)+E(f14(x57651,f221(x57651),f315(f315(f297(x57651),x57652),f177(f909(x57651,a899)))),x57652)
% 168.50/168.38 [5766]~P110(x57661)+E(f15(x57661,f222(x57661),f315(f315(f297(x57661),x57662),f177(f909(x57661,a899)))),x57662)
% 168.50/168.38 [5827]E(f315(f315(f3(a901),x58271),f315(f315(f3(a901),x58271),x58272)),x58272)+~P1(f315(f315(f223(a901),x58272),x58271))
% 168.50/168.38 [5828]E(f315(f315(f73(a901),x58281),f315(f315(f3(a901),x58282),x58281)),x58282)+~P1(f315(f315(f223(a901),x58281),x58282))
% 168.50/168.38 [5850]E(f38(a901,f315(f315(f3(a901),x58501),x58502),x58502),f38(a901,x58501,x58502))+P1(f315(f315(f224(a901),x58501),x58502))
% 168.50/168.38 [5861]E(f315(f72(a1),f315(f315(f29(a1),x58611),f315(f72(a1),x58612))),f281(x58611,x58612))+P1(f315(f315(f223(a1),f2(a1)),x58612))
% 168.50/168.38 [5863]~E(x58632,f2(a901))+P1(f315(f315(f224(a901),f2(a901)),f315(f315(f232(a901),x58631),x58632)))
% 168.50/168.38 [5926]~P97(x59261)+E(f315(f315(f73(x59261),f315(f72(x59261),f71(x59261))),f315(f92(x59261),x59262)),f315(f92(x59261),f315(f315(f73(a1),x59262),a86)))
% 168.50/168.38 [5928]E(f315(f315(f232(a901),f315(f92(a901),x59281)),x59282),f315(f315(f232(a901),f2(a901)),x59282))+~P1(f315(a182,f315(f92(a1),x59281)))
% 168.50/168.38 [6035]E(f315(f130(a901),f128(a901,f315(f290(a901,x60351),x60352))),x60351)+~P1(f315(f315(f224(a901),x60351),x60352))
% 168.50/168.38 [6051]E(f315(f315(f74(a901),f315(f92(a901),x60511)),f315(f92(a901),x60512)),f315(f92(a901),f315(f315(f74(a1),x60511),x60512)))+P1(f315(f315(f224(a1),x60511),a76))
% 168.50/168.38 [6057]~P129(x60571)+P1(f315(f315(f223(x60571),f2(x60571)),f315(f315(f74(x60571),x60572),x60572)))
% 168.50/168.38 [6069]E(f315(f315(f3(a901),f315(a101,x60691)),x60692),f315(a101,f315(f315(f3(a901),x60691),x60692)))+~P1(f315(f315(f223(a901),x60692),x60691))
% 168.50/168.38 [6073]E(f38(a901,f315(f315(f3(a901),x60731),x60732),x60732),f38(a901,x60731,x60732))+~P1(f315(f315(f223(a901),x60732),x60731))
% 168.50/168.38 [6128]E(f315(f315(f232(a901),f315(a93,x61281)),x61282),f315(a93,f315(f315(f232(a1),x61281),x61282)))+~P1(f315(f315(f223(a1),f2(a1)),x61281))
% 168.50/168.38 [6146]P1(f315(f126(x61461),x61462))+P1(f315(f315(f224(a901),f648(x61462,x61461)),f315(f178(f902(x61461)),x61462)))
% 168.50/168.38 [6147]P1(f315(f126(x61471),x61472))+P1(f315(f315(f224(a901),f654(x61472,x61471)),f315(f178(f902(x61471)),x61472)))
% 168.50/168.38 [6161]~E(x61611,f102(x61612))+~P1(f315(f315(f224(a901),f2(a901)),f315(f178(f902(x61612)),x61611)))
% 168.50/168.38 [6172]E(f133(a901,f128(a901,f315(f290(a901,x61721),x61722))),f315(f315(f3(a901),x61722),f71(a901)))+~P1(f315(f315(f224(a901),x61721),x61722))
% 168.50/168.38 [6175]E(f315(f315(f73(a1),x61751),f315(f89(a1),f315(a101,f331(x61752,x61751)))),x61752)+~P1(f315(f315(f224(a1),x61751),x61752))
% 168.50/168.38 [6182]E(x61821,f2(a901))+E(f315(f315(f74(a901),x61822),f315(f315(f232(a901),x61822),f315(f315(f3(a901),x61821),f71(a901)))),f315(f315(f232(a901),x61822),x61821))
% 168.50/168.38 [6211]E(f315(f315(f74(a901),f315(a93,x62111)),f315(a93,x62112)),f315(a93,f315(f315(f74(a1),x62111),x62112)))+~P1(f315(f315(f223(a1),f2(a1)),x62111))
% 168.50/168.38 [6212]E(f315(f315(f29(a901),f315(a93,x62121)),f315(a93,x62122)),f315(a93,f315(f315(f29(a1),x62121),x62122)))+~P1(f315(f315(f223(a1),f2(a1)),x62121))
% 168.50/168.38 [6227]~P121(x62271)+E(f315(f315(f73(x62271),x62272),x62272),f315(f315(f74(x62271),f315(f315(f73(x62271),f71(x62271)),f71(x62271))),x62272))
% 168.50/168.38 [6250]E(f315(f315(f3(a1),f315(f89(a1),x62501)),f315(f89(a1),x62502)),f315(f89(a1),f315(f315(f3(a901),x62501),x62502)))+~P1(f315(f315(f223(a901),x62502),x62501))
% 168.50/168.38 [6252]E(f315(f315(f240(a1,a1),f315(f92(a1),a86)),f315(f315(f73(a1),x62521),x62522)),f43(x62521,x62522))+~P1(f315(f315(f223(a1),x62522),f2(a1)))
% 168.50/168.38 [6287]E(f168(x62871,x62872),f102(f902(x62871)))+P1(f315(f315(f317(f902(x62871)),f647(x62872,x62871)),f315(f161(f902(x62871)),x62872)))
% 168.50/168.38 [6296]E(f105(a1,f315(f118(a1),x62961),f117(x62962,f315(f315(f73(a1),x62961),f71(a1)))),f117(x62962,x62961))+P1(f315(f315(f224(a1),x62962),x62961))
% 168.50/168.38 [6350]~P1(f315(f315(f275(a901),x63501),x63502))+P1(f315(f315(f275(a901),x63501),f315(f315(f73(a901),x63502),x63501)))
% 168.50/168.38 [6372]E(f315(f315(f140(a1),x63721),f167(f315(f315(f73(a1),x63721),f71(a1)),x63722)),f167(x63721,x63722))+~P1(f315(f315(f223(a1),x63721),x63722))
% 168.50/168.38 [6414]~P1(f315(f315(f224(a901),x64142),x64141))+P1(f315(f315(f224(a901),f2(a901)),f315(f315(f3(a901),x64141),x64142)))
% 168.50/168.38 [6447]~P1(f315(f315(f224(a901),x64471),f315(a93,x64472)))+P1(f315(f315(f224(a1),f315(f89(a1),x64471)),x64472))
% 168.50/168.38 [6476]~P110(x64761)+E(f315(f315(f99(f909(x64761,a899)),f315(f270(x64761),x64762)),f315(f315(f297(x64761),x64762),f177(f909(x64761,a899)))),f315(f289(x64761),x64762))
% 168.50/168.38 [6477]~P1(f315(f315(f223(a1),f2(a1)),x64771))+P1(f315(f315(f223(a1),f2(a1)),f315(f315(f232(a1),x64771),x64772)))
% 168.50/168.38 [6480]~P1(f315(f315(f224(a901),f2(a901)),x64801))+P1(f315(f315(f224(a901),f2(a901)),f315(f315(f232(a901),x64801),x64802)))
% 168.50/168.38 [6508]~E(f315(x65081,f2(a901)),f2(a901))+E(f315(f315(f8(a901,a901),x65081),f291(a901,f315(a101,f2(a901)),x65082)),f315(f315(f8(a901,a901),x65081),f291(a901,f2(a901),x65082)))
% 168.50/168.38 [6575]~P97(x65751)+E(f315(f315(f74(x65751),f315(f315(f73(x65751),f71(x65751)),f71(x65751))),f315(f92(x65751),x65752)),f315(f92(x65751),f315(f315(f73(a1),x65752),x65752)))
% 168.50/168.38 [6594]E(f315(f315(f297(a1),x65941),f291(a1,f315(f315(f73(a1),x65941),f71(a1)),x65942)),f291(a1,x65941,x65942))+P1(f315(f315(f224(a1),x65942),x65941))
% 168.50/168.38 [6595]P1(f315(f315(f224(a901),x65951),f315(a93,x65952)))+~P1(f315(f315(f224(a1),f315(f89(a1),x65951)),x65952))
% 168.50/168.38 [6695]P1(f315(f315(f275(a901),x66951),x66952))+~P1(f315(f315(f275(a901),x66951),f315(f315(f73(a901),x66952),x66951)))
% 168.50/168.38 [6700]E(f315(a93,f315(f315(f29(a1),f315(f92(a1),x67001)),f315(f92(a1),x67002))),f315(f315(f29(a901),f315(f92(a901),x67001)),f315(f92(a901),x67002)))+P1(f315(a182,f315(f92(a1),x67001)))
% 168.50/168.38 [6761]P1(f315(f315(f224(a901),x67611),x67612))+~P1(f315(f315(f224(a901),f2(a901)),f315(f315(f3(a901),x67612),x67611)))
% 168.50/168.38 [6804]P1(f315(f315(f224(a901),f2(a901)),x68041))+~P1(f315(f315(f224(a901),f2(a901)),f315(f315(f74(a901),x68042),x68041)))
% 168.50/168.38 [6805]P1(f315(f315(f224(a901),f2(a901)),x68051))+~P1(f315(f315(f224(a901),f2(a901)),f315(f315(f74(a901),x68051),x68052)))
% 168.50/168.38 [6824]~P1(f315(f315(f223(a1),x68241),f2(a1)))+E(f315(f315(f74(a901),f315(a93,f315(f72(a1),x68241))),f315(a93,f315(f72(a1),x68242))),f315(a93,f315(f315(f74(a1),x68241),x68242)))
% 168.50/168.38 [6886]~E(x68862,f177(f909(x68861,a899)))+P1(f315(f315(f223(f909(x68861,a899)),x68862),f315(f72(f909(x68861,a899)),x68862)))
% 168.50/168.38 [6948]~P97(x69481)+E(f315(f315(f73(x69481),f315(f315(f73(x69481),f2(x69481)),f315(f92(x69481),x69482))),f315(f92(x69481),x69482)),f315(f92(x69481),f315(f315(f73(a1),x69482),x69482)))
% 168.50/168.38 [7004]~P1(f315(f315(f224(a1),x70041),x70042))+P1(f315(f315(f223(a1),f315(f315(f73(a1),x70041),f71(a1))),x70042))
% 168.50/168.38 [7074]E(x70741,f2(a901))+~P1(f315(f315(f223(a1),f315(f89(a1),x70742)),f315(f72(a1),f315(f89(a1),x70741))))
% 168.50/168.38 [7075]E(x70751,f2(a901))+~P1(f315(f315(f223(a1),f315(f89(a1),x70751)),f315(f72(a1),f315(f89(a1),x70752))))
% 168.50/168.38 [7179]E(f315(f315(f240(a1,a1),f315(f92(a1),a86)),f315(f315(f73(a1),x71791),x71792)),f43(x71791,x71792))+~P1(f315(f315(f223(a1),f2(a1)),f315(f315(f73(a1),x71791),x71792)))
% 168.50/168.38 [7223]~P27(x72231,x72232)+P39(x72231,f315(f239(f909(f908(x72231,x72231),a899),f909(f908(x72231,x72231),a899)),x72232))
% 168.50/168.38 [7242]~P1(f315(f315(f223(a901),f315(a101,f2(a901))),x72421))+P1(f315(f315(f223(a901),f315(a101,f2(a901))),f315(f315(f232(a901),x72421),x72422)))
% 168.50/168.38 [7422]~P1(f315(f315(f223(a1),x74221),x74222))+P1(f315(f315(f223(a1),f315(f315(f73(a1),x74221),x74221)),f315(f315(f73(a1),x74222),x74222)))
% 168.50/168.38 [7427]~P1(f315(f315(f224(a1),x74271),x74272))+P1(f315(f315(f224(a1),f315(f315(f73(a1),x74271),x74271)),f315(f315(f73(a1),x74272),x74272)))
% 168.50/168.38 [7485]~P1(f315(f315(f224(a901),f2(a901)),x74851))+P1(f315(f315(f224(a901),f315(f315(f3(a901),x74851),f315(a101,x74852))),x74851))
% 168.50/168.38 [7520]P1(f315(f315(f223(a901),f315(a101,f2(a901))),x75201))+~P1(f315(f315(f223(a901),f315(a101,f2(a901))),f315(f315(f74(a901),x75202),x75201)))
% 168.50/168.38 [7521]P1(f315(f315(f223(a901),f315(a101,f2(a901))),x75211))+~P1(f315(f315(f223(a901),f315(a101,f2(a901))),f315(f315(f74(a901),x75211),x75212)))
% 168.50/168.38 [7525]P1(f315(f315(f223(a901),f315(f315(f153(a901),x75251),x75252)),f315(f154(a901),x75251)))+~P1(f315(f315(f224(a901),x75252),f315(f178(f902(a901)),x75251)))
% 168.50/168.38 [7562]P1(f315(f315(f224(a1),x75621),x75622))+~P1(f315(f315(f223(a1),f315(f315(f73(a1),x75621),f71(a1))),x75622))
% 168.50/168.38 [7604]P1(f315(f54(x76041),f230(f909(x76041,a899))))+~P1(f315(f54(f909(x76042,x76041)),f230(f909(f909(x76042,x76041),a899))))
% 168.50/168.38 [7605]P1(f315(f54(x76051),f230(f909(x76051,a899))))+~P1(f315(f54(f907(x76052,x76051)),f230(f909(f907(x76052,x76051),a899))))
% 168.50/168.38 [7606]P1(f315(f54(x76061),f230(f909(x76061,a899))))+~P1(f315(f54(f907(x76061,x76062)),f230(f909(f907(x76061,x76062),a899))))
% 168.50/168.38 [7645]E(x76451,f177(f909(x76452,a899)))+~P1(f315(f315(f223(f909(x76452,a899)),x76451),f315(f72(f909(x76452,a899)),x76451)))
% 168.50/168.38 [7786]E(f315(f131(f902(x77861),f902(x77861),f123(x77861),f102(x77861)),x77862),f102(x77861))+P1(f315(f315(f317(f902(x77861)),f678(x77862,x77861)),f315(f161(f902(x77861)),x77862)))
% 168.50/168.38 [7787]E(f315(f131(f902(x77871),f902(x77871),f123(x77871),f102(x77871)),x77872),f102(x77871))+P1(f315(f315(f317(f902(x77871)),f679(x77872,x77871)),f315(f161(f902(x77871)),x77872)))
% 168.50/168.38 [8023]P1(f315(f315(f223(a1),x80231),x80232))+~P1(f315(f315(f223(a1),f315(f315(f73(a1),x80231),x80231)),f315(f315(f73(a1),x80232),x80232)))
% 168.50/168.38 [8028]P1(f315(f315(f224(a1),x80281),x80282))+~P1(f315(f315(f224(a1),f315(f315(f73(a1),x80281),x80281)),f315(f315(f73(a1),x80282),x80282)))
% 168.50/168.38 [8122]~P121(x81221)+E(f315(f315(f74(x81221),f315(f315(f73(x81221),f71(x81221)),f71(x81221))),f315(f315(f8(a901,x81221),f89(x81221)),f291(a901,f71(a901),x81222))),f315(f315(f74(x81221),f315(f89(x81221),x81222)),f315(f315(f73(x81221),f315(f89(x81221),x81222)),f71(x81221))))
% 168.50/168.38 [8172]P1(f315(f315(f317(a901),x81721),x81722))+~P1(f315(f315(f317(a1),f315(f89(a1),x81721)),f315(f298(a901,a1,f89(a1)),x81722)))
% 168.50/168.38 [8332]~P1(f315(f54(x83321),x83322))+E(f315(f298(a901,x83321,f544(x83322,x83321)),f315(f250(a901),f315(f315(f9(a901,a901,a899),f224(a901)),f545(x83322,x83321)))),x83322)
% 168.50/168.38 [8611]P55(x86111,x86112)+P1(f315(f315(f317(f908(x86111,x86111)),f315(f315(f240(x86111,x86111),f387(x86112,x86111)),f387(x86112,x86111))),x86112))
% 168.50/168.38 [8612]P40(x86121,x86122)+P1(f315(f315(f317(f908(x86121,x86121)),f315(f315(f240(x86121,x86121),f770(x86122,x86121)),f773(x86122,x86121))),x86122))
% 168.50/168.38 [8613]P40(x86131,x86132)+P1(f315(f315(f317(f908(x86131,x86131)),f315(f315(f240(x86131,x86131),f773(x86132,x86131)),f774(x86132,x86131))),x86132))
% 168.50/168.38 [8614]P41(x86141,x86142)+P1(f315(f315(f317(f908(x86141,x86141)),f315(f315(f240(x86141,x86141),f689(x86142,x86141)),f688(x86142,x86141))),x86142))
% 168.50/168.38 [8615]P41(x86151,x86152)+P1(f315(f315(f317(f908(x86151,x86151)),f315(f315(f240(x86151,x86151),f688(x86152,x86151)),f689(x86152,x86151))),x86152))
% 168.50/168.38 [8616]P53(x86161,x86162)+P1(f315(f315(f317(f908(x86161,x86161)),f315(f315(f240(x86161,x86161),f785(x86162,x86161)),f786(x86162,x86161))),x86162))
% 168.50/168.38 [8757]~P97(x87571)+E(f315(f315(f3(x87571),f71(x87571)),f315(f92(x87571),x87572)),f315(f92(x87571),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f72(a1),x87572))))
% 168.50/168.38 [8882]~P1(f315(f315(f224(f909(a901,a899)),x88821),x88822))+P1(f315(f315(f224(f909(a1,a899)),f315(f298(a901,a1,f89(a1)),x88821)),f315(f298(a901,a1,f89(a1)),x88822)))
% 168.50/168.38 [8916]~P1(f315(f315(f224(a1),x89161),x89162))+P1(f315(f315(f223(a1),f315(f315(f3(a1),f315(f315(f73(a1),x89161),x89161)),a86)),f315(f315(f73(a1),x89162),x89162)))
% 168.50/168.38 [8918]~P1(f315(f315(f224(a1),x89181),x89182))+P1(f315(f315(f224(a1),f315(f315(f3(a1),f315(f315(f73(a1),x89181),x89181)),a86)),f315(f315(f73(a1),x89182),x89182)))
% 168.50/168.38 [8991]~P1(f315(f315(f317(a901),x89911),f315(f161(a901),x89912)))+P1(f315(f315(f223(a901),x89911),f315(f131(a901,a901,f73(a901),f2(a901)),x89912)))
% 168.50/168.38 [9081]P48(x90811,x90812)+~P1(f315(f315(f317(f908(x90811,x90811)),f315(f315(f240(x90811,x90811),f373(x90812,x90811)),f373(x90812,x90811))),x90812))
% 168.50/168.38 [9082]P40(x90821,x90822)+~P1(f315(f315(f317(f908(x90821,x90821)),f315(f315(f240(x90821,x90821),f770(x90822,x90821)),f774(x90822,x90821))),x90822))
% 168.50/168.38 [9083]P53(x90831,x90832)+~P1(f315(f315(f317(f908(x90831,x90831)),f315(f315(f240(x90831,x90831),f786(x90832,x90831)),f785(x90832,x90831))),x90832))
% 168.50/168.38 [9222]~P1(f315(f315(f223(f909(a1,a899)),f315(f298(a901,a1,f89(a1)),x92221)),f315(f298(a901,a1,f89(a1)),x92222)))+P1(f315(f315(f223(f909(a901,a899)),x92221),x92222))
% 168.50/168.38 [9223]~P1(f315(f315(f224(f909(a1,a899)),f315(f298(a901,a1,f89(a1)),x92231)),f315(f298(a901,a1,f89(a1)),x92232)))+P1(f315(f315(f224(f909(a901,a899)),x92231),x92232))
% 168.50/168.38 [9308]P1(f315(f315(f224(a1),x93081),x93082))+~P1(f315(f315(f223(a1),f315(f315(f3(a1),f315(f315(f73(a1),x93081),x93081)),a86)),f315(f315(f73(a1),x93082),x93082)))
% 168.50/168.38 [9310]P1(f315(f315(f224(a1),x93101),x93102))+~P1(f315(f315(f224(a1),f315(f315(f3(a1),f315(f315(f73(a1),x93101),x93101)),a86)),f315(f315(f73(a1),x93102),x93102)))
% 168.50/168.38 [10205]~P106(x102051)+E(f105(f902(x102051),f315(f118(f902(x102051)),f102(x102051)),f315(f315(f315(f85(f903(f902(x102051))),f315(f315(f224(a1),f2(a1)),x102052)),f315(f107(f908(x102051,f902(x102051)),f902(x102051),f120(x102051,f902(x102051),f121(x102051,f315(f315(f3(a1),x102052),f71(a1))),f121(f902(x102051),f315(f315(f3(a1),x102052),f71(a1))))),f315(f245(x102051,f902(x102051),f903(f902(x102051))),f315(f315(f10(f909(f902(x102051),f902(x102051)),f909(f902(x102051),f903(f902(x102051))),x102051),f315(f10(f902(x102051),f903(f902(x102051)),f902(x102051)),f118(f902(x102051)))),f140(x102051))))),f104(f902(x102051)))),f121(f902(x102051),x102052))
% 168.50/168.38 [10227]~P1(f315(f54(x102271),x102272))+E(f315(f178(f902(x102271)),f83(f902(x102271),f315(f315(f20(f902(x102271),a899,a899),f315(f315(f10(a899,f909(a899,a899),f902(x102271)),a313),f315(f315(f9(f902(x102271),f909(x102271,a899),a899),f315(f315(f10(f909(x102271,a899),f909(f909(x102271,a899),a899),f902(x102271)),a312),f161(x102271))),x102272))),f126(x102271)))),f203(x102271,x102272))
% 168.50/168.38 [6171]E(f315(f315(f73(a901),f315(f315(f3(a901),x61711),x61712)),x61712),x61711)+~P1(f315(f315(f223(a901),x61712),x61711))
% 168.50/168.38 [6246]E(f315(f315(f29(a901),f315(f315(f74(a901),x62461),x62462)),x62462),x62461)+~P1(f315(f315(f224(a901),f2(a901)),x62462))
% 168.50/168.38 [6247]E(f315(f315(f29(a901),f315(f315(f74(a901),x62471),x62472)),x62471),x62472)+~P1(f315(f315(f224(a901),f2(a901)),x62471))
% 168.50/168.38 [6251]~P72(x62511)+E(f315(f315(f8(a901,x62511),f315(f153(x62511),x62512)),f315(f290(a901,f2(a901)),f315(f178(f902(x62511)),x62512))),f315(f154(x62511),x62512))
% 168.50/168.38 [6364]E(f38(a901,f315(a101,f315(f315(f74(a901),x63641),x63642)),x63641),f71(a901))+~P1(f315(f315(f224(a901),f71(a901)),x63641))
% 168.50/168.38 [6370]E(f315(a101,f315(f315(f73(a901),f315(f92(a901),x63701)),x63702)),f315(f315(f73(a901),f71(a901)),x63702))+~P1(f315(a182,f315(f92(a1),x63701)))
% 168.50/168.38 [6399]E(f315(a93,f315(f315(f232(a1),f315(f92(a1),x63991)),x63992)),f315(f315(f232(a901),f315(f92(a901),x63991)),x63992))+P1(f315(a182,f315(f92(a1),x63991)))
% 168.50/168.38 [6649]E(f315(f315(f3(a901),x66491),f315(f92(a901),f315(f315(f73(a1),x66492),a86))),f315(f315(f3(a901),f315(a101,x66491)),f315(f92(a901),x66492)))+~P1(f315(f315(f224(a1),a76),x66492))
% 168.50/168.38 [6731]E(x67311,f2(a901))+E(f315(a101,f315(f315(f73(a901),f315(f315(f3(a901),x67311),f71(a901))),x67312)),f315(f315(f73(a901),x67311),x67312))
% 168.50/168.38 [6774]E(x67741,f2(a1))+P1(f315(f315(f224(a1),f2(a1)),f315(f315(f232(a1),f315(f69(a1),x67741)),x67742)))
% 168.50/168.38 [6789]~E(x67892,f2(a901))+P1(f315(f315(f224(a1),f2(a1)),f315(f315(f232(a1),f315(f69(a1),x67891)),x67892)))
% 168.50/168.38 [6827]E(x68271,f2(a901))+E(f315(f315(f73(a901),x68272),f315(f315(f74(a901),f315(f315(f3(a901),x68271),f71(a901))),x68272)),f315(f315(f74(a901),x68271),x68272))
% 168.50/168.38 [6879]~P1(f315(f315(f223(a1),x68791),x68792))+P1(f315(f315(f224(a1),f315(f315(f73(a1),x68791),a86)),x68792))
% 168.50/168.38 [7008]E(f315(f315(f140(a901),x70081),f128(a901,f315(f290(a901,f315(a101,x70081)),x70082))),f128(a901,f315(f290(a901,x70081),x70082)))+~P1(f315(f315(f224(a901),x70081),x70082))
% 168.50/168.38 [7214]E(x72141,x72142)+~E(f315(f315(f3(a1),f315(f315(f73(a1),x72141),x72141)),a86),f315(f315(f3(a1),f315(f315(f73(a1),x72142),x72142)),a86))
% 168.50/168.38 [7217]E(x72171,f102(x72172))+E(f254(x72172,f315(f315(f143(x72172,f908(a88,x72172)),f315(f240(a88,x72172),f71(a88))),x72171)),f263(x72172,x72171))
% 168.50/168.38 [7455]P1(f315(f315(f223(a1),x74551),x74552))+~P1(f315(f315(f224(a1),f315(f315(f73(a1),x74551),a86)),x74552))
% 168.50/168.38 [7927]~P1(f315(f315(f224(a901),x79271),x79272))+P1(f315(f315(f317(f908(a901,a901)),f315(f315(f240(a901,a901),x79271),x79272)),a228))
% 168.50/168.38 [8148]~P1(f315(f315(f224(a88),f2(a88)),x81481))+P1(f315(f315(f224(a88),f315(f239(a88,f908(a88,a88)),f315(f255(x81481),x81482))),x81481))
% 168.50/168.38 [8413]~P40(x84131,x84132)+P40(x84131,f315(f315(f99(f909(f908(x84131,x84131),a899)),x84132),f295(x84131,f177(f909(f908(x84131,x84131),a899)))))
% 168.50/168.38 [8414]~P41(x84141,x84142)+P41(x84141,f315(f315(f99(f909(f908(x84141,x84141),a899)),x84142),f295(x84141,f177(f909(f908(x84141,x84141),a899)))))
% 168.50/168.38 [8462]~P89(x84621)+P1(f315(f315(f223(x84621),f315(f69(x84621),f315(f154(x84621),x84622))),f315(f154(x84621),f315(f315(f143(x84621,x84621),f69(x84621)),x84622))))
% 168.50/168.38 [8488]P1(f315(f315(f224(a901),x84881),x84882))+~P1(f315(f315(f317(f908(a901,a901)),f315(f315(f240(a901,a901),x84881),x84882)),a228))
% 168.50/168.38 [8635]E(f315(f315(f240(x86351,x86351),f610(x86352,x86351)),f610(x86352,x86351)),x86352)+~P1(f315(f315(f317(f908(x86351,x86351)),x86352),f295(x86351,f177(f909(f908(x86351,x86351),a899)))))
% 168.50/168.38 [8679]E(f315(f290(a901,x86791),f315(f315(f73(a901),x86791),f315(f28(a901),x86792))),x86792)+~P1(f315(f315(f223(f909(a901,a899)),x86792),f315(f290(a901,x86791),f315(f315(f73(a901),x86791),f315(f28(a901),x86792)))))
% 168.50/168.38 [8909]P41(x89091,x89092)+~P41(x89091,f315(f315(f99(f909(f908(x89091,x89091),a899)),x89092),f295(x89091,f177(f909(f908(x89091,x89091),a899)))))
% 168.50/168.38 [9036]E(f315(f315(f29(a1),f315(f92(a1),f315(f315(f3(a1),f315(f315(f73(a1),x90361),x90361)),a86))),f315(f92(a1),f315(f315(f73(a1),x90362),x90362))),f315(f315(f29(a1),f315(f92(a1),x90361)),f315(f92(a1),x90362)))+~P1(f315(f315(f223(a1),f2(a1)),f315(f92(a1),x90362)))
% 168.50/168.38 [9126]~P40(x91261,x91262)+P1(f315(f315(f223(f909(f908(x91261,x91261),a899)),f315(f315(f277(x91261,x91261,x91261),x91262),x91262)),x91262))
% 168.50/168.38 [9152]E(f166(f902(x91521),f315(f315(f10(a899,a899,f902(x91521)),a310),f315(f315(f9(f902(x91521),f902(x91521),a899),a312),f102(x91521))),x91522),f168(x91521,f168(x91521,x91522)))+~P13(a901,f315(f157(a901),f315(f315(f143(f902(x91521),a901),f178(f902(x91521))),x91522)))
% 168.50/168.38 [9155]E(f315(f315(f29(a1),f315(f92(a1),f315(f315(f3(a1),f315(f315(f73(a1),x91551),x91551)),a86))),f315(f92(a1),f315(f315(f73(a1),x91552),x91552))),f315(f315(f29(a1),f315(f315(f73(a1),f315(f92(a1),x91551)),f71(a1))),f315(f92(a1),x91552)))+P1(f315(f315(f223(a1),f2(a1)),f315(f92(a1),x91552)))
% 168.50/168.38 [10003]P1(f315(a182,x100032))+E(f315(f315(f79(a1,a901),f315(f315(f3(a1),x100031),x100032)),f315(f315(f20(a1,a901,a901),f315(f315(f9(a1,a901,f909(a901,a901)),f315(f315(f10(a899,f909(a901,f909(a901,a901)),a1),f85(a901)),a182)),f2(a901))),a93)),f315(f315(f3(a901),f315(a93,x100031)),f315(a93,x100032)))
% 168.50/168.38 [10011]E(f315(f315(f79(a1,a901),f315(f92(a1),f315(f315(f73(a1),x100111),f315(f72(a1),x100112)))),f315(f315(f20(a1,a901,a901),f315(f315(f9(a1,a901,f909(a901,a901)),f315(f315(f10(a899,f909(a901,f909(a901,a901)),a1),f85(a901)),a182)),f2(a901))),a93)),f315(f315(f3(a901),f315(f92(a901),x100111)),f315(f92(a901),x100112)))+P1(f315(f315(f224(a1),x100112),a76))
% 168.50/168.38 [10012]~P27(x100121,x100122)+P1(f315(f315(f223(f909(f908(x100121,x100121),a899)),f315(f315(f277(x100121,x100121,x100121),f315(f239(f909(f908(x100121,x100121),a899),f909(f908(x100121,x100121),a899)),x100122)),f315(f244(f909(f908(x100121,x100121),a899),f909(f908(x100121,x100121),a899)),x100122))),f315(f239(f909(f908(x100121,x100121),a899),f909(f908(x100121,x100121),a899)),x100122)))
% 168.50/168.38 [10067]~E(f315(f28(a901),f315(f250(a901),f315(f315(f20(a901,a899,a899),f315(f315(f10(a899,f909(a899,a899),a901),a313),f315(f315(f9(a901,f909(a901,a899),a899),f317(a901)),x100671))),f315(f315(f9(a901,a901,a899),f224(a901)),f315(a101,x100672))))),f2(a901))+~P1(f315(f315(f317(a901),f2(a901)),x100671))
% 168.50/168.38 [10078]E(f287(a901,f315(f315(f20(a901,f909(a901,a899),f909(a901,a899)),f315(f315(f10(f909(a901,f909(a899,a899)),f909(f909(a901,a899),f909(a901,a899)),a901),f20(a901,a899,a899)),f315(f315(f10(f909(a901,a899),f909(a901,f909(a899,a899)),a901),f315(f10(a899,f909(a899,a899),a901),a313)),f275(a901)))),f315(f315(f10(f909(a901,a899),f909(a901,a899),a901),f315(f10(a899,a899,a901),a310)),f315(f9(a901,a901,a899),f275(a901)))),x100781,x100782),f177(f909(a901,a899)))+~P1(f315(f315(f275(a901),x100782),x100781))
% 168.50/168.38 [10083]E(f288(a901,f275(a901),f315(f315(f20(a901,f909(a901,a899),f909(a901,a899)),f315(f315(f10(f909(a901,f909(a899,a899)),f909(f909(a901,a899),f909(a901,a899)),a901),f20(a901,a899,a899)),f315(f315(f10(f909(a901,a899),f909(a901,f909(a899,a899)),a901),f315(f10(a899,f909(a899,a899),a901),a313)),f275(a901)))),f315(f315(f10(f909(a901,a899),f909(a901,a899),a901),f315(f10(a899,a899,a901),a310)),f315(f9(a901,a901,a899),f275(a901)))),x100831,x100832),f177(f909(a901,a899)))+P1(f315(f315(f275(a901),x100831),x100832))
% 168.50/168.38 [10084]E(f285(a901,f275(a901),f315(f315(f20(a901,f909(a901,a899),f909(a901,a899)),f315(f315(f10(f909(a901,f909(a899,a899)),f909(f909(a901,a899),f909(a901,a899)),a901),f20(a901,a899,a899)),f315(f315(f10(f909(a901,a899),f909(a901,f909(a899,a899)),a901),f315(f10(a899,f909(a899,a899),a901),a313)),f275(a901)))),f315(f315(f10(f909(a901,a899),f909(a901,a899),a901),f315(f10(a899,a899,a901),a310)),f315(f9(a901,a901,a899),f275(a901)))),x100841,x100842),f177(f909(a901,a899)))+P1(f315(f315(f275(a901),x100841),x100842))
% 168.50/168.38 [10088]E(f288(a901,f275(a901),f315(f315(f20(a901,f909(a901,a899),f909(a901,a899)),f315(f315(f10(f909(a901,f909(a899,a899)),f909(f909(a901,a899),f909(a901,a899)),a901),f20(a901,a899,a899)),f315(f315(f10(f909(a901,a899),f909(a901,f909(a899,a899)),a901),f315(f10(a899,f909(a899,a899),a901),a313)),f275(a901)))),f315(f315(f10(f909(a901,a899),f909(a901,a899),a901),f315(f10(a899,a899,a901),a310)),f315(f9(a901,a901,a899),f275(a901)))),x100881,x100882),f177(f909(a901,a899)))+~P1(f315(f315(f275(a901),x100882),x100881))
% 168.50/168.38 [10090]E(f285(a901,f275(a901),f315(f315(f20(a901,f909(a901,a899),f909(a901,a899)),f315(f315(f10(f909(a901,f909(a899,a899)),f909(f909(a901,a899),f909(a901,a899)),a901),f20(a901,a899,a899)),f315(f315(f10(f909(a901,a899),f909(a901,f909(a899,a899)),a901),f315(f10(a899,f909(a899,a899),a901),a313)),f275(a901)))),f315(f315(f10(f909(a901,a899),f909(a901,a899),a901),f315(f10(a899,a899,a901),a310)),f315(f9(a901,a901,a899),f275(a901)))),x100901,x100902),f177(f909(a901,a899)))+~P1(f315(f315(f275(a901),x100902),x100901))
% 168.50/168.38 [10133]E(f38(a1,f315(f92(a1),f315(f315(f3(a1),f315(f315(f73(a1),x101331),x101331)),a86)),f315(f92(a1),f315(f315(f73(a1),x101332),x101332))),f315(f315(f73(a1),f315(f315(f74(a1),f315(f92(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),f38(a1,f315(f92(a1),x101331),f315(f92(a1),x101332)))),f71(a1)))+~P1(f315(f315(f223(a1),f2(a1)),f315(f92(a1),x101332)))
% 168.50/168.38 [10142]E(f38(a1,f315(f92(a1),f315(f315(f3(a1),f315(f315(f73(a1),x101421),x101421)),a86)),f315(f92(a1),f315(f315(f73(a1),x101422),x101422))),f315(f315(f3(a1),f315(f315(f74(a1),f315(f92(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),f38(a1,f315(f315(f73(a1),f315(f92(a1),x101421)),f71(a1)),f315(f92(a1),x101422)))),f71(a1)))+P1(f315(f315(f223(a1),f2(a1)),f315(f92(a1),x101422)))
% 168.50/168.38 [10196]~P5(x101961)+E(f30(x101961,f315(f250(x101961),f315(f315(f10(f909(x101961,a899),a899,x101961),f81(x101961)),f315(f315(f10(f909(x101961,a899),f909(x101961,a899),x101961),f315(f20(x101961,a899,a899),f315(f315(f10(a899,f909(a899,a899),x101961),a318),f315(f315(f9(x101961,f909(x101961,a899),a899),f317(x101961)),x101962)))),f223(x101961))))),f31(x101961,x101962))
% 168.50/168.38 [10220]~P39(x102201,x102202)+P61(x102201,f315(f315(f9(x102201,f909(f908(x102201,x102201),a899),f909(x102201,a899)),f315(f315(f10(f909(x102201,f909(f909(f908(x102201,x102201),a899),a899)),f909(f909(f908(x102201,x102201),a899),f909(x102201,a899)),x102201),f9(x102201,f909(f908(x102201,x102201),a899),a899)),f315(f315(f10(f909(x102201,f908(x102201,x102201)),f909(x102201,f909(f909(f908(x102201,x102201),a899),a899)),x102201),f315(f10(f908(x102201,x102201),f909(f909(f908(x102201,x102201),a899),a899),x102201),f317(f908(x102201,x102201)))),f240(x102201,x102201)))),x102202))
% 168.50/168.38 [10221]~P8(x102211,f230(f909(x102211,a899)),x102212)+P7(x102211,f315(f315(f9(x102211,f909(f908(x102211,x102211),a899),f909(x102211,a899)),f315(f315(f10(f909(x102211,f909(f909(f908(x102211,x102211),a899),a899)),f909(f909(f908(x102211,x102211),a899),f909(x102211,a899)),x102211),f9(x102211,f909(f908(x102211,x102211),a899),a899)),f315(f315(f10(f909(x102211,f908(x102211,x102211)),f909(x102211,f909(f909(f908(x102211,x102211),a899),a899)),x102211),f315(f10(f908(x102211,x102211),f909(f909(f908(x102211,x102211),a899),a899),x102211),f317(f908(x102211,x102211)))),f240(x102211,x102211)))),x102212))
% 168.50/168.38 [10264]P39(x102641,x102642)+~P61(x102641,f315(f315(f9(x102641,f909(f908(x102641,x102641),a899),f909(x102641,a899)),f315(f315(f10(f909(x102641,f909(f909(f908(x102641,x102641),a899),a899)),f909(f909(f908(x102641,x102641),a899),f909(x102641,a899)),x102641),f9(x102641,f909(f908(x102641,x102641),a899),a899)),f315(f315(f10(f909(x102641,f908(x102641,x102641)),f909(x102641,f909(f909(f908(x102641,x102641),a899),a899)),x102641),f315(f10(f908(x102641,x102641),f909(f909(f908(x102641,x102641),a899),a899),x102641),f317(f908(x102641,x102641)))),f240(x102641,x102641)))),x102642))
% 168.50/168.38 [10265]P8(x102651,f230(f909(x102651,a899)),x102652)+~P7(x102651,f315(f315(f9(x102651,f909(f908(x102651,x102651),a899),f909(x102651,a899)),f315(f315(f10(f909(x102651,f909(f909(f908(x102651,x102651),a899),a899)),f909(f909(f908(x102651,x102651),a899),f909(x102651,a899)),x102651),f9(x102651,f909(f908(x102651,x102651),a899),a899)),f315(f315(f10(f909(x102651,f908(x102651,x102651)),f909(x102651,f909(f909(f908(x102651,x102651),a899),a899)),x102651),f315(f10(f908(x102651,x102651),f909(f909(f908(x102651,x102651),a899),a899),x102651),f317(f908(x102651,x102651)))),f240(x102651,x102651)))),x102652))
% 168.50/168.38 [7402]E(f315(f315(f73(a901),f315(f92(a901),f315(f315(f3(a1),x74021),a86))),x74022),f315(a101,f315(f315(f73(a901),f315(f92(a901),x74021)),x74022)))+P1(f315(a182,f315(f92(a1),x74021)))
% 168.50/168.38 [7845]~P97(x78451)+E(f315(f315(f73(x78451),f315(f315(f73(x78451),f71(x78451)),f315(f92(x78451),x78452))),f315(f92(x78451),x78452)),f315(f92(x78451),f315(f315(f3(a1),f315(f315(f73(a1),x78452),x78452)),a86)))
% 168.50/168.38 [8490]~P1(f315(f315(f223(a1),x84901),x84902))+P1(f315(f315(f223(a1),f315(f315(f73(a1),x84901),x84901)),f315(f315(f3(a1),f315(f315(f73(a1),x84902),x84902)),a86)))
% 168.50/168.38 [8492]~P1(f315(f315(f223(a1),x84921),x84922))+P1(f315(f315(f224(a1),f315(f315(f73(a1),x84921),x84921)),f315(f315(f3(a1),f315(f315(f73(a1),x84922),x84922)),a86)))
% 168.50/168.38 [8920]P1(f315(f315(f223(a1),x89201),x89202))+~P1(f315(f315(f223(a1),f315(f315(f73(a1),x89201),x89201)),f315(f315(f3(a1),f315(f315(f73(a1),x89202),x89202)),a86)))
% 168.50/168.38 [8922]P1(f315(f315(f223(a1),x89221),x89222))+~P1(f315(f315(f224(a1),f315(f315(f73(a1),x89221),x89221)),f315(f315(f3(a1),f315(f315(f73(a1),x89222),x89222)),a86)))
% 168.50/168.38 [9211]~P1(f315(f315(f223(a1),x92111),x92112))+P1(f315(f315(f223(a1),f315(f315(f3(a1),f315(f315(f73(a1),x92111),x92111)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),x92112),x92112)),a86)))
% 168.50/168.38 [9213]~P1(f315(f315(f224(a1),x92131),x92132))+P1(f315(f315(f224(a1),f315(f315(f3(a1),f315(f315(f73(a1),x92131),x92131)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),x92132),x92132)),a86)))
% 168.50/168.38 [9484]P1(f315(f315(f223(a1),x94841),x94842))+~P1(f315(f315(f223(a1),f315(f315(f3(a1),f315(f315(f73(a1),x94841),x94841)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),x94842),x94842)),a86)))
% 168.50/168.38 [9486]P1(f315(f315(f224(a1),x94861),x94862))+~P1(f315(f315(f224(a1),f315(f315(f3(a1),f315(f315(f73(a1),x94861),x94861)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),x94862),x94862)),a86)))
% 168.50/168.38 [9519]~P1(f315(f54(x95191),x95192))+P1(f315(f54(f909(x95191,a899)),f315(f250(f909(x95191,a899)),f315(f315(f9(f909(x95191,a899),f909(x95191,a899),a899),f223(f909(x95191,a899))),x95192))))
% 168.50/168.38 [9571]~E(f315(f273(f908(a901,a901),f908(a901,a901),a97),f315(f315(f297(f908(a901,a901)),x95711),f177(f909(f908(a901,a901),a899)))),f315(f273(f908(a901,a901),f908(a901,a901),a97),f315(f315(f297(f908(a901,a901)),x95712),f177(f909(f908(a901,a901),a899)))))+P1(f315(f315(f317(f908(f908(a901,a901),f908(a901,a901))),f315(f315(f240(f908(a901,a901),f908(a901,a901)),x95711),x95712)),a97))
% 168.50/168.38 [9665]E(f315(f273(f908(a901,a901),f908(a901,a901),a97),f315(f315(f297(f908(a901,a901)),x96651),f177(f909(f908(a901,a901),a899)))),f315(f273(f908(a901,a901),f908(a901,a901),a97),f315(f315(f297(f908(a901,a901)),x96652),f177(f909(f908(a901,a901),a899)))))+~P1(f315(f315(f317(f908(f908(a901,a901),f908(a901,a901))),f315(f315(f240(f908(a901,a901),f908(a901,a901)),x96651),x96652)),a97))
% 168.50/168.38 [9701]P1(f315(f315(f223(a1),f2(a1)),f625(x97011,x97012)))+E(f315(f250(a1),f315(f315(f20(a1,a899,a899),f315(f315(f10(a899,f909(a899,a899),a1),a313),f315(f223(a1),f2(a1)))),x97011)),f315(f250(a1),f315(f315(f20(a1,a899,a899),f315(f315(f10(a899,f909(a899,a899),a1),a313),f315(f223(a1),f2(a1)))),x97012)))
% 168.50/168.38 [10204]~P5(x102041)+E(f31(x102041,f315(f250(x102041),f315(f315(f10(f909(x102041,a899),a899,x102041),f81(x102041)),f315(f315(f10(f909(x102041,a899),f909(x102041,a899),x102041),f315(f20(x102041,a899,a899),f315(f315(f10(a899,f909(a899,a899),x102041),a318),f315(f315(f9(x102041,f909(x102041,a899),a899),f317(x102041)),x102042)))),f315(f9(x102041,x102041,a899),f223(x102041)))))),f30(x102041,x102042))
% 168.50/168.38 [10226]P1(f315(f315(f317(a901),f2(a901)),x102261))+E(f315(f28(a901),f315(f250(a901),f315(f315(f20(a901,a899,a899),f315(f315(f10(a899,f909(a899,a899),a901),a313),f315(f315(f9(a901,f909(a901,a899),a899),f315(f315(f10(a901,f909(f909(a901,a899),a899),a901),f317(a901)),a101)),x102261))),f315(f315(f9(a901,a901,a899),f224(a901)),x102262)))),f315(f28(a901),f315(f250(a901),f315(f315(f20(a901,a899,a899),f315(f315(f10(a899,f909(a899,a899),a901),a313),f315(f315(f9(a901,f909(a901,a899),a899),f317(a901)),x102261))),f315(f315(f9(a901,a901,a899),f224(a901)),f315(a101,x102262))))))
% 168.50/168.38 [10284]P1(f315(f315(f275(a901),x102841),x102842))+~P1(f315(f315(f317(a901),x102842),f283(a901,f315(f315(f20(a901,f909(a901,a899),f909(a901,a899)),f315(f315(f10(f909(a901,f909(a899,a899)),f909(f909(a901,a899),f909(a901,a899)),a901),f20(a901,a899,a899)),f315(f315(f10(f909(a901,a899),f909(a901,f909(a899,a899)),a901),f315(f10(a899,f909(a899,a899),a901),a313)),f275(a901)))),f315(f315(f10(f909(a901,a899),f909(a901,a899),a901),f315(f10(a899,a899,a901),a310)),f315(f9(a901,a901,a899),f275(a901)))),x102841)))
% 168.50/168.38 [10285]P1(f315(f315(f275(a901),x102851),x102852))+~P1(f315(f315(f317(a901),x102851),f286(a901,f315(f315(f20(a901,f909(a901,a899),f909(a901,a899)),f315(f315(f10(f909(a901,f909(a899,a899)),f909(f909(a901,a899),f909(a901,a899)),a901),f20(a901,a899,a899)),f315(f315(f10(f909(a901,a899),f909(a901,f909(a899,a899)),a901),f315(f10(a899,f909(a899,a899),a901),a313)),f275(a901)))),f315(f315(f10(f909(a901,a899),f909(a901,a899),a901),f315(f10(a899,a899,a901),a310)),f315(f9(a901,a901,a899),f275(a901)))),x102852)))
% 168.50/168.38 [10286]~P1(f315(f315(f275(a901),x102861),x102862))+~P1(f315(f315(f317(a901),x102862),f286(a901,f315(f315(f20(a901,f909(a901,a899),f909(a901,a899)),f315(f315(f10(f909(a901,f909(a899,a899)),f909(f909(a901,a899),f909(a901,a899)),a901),f20(a901,a899,a899)),f315(f315(f10(f909(a901,a899),f909(a901,f909(a899,a899)),a901),f315(f10(a899,f909(a899,a899),a901),a313)),f275(a901)))),f315(f315(f10(f909(a901,a899),f909(a901,a899),a901),f315(f10(a899,a899,a901),a310)),f315(f9(a901,a901,a899),f275(a901)))),x102861)))
% 168.50/168.38 [10287]~P1(f315(f315(f275(a901),x102871),x102872))+~P1(f315(f315(f317(a901),x102871),f283(a901,f315(f315(f20(a901,f909(a901,a899),f909(a901,a899)),f315(f315(f10(f909(a901,f909(a899,a899)),f909(f909(a901,a899),f909(a901,a899)),a901),f20(a901,a899,a899)),f315(f315(f10(f909(a901,a899),f909(a901,f909(a899,a899)),a901),f315(f10(a899,f909(a899,a899),a901),a313)),f275(a901)))),f315(f315(f10(f909(a901,a899),f909(a901,a899),a901),f315(f10(a899,a899,a901),a310)),f315(f9(a901,a901,a899),f275(a901)))),x102872)))
% 168.50/168.38 [7712]~P97(x77121)+E(f315(f315(f74(x77121),x77122),f315(f92(x77121),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))),x77122)
% 168.50/168.38 [7975]~P97(x79751)+E(f315(f315(f73(x79751),f315(f92(x79751),x79752)),f71(x79751)),f315(f92(x79751),f315(f315(f73(a1),x79752),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))))
% 168.50/168.38 [8120]P1(f315(f315(f223(a1),f2(a1)),f315(f92(a1),x81202)))+E(f315(f315(f232(a1),x81201),f315(f92(a901),f315(f315(f3(a1),f315(f315(f73(a1),x81202),x81202)),a86))),f71(a1))
% 168.50/168.38 [9546]~P1(f315(f315(f223(a1),f2(a1)),f315(f92(a1),x95462)))+E(f315(f315(f232(a1),x95461),f315(f92(a901),f315(f315(f3(a1),f315(f315(f73(a1),x95462),x95462)),a86))),f315(f315(f79(a1,a1),f315(f315(f232(a1),x95461),f315(f92(a901),x95462))),f315(f315(f20(a1,a1,a1),f315(f315(f10(a1,f909(a1,a1),a1),f74(a1)),f315(f74(a1),x95461))),f7(a1))))
% 168.50/168.38 [9922]~P1(f315(f315(f223(a901),f632(x99222,x99221)),f315(x99221,f632(x99222,x99221))))+P1(f315(f54(a901),f315(f250(a901),f315(f315(f9(a901,a901,a899),f315(f315(f10(a901,f909(a901,a899),a901),f223(a901)),x99221)),x99222))))
% 168.50/168.38 [10057]~P1(f315(f315(f223(a901),f315(f92(a901),x100571)),f315(a101,x100572)))+P1(f315(f315(f79(a1,a899),f315(f92(a1),f315(f315(f73(a1),x100571),a86))),f315(f315(f20(a1,a899,a899),f315(f315(f10(a899,f909(a899,a899),a1),a318),f315(f315(f10(a899,a899,a1),a310),a182))),f315(f315(f9(a1,a901,a899),f315(f315(f10(a901,f909(a901,a899),a1),f223(a901)),a93)),x100572))))
% 168.50/168.38 [10058]~P1(f315(f315(f224(a901),f315(f92(a901),x100581)),f315(a101,x100582)))+P1(f315(f315(f79(a1,a899),f315(f92(a1),f315(f315(f73(a1),x100581),a86))),f315(f315(f20(a1,a899,a899),f315(f315(f10(a899,f909(a899,a899),a1),a318),f315(f315(f10(a899,a899,a1),a310),a182))),f315(f315(f9(a1,a901,a899),f315(f315(f10(a901,f909(a901,a899),a1),f224(a901)),a93)),x100582))))
% 168.50/168.38 [10117]P1(f315(f315(f223(a901),f315(f92(a901),x101171)),f315(a101,x101172)))+~P1(f315(f315(f79(a1,a899),f315(f92(a1),f315(f315(f73(a1),x101171),a86))),f315(f315(f20(a1,a899,a899),f315(f315(f10(a899,f909(a899,a899),a1),a318),f315(f315(f10(a899,a899,a1),a310),a182))),f315(f315(f9(a1,a901,a899),f315(f315(f10(a901,f909(a901,a899),a1),f223(a901)),a93)),x101172))))
% 168.50/168.38 [10118]P1(f315(f315(f224(a901),f315(f92(a901),x101181)),f315(a101,x101182)))+~P1(f315(f315(f79(a1,a899),f315(f92(a1),f315(f315(f73(a1),x101181),a86))),f315(f315(f20(a1,a899,a899),f315(f315(f10(a899,f909(a899,a899),a1),a318),f315(f315(f10(a899,a899,a1),a310),a182))),f315(f315(f9(a1,a901,a899),f315(f315(f10(a901,f909(a901,a899),a1),f224(a901)),a93)),x101182))))
% 168.50/168.38 [10148]~P1(f315(f315(f223(a901),f315(a101,x101482)),f315(f92(a901),x101481)))+P1(f315(f315(f79(a1,a899),f315(f92(a1),f315(f315(f73(a1),x101481),a86))),f315(f315(f20(a1,a899,a899),f315(f315(f10(a899,f909(a899,a899),a1),a313),f315(f315(f10(a899,a899,a1),a310),a182))),f315(f315(f20(a1,a899,a899),f315(f315(f10(a899,f909(a899,a899),a1),a318),f315(f315(f10(a899,a899,a1),a310),a182))),f315(f315(f10(a901,a899,a1),f315(f223(a901),x101482)),a93)))))
% 168.50/168.38 [10149]~P1(f315(f315(f224(a901),f315(a101,x101492)),f315(f92(a901),x101491)))+P1(f315(f315(f79(a1,a899),f315(f92(a1),f315(f315(f73(a1),x101491),a86))),f315(f315(f20(a1,a899,a899),f315(f315(f10(a899,f909(a899,a899),a1),a313),f315(f315(f10(a899,a899,a1),a310),a182))),f315(f315(f20(a1,a899,a899),f315(f315(f10(a899,f909(a899,a899),a1),a318),f315(f315(f10(a899,a899,a1),a310),a182))),f315(f315(f10(a901,a899,a1),f315(f224(a901),x101492)),a93)))))
% 168.50/168.38 [10194]P1(f315(f315(f223(a901),f315(a101,x101941)),f315(f92(a901),x101942)))+~P1(f315(f315(f79(a1,a899),f315(f92(a1),f315(f315(f73(a1),x101942),a86))),f315(f315(f20(a1,a899,a899),f315(f315(f10(a899,f909(a899,a899),a1),a313),f315(f315(f10(a899,a899,a1),a310),a182))),f315(f315(f20(a1,a899,a899),f315(f315(f10(a899,f909(a899,a899),a1),a318),f315(f315(f10(a899,a899,a1),a310),a182))),f315(f315(f10(a901,a899,a1),f315(f223(a901),x101941)),a93)))))
% 168.50/168.38 [10195]P1(f315(f315(f224(a901),f315(a101,x101951)),f315(f92(a901),x101952)))+~P1(f315(f315(f79(a1,a899),f315(f92(a1),f315(f315(f73(a1),x101952),a86))),f315(f315(f20(a1,a899,a899),f315(f315(f10(a899,f909(a899,a899),a1),a313),f315(f315(f10(a899,a899,a1),a310),a182))),f315(f315(f20(a1,a899,a899),f315(f315(f10(a899,f909(a899,a899),a1),a318),f315(f315(f10(a899,a899,a1),a310),a182))),f315(f315(f10(a901,a899,a1),f315(f224(a901),x101951)),a93)))))
% 168.50/168.38 [10274]~P1(f315(f315(f317(a901),f2(a901)),x102741))+E(f315(a101,f315(f28(a901),f315(f250(a901),f315(f315(f20(a901,a899,a899),f315(f315(f10(a899,f909(a899,a899),a901),a313),f315(f315(f9(a901,f909(a901,a899),a899),f315(f315(f10(a901,f909(f909(a901,a899),a899),a901),f317(a901)),a101)),x102741))),f315(f315(f9(a901,a901,a899),f224(a901)),x102742))))),f315(f28(a901),f315(f250(a901),f315(f315(f20(a901,a899,a899),f315(f315(f10(a899,f909(a899,a899),a901),a313),f315(f315(f9(a901,f909(a901,a899),a899),f317(a901)),x102741))),f315(f315(f9(a901,a901,a899),f224(a901)),f315(a101,x102742))))))
% 168.50/168.38 [8662]~P97(x86621)+E(f315(f315(f74(x86621),f315(f92(x86621),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))),x86622),x86622)
% 168.50/168.38 [8723]~P97(x87231)+E(f315(f315(f73(x87231),f71(x87231)),f315(f92(x87231),x87232)),f315(f92(x87231),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),x87232)))
% 168.50/168.38 [8785]~P97(x87851)+E(f315(f315(f3(x87851),f315(f92(x87851),x87852)),f71(x87851)),f315(f92(x87851),f315(f315(f73(a1),x87852),f315(f72(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))))
% 168.50/168.38 [8939]~P1(f315(f315(f224(a901),f315(f92(a901),a76)),x89392))+E(f315(f315(f3(a901),x89391),f315(f315(f3(a901),x89392),f315(f92(a901),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),f315(f315(f3(a901),f315(a101,x89391)),x89392))
% 168.50/168.38 [9589]~P121(x95891)+E(f315(f315(f74(x95891),x95892),x95892),f315(f315(f232(x95891),x95892),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))))
% 168.50/168.38 [9590]~P84(x95901)+E(f315(f315(f232(x95901),x95902),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),f315(f315(f74(x95901),x95902),x95902))
% 168.50/168.38 [9592]~P97(x95921)+E(f315(f315(f74(x95921),x95922),f315(f92(x95921),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),f315(f315(f73(x95921),x95922),x95922))
% 168.50/168.38 [9840]~P114(x98401)+E(f315(f315(f232(x98401),f315(f69(x98401),x98402)),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),f315(f315(f232(x98401),x98402),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))))
% 168.50/168.38 [9841]~P143(x98411)+E(f315(f315(f232(x98411),f315(f72(x98411),x98412)),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),f315(f315(f232(x98411),x98412),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))))
% 168.50/168.38 [9837]~P97(x98371)+E(f315(f315(f74(x98371),f315(f92(x98371),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),x98372),f315(f315(f73(x98371),x98372),x98372))
% 168.50/168.38 [9955]~P114(x99551)+E(f315(f69(x99551),f315(f315(f232(x99551),x99552),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))))),f315(f315(f232(x99551),x99552),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))))
% 168.50/168.38 [10019]~P114(x100191)+P1(f315(f315(f223(x100191),f2(x100191)),f315(f315(f232(x100191),x100192),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))))))
% 168.50/168.38 [10185]~E(f315(a101,x101852),f315(f92(a901),x101851))+P1(f315(f315(f79(a1,a899),f315(f92(a1),f315(f315(f73(a1),x101851),a86))),f315(f315(f20(a1,a899,a899),f315(f315(f10(a899,f909(a899,a899),a1),a313),f315(f315(f10(a899,a899,a1),a310),a182))),f315(f315(f20(a1,a899,a899),f315(f315(f10(a899,f909(a899,a899),a1),a318),f315(f315(f10(a899,a899,a1),a310),a182))),f315(f315(f9(a1,a901,a899),f315(f315(f10(a901,f909(a901,a899),a1),a312),a93)),x101852)))))
% 168.50/168.38 [10186]~E(f315(f92(a901),x101861),f315(a101,x101862))+P1(f315(f315(f79(a1,a899),f315(f92(a1),f315(f315(f73(a1),x101861),a86))),f315(f315(f20(a1,a899,a899),f315(f315(f10(a899,f909(a899,a899),a1),a313),f315(f315(f10(a899,a899,a1),a310),a182))),f315(f315(f20(a1,a899,a899),f315(f315(f10(a899,f909(a899,a899),a1),a318),f315(f315(f10(a899,a899,a1),a310),a182))),f315(f315(f9(a1,a901,a899),f315(f315(f10(a901,f909(a901,a899),a1),a312),a93)),x101862)))))
% 168.50/168.38 [10229]E(f315(a101,x102291),f315(f92(a901),x102292))+~P1(f315(f315(f79(a1,a899),f315(f92(a1),f315(f315(f73(a1),x102292),a86))),f315(f315(f20(a1,a899,a899),f315(f315(f10(a899,f909(a899,a899),a1),a313),f315(f315(f10(a899,a899,a1),a310),a182))),f315(f315(f20(a1,a899,a899),f315(f315(f10(a899,f909(a899,a899),a1),a318),f315(f315(f10(a899,a899,a1),a310),a182))),f315(f315(f9(a1,a901,a899),f315(f315(f10(a901,f909(a901,a899),a1),a312),a93)),x102291)))))
% 168.50/168.38 [10230]E(f315(f92(a901),x102301),f315(a101,x102302))+~P1(f315(f315(f79(a1,a899),f315(f92(a1),f315(f315(f73(a1),x102301),a86))),f315(f315(f20(a1,a899,a899),f315(f315(f10(a899,f909(a899,a899),a1),a313),f315(f315(f10(a899,a899,a1),a310),a182))),f315(f315(f20(a1,a899,a899),f315(f315(f10(a899,f909(a899,a899),a1),a318),f315(f315(f10(a899,a899,a1),a310),a182))),f315(f315(f9(a1,a901,a899),f315(f315(f10(a901,f909(a901,a899),a1),a312),a93)),x102302)))))
% 168.50/168.38 [10275]~P16(x102751,x102752)+P1(f315(f315(f317(f909(x102751,a899)),f793(x102752,x102751)),f315(f315(f10(f909(x102751,a899),a899,f909(x102751,a899)),f80(x102751)),f315(f315(f10(f909(x102751,a899),f909(x102751,a899),f909(x102751,a899)),f315(f20(x102751,a899,a899),f315(f315(f10(a899,f909(a899,a899),x102751),a313),f315(f315(f20(x102751,x102751,a899),x102752),f7(x102751))))),f315(f315(f9(f909(x102751,a899),f909(x102751,f909(x102751,a899)),f909(x102751,a899)),f315(f315(f10(f909(f909(x102751,a899),a899),f909(f909(x102751,f909(x102751,a899)),f909(x102751,a899)),f909(x102751,a899)),f10(f909(x102751,a899),a899,x102751)),a312)),x102752)))))
% 168.50/168.38 [10017]~P97(x100171)+E(f315(f315(f232(x100171),f315(f92(x100171),a86)),f315(f315(f74(a901),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),x100172)),f71(x100171))
% 168.50/168.38 [10018]~P143(x100181)+E(f315(f315(f232(x100181),f315(f72(x100181),f71(x100181))),f315(f315(f74(a901),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),x100182)),f71(x100181))
% 168.50/168.38 [10021]~P84(x100211)+E(f315(f315(f232(x100211),x100212),f315(f92(a901),f315(f315(f3(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))),a86))),f315(f315(f74(x100211),f315(f315(f74(x100211),x100212),x100212)),x100212))
% 168.50/168.38 [10209]~P1(f315(f315(f223(a1),f2(a1)),x102092))+E(f38(a1,f315(f315(f73(a1),f71(a1)),f315(f315(f74(a1),f315(f92(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),x102091)),f315(f315(f74(a1),f315(f92(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),x102092)),f315(f315(f73(a1),f71(a1)),f315(f315(f74(a1),f315(f92(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),f38(a1,x102091,x102092))))
% 168.50/168.38 [10232]~P1(f315(f315(f223(a1),f2(a1)),x102322))+E(f315(f315(f29(a1),f315(f315(f73(a1),f71(a1)),f315(f315(f74(a1),f315(f92(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),x102321))),f315(f315(f74(a1),f315(f92(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),x102322)),f315(f315(f29(a1),x102321),x102322))
% 168.50/168.38 [10234]~P1(f315(f315(f223(a1),x102342),f2(a1)))+E(f315(f315(f29(a1),f315(f315(f73(a1),f71(a1)),f315(f315(f74(a1),f315(f92(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),x102341))),f315(f315(f74(a1),f315(f92(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),x102342)),f315(f315(f29(a1),f315(f315(f73(a1),x102341),f71(a1))),x102342))
% 168.50/168.38 [10235]~P1(f315(f315(f223(a1),x102352),f2(a1)))+E(f38(a1,f315(f315(f73(a1),f71(a1)),f315(f315(f74(a1),f315(f92(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),x102351)),f315(f315(f74(a1),f315(f92(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),x102352)),f315(f315(f3(a1),f315(f315(f74(a1),f315(f92(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),f38(a1,f315(f315(f73(a1),x102351),f71(a1)),x102352))),f71(a1)))
% 168.50/168.38 [10108]~P97(x101081)+E(f315(f315(f232(x101081),f315(f92(x101081),a86)),f315(a101,f315(f315(f74(a901),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),x101082))),f315(f92(x101081),a86))
% 168.50/168.38 [10110]~P143(x101101)+E(f315(f315(f232(x101101),f315(f72(x101101),f71(x101101))),f315(a101,f315(f315(f74(a901),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),x101102))),f315(f72(x101101),f71(x101101)))
% 168.50/168.38 [5020]P40(x50201,x50202)+~P8(x50201,x50203,x50202)
% 168.50/168.38 [5022]P53(x50221,x50222)+~P8(x50221,x50223,x50222)
% 168.50/168.38 [5195]~P8(x51951,x51952,x51953)+P54(x51951,x51952,x51953)
% 168.50/168.38 [8187]~E(x81872,x81873)+P36(x81871,x81871,a312,x81872,x81873)
% 168.50/168.38 [8736]E(x87361,x87362)+~P36(x87363,x87363,a312,x87361,x87362)
% 168.50/168.38 [4824]E(f158(x48241,x48242,x48243),f102(x48241))+~E(x48242,f2(a901))
% 168.50/168.38 [4992]~E(f158(x49922,x49921,x49923),f102(x49922))+E(x49921,f2(a901))
% 168.50/168.38 [5200]~P39(x52001,x52003)+P39(x52001,f309(x52001,x52002,x52003))
% 168.50/168.38 [5310]~P31(x53101,x53102,x53103)+P33(a1,x53101,f167(x53102,x53103))
% 168.50/168.38 [5359]P28(x53591,x53592,x53593)+~P28(x53591,f315(a101,x53592),x53593)
% 168.50/168.38 [5379]P31(x53791,x53792,x53793)+~P33(a1,x53791,f167(x53792,x53793))
% 168.50/168.38 [5450]~P8(x54501,x54502,x54503)+P8(f902(x54501),f150(x54501,x54502),f147(x54501,x54503))
% 168.50/168.38 [5451]~P54(x54511,x54512,x54513)+P54(f902(x54511),f150(x54511,x54512),f147(x54511,x54513))
% 168.50/168.38 [5564]P57(x55641,x55642,x55643)+~E(f597(x55643,x55642,x55641),f598(x55643,x55642,x55641))
% 168.50/168.38 [5565]P56(x55651,x55652,x55653)+~E(f600(x55653,x55652,x55651),f601(x55653,x55652,x55651))
% 168.50/168.38 [6549]P29(x65491,x65492,x65493)+~P28(x65491,f649(x65493,x65492,x65491),f767(x65493,x65492,x65491))
% 168.50/168.38 [8193]~E(x81932,x81933)+P26(x81931,x81931,f25(x81931),x81932,x81933)
% 168.50/168.38 [8744]E(x87441,x87442)+~P26(x87443,x87443,f25(x87443),x87441,x87442)
% 168.50/168.38 [4779]~E(f315(f157(x47792),x47791),x47793)+E(x47791,f315(f157(x47792),x47793))
% 168.50/168.38 [4780]~E(x47802,f315(f157(x47801),x47803))+E(f315(f157(x47801),x47802),x47803)
% 168.50/168.38 [4830]E(x48301,x48302)+~E(f315(f157(x48303),x48301),f315(f157(x48303),x48302))
% 168.50/168.38 [5046]~P7(x50463,x50461)+P1(f315(f315(x50461,x50462),x50462))
% 168.50/168.38 [5047]~P45(x50473,x50471)+P1(f315(f315(x50471,x50472),x50472))
% 168.50/168.38 [5049]~P61(x50491,x50492)+P1(f315(f303(x50491,x50492),x50493))
% 168.50/168.38 [5115]~P39(x51151,x51152)+P39(f902(x51151),f315(f132(x51151,x51152),x51153))
% 168.50/168.38 [5120]~P1(f315(x51202,x51203))+~E(f315(f250(x51201),x51202),f177(f909(x51201,a899)))
% 168.50/168.38 [5121]~P1(f315(x51212,x51213))+~E(f177(f909(x51211,a899)),f315(f250(x51211),x51212))
% 168.50/168.38 [5133]E(x51331,f2(a901))+E(f133(x51332,f158(x51332,x51331,x51333)),x51333)
% 168.50/168.38 [5152]~P1(f315(x51521,x51523))+P1(f315(x51521,f83(x51522,x51521)))
% 168.50/168.38 [5153]~P1(f315(x51531,x51533))+P1(f315(x51531,f719(x51531,x51532)))
% 168.50/168.38 [5165]E(x51651,f2(a901))+E(f315(f130(x51652),f158(x51652,x51651,x51653)),x51653)
% 168.50/168.38 [5271]~E(x52712,x52713)+P1(f315(f315(f317(x52711),x52712),f315(a312,x52713)))
% 168.50/168.38 [5287]~E(x52872,f2(a901))+E(f315(f161(x52871),f158(x52871,x52872,x52873)),f177(f909(x52871,a899)))
% 168.50/168.38 [5332]E(f315(f157(x53321),x53322),f315(f315(f140(x53321),x53323),f102(x53321)))+~E(x53322,f315(f315(f140(x53321),x53323),f102(x53321)))
% 168.50/168.38 [5333]~E(x53333,f315(f315(f140(x53331),x53332),f102(x53331)))+E(f315(f315(f140(x53331),x53332),f102(x53331)),f315(f157(x53331),x53333))
% 168.50/168.38 [5375]~P35(x53751,x53752,x53753)+P35(x53751,x53752,f315(f157(x53751),x53753))
% 168.50/168.38 [5376]~P33(x53761,x53762,x53763)+P33(x53761,x53762,f315(f157(x53761),x53763))
% 168.50/168.38 [5380]E(f315(f28(x53801),f842(x53802,x53803,x53801)),x53802)+~E(f315(f28(x53801),x53803),f315(a101,x53802))
% 168.50/168.38 [5387]~P39(x53871,x53873)+P1(f315(f315(f317(x53871),x53872),f304(x53871,x53873)))
% 168.50/168.38 [5391]~E(f315(f157(x53912),x53911),f315(f315(f140(x53912),x53913),f102(x53912)))+E(x53911,f315(f315(f140(x53912),x53913),f102(x53912)))
% 168.50/168.38 [5392]~E(f315(f315(f140(x53922),x53923),f102(x53922)),f315(f157(x53922),x53921))+E(x53921,f315(f315(f140(x53922),x53923),f102(x53922)))
% 168.50/168.38 [5415]E(f78(f908(a901,a901),f41(x54151,x54152)),x54153)+~P1(f315(f41(x54151,x54152),x54153))
% 168.50/168.38 [5454]P35(x54541,x54542,x54543)+~P35(x54541,x54542,f315(f157(x54541),x54543))
% 168.50/168.38 [5455]P33(x54551,x54552,x54553)+~P33(x54551,x54552,f315(f157(x54551),x54553))
% 168.50/168.38 [5494]P1(f315(f315(x54941,x54942),x54942))+~P1(f315(f258(x54943,x54941),x54942))
% 168.50/168.38 [5495]~P1(f315(f315(x54952,x54953),x54953))+P1(f315(f258(x54951,x54952),x54953))
% 168.50/168.38 [5517]~E(x55172,f102(x55171))+P1(f315(f315(f317(f902(x55171)),x55172),f150(x55171,x55173)))
% 168.50/168.38 [5527]~P54(x55271,x55272,x55273)+P54(x55271,x55272,f315(f274(x55271,x55271),x55273))
% 168.50/168.38 [5528]~P57(x55281,x55282,x55283)+P57(x55281,x55282,f315(f274(x55281,x55281),x55283))
% 168.50/168.38 [5545]~P62(x55451)+E(f38(x55451,f38(x55451,x55452,x55453),x55453),f38(x55451,x55452,x55453))
% 168.50/168.38 [5649]E(x56491,x56492)+~P1(f315(f315(f317(x56493),x56491),f315(a312,x56492)))
% 168.50/168.38 [5697]~P147(x56971)+E(f179(x56971,x56972,f2(a901),x56973),x56973)
% 168.50/168.38 [5719]P54(x57191,x57192,x57193)+~P54(x57191,x57192,f315(f274(x57191,x57191),x57193))
% 168.50/168.38 [5720]P57(x57201,x57202,x57203)+~P57(x57201,x57202,f315(f274(x57201,x57201),x57203))
% 168.50/168.38 [5724]~P110(x57242)+E(f139(x57241,x57242,x57243,f102(x57241)),f102(x57241))
% 168.50/168.38 [5736]E(f159(x57361,x57362,f141(x57361,x57363)),f141(x57361,f159(x57361,x57362,x57363)))+~P1(f315(f126(x57361),x57363))
% 168.50/168.38 [5835]~P1(f315(f315(x58353,x58352),x58352))+P1(f315(f315(f317(x58351),x58352),f258(x58351,x58353)))
% 168.50/168.38 [5837]E(f315(f125(x58371,x58372),x58373),f102(x58371))+P1(f315(x58372,f686(x58373,x58372,x58371)))
% 168.50/168.38 [5905]E(f61(x59051,x59052,x59053),x59052)+P1(f315(x59053,f720(x59052,x59051,x59053)))
% 168.50/168.38 [6001]~P1(f315(f126(x60011),x60012))+P1(f315(f126(x60011),f165(x60011,x60012,x60013)))
% 168.50/168.38 [6002]~P1(f315(f126(x60021),x60023))+P1(f315(f126(x60021),f159(x60021,x60022,x60023)))
% 168.50/168.38 [6003]~P1(f315(f126(x60031),x60033))+P1(f315(f126(x60031),f166(x60031,x60032,x60033)))
% 168.50/168.38 [6004]~P1(f315(f126(x60041),x60043))+P1(f315(f126(x60041),f129(x60041,x60042,x60043)))
% 168.50/168.38 [6005]~P149(x60051,x60052,x60053)+P1(f315(x60051,f38(a1,x60052,x60053)))
% 168.50/168.38 [6021]~P35(x60213,x60211,x60212)+P1(f315(x60211,f732(x60212,x60211,x60213)))
% 168.50/168.38 [6022]~P37(x60223,x60221,x60222)+P1(f315(x60221,f739(x60222,x60221,x60223)))
% 168.50/168.38 [6023]~P37(x60233,x60231,x60232)+P1(f315(x60231,f749(x60232,x60231,x60233)))
% 168.50/168.38 [6024]~P35(x60243,x60241,x60242)+P1(f315(x60241,f777(x60242,x60241,x60243)))
% 168.50/168.38 [6025]~P35(x60253,x60251,x60252)+P1(f315(x60251,f778(x60251,x60252,x60253)))
% 168.50/168.38 [6030]P1(f315(f315(x60301,x60302),x60302))+~P1(f315(f315(f317(x60303),x60302),f258(x60303,x60301)))
% 168.50/168.38 [6045]E(f315(f125(x60451,x60452),x60453),f166(x60451,x60452,x60453))+P1(f315(x60452,f704(x60453,x60452,x60451)))
% 168.50/168.38 [6085]~P1(f315(f126(x60851),x60853))+P1(f315(f126(f902(x60851)),f48(x60851,x60852,x60853)))
% 168.50/168.38 [6122]~P111(x61221)+E(f315(f315(f90(f909(x61221,a899)),f315(f270(x61221),x61222)),f291(x61221,x61222,x61223)),f177(f909(x61221,a899)))
% 168.50/168.38 [6123]~P111(x61231)+E(f315(f315(f90(f909(x61231,a899)),f315(f289(x61231),x61232)),f294(x61231,x61232,x61233)),f177(f909(x61231,a899)))
% 168.50/168.38 [6124]~P111(x61241)+E(f315(f315(f90(f909(x61241,a899)),f315(f289(x61241),x61242)),f293(x61241,x61242,x61243)),f177(f909(x61241,a899)))
% 168.50/168.38 [6359]E(f315(f125(x63591,x63592),x63593),x63593)+~P1(f315(x63592,f687(x63593,x63592,x63591)))
% 168.50/168.38 [6361]E(f315(f315(f297(x63611),f843(x63612,x63613,x63611)),f842(x63612,x63613,x63611)),x63613)+~E(f315(f28(x63611),x63613),f315(a101,x63612))
% 168.50/168.38 [6377]P149(x63771,x63772,x63773)+~P1(f315(x63771,f38(a1,x63772,x63773)))
% 168.50/168.38 [6429]P33(x64291,x64292,x64293)+~P1(f315(x64292,f745(x64293,x64292,x64291)))
% 168.50/168.38 [6430]P33(x64301,x64302,x64303)+~P1(f315(x64302,f747(x64302,x64303,x64301)))
% 168.50/168.38 [6431]P33(x64311,x64312,x64313)+~P1(f315(x64312,f748(x64313,x64312,x64311)))
% 168.50/168.38 [6432]P31(x64321,x64322,x64323)+~P1(f315(x64321,f766(x64323,x64322,x64321)))
% 168.50/168.38 [6433]P32(x64331,x64332,x64333)+~P1(f315(x64331,f812(x64333,x64332,x64331)))
% 168.50/168.38 [6435]E(f166(x64351,x64352,x64353),x64353)+~P1(f315(x64352,f700(x64353,x64352,x64351)))
% 168.50/168.38 [6518]~P1(f315(x65182,f377(x65183,x65182,x65181)))+P1(f315(f236(x65181,x65182),x65183))
% 168.50/168.38 [6519]~P1(f315(x65192,f676(x65193,x65192,x65191)))+P1(f315(f149(x65191,x65192),x65193))
% 168.50/168.38 [6775]~P1(f315(f303(x67751,x67752),f369(x67753,x67752,x67751)))+P1(f315(f303(x67751,x67752),x67753))
% 168.50/168.38 [6776]~P1(f315(f303(x67761,x67762),f378(x67763,x67762,x67761)))+P1(f315(f303(x67761,x67762),x67763))
% 168.50/168.38 [7403]~P62(x74031)+E(f315(f315(f73(x74031),f315(f315(f74(x74031),x74032),f315(f315(f29(x74031),x74033),x74032))),f38(x74031,x74033,x74032)),x74033)
% 168.50/168.38 [7433]P31(x74331,x74332,x74333)+P1(f315(f315(f317(a1),f766(x74333,x74332,x74331)),f291(a1,x74332,x74333)))
% 168.50/168.38 [7866]E(f315(f315(f240(x78661,x78661),f470(x78662,x78663,x78661)),f470(x78662,x78663,x78661)),x78663)+~P1(f315(f315(f317(f908(x78661,x78661)),x78663),f251(x78661,x78662)))
% 168.50/168.38 [7983]~P1(f315(f315(f317(x79831),f494(x79833,x79832,x79831)),f304(x79831,x79833)))+P1(f315(f315(f317(x79831),x79832),f304(x79831,x79833)))
% 168.50/168.38 [7984]~P1(f315(f315(f317(x79841),f584(x79843,x79842,x79841)),f304(x79841,x79843)))+P1(f315(f315(f317(x79841),x79842),f304(x79841,x79843)))
% 168.50/168.38 [7985]~P1(f315(f315(f317(x79851),f586(x79853,x79852,x79851)),f304(x79851,x79853)))+P1(f315(f315(f317(x79851),x79852),f304(x79851,x79853)))
% 168.50/168.38 [8078]P35(a1,x80781,f167(x80782,x80783))+P31(f315(f66(a899,a899,a1,a310),x80781),x80782,x80783)
% 168.50/168.38 [8167]~P62(x81671)+E(f315(f315(f73(x81671),f315(f315(f74(x81671),f315(f315(f29(x81671),x81672),x81673)),x81673)),f38(x81671,x81672,x81673)),x81672)
% 168.50/168.38 [8214]~E(f315(f28(x82141),x82142),f315(a101,x82143))+~P1(f315(f315(f317(x82141),f843(x82143,x82142,x82141)),f842(x82143,x82142,x82141)))
% 168.50/168.38 [8654]~P35(a1,x86541,f167(x86542,x86543))+~P31(f315(f66(a899,a899,a1,a310),x86541),x86542,x86543)
% 168.50/168.38 [8841]P1(f315(f315(f223(f909(f908(x88411,x88411),a899)),f295(x88411,x88412)),f295(x88411,x88413)))+~P1(f315(f315(f223(f909(f908(x88411,x88411),a899)),x88412),f295(x88411,x88413)))
% 168.50/168.38 [9122]E(x91221,f102(x91222))+~P1(f315(f315(f317(f908(f902(x91222),f902(x91222))),f315(f315(f240(f902(x91222),f902(x91222)),x91221),f102(x91222))),f147(x91222,x91223)))
% 168.50/168.38 [9146]E(x91461,f102(x91462))+~P1(f315(f315(f317(f908(f902(x91462),f902(x91462))),f315(f315(f240(f902(x91462),f902(x91462)),f102(x91462)),x91461)),f147(x91462,x91463)))
% 168.50/168.38 [9271]E(f315(f315(f140(x92711),f672(x92712,x92713,x92711)),f673(x92712,x92713,x92711)),x92713)+~P1(f315(f315(f317(f908(f902(x92711),f902(x92711))),f315(f315(f240(f902(x92711),f902(x92711)),f102(x92711)),x92713)),f136(x92711,x92712)))
% 168.50/168.38 [9512]~P129(x95121)+~P1(f315(f315(f224(x95121),f315(f315(f73(x95121),f315(f315(f74(x95121),x95122),x95122)),f315(f315(f74(x95121),x95123),x95123))),f2(x95121)))
% 168.50/168.38 [9563]P1(f315(f54(x95631),x95632))+~P1(f315(f315(f317(f908(f909(x95631,a899),f909(x95631,a899))),f315(f315(f240(f909(x95631,a899),f909(x95631,a899)),x95633),x95632)),f302(x95631)))
% 168.50/168.38 [9866]~P49(x98661,x98662,x98663)+P1(f315(f315(f223(a1),f315(f315(f66(f908(a1,a1),a1,x98661,f239(a1,a1)),f201(x98661)),f219(x98661,x98662,f216(x98661,x98663)))),f2(a1)))
% 168.50/168.38 [9867]~P50(x98671,x98672,x98673)+P1(f315(f315(f224(a1),f315(f315(f66(f908(a1,a1),a1,x98671,f239(a1,a1)),f201(x98671)),f219(x98671,x98672,f216(x98671,x98673)))),f2(a1)))
% 168.50/168.38 [9985]P50(x99851,x99852,x99853)+~P1(f315(f315(f224(a1),f315(f315(f66(f908(a1,a1),a1,x99851,f239(a1,a1)),f201(x99851)),f219(x99851,x99852,f216(x99851,x99853)))),f2(a1)))
% 168.50/168.38 [9986]P49(x99861,x99862,x99863)+~P1(f315(f315(f223(a1),f315(f315(f66(f908(a1,a1),a1,x99861,f239(a1,a1)),f201(x99861)),f219(x99861,x99862,f216(x99861,x99863)))),f2(a1)))
% 168.50/168.38 [10337]~P114(x103371)+~P1(f315(f315(f224(x103371),f315(f315(f73(x103371),f315(f315(f232(x103371),x103372),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))))),f315(f315(f232(x103371),x103373),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))))),f2(x103371)))
% 168.50/168.38 [4809]~E(x48093,f102(x48091))+E(f315(f315(f123(x48091),x48092),x48093),x48092)
% 168.50/168.38 [4810]~E(x48102,f102(x48101))+E(f315(f315(f123(x48101),x48102),x48103),x48103)
% 168.50/168.38 [4816]~E(x48162,f2(a901))+E(f315(f315(f164(x48161),x48162),x48163),f102(x48161))
% 168.50/168.38 [4825]~E(x48253,f102(x48251))+E(f315(f315(f164(x48251),x48252),x48253),f102(x48251))
% 168.50/168.38 [4864]~E(x48641,x48643)+E(x48641,f315(f315(f123(x48642),f102(x48642)),x48643))
% 168.50/168.38 [4955]~P2(x49552)+E(f315(f177(f909(x49551,x49552)),x49553),f177(x49552))
% 168.50/168.38 [4956]~P118(x49562)+E(f315(f230(f909(x49561,x49562)),x49563),f230(x49562))
% 168.50/168.38 [4974]E(x49741,f102(x49742))+~E(f315(f315(f123(x49742),x49743),x49741),x49743)
% 168.50/168.38 [4975]E(x49751,f102(x49752))+~E(f315(f315(f123(x49752),x49751),x49753),x49753)
% 168.50/168.38 [4983]E(x49831,f102(x49832))+~E(f315(f315(f123(x49832),x49833),x49831),f102(x49832))
% 168.50/168.38 [4984]E(x49841,f102(x49842))+~E(f315(f315(f123(x49842),x49841),x49843),f102(x49842))
% 168.50/168.38 [5013]~E(x50132,f2(a901))+E(f315(f315(f74(a901),x50131),x50132),f315(f315(f74(a901),x50133),x50132))
% 168.50/168.38 [5015]~E(x50151,f2(a901))+E(f315(f315(f74(a901),x50151),x50152),f315(f315(f74(a901),x50151),x50153))
% 168.50/168.38 [5073]~P80(x50731)+E(f315(f315(f99(x50731),x50732),x50733),f315(f315(f99(x50731),x50733),x50732))
% 168.50/168.38 [5075]~P103(x50751)+E(f315(f315(f99(x50751),x50752),x50753),f315(f315(f99(x50751),x50753),x50752))
% 168.50/168.38 [5076]~P121(x50761)+E(f315(f315(f74(x50761),x50762),x50763),f315(f315(f74(x50761),x50763),x50762))
% 168.50/168.38 [5077]~P80(x50771)+E(f315(f315(f90(x50771),x50772),x50773),f315(f315(f90(x50771),x50773),x50772))
% 168.50/168.38 [5079]~P104(x50791)+E(f315(f315(f90(x50791),x50792),x50793),f315(f315(f90(x50791),x50793),x50792))
% 168.50/168.38 [5080]~P121(x50801)+E(f315(f315(f73(x50801),x50802),x50803),f315(f315(f73(x50801),x50803),x50802))
% 168.50/168.38 [5082]~P110(x50821)+E(f315(f315(f221(x50821),x50822),x50823),f315(f315(f221(x50821),x50823),x50822))
% 168.50/168.38 [5084]~P110(x50841)+E(f315(f315(f222(x50841),x50842),x50843),f315(f315(f222(x50841),x50843),x50842))
% 168.50/168.38 [5147]E(f38(a901,x51471,x51472),f2(a901))+~E(x51471,f315(f315(f74(a901),x51472),x51473))
% 168.50/168.38 [5148]E(f38(a1,x51481,x51482),f2(a1))+~E(x51481,f315(f315(f74(a1),x51482),x51483))
% 168.50/168.38 [5212]E(x52121,x52122)+~E(f315(f315(f73(a901),x52123),x52121),f315(f315(f73(a901),x52123),x52122))
% 168.50/168.38 [5213]E(x52131,x52132)+~E(f315(f315(f73(a901),x52131),x52133),f315(f315(f73(a901),x52132),x52133))
% 168.50/168.38 [5223]~P98(x52231)+E(f315(f315(f90(x52231),x52232),f315(f72(x52231),x52233)),f315(f315(f3(x52231),x52232),x52233))
% 168.50/168.38 [5224]~P69(x52241)+E(f315(f315(f73(x52241),x52242),f315(f72(x52241),x52243)),f315(f315(f3(x52241),x52242),x52243))
% 168.50/168.38 [5225]~P76(x52251)+E(f315(f315(f73(x52251),x52252),f315(f72(x52251),x52253)),f315(f315(f3(x52251),x52252),x52253))
% 168.50/168.38 [5226]~P116(x52261)+E(f315(f315(f73(x52261),x52262),f315(f72(x52261),x52263)),f315(f315(f3(x52261),x52262),x52263))
% 168.50/168.38 [5227]~P76(x52271)+E(f315(f315(f3(x52271),x52272),f315(f72(x52271),x52273)),f315(f315(f73(x52271),x52272),x52273))
% 168.50/168.38 [5265]~P1(f315(x52653,x52652))+P1(f315(f315(f317(x52651),x52652),x52653))
% 168.50/168.38 [5267]~P72(x52672)+E(f315(f315(f8(x52671,x52672),x52673),f177(f909(x52671,a899))),f2(x52672))
% 168.50/168.38 [5269]~P77(x52692)+E(f315(f315(f11(x52691,x52692),x52693),f177(f909(x52691,a899))),f71(x52692))
% 168.50/168.38 [5322]~E(x53222,f315(f315(f73(a901),x53221),x53223))+P1(f315(f315(f223(a901),x53221),x53222))
% 168.50/168.38 [5325]~E(x53252,f177(f909(x53251,a899)))+E(f315(f315(f53(x53251),x53252),x53253),f177(f909(f909(x53251,a899),a899)))
% 168.50/168.38 [5326]~E(x53262,f177(f909(x53261,a899)))+E(f177(f909(f909(x53261,a899),a899)),f315(f315(f53(x53261),x53262),x53263))
% 168.50/168.38 [5395]~E(f315(f272(x53952,x53953),x53951),f177(f909(x53953,a899)))+E(x53951,f177(f909(f908(x53952,x53953),a899)))
% 168.50/168.38 [5396]~E(f315(f252(x53962,x53963),x53961),f177(f909(x53962,a899)))+E(x53961,f177(f909(f908(x53962,x53963),a899)))
% 168.50/168.38 [5428]E(f315(f272(x54281,x54282),x54283),f177(f909(x54282,a899)))+~E(x54283,f177(f909(f908(x54281,x54282),a899)))
% 168.50/168.38 [5429]E(f315(f252(x54291,x54292),x54293),f177(f909(x54291,a899)))+~E(x54293,f177(f909(f908(x54291,x54292),a899)))
% 168.50/168.38 [5432]E(f262(x54321,x54322,x54323),f315(f315(f3(a88),x54322),x54323))+P1(f315(f315(f224(a88),x54322),x54323))
% 168.50/168.38 [5448]P1(f315(x54481,x54482))+~P1(f315(f315(f317(x54483),x54482),x54481))
% 168.50/168.38 [5487]E(x54871,x54872)+~E(f315(f72(f909(x54873,a899)),x54871),f315(f72(f909(x54873,a899)),x54872))
% 168.50/168.38 [5498]~E(x54981,f177(f909(x54982,a899)))+~P1(f315(f315(f317(x54982),x54983),x54981))
% 168.50/168.38 [5529]~E(x55292,f315(f315(f73(a1),x55291),f315(f89(a1),x55293)))+P1(f315(f315(f223(a1),x55291),x55292))
% 168.50/168.38 [5543]E(f315(f315(f297(x55431),x55432),x55433),x55433)+~P1(f315(f315(f317(x55431),x55432),x55433))
% 168.50/168.38 [5554]E(x55541,f177(f909(x55542,a899)))+~E(f315(f315(f53(x55542),x55541),x55543),f177(f909(f909(x55542,a899),a899)))
% 168.50/168.38 [5555]E(x55551,f177(f909(x55552,a899)))+~E(f177(f909(f909(x55552,a899),a899)),f315(f315(f53(x55552),x55551),x55553))
% 168.50/168.38 [5562]~P112(x55621)+E(f315(f315(f74(x55621),f315(f72(x55621),x55622)),f315(f72(x55621),x55623)),f315(f315(f74(x55621),x55622),x55623))
% 168.50/168.38 [5563]~P65(x55631)+E(f315(f315(f279(x55631),f315(f72(x55631),x55632)),f315(f72(x55631),x55633)),f315(f315(f279(x55631),x55632),x55633))
% 168.50/168.38 [5595]~P1(f315(x55953,x55952))+P1(f315(f315(f317(x55951),x55952),f315(f250(x55951),x55953)))
% 168.50/168.38 [5622]E(x56221,f2(a901))+E(f315(f161(x56222),f158(x56222,x56221,x56223)),f315(f315(f297(x56222),x56223),f177(f909(x56222,a899))))
% 168.50/168.38 [5642]E(f159(x56421,x56422,x56423),x56423)+P1(f315(f315(f317(x56421),x56422),f315(f161(x56421),x56423)))
% 168.50/168.38 [5728]~P1(f315(f126(x57281),x57283))+P1(f315(f126(x57281),f315(f125(x57281,x57282),x57283)))
% 168.50/168.38 [5771]~P62(x57711)+E(f315(f315(f29(x57711),f38(x57711,x57712,x57713)),x57713),f2(x57711))
% 168.50/168.38 [5790]E(f165(x57901,f315(f315(f140(x57901),x57902),f102(x57901)),x57903),f102(x57901))+P1(f315(f315(f317(a901),f2(a901)),x57903))
% 168.50/168.38 [5796]E(x57961,f2(a901))+E(f315(f160(x57962),f158(x57962,x57961,x57963)),f158(x57962,f315(f315(f3(a901),x57961),f71(a901)),x57963))
% 168.50/168.38 [5847]E(f315(f315(f140(x58471),x58472),x58473),f129(x58471,x58472,x58473))+P1(f315(f315(f317(x58471),x58472),f315(f161(x58471),x58473)))
% 168.50/168.38 [5856]E(x58561,x58562)+~E(f315(f315(f74(a901),f315(a101,x58563)),x58561),f315(f315(f74(a901),f315(a101,x58563)),x58562))
% 168.50/168.38 [5857]~E(x58572,f315(f315(f73(a1),x58571),f315(f89(a1),f315(a101,x58573))))+P1(f315(f315(f224(a1),x58571),x58572))
% 168.50/168.38 [5927]~P32(x59271,x59272,x59273)+P33(a901,x59271,f128(a901,f315(f290(a901,x59272),x59273)))
% 168.50/168.38 [5980]~E(x59803,f102(x59801))+E(f315(f315(f315(f172(f902(x59801),f902(x59801)),x59802),f156(x59801)),x59803),f102(x59801))
% 168.50/168.38 [5984]P1(f315(x59841,x59842))+~P1(f315(f315(f317(x59843),x59842),f315(f250(x59843),x59841)))
% 168.50/168.38 [6016]E(x60161,x60162)+~E(f315(f315(f297(x60163),x60161),f177(f909(x60163,a899))),f315(f315(f297(x60163),x60162),f177(f909(x60163,a899))))
% 168.50/168.38 [6032]~P111(x60321)+E(f315(f315(f90(f909(x60321,a899)),f315(f270(x60321),x60322)),f315(f290(x60321,x60322),x60323)),f177(f909(x60321,a899)))
% 168.50/168.38 [6071]E(f129(x60711,x60712,x60713),x60713)+~P1(f315(f315(f317(x60711),x60712),f315(f161(x60711),x60713)))
% 168.50/168.38 [6094]~P82(x60941)+E(f315(f298(x60941,x60941,f72(x60941)),f315(f290(x60941,x60942),x60943)),f293(x60941,f315(f72(x60941),x60943),f315(f72(x60941),x60942)))
% 168.50/168.38 [6105]E(f315(f178(f902(x61051)),f159(x61051,x61052,x61053)),f315(f178(f902(x61051)),x61053))+P1(f315(f315(f317(x61051),x61052),f315(f161(x61051),x61053)))
% 168.50/168.38 [6160]~P111(x61601)+E(f315(f315(f90(f909(x61601,a899)),f315(f290(x61601,x61602),x61603)),f315(f271(x61601),x61603)),f177(f909(x61601,a899)))
% 168.50/168.38 [6180]~P82(x61801)+E(f315(f298(x61801,x61801,f72(x61801)),f291(x61801,x61802,x61803)),f291(x61801,f315(f72(x61801),x61803),f315(f72(x61801),x61802)))
% 168.50/168.38 [6181]~P82(x61811)+E(f315(f298(x61811,x61811,f72(x61811)),f294(x61811,x61812,x61813)),f294(x61811,f315(f72(x61811),x61813),f315(f72(x61811),x61812)))
% 168.50/168.38 [6248]E(f165(x62481,f315(f315(f140(x62481),x62482),f102(x62481)),x62483),f315(f315(f140(x62481),x62482),f102(x62481)))+~P1(f315(f315(f317(a901),f2(a901)),x62483))
% 168.50/168.38 [6253]P32(x62531,x62532,x62533)+~P33(a901,x62531,f128(a901,f315(f290(a901,x62532),x62533)))
% 168.50/168.38 [6256]~P82(x62561)+E(f315(f298(x62561,x62561,f72(x62561)),f293(x62561,x62562,x62563)),f315(f290(x62561,f315(f72(x62561),x62563)),f315(f72(x62561),x62562)))
% 168.50/168.38 [6278]~P63(x62781)+E(f38(x62781,f315(f72(x62781),f38(x62781,x62782,x62783)),x62783),f38(x62781,f315(f72(x62781),x62782),x62783))
% 168.50/168.38 [6375]~P1(f315(f54(f908(x63752,x63751)),x63753))+P1(f315(f54(x63751),f315(f272(x63752,x63751),x63753)))
% 168.50/168.38 [6376]~P1(f315(f54(f908(x63761,x63762)),x63763))+P1(f315(f54(x63761),f315(f252(x63761,x63762),x63763)))
% 168.50/168.38 [6381]~P111(x63811)+E(f315(f315(f90(f909(x63811,a899)),f291(x63811,x63812,x63813)),f315(f292(x63811),x63813)),f177(f909(x63811,a899)))
% 168.50/168.38 [6382]~P111(x63821)+E(f315(f315(f90(f909(x63821,a899)),f294(x63821,x63822,x63823)),f315(f271(x63821),x63823)),f177(f909(x63821,a899)))
% 168.50/168.38 [6383]~P111(x63831)+E(f315(f315(f90(f909(x63831,a899)),f293(x63831,x63832,x63833)),f315(f292(x63831),x63833)),f177(f909(x63831,a899)))
% 168.50/168.38 [6456]E(f315(f315(f153(x64561),x64562),f608(x64562,x64563,x64561)),x64563)+~P1(f315(f315(f317(x64561),x64563),f315(f161(x64561),x64562)))
% 168.50/168.38 [6605]E(x66051,f102(x66052))+~E(f315(f315(f315(f172(f902(x66052),f902(x66052)),x66053),f156(x66052)),x66051),f102(x66052))
% 168.50/168.38 [6711]~P1(f315(f54(f908(x67112,x67111)),x67113))+P1(f315(f54(f908(x67111,x67112)),f315(f274(x67112,x67111),x67113)))
% 168.50/168.38 [6734]E(x67341,x67342)+~E(f278(a901,f275(a901),x67343,x67341),f315(f315(f297(a901),x67342),f177(f909(a901,a899))))
% 168.50/168.38 [6735]E(x67351,x67352)+~E(f278(a901,f275(a901),x67351,x67352),f315(f315(f297(a901),x67353),f177(f909(a901,a899))))
% 168.50/168.38 [6870]P57(x68701,x68702,x68703)+P1(f315(f315(f317(x68701),f598(x68703,x68702,x68701)),x68702))
% 168.50/168.38 [6871]P57(x68711,x68712,x68713)+P1(f315(f315(f317(x68711),f597(x68713,x68712,x68711)),x68712))
% 168.50/168.38 [6882]P1(f315(f303(x68821,x68822),x68823))+P1(f315(f315(x68822,f369(x68823,x68822,x68821)),x68823))
% 168.50/168.38 [6883]P1(f315(f303(x68831,x68832),x68833))+P1(f315(f315(x68832,f378(x68833,x68832,x68831)),x68833))
% 168.50/168.38 [6914]E(f315(f178(f902(x69141)),f159(x69141,x69142,x69143)),f315(f315(f3(a901),f315(f178(f902(x69141)),x69143)),f71(a901)))+~P1(f315(f315(f317(x69141),x69142),f315(f161(x69141),x69143)))
% 168.50/168.38 [6953]P1(f315(f236(x69531,x69532),x69533))+P1(f315(f315(f317(x69531),f377(x69533,x69532,x69531)),x69533))
% 168.50/168.38 [6962]~P1(f315(f54(f908(x69622,x69621)),f315(f274(x69621,x69622),x69623)))+P1(f315(f54(f908(x69621,x69622)),x69623))
% 168.50/168.38 [7020]~P1(f315(f315(f317(x70201),x70202),f315(f161(x70201),f103(x70201,x70203))))+P1(f315(f315(f317(x70201),x70202),f315(f161(x70201),x70203)))
% 168.50/168.38 [7026]P29(x70261,x70262,x70263)+P1(f315(f315(f317(f900(x70261)),f767(x70263,x70262,x70261)),x70263))
% 168.50/168.38 [7056]E(f315(f125(x70561,x70562),x70563),x70563)+P1(f315(f315(f317(x70561),f687(x70563,x70562,x70561)),f315(f161(x70561),x70563)))
% 168.50/168.38 [7072]E(f315(f125(x70721,x70722),x70723),f102(x70721))+P1(f315(f315(f317(x70721),f686(x70723,x70722,x70721)),f315(f161(x70721),x70723)))
% 168.50/168.38 [7098]P33(x70981,x70982,x70983)+P1(f315(f315(f317(x70981),f745(x70983,x70982,x70981)),f315(f161(x70981),x70983)))
% 168.50/168.38 [7099]P33(x70991,x70992,x70993)+P1(f315(f315(f317(x70991),f748(x70993,x70992,x70991)),f315(f161(x70991),x70993)))
% 168.50/168.38 [7100]P33(x71001,x71002,x71003)+P1(f315(f315(f317(x71001),f747(x71002,x71003,x71001)),f315(f161(x71001),x71003)))
% 168.50/168.38 [7103]E(f166(x71031,x71032,x71033),x71033)+P1(f315(f315(f317(x71031),f700(x71033,x71032,x71031)),f315(f161(x71031),x71033)))
% 168.50/168.38 [7180]P1(f315(f149(x71801,x71802),x71803))+P1(f315(f315(f317(x71801),f676(x71803,x71802,x71801)),f315(f161(x71801),x71803)))
% 168.50/168.38 [7189]~P35(x71891,x71893,x71892)+P1(f315(f315(f317(x71891),f732(x71892,x71893,x71891)),f315(f161(x71891),x71892)))
% 168.50/168.38 [7190]~P37(x71901,x71903,x71902)+P1(f315(f315(f317(x71901),f739(x71902,x71903,x71901)),f315(f161(x71901),x71902)))
% 168.50/168.38 [7191]~P37(x71911,x71913,x71912)+P1(f315(f315(f317(x71911),f749(x71912,x71913,x71911)),f315(f161(x71911),x71912)))
% 168.50/168.38 [7192]~P35(x71921,x71923,x71922)+P1(f315(f315(f317(x71921),f777(x71922,x71923,x71921)),f315(f161(x71921),x71922)))
% 168.50/168.38 [7193]~P35(x71931,x71932,x71933)+P1(f315(f315(f317(x71931),f778(x71932,x71933,x71931)),f315(f161(x71931),x71933)))
% 168.50/168.38 [7227]P1(f315(f315(f317(x72271),x72272),f883(x72273,x72272,x72271)))+~P1(f315(f315(f317(x72271),x72272),f30(f909(x72271,a899),x72273)))
% 168.50/168.38 [7228]~P72(x72281)+E(f315(f315(f73(x72281),f315(f315(f8(a901,x72281),x72282),f315(f270(a901),x72283))),f315(x72282,x72283)),f315(f315(f8(a901,x72281),x72282),f315(f270(a901),f315(a101,x72283))))
% 168.50/168.38 [7240]P32(x72401,x72402,x72403)+P1(f315(f315(f317(a901),f812(x72403,x72402,x72401)),f315(f290(a901,x72402),x72403)))
% 168.50/168.38 [7320]~P35(x73202,x73201,x73203)+P1(f315(x73201,f315(f315(f153(x73202),x73203),f736(x73203,x73201,x73202))))
% 168.50/168.38 [7333]~P1(f315(f315(f317(x73331),x73332),f370(x73332,x73333,x73331)))+P1(f315(f315(f317(x73331),x73332),f31(f909(x73331,a899),x73333)))
% 168.50/168.38 [7366]~P72(x73661)+E(f315(f315(f73(x73661),f315(f315(f8(a901,x73661),x73662),f315(f289(a901),x73663))),f315(x73662,f315(a101,x73663))),f315(f315(f8(a901,x73661),x73662),f315(f289(a901),f315(a101,x73663))))
% 168.50/168.38 [7507]P1(f315(f315(f317(f902(x75071)),x75072),f150(x75071,x75073)))+P1(f315(f315(f317(x75071),f640(x75073,x75072,x75071)),f315(f161(x75071),x75072)))
% 168.50/168.38 [7523]~P1(f315(f315(f317(f902(x75231)),x75232),f150(x75231,f304(x75231,x75233))))+P1(f315(f315(f317(f902(x75231)),x75232),f304(f902(x75231),f146(x75231,x75233))))
% 168.50/168.38 [7547]~P1(f315(f315(f317(f902(x75471)),x75472),f304(f902(x75471),f146(x75471,x75473))))+P1(f315(f315(f317(f902(x75471)),x75472),f150(x75471,f304(x75471,x75473))))
% 168.50/168.38 [7580]E(f315(f315(f315(f172(f902(x75801),f902(x75801)),x75802),f156(x75801)),x75803),x75803)+~P1(f315(f315(f223(a901),f315(f178(f902(x75801)),x75803)),f71(a901)))
% 168.50/168.38 [7613]E(f315(f315(f123(x76131),f737(x76132,x76133,x76131)),f315(f315(f140(x76131),x76133),f738(x76132,x76133,x76131))),x76132)+~P1(f315(f315(f317(x76131),x76133),f315(f161(x76131),x76132)))
% 168.50/168.38 [7614]E(f315(f315(f123(x76141),f741(x76142,x76143,x76141)),f315(f315(f140(x76141),x76143),f742(x76142,x76143,x76141))),x76142)+~P1(f315(f315(f317(x76141),x76143),f315(f161(x76141),x76142)))
% 168.50/168.38 [7615]E(f315(f315(f123(x76151),f743(x76152,x76153,x76151)),f315(f315(f140(x76151),x76153),f744(x76152,x76153,x76151))),x76152)+~P1(f315(f315(f317(x76151),x76153),f315(f161(x76151),x76152)))
% 168.50/168.38 [7637]~P25(x76371,x76372,x76373,f230(f909(x76371,a899)))+P25(f902(x76371),f902(x76372),f315(f143(x76371,x76372),x76373),f230(f909(f902(x76371),a899)))
% 168.50/168.38 [7788]E(x77881,f315(f315(f73(a901),f315(f315(f74(a901),f315(f239(a901,a901),x77882)),x77883)),f315(f244(a901,a901),x77882)))+~P1(f315(f41(x77881,x77883),x77882))
% 168.50/168.38 [7796]P25(x77961,x77962,x77963,f230(f909(x77961,a899)))+~P25(f902(x77961),f902(x77962),f315(f143(x77961,x77962),x77963),f230(f909(f902(x77961),a899)))
% 168.50/168.38 [7841]P1(f315(f315(f317(f909(x78411,a899)),f370(x78412,x78413,x78411)),x78413))+P1(f315(f315(f317(x78411),x78412),f31(f909(x78411,a899),x78413)))
% 168.50/168.38 [7931]P1(f315(f315(f317(f902(x79311)),x79312),f150(x79311,x79313)))+~P1(f315(f315(f317(x79311),f640(x79313,x79312,x79311)),x79313))
% 168.50/168.38 [8032]P33(x80321,x80322,x80323)+~P1(f315(x80322,f315(f315(f153(x80321),x80323),f746(x80323,x80322,x80321))))
% 168.50/168.38 [8057]E(x80571,x80572)+~E(f315(f315(f9(x80573,f909(x80573,a899),a899),f317(x80573)),x80571),f315(f315(f9(x80573,f909(x80573,a899),a899),f317(x80573)),x80572))
% 168.50/168.38 [8065]~P1(f315(f315(f317(f908(x80651,x80651)),x80653),f251(x80651,x80652)))+P1(f315(f315(f317(x80651),f470(x80652,x80653,x80651)),x80652))
% 168.50/168.38 [8067]~P1(f315(f315(f317(x80671),x80673),f30(f909(x80671,a899),x80672)))+P1(f315(f315(f317(f909(x80671,a899)),f883(x80672,x80673,x80671)),x80672))
% 168.50/168.38 [8188]P25(x81881,x81882,f84(x81882,x81881,f230(f909(x81882,a899)),x81883),f230(f909(x81881,a899)))+~E(f315(f298(x81882,x81881,x81883),f230(f909(x81882,a899))),f230(f909(x81881,a899)))
% 168.50/168.38 [8243]~P1(f315(f315(f317(x82431),x82432),f315(f161(x82431),f741(x82433,x82432,x82431))))+~P1(f315(f315(f317(x82431),x82432),f315(f161(x82431),x82433)))
% 168.50/168.38 [8244]~P1(f315(f315(f317(x82441),x82442),f315(f161(x82441),f744(x82443,x82442,x82441))))+~P1(f315(f315(f317(x82441),x82442),f315(f161(x82441),x82443)))
% 168.50/168.38 [8273]P32(f315(f66(a899,a899,a901,a310),x82731),x82732,x82733)+P35(a901,x82731,f128(a901,f315(f290(a901,x82732),x82733)))
% 168.50/168.38 [8433]E(x84331,f102(x84332))+P1(f315(f315(f317(x84332),f315(f239(x84332,f908(a88,a88)),f315(f263(x84332,x84331),x84333))),f315(f161(x84332),x84331)))
% 168.50/168.38 [8532]~P71(x85321)+E(f315(f131(x85321,x85321,f315(f9(x85321,x85321,x85321),f73(x85321)),x85322),f315(f157(x85321),x85323)),f315(f131(x85321,x85321,f73(x85321),x85322),x85323))
% 168.50/168.38 [8724]~P25(x87242,x87241,x87243,f230(f909(x87242,a899)))+E(f315(f298(x87241,x87242,f84(x87242,x87241,f230(f909(x87242,a899)),x87243)),f230(f909(x87241,a899))),f230(f909(x87242,a899)))
% 168.50/168.38 [8794]~P32(f315(f66(a899,a899,a901,a310),x87941),x87942,x87943)+~P35(a901,x87941,f128(a901,f315(f290(a901,x87942),x87943)))
% 168.50/168.38 [9042]~P110(x90421)+E(f315(f161(x90421),f138(x90421,x90421,f7(x90421),x90422,x90423)),f315(f315(f297(x90421),x90422),f315(f161(x90421),x90423)))
% 168.50/168.38 [9051]~E(f315(x90513,f315(f84(x90511,x90512,f230(f909(x90511,a899)),x90513),f792(x90513,x90512,x90511))),f792(x90513,x90512,x90511))+E(f315(f298(x90511,x90512,x90513),f230(f909(x90511,a899))),f230(f909(x90512,a899)))
% 168.50/168.38 [9053]P1(f315(f315(f224(a901),f2(a901)),f605(x90531,x90532,x90533)))+~P1(f315(f315(f317(f908(x90533,x90533)),x90532),f315(f315(f277(x90533,x90533,x90533),x90531),f295(x90533,x90531))))
% 168.50/168.38 [9329]~P59(x93291,x93292)+~P1(f315(f315(f317(f908(x93291,x93291)),f315(f315(f240(x93291,x93291),x93293),x93293)),f315(f315(f277(x93291,x93291,x93291),x93292),f295(x93291,x93292))))
% 168.50/168.38 [9467]~E(f315(f315(f90(f909(f908(x94671,x94671),a899)),f315(f274(x94671,x94671),x94672)),f295(x94671,x94672)),f177(f909(f908(x94671,x94671),a899)))+~P1(f315(f315(f317(f908(x94671,x94671)),f315(f315(f240(x94671,x94671),x94673),x94673)),f315(f315(f277(x94671,x94671,x94671),x94672),f295(x94671,x94672))))
% 168.50/168.38 [9658]~P1(f315(f54(x96581),x96582))+P1(f315(f315(f223(a901),f315(f28(x96581),f315(f315(f3(f909(x96581,a899)),x96582),f315(f315(f297(x96581),x96583),f177(f909(x96581,a899)))))),f315(f28(x96581),x96582)))
% 168.50/168.38 [5135]~E(x51353,f102(x51351))+E(f133(x51351,f315(f315(f140(x51351),x51352),x51353)),x51352)
% 168.50/168.38 [5144]~E(x51443,f102(x51441))+E(f103(x51441,f315(f315(f140(x51441),x51442),x51443)),f102(x51441))
% 168.50/168.38 [5174]E(x51741,f102(x51742))+E(f133(x51742,f315(f315(f140(x51742),x51743),x51741)),f133(x51742,x51741))
% 168.50/168.38 [5176]E(x51761,f102(x51762))+E(f133(x51762,f315(f315(f123(x51762),x51763),x51761)),f133(x51762,x51761))
% 168.50/168.38 [5182]~E(x51823,f102(x51821))+E(f103(x51821,f315(f315(f123(x51821),x51822),x51823)),f103(x51821,x51822))
% 168.50/168.38 [5184]~E(x51843,f102(x51841))+E(f133(x51841,f315(f315(f123(x51841),x51842),x51843)),f133(x51841,x51842))
% 168.50/168.38 [5217]E(x52171,f102(x52172))+E(f315(f130(x52172),f315(f315(f123(x52172),x52171),x52173)),f315(f130(x52172),x52171))
% 168.50/168.38 [5245]~E(x52452,f102(x52451))+E(f315(f130(x52451),f315(f315(f123(x52451),x52452),x52453)),f315(f130(x52451),x52453))
% 168.50/168.38 [5298]~P80(x52981)+E(f315(f315(f99(x52981),x52982),f315(f315(f90(x52981),x52982),x52983)),x52982)
% 168.50/168.38 [5299]~P80(x52991)+E(f315(f315(f90(x52991),x52992),f315(f315(f99(x52991),x52992),x52993)),x52992)
% 168.50/168.38 [5300]~P110(x53001)+E(f315(f315(f221(x53001),x53002),f315(f315(f222(x53001),x53002),x53003)),x53002)
% 168.50/168.38 [5301]~P110(x53011)+E(f315(f315(f222(x53011),x53012),f315(f315(f221(x53011),x53012),x53013)),x53012)
% 168.50/168.38 [5320]~P62(x53201)+E(f38(x53201,f315(f315(f74(x53201),x53202),x53203),x53203),f2(x53201))
% 168.50/168.38 [5321]~P62(x53211)+E(f38(x53211,f315(f315(f74(x53211),x53212),x53213),x53212),f2(x53211))
% 168.50/168.38 [5390]~P69(x53901)+E(f315(f72(x53901),f315(f315(f3(x53901),x53902),x53903)),f315(f315(f3(x53901),x53903),x53902))
% 168.50/168.38 [5452]E(x54521,f102(x54522))+E(f103(x54522,f315(f315(f140(x54522),x54523),x54521)),f315(f315(f140(x54522),x54523),f103(x54522,x54521)))
% 168.50/168.38 [5453]E(x54531,f102(x54532))+E(f103(x54532,f315(f315(f123(x54532),x54533),x54531)),f315(f315(f123(x54532),x54533),f103(x54532,x54531)))
% 168.50/168.38 [5456]~P5(x54561)+E(f30(x54561,f315(f315(f297(x54561),x54562),x54563)),f315(f315(f99(x54561),x54562),f30(x54561,x54563)))
% 168.50/168.38 [5457]~P5(x54571)+E(f31(x54571,f315(f315(f297(x54571),x54572),x54573)),f315(f315(f90(x54571),x54572),f31(x54571,x54573)))
% 168.50/168.38 [5503]~P80(x55031)+E(f315(f315(f99(x55031),x55032),f315(f315(f99(x55031),x55032),x55033)),f315(f315(f99(x55031),x55032),x55033))
% 168.50/168.38 [5505]~P103(x55051)+E(f315(f315(f99(x55051),x55052),f315(f315(f99(x55051),x55052),x55053)),f315(f315(f99(x55051),x55052),x55053))
% 168.50/168.38 [5506]~P99(x55061)+E(f315(f315(f74(x55061),x55062),f315(f315(f74(x55061),x55062),x55063)),f315(f315(f74(x55061),x55062),x55063))
% 168.50/168.38 [5507]~P80(x55071)+E(f315(f315(f90(x55071),x55072),f315(f315(f90(x55071),x55072),x55073)),f315(f315(f90(x55071),x55072),x55073))
% 168.50/168.38 [5509]~P104(x55091)+E(f315(f315(f90(x55091),x55092),f315(f315(f90(x55091),x55092),x55093)),f315(f315(f90(x55091),x55092),x55093))
% 168.50/168.38 [5511]~P110(x55111)+E(f315(f315(f221(x55111),x55112),f315(f315(f221(x55111),x55112),x55113)),f315(f315(f221(x55111),x55112),x55113))
% 168.50/168.38 [5513]~P110(x55131)+E(f315(f315(f222(x55131),x55132),f315(f315(f222(x55131),x55132),x55133)),f315(f315(f222(x55131),x55132),x55133))
% 168.50/168.38 [5520]~P62(x55201)+E(f38(x55201,f315(f315(f73(x55201),x55202),x55203),x55203),f38(x55201,x55202,x55203))
% 168.50/168.38 [5521]~P62(x55211)+E(f38(x55211,f315(f315(f73(x55211),x55212),x55213),x55212),f38(x55211,x55213,x55212))
% 168.50/168.38 [5530]~P112(x55301)+E(f315(f315(f74(x55301),x55302),f315(f72(x55301),x55303)),f315(f72(x55301),f315(f315(f74(x55301),x55302),x55303)))
% 168.50/168.38 [5531]~P65(x55311)+E(f315(f315(f279(x55311),x55312),f315(f72(x55311),x55313)),f315(f72(x55311),f315(f315(f279(x55311),x55312),x55313)))
% 168.50/168.38 [5532]~P85(x55321)+E(f315(f315(f73(x55321),x55322),f315(f154(x55321),x55323)),f315(f154(x55321),f315(f315(f140(x55321),x55322),x55323)))
% 168.50/168.38 [5560]~P112(x55601)+E(f315(f315(f74(x55601),f315(f72(x55601),x55602)),x55603),f315(f315(f74(x55601),x55602),f315(f72(x55601),x55603)))
% 168.50/168.38 [5566]~P8(x55661,x55662,x55663)+E(f30(f909(x55661,a899),f315(f315(f53(x55661),x55662),x55663)),x55662)
% 168.50/168.38 [5634]~P117(x56341)+E(f315(f315(f74(x56341),x56342),f315(f315(f232(x56341),x56342),x56343)),f315(f315(f232(x56341),x56342),f315(a101,x56343)))
% 168.50/168.38 [5635]~P121(x56351)+E(f315(f315(f74(x56351),x56352),f315(f315(f232(x56351),x56352),x56353)),f315(f315(f232(x56351),x56352),f315(a101,x56353)))
% 168.50/168.38 [5645]~P76(x56451)+E(f315(f315(f73(x56451),f315(f72(x56451),x56452)),f315(f315(f73(x56451),x56452),x56453)),x56453)
% 168.50/168.38 [5668]~P147(x56681)+E(f315(f315(f232(x56681),f315(f89(x56681),x56682)),x56683),f315(f89(x56681),f315(f315(f232(a901),x56682),x56683)))
% 168.50/168.38 [5669]~P143(x56691)+E(f315(f315(f232(x56691),f315(f91(x56691),x56692)),x56693),f315(f91(x56691),f315(f315(f232(a1),x56692),x56693)))
% 168.50/168.38 [5675]~P89(x56751)+E(f315(f69(x56751),f315(f315(f3(x56751),x56752),x56753)),f315(f69(x56751),f315(f315(f3(x56751),x56753),x56752)))
% 168.50/168.38 [5678]~P114(x56781)+E(f315(f315(f74(x56781),f75(x56781,x56782)),f75(x56781,x56783)),f75(x56781,f315(f315(f74(x56781),x56782),x56783)))
% 168.50/168.38 [5682]E(x56821,f102(x56822))+E(f315(f315(f123(x56822),f315(f160(x56822),x56821)),x56823),f315(f160(x56822),f315(f315(f123(x56822),x56821),x56823)))
% 168.50/168.38 [5688]~E(x56882,f315(a101,f315(f315(f73(a901),x56881),x56883)))+P1(f315(f315(f224(a901),x56881),x56882))
% 168.50/168.38 [5689]~P114(x56891)+E(f315(f315(f232(x56891),f315(f69(x56891),x56892)),x56893),f315(f69(x56891),f315(f315(f232(x56891),x56892),x56893)))
% 168.50/168.38 [5690]~P112(x56901)+E(f315(f315(f74(x56901),f315(f72(x56901),x56902)),x56903),f315(f72(x56901),f315(f315(f74(x56901),x56902),x56903)))
% 168.50/168.38 [5691]~P125(x56911)+E(f315(f315(f279(x56911),f315(f72(x56911),x56912)),x56913),f315(f72(x56911),f315(f315(f279(x56911),x56912),x56913)))
% 168.50/168.38 [5789]E(f565(x57891,x57892,x57893),f575(x57891,x57892,x57893))+E(f315(f315(f90(f909(x57893,a899)),x57892),x57891),f177(f909(x57893,a899)))
% 168.50/168.38 [5804]~P72(x58042)+E(f315(f315(f8(x58041,x58042),f315(f18(x58042,x58041),f2(x58042))),x58043),f2(x58042))
% 168.50/168.38 [5805]~P77(x58052)+E(f315(f315(f11(x58051,x58052),f315(f18(x58052,x58051),f71(x58052))),x58053),f71(x58052))
% 168.50/168.38 [5807]~P97(x58071)+E(f315(f315(f3(x58071),f315(f92(x58071),x58072)),f315(f92(x58071),x58073)),f315(f92(x58071),f315(f315(f3(a1),x58072),x58073)))
% 168.50/168.38 [5810]~P147(x58101)+E(f315(f315(f74(x58101),f315(f89(x58101),x58102)),f315(f89(x58101),x58103)),f315(f89(x58101),f315(f315(f74(a901),x58102),x58103)))
% 168.50/168.38 [5811]~P147(x58111)+E(f315(f315(f73(x58111),f315(f89(x58111),x58112)),f315(f89(x58111),x58113)),f315(f89(x58111),f315(f315(f73(a901),x58112),x58113)))
% 168.50/168.38 [5812]~P143(x58121)+E(f315(f315(f3(x58121),f315(f91(x58121),x58122)),f315(f91(x58121),x58123)),f315(f91(x58121),f315(f315(f3(a1),x58122),x58123)))
% 168.50/168.38 [5813]~P143(x58131)+E(f315(f315(f74(x58131),f315(f91(x58131),x58132)),f315(f91(x58131),x58133)),f315(f91(x58131),f315(f315(f74(a1),x58132),x58133)))
% 168.50/168.38 [5814]~P143(x58141)+E(f315(f315(f73(x58141),f315(f91(x58141),x58142)),f315(f91(x58141),x58143)),f315(f91(x58141),f315(f315(f73(a1),x58142),x58143)))
% 168.50/168.38 [5815]~P97(x58151)+E(f315(f315(f74(x58151),f315(f92(x58151),x58152)),f315(f92(x58151),x58153)),f315(f92(x58151),f315(f315(f74(a1),x58152),x58153)))
% 168.50/168.38 [5816]~P97(x58161)+E(f315(f315(f73(x58161),f315(f92(x58161),x58162)),f315(f92(x58161),x58163)),f315(f92(x58161),f315(f315(f73(a1),x58162),x58163)))
% 168.50/168.38 [5864]~E(x58643,x58642)+P1(f315(f315(f223(f909(x58641,a899)),x58642),x58643))
% 168.50/168.38 [5870]~E(x58702,x58703)+P1(f315(f315(f223(f909(x58701,a899)),x58702),x58703))
% 168.50/168.38 [5875]~P114(x58751)+E(f315(f315(f74(x58751),f315(f69(x58751),x58752)),f315(f69(x58751),x58753)),f315(f69(x58751),f315(f315(f74(x58751),x58752),x58753)))
% 168.50/168.38 [5876]~P67(x58761)+E(f315(f315(f279(x58761),f315(f69(x58761),x58762)),f315(f69(x58761),x58763)),f315(f69(x58761),f315(f315(f279(x58761),x58762),x58763)))
% 168.50/168.38 [5877]~P98(x58771)+E(f315(f315(f90(x58771),f315(f72(x58771),x58772)),f315(f72(x58771),x58773)),f315(f72(x58771),f315(f315(f99(x58771),x58772),x58773)))
% 168.50/168.38 [5878]~P98(x58781)+E(f315(f315(f99(x58781),f315(f72(x58781),x58782)),f315(f72(x58781),x58783)),f315(f72(x58781),f315(f315(f90(x58781),x58782),x58783)))
% 168.50/168.38 [5879]~P76(x58791)+E(f315(f315(f73(x58791),f315(f72(x58791),x58792)),f315(f72(x58791),x58793)),f315(f72(x58791),f315(f315(f73(x58791),x58793),x58792)))
% 168.50/168.38 [5880]~P69(x58801)+E(f315(f315(f73(x58801),f315(f72(x58801),x58802)),f315(f72(x58801),x58803)),f315(f72(x58801),f315(f315(f73(x58801),x58802),x58803)))
% 168.50/168.38 [5881]~P78(x58811)+E(f315(f315(f222(x58811),f315(f72(x58811),x58812)),f315(f72(x58811),x58813)),f315(f72(x58811),f315(f315(f221(x58811),x58812),x58813)))
% 168.50/168.38 [5882]~P78(x58821)+E(f315(f315(f221(x58821),f315(f72(x58821),x58822)),f315(f72(x58821),x58823)),f315(f72(x58821),f315(f315(f222(x58821),x58822),x58823)))
% 168.50/168.38 [5883]~P85(x58831)+E(f315(f315(f73(x58831),f315(f154(x58831),x58832)),f315(f154(x58831),x58833)),f315(f154(x58831),f315(f315(f123(x58831),x58832),x58833)))
% 168.50/168.38 [5884]E(x58841,f177(f909(x58842,a899)))+~E(f315(f315(f99(f909(x58842,a899)),x58843),x58841),f177(f909(x58842,a899)))
% 168.50/168.38 [5885]E(x58851,f177(f909(x58852,a899)))+~E(f315(f315(f99(f909(x58852,a899)),x58851),x58853),f177(f909(x58852,a899)))
% 168.50/168.38 [5886]~P150(x58861,x58862,x58863)+P1(f315(x58861,f315(f315(f29(a1),x58862),x58863)))
% 168.50/168.38 [5951]~P1(f315(f54(x59511),x59513))+P1(f315(f54(x59511),f315(f315(f297(x59511),x59512),x59513)))
% 168.50/168.38 [5952]~P1(f315(f126(x59521),x59523))+P1(f315(f126(x59521),f315(f315(f164(x59521),x59522),x59523)))
% 168.50/168.38 [5953]~P1(f315(f126(x59531),x59533))+P1(f315(f126(x59531),f315(f315(f127(x59531),x59532),x59533)))
% 168.50/168.38 [5985]~P80(x59851)+P1(f315(f315(f223(x59851),x59852),f315(f315(f99(x59851),x59853),x59852)))
% 168.50/168.38 [5986]~P103(x59861)+P1(f315(f315(f223(x59861),x59862),f315(f315(f99(x59861),x59863),x59862)))
% 168.50/168.38 [5987]~P80(x59871)+P1(f315(f315(f223(x59871),x59872),f315(f315(f99(x59871),x59872),x59873)))
% 168.50/168.38 [5988]~P103(x59881)+P1(f315(f315(f223(x59881),x59882),f315(f315(f99(x59881),x59882),x59883)))
% 168.50/168.38 [5989]~P110(x59891)+P1(f315(f315(f223(x59891),x59892),f315(f315(f222(x59891),x59893),x59892)))
% 168.50/168.38 [5990]~P110(x59901)+P1(f315(f315(f223(x59901),x59902),f315(f315(f222(x59901),x59902),x59903)))
% 168.50/168.38 [5991]~P121(x59911)+P1(f315(f315(f275(x59911),x59912),f315(f315(f74(x59911),x59913),x59912)))
% 168.50/168.38 [5992]~P121(x59921)+P1(f315(f315(f275(x59921),x59922),f315(f315(f74(x59921),x59922),x59923)))
% 168.50/168.38 [6006]~E(x60061,f2(a901))+E(f315(f315(f29(a901),f315(f315(f74(a901),x60061),x60062)),f315(f315(f74(a901),x60061),x60063)),f2(a901))
% 168.50/168.38 [6087]~P97(x60871)+E(f315(f315(f3(x60871),f315(f92(x60871),x60872)),f315(f92(x60871),x60873)),f315(f92(x60871),f315(f315(f73(a1),x60872),f315(f72(a1),x60873))))
% 168.50/168.38 [6148]E(x61481,f2(a901))+E(f315(f315(f29(a901),f315(f315(f74(a901),x61481),x61482)),f315(f315(f74(a901),x61481),x61483)),f315(f315(f29(a901),x61482),x61483))
% 168.50/168.38 [6178]E(f141(x61781,f315(f315(f140(x61781),x61782),x61783)),f315(f315(f140(x61781),x61782),f141(x61781,x61783)))+P1(f315(f315(f317(x61781),x61782),f315(f161(x61781),x61783)))
% 168.50/168.38 [6215]P150(x62151,x62152,x62153)+~P1(f315(x62151,f315(f315(f29(a1),x62152),x62153)))
% 168.50/168.38 [6292]E(x62921,f102(x62922))+E(f315(f315(f140(x62922),f315(f130(x62922),x62921)),f315(f315(f164(x62922),x62923),f315(f160(x62922),x62921))),f315(f315(f164(x62922),f315(a101,x62923)),x62921))
% 168.50/168.38 [6299]E(f315(f315(f3(f909(x62991,a899)),x62992),x62993),x62992)+~E(f315(f315(f90(f909(x62991,a899)),x62992),x62993),f177(f909(x62991,a899)))
% 168.50/168.38 [6313]E(f141(x63131,f315(f315(f140(x63131),x63132),x63133)),f141(x63131,x63133))+~P1(f315(f315(f317(x63131),x63132),f315(f161(x63131),x63133)))
% 168.50/168.38 [6343]~P1(f315(f315(f223(a901),x63431),x63433))+P1(f315(f315(f223(a901),x63431),f315(f315(f73(a901),x63432),x63433)))
% 168.50/168.38 [6345]~P1(f315(f315(f223(a901),x63451),x63452))+P1(f315(f315(f223(a901),x63451),f315(f315(f73(a901),x63452),x63453)))
% 168.50/168.38 [6347]~P1(f315(f315(f224(a901),x63471),x63473))+P1(f315(f315(f224(a901),x63471),f315(f315(f73(a901),x63472),x63473)))
% 168.50/168.38 [6349]~P1(f315(f315(f224(a901),x63491),x63492))+P1(f315(f315(f224(a901),x63491),f315(f315(f73(a901),x63492),x63493)))
% 168.50/168.38 [6389]P1(f315(f54(x63891),x63892))+~P1(f315(f54(x63891),f315(f315(f297(x63891),x63893),x63892)))
% 168.50/168.38 [6390]P1(f315(f126(x63901),x63902))+~P1(f315(f126(x63901),f315(f315(f140(x63901),x63903),x63902)))
% 168.50/168.38 [6391]P1(f315(f126(x63911),x63912))+~P1(f315(f126(x63911),f315(f315(f123(x63911),x63913),x63912)))
% 168.50/168.38 [6392]P1(f315(f126(x63921),x63922))+~P1(f315(f126(x63921),f315(f315(f123(x63921),x63922),x63923)))
% 168.50/168.38 [6446]~P121(x64461)+E(f315(f315(f73(x64461),x64462),f315(f315(f74(x64461),x64463),x64462)),f315(f315(f74(x64461),f315(f315(f73(x64461),x64463),f71(x64461))),x64462))
% 168.50/168.38 [6493]~E(x64931,x64932)+~P1(f315(f315(f224(f909(x64933,a899)),x64931),x64932))
% 168.50/168.38 [6540]P1(f315(f315(f317(x65401),x65402),x65403))+P1(f315(f315(f317(x65401),x65402),f315(f72(f909(x65401,a899)),x65403)))
% 168.50/168.38 [6546]E(f133(x65461,f315(f315(f127(x65461),x65462),x65463)),f133(x65461,x65463))+~P1(f315(f315(f224(a901),x65462),f315(f178(f902(x65461)),x65463)))
% 168.50/168.38 [6547]E(f315(f315(f164(x65471),x65472),f103(x65471,x65473)),f315(f315(f164(x65471),x65472),x65473))+~P1(f315(f315(f224(a901),x65472),f315(f178(f902(x65471)),x65473)))
% 168.50/168.38 [6607]E(f315(f315(f315(f172(f902(x66071),f902(x66071)),x66072),f156(x66071)),x66073),x66073)+~E(f38(a901,x66072,f315(f178(f902(x66071)),x66073)),f2(a901))
% 168.50/168.38 [6614]~P8(x66141,x66143,x66142)+E(f315(f315(f277(x66141,x66141,x66141),f315(f274(x66141,x66141),x66142)),x66142),x66142)
% 168.50/168.38 [6657]~E(f315(f315(f99(f909(x66571,a899)),x66572),x66573),x66573)+P1(f315(f315(f223(f909(x66571,a899)),x66572),x66573))
% 168.50/168.38 [6662]~P56(x66621,x66621,x66623)+P56(x66621,x66621,f315(f315(f172(f908(x66621,x66621),a899),x66622),x66623))
% 168.50/168.38 [6665]~P1(f315(f315(f317(x66651),x66653),f315(f161(x66651),x66652)))+P1(f315(f315(f224(a901),f2(a901)),f315(f178(f902(x66651)),x66652)))
% 168.50/168.38 [6693]~P89(x66931)+E(f315(f69(x66931),f315(f315(f73(x66931),f315(f69(x66931),x66932)),f315(f69(x66931),x66933))),f315(f315(f73(x66931),f315(f69(x66931),x66932)),f315(f69(x66931),x66933)))
% 168.50/168.38 [6704]E(f315(f315(f29(a901),f315(f315(f74(a901),x67041),x67042)),f315(f315(f74(a901),x67041),x67043)),f315(f315(f29(a901),x67042),x67043))+~P1(f315(f315(f224(a901),f2(a901)),x67041))
% 168.50/168.38 [6847]~P1(f315(f54(x68471),x68473))+E(f315(f315(f57(x68471,f909(x68471,a899),f297(x68471)),x68472),x68473),f315(f315(f99(f909(x68471,a899)),x68473),x68472))
% 168.50/168.38 [6907]E(f315(f315(f99(f909(x69071,a899)),x69072),x69073),x69072)+~P1(f315(f315(f223(f909(x69071,a899)),x69073),x69072))
% 168.50/168.38 [6909]E(f315(f315(f99(f909(x69091,a899)),x69092),x69093),x69093)+~P1(f315(f315(f223(f909(x69091,a899)),x69092),x69093))
% 168.50/168.38 [6910]E(f315(f315(f90(f909(x69101,a899)),x69102),x69103),x69103)+~P1(f315(f315(f223(f909(x69101,a899)),x69103),x69102))
% 168.50/168.38 [6911]E(f315(f315(f90(f909(x69111,a899)),x69112),x69113),x69112)+~P1(f315(f315(f223(f909(x69111,a899)),x69112),x69113))
% 168.50/168.38 [6960]~P1(f315(f126(x69601),x69602))+E(f315(f315(f3(f909(x69601,a899)),f315(f161(x69601),x69602)),f315(f315(f297(x69601),x69603),f177(f909(x69601,a899)))),f315(f161(x69601),f159(x69601,x69603,x69602)))
% 168.50/168.38 [7015]P39(x70151,x70152)+~P39(x70151,f315(f315(f172(f908(x70151,x70151),a899),x70153),x70152))
% 168.50/168.38 [7033]~E(x70331,f2(a901))+P1(f315(f315(f275(a901),f315(f315(f74(a901),x70331),x70332)),f315(f315(f74(a901),x70331),x70333)))
% 168.50/168.38 [7084]P1(f315(f42(x70841,x70842),f315(a44,x70843)))+~P1(f315(f42(f315(f72(a1),x70841),f315(f72(a1),x70842)),x70843))
% 168.50/168.38 [7089]E(f315(f315(f3(f909(x70891,a899)),f315(f315(f297(x70891),x70892),x70893)),f315(f315(f297(x70891),x70892),f177(f909(x70891,a899)))),x70893)+P1(f315(f315(f317(x70891),x70892),x70893))
% 168.50/168.38 [7112]E(f315(f315(f90(f909(x71121,a899)),f315(f161(x71121),x71122)),f315(f161(x71121),x71123)),f177(f909(x71121,a899)))+~P1(f315(f126(x71121),f315(f315(f123(x71121),x71122),x71123)))
% 168.50/168.38 [7127]~P1(f315(f315(f317(x71271),x71272),f315(f161(x71271),x71273)))+~P1(f315(f126(x71271),f315(f315(f140(x71271),x71272),x71273)))
% 168.50/168.38 [7199]P33(x71991,x71992,x71993)+P1(f315(f315(f224(a901),f746(x71993,x71992,x71991)),f315(f178(f902(x71991)),x71993)))
% 168.50/168.38 [7209]E(f315(f315(f90(f909(x72091,a899)),x72092),x72093),f177(f909(x72091,a899)))+P1(f315(f315(f317(x72091),f565(x72093,x72092,x72091)),x72092))
% 168.50/168.38 [7210]E(f315(f315(f90(f909(x72101,a899)),x72102),x72103),f177(f909(x72101,a899)))+P1(f315(f315(f317(x72101),f575(x72103,x72102,x72101)),x72103))
% 168.50/168.38 [7213]E(f103(x72131,f315(f315(f164(x72131),x72132),x72133)),f315(f315(f164(x72131),f315(f315(f3(a901),x72132),f71(a901))),x72133))+~P1(f315(f315(f223(a901),x72132),f315(f178(f902(x72131)),x72133)))
% 168.50/168.38 [7273]~P35(x72733,x72732,x72731)+P1(f315(f315(f224(a901),f736(x72731,x72732,x72733)),f315(f178(f902(x72733)),x72731)))
% 168.50/168.38 [7293]P1(f315(f315(f224(a901),f2(a901)),x72931))+P1(f315(f315(f223(a901),f315(f315(f74(a901),x72932),x72931)),f315(f315(f74(a901),x72933),x72931)))
% 168.50/168.38 [7294]P1(f315(f315(f224(a901),f2(a901)),x72941))+P1(f315(f315(f223(a901),f315(f315(f74(a901),x72941),x72942)),f315(f315(f74(a901),x72941),x72943)))
% 168.50/168.38 [7297]~P1(f315(f315(f317(x72971),x72972),x72973))+~P1(f315(f315(f317(x72971),x72972),f315(f72(f909(x72971,a899)),x72973)))
% 168.50/168.38 [7303]~P1(f315(f315(f224(f909(x73031,a899)),x73032),x73033))+P1(f315(f315(f223(f909(x73031,a899)),x73032),x73033))
% 168.50/168.38 [7411]~P1(f315(f315(f223(a901),x74113),x74112))+P1(f315(f315(f223(a901),f315(f315(f3(a901),x74111),x74112)),f315(f315(f3(a901),x74111),x74113)))
% 168.50/168.38 [7412]~P1(f315(f315(f223(a901),x74121),x74123))+P1(f315(f315(f223(a901),f315(f315(f3(a901),x74121),x74122)),f315(f315(f3(a901),x74123),x74122)))
% 168.50/168.38 [7414]~P1(f315(f315(f223(a901),x74142),x74143))+P1(f315(f315(f223(a901),f315(f315(f74(a901),x74141),x74142)),f315(f315(f74(a901),x74141),x74143)))
% 168.50/168.38 [7416]~P1(f315(f315(f223(a901),x74161),x74163))+P1(f315(f315(f223(a901),f315(f315(f74(a901),x74161),x74162)),f315(f315(f74(a901),x74163),x74162)))
% 168.50/168.38 [7417]~P1(f315(f315(f223(a901),x74172),x74173))+P1(f315(f315(f223(a901),f315(f315(f73(a901),x74171),x74172)),f315(f315(f73(a901),x74171),x74173)))
% 168.50/168.38 [7418]~P1(f315(f315(f223(a901),x74181),x74183))+P1(f315(f315(f223(a901),f315(f315(f73(a901),x74181),x74182)),f315(f315(f73(a901),x74183),x74182)))
% 168.50/168.38 [7419]~P1(f315(f315(f223(a901),x74191),x74193))+P1(f315(f315(f223(a901),f315(f315(f29(a901),x74191),x74192)),f315(f315(f29(a901),x74193),x74192)))
% 168.50/168.38 [7420]~P1(f315(f315(f223(a1),x74202),x74203))+P1(f315(f315(f223(a1),f315(f315(f73(a1),x74201),x74202)),f315(f315(f73(a1),x74201),x74203)))
% 168.50/168.38 [7423]~P1(f315(f315(f224(a901),x74232),x74233))+P1(f315(f315(f224(a901),f315(f315(f73(a901),x74231),x74232)),f315(f315(f73(a901),x74231),x74233)))
% 168.50/168.38 [7424]~P1(f315(f315(f224(a901),x74241),x74243))+P1(f315(f315(f224(a901),f315(f315(f73(a901),x74241),x74242)),f315(f315(f73(a901),x74243),x74242)))
% 168.50/168.38 [7425]~P1(f315(f315(f224(a1),x74251),x74253))+P1(f315(f315(f224(a1),f315(f315(f73(a1),x74251),x74252)),f315(f315(f73(a1),x74253),x74252)))
% 168.50/168.38 [7428]~P1(f315(f315(f275(a901),x74282),x74283))+P1(f315(f315(f275(a901),f315(f315(f74(a901),x74281),x74282)),f315(f315(f74(a901),x74281),x74283)))
% 168.50/168.38 [7506]E(x75061,x75062)+~P1(f315(f315(f317(x75063),x75061),f315(f315(f297(x75063),x75062),f177(f909(x75063,a899)))))
% 168.50/168.38 [7508]~E(f315(f315(f90(f909(x75081,a899)),x75082),x75083),f177(f909(x75081,a899)))+P1(f315(f315(f223(f909(x75081,a899)),x75082),f315(f72(f909(x75081,a899)),x75083)))
% 168.50/168.38 [7513]P1(f315(f315(f317(f909(x75131,a899)),x75132),f315(f296(x75131),x75133)))+~P1(f315(f315(f223(f909(x75131,a899)),x75132),x75133))
% 168.50/168.38 [7564]E(f315(f315(f140(x75641),f315(f315(f153(x75641),x75642),x75643)),f315(f315(f127(x75641),f315(a101,x75643)),x75642)),f315(f315(f127(x75641),x75643),x75642))+~P1(f315(f315(f224(a901),x75643),f315(f178(f902(x75641)),x75642)))
% 168.50/168.38 [7590]P1(f315(f315(f317(f908(x75901,x75901)),x75902),f295(x75901,x75903)))+~P1(f315(f315(f317(f908(x75901,x75901)),x75902),x75903))
% 168.50/168.38 [7599]~P1(f315(f315(f317(f909(x75991,a899)),x75992),f315(f296(x75991),x75993)))+P1(f315(f315(f223(f909(x75991,a899)),x75992),x75993))
% 168.50/168.38 [7643]P1(f315(f315(f223(f909(x76431,a899)),x76432),f30(f909(x76431,a899),x76433)))+~P1(f315(f315(f317(f909(x76431,a899)),x76432),x76433))
% 168.50/168.38 [7668]~P143(x76681)+E(f315(f315(f74(x76681),f315(f315(f232(x76681),f315(f72(x76681),f71(x76681))),x76682)),f315(f315(f232(x76681),x76683),x76682)),f315(f315(f232(x76681),f315(f72(x76681),x76683)),x76682))
% 168.50/168.38 [7690]E(f315(f315(f153(x76901),x76902),f315(f315(f3(a901),f315(f178(f902(x76901)),x76902)),f315(a101,x76903))),f315(f315(f153(x76901),f315(f157(x76901),x76902)),x76903))+~P1(f315(f315(f224(a901),x76903),f315(f178(f902(x76901)),x76902)))
% 168.50/168.38 [7707]~E(f315(f315(f90(f909(x77071,a899)),f865(x77073,x77072,x77071)),x77073),f177(f909(x77071,a899)))+E(f315(f315(f90(f909(x77071,a899)),f30(f909(x77071,a899),x77072)),x77073),f177(f909(x77071,a899)))
% 168.50/168.38 [7771]~P1(f315(f315(f317(x77713),x77712),f315(f161(x77713),x77711)))+P1(f315(f315(f224(a901),f608(x77711,x77712,x77713)),f315(f178(f902(x77713)),x77711)))
% 168.50/168.38 [7779]P1(f315(f315(f317(x77791),f315(f315(f153(x77791),x77792),x77793)),f315(f161(x77791),x77792)))+~P1(f315(f315(f224(a901),x77793),f315(f178(f902(x77791)),x77792)))
% 168.50/168.38 [7877]~P1(f315(x78772,f701(x78773,x78772,x78771)))+E(f315(f315(f127(x78771),f315(f178(f902(x78771)),f166(x78771,x78772,x78773))),x78773),f102(x78771))
% 168.50/168.38 [7890]P1(f315(f315(f223(f909(f902(x78901),a899)),f150(x78901,x78902)),f150(x78901,x78903)))+~P1(f315(f315(f223(f909(x78901,a899)),x78902),x78903))
% 168.50/168.38 [7891]P1(f315(f315(f223(f909(f902(x78911),a899)),f149(x78911,x78912)),f149(x78911,x78913)))+~P1(f315(f315(f223(f909(x78911,a899)),x78912),x78913))
% 168.50/168.38 [7917]E(f315(f315(f90(f909(x79171,a899)),f30(f909(x79171,a899),x79172)),x79173),f177(f909(x79171,a899)))+P1(f315(f315(f317(f909(x79171,a899)),f865(x79173,x79172,x79171)),x79172))
% 168.50/168.38 [7919]~P1(f315(f315(f317(f909(x79191,a899)),x79193),x79192))+P1(f315(f315(f223(f909(x79191,a899)),f31(f909(x79191,a899),x79192)),x79193))
% 168.50/168.38 [7921]E(f315(f315(f90(f909(x79211,a899)),x79212),x79213),f177(f909(x79211,a899)))+~P1(f315(f315(f223(f909(x79211,a899)),x79212),f315(f72(f909(x79211,a899)),x79213)))
% 168.50/168.38 [7970]E(f315(f315(f3(a901),f315(f315(f73(a901),f315(f154(a901),x79701)),x79702)),f315(f315(f153(a901),x79701),x79703)),f315(f154(a901),f315(f315(f148(a901,x79701),x79703),x79702)))+~P1(f315(f315(f224(a901),x79703),f315(f178(f902(a901)),x79701)))
% 168.50/168.38 [8021]P1(f315(f315(f223(a901),x80211),x80212))+~P1(f315(f315(f223(a901),f315(f315(f73(a901),x80213),x80211)),f315(f315(f73(a901),x80213),x80212)))
% 168.50/168.38 [8024]P1(f315(f315(f224(a901),x80241),x80242))+~P1(f315(f315(f224(a901),f315(f315(f73(a901),x80243),x80241)),f315(f315(f73(a901),x80243),x80242)))
% 168.50/168.38 [8025]P1(f315(f315(f224(a901),x80251),x80252))+~P1(f315(f315(f224(a901),f315(f315(f74(a901),x80253),x80251)),f315(f315(f74(a901),x80253),x80252)))
% 168.50/168.38 [8026]P1(f315(f315(f224(a901),x80261),x80262))+~P1(f315(f315(f224(a901),f315(f315(f74(a901),x80261),x80263)),f315(f315(f74(a901),x80262),x80263)))
% 168.50/168.38 [8055]P1(f315(f315(f224(a901),f2(a901)),x80551))+~P1(f315(f315(f224(a901),f315(f315(f74(a901),x80552),x80551)),f315(f315(f74(a901),x80553),x80551)))
% 168.50/168.38 [8056]P1(f315(f315(f224(a901),f2(a901)),x80561))+~P1(f315(f315(f224(a901),f315(f315(f74(a901),x80561),x80562)),f315(f315(f74(a901),x80561),x80563)))
% 168.50/168.38 [8130]E(f235(x81301,x81302,x81303),x81302)+~P1(f315(f315(f223(f909(x81301,a899)),x81303),f315(f315(f297(x81301),x81302),f177(f909(x81301,a899)))))
% 168.50/168.38 [8181]~P1(f315(f126(x81811),x81813))+E(f315(f125(x81811,f315(f315(f10(a899,a899,x81811),a310),f315(a312,x81812))),x81813),f159(x81811,x81812,x81813))
% 168.50/168.38 [8206]E(f315(f315(f127(x82061),f315(f178(f902(x82061)),f166(x82061,x82062,x82063))),x82063),f102(x82061))+P1(f315(f315(f317(x82061),f701(x82063,x82062,x82061)),f315(f161(x82061),x82063)))
% 168.50/168.38 [8210]E(f315(f315(f123(x82101),f315(f315(f164(x82101),x82102),x82103)),f315(f315(f140(x82101),f315(f315(f153(x82101),x82103),x82102)),f102(x82101))),f315(f315(f164(x82101),f315(a101,x82102)),x82103))+~P1(f315(f315(f224(a901),x82102),f315(f178(f902(x82101)),x82103)))
% 168.50/168.38 [8278]E(f315(f125(x82781,f315(f315(f10(a899,a899,x82781),a310),f315(a312,x82782))),x82783),x82783)+P1(f315(f315(f317(x82781),x82782),f315(f161(x82781),x82783)))
% 168.50/168.38 [8284]P1(f315(f315(f223(f909(f909(x82841,a899),a899)),f236(x82841,x82842)),f236(x82841,x82843)))+~P1(f315(f315(f223(f909(x82841,a899)),x82842),x82843))
% 168.50/168.38 [8323]~P1(f315(f126(x83231),x83233))+P1(f315(f126(x83231),f315(f315(f315(f172(f902(x83231),f902(x83231)),x83232),f156(x83231)),x83233)))
% 168.50/168.38 [8329]~P1(f315(f315(f224(a901),x83292),x83293))+P1(f315(f315(f224(a901),f315(f315(f74(a901),f315(a101,x83291)),x83292)),f315(f315(f74(a901),f315(a101,x83291)),x83293)))
% 168.50/168.38 [8349]P1(f315(f315(f223(f909(f909(x83491,a899),a899)),f315(f296(x83491),x83492)),f315(f296(x83491),x83493)))+~P1(f315(f315(f223(f909(x83491,a899)),x83492),x83493))
% 168.50/168.38 [8418]~E(f315(f298(x84181,x84182,x84183),f230(f909(x84181,a899))),f230(f909(x84182,a899)))+E(f315(f66(x84181,x84182,x84182,x84183),f84(x84181,x84182,f230(f909(x84181,a899)),x84183)),f25(x84182))
% 168.50/168.38 [8512]~P1(f315(f315(f223(f909(x85121,a899)),x85123),x85122))+P1(f315(f315(f223(f909(x85121,a899)),f315(f72(f909(x85121,a899)),x85122)),f315(f72(f909(x85121,a899)),x85123)))
% 168.50/168.38 [8546]E(f315(f298(a901,a901,f315(f315(f9(a901,a901,a901),f3(a901)),x85461)),f315(f290(a901,x85462),x85463)),f315(f290(a901,f315(f315(f3(a901),x85462),x85461)),f315(f315(f3(a901),x85463),x85461)))+~P1(f315(f315(f224(a901),x85461),x85463))
% 168.50/168.38 [8572]~P85(x85721)+E(f315(f315(f73(x85721),x85722),f315(f131(x85721,x85721,f73(x85721),f2(x85721)),x85723)),f315(f131(x85721,x85721,f73(x85721),x85722),x85723))
% 168.50/168.38 [8648]~P89(x86481)+P1(f315(f315(f223(x86481),f315(f69(x86481),f315(f315(f3(x86481),x86482),x86483))),f315(f315(f73(x86481),f315(f69(x86481),x86482)),f315(f69(x86481),x86483))))
% 168.50/168.38 [8649]~P89(x86491)+P1(f315(f315(f223(x86491),f315(f69(x86491),f315(f315(f73(x86491),x86492),x86493))),f315(f315(f73(x86491),f315(f69(x86491),x86492)),f315(f69(x86491),x86493))))
% 168.50/168.38 [8660]E(f315(f315(f73(a1),f315(f315(f74(a1),x86601),f38(a1,f315(f315(f29(a1),x86602),x86601),x86603))),f38(a1,x86602,x86601)),f38(a1,x86602,f315(f315(f74(a1),x86601),x86603)))+~P1(f315(f315(f224(a1),f2(a1)),x86603))
% 168.50/168.38 [8666]E(f315(f315(f123(x86661),f315(f315(f164(x86661),x86662),x86663)),f315(f315(f140(x86661),f315(f130(x86661),f315(f315(f127(x86661),x86662),x86663))),f102(x86661))),f315(f315(f164(x86661),f315(a101,x86662)),x86663))+~P1(f315(f315(f224(a901),x86662),f315(f178(f902(x86661)),x86663)))
% 168.50/168.38 [8686]E(f315(f256(x86861,f315(f315(f143(x86861,f908(a88,x86861)),f315(f240(a88,x86861),f71(a88))),x86862)),f315(a5,x86863)),f315(f315(f153(x86861),x86862),x86863))+~P1(f315(f315(f224(a901),x86863),f315(f178(f902(x86861)),x86862)))
% 168.50/168.38 [8754]P1(f315(f315(f317(f908(x87541,x87541)),x87542),f315(f315(f277(x87541,x87541,x87541),x87543),f295(x87541,x87543))))+~P1(f315(f315(f317(f908(x87541,x87541)),x87542),x87543))
% 168.50/168.38 [8765]E(f315(f298(x87651,x87652,x87653),f230(f909(x87651,a899))),f230(f909(x87652,a899)))+~E(f315(f66(x87651,x87652,x87652,x87653),f84(x87651,x87652,f230(f909(x87651,a899)),x87653)),f25(x87652))
% 168.50/168.38 [8774]P1(f315(f315(f223(a901),x87741),x87742))+~P1(f315(f315(f223(a901),f315(f315(f74(a901),f315(a101,x87743)),x87741)),f315(f315(f74(a901),f315(a101,x87743)),x87742)))
% 168.50/168.38 [8790]P1(f315(f315(f223(f909(x87901,a899)),x87902),x87903))+~P1(f315(f315(f223(f909(x87901,a899)),f315(f72(f909(x87901,a899)),x87903)),f315(f72(f909(x87901,a899)),x87902)))
% 168.50/168.38 [8813]P1(f315(f126(x88131),x88132))+~P1(f315(f126(x88131),f315(f315(f315(f172(f902(x88131),f902(x88131)),x88133),f156(x88131)),x88132)))
% 168.50/168.38 [8886]E(f315(f273(x88861,x88861,f295(x88861,x88862)),x88863),x88863)+~P1(f315(f315(f223(f909(x88861,a899)),f315(f273(x88861,x88861,x88862),x88863)),x88863))
% 168.50/168.38 [8934]~P110(x89341)+P13(x89341,f315(f125(x89341,f315(f315(f9(x89341,x89341,a899),a312),f315(x89342,x89343))),x89343))
% 168.50/168.38 [8941]~P1(f315(f315(f223(a901),x89411),x89412))+P1(f315(f315(f223(a901),x89411),f315(f131(a901,a901,f73(a901),x89412),x89413)))
% 168.50/168.38 [9027]~P1(f315(f315(f317(f908(x90271,x90271)),x90272),f295(x90271,x90273)))+P1(f315(f315(f317(f908(x90271,x90271)),x90272),f315(f315(f172(f908(x90271,x90271),a899),f602(x90273,x90272,x90271)),x90273)))
% 168.50/168.38 [9109]~P85(x91091)+E(f315(f315(f73(x91091),x91092),f315(f131(x91091,x91091,f315(f9(x91091,x91091,x91091),f73(x91091)),f2(x91091)),f315(f157(x91091),x91093))),f315(f131(x91091,x91091,f73(x91091),x91092),x91093))
% 168.50/168.38 [9226]~P26(x92262,x92261,x92263,f230(f909(x92262,a899)),f230(f909(x92261,a899)))+E(f84(x92261,x92262,f230(f909(x92261,a899)),f84(x92262,x92261,f230(f909(x92262,a899)),x92263)),x92263)
% 168.50/168.38 [9381]P56(x93811,x93812,x93813)+P1(f315(f315(f317(f908(x93811,x93812)),f315(f315(f240(x93811,x93812),f603(x93813,x93812,x93811)),f601(x93813,x93812,x93811))),x93813))
% 168.50/168.38 [9382]P56(x93821,x93822,x93823)+P1(f315(f315(f317(f908(x93821,x93822)),f315(f315(f240(x93821,x93822),f603(x93823,x93822,x93821)),f600(x93823,x93822,x93821))),x93823))
% 168.50/168.38 [9452]~P1(f315(f315(f317(f908(x94521,x94521)),x94522),f315(f315(f277(x94521,x94521,x94521),x94523),f295(x94521,x94523))))+P1(f315(f315(f317(f908(x94521,x94521)),x94522),f315(f315(f172(f908(x94521,x94521),a899),f605(x94523,x94522,x94521)),x94523)))
% 168.50/168.38 [9453]~P1(f315(x94531,f315(f315(f153(x94532),x94533),f315(f178(f902(x94532)),f166(x94532,x94531,x94533)))))+~P1(f315(f315(f224(a901),f315(f178(f902(x94532)),f166(x94532,x94531,x94533))),f315(f178(f902(x94532)),x94533)))
% 168.50/168.38 [9544]~P1(f315(f315(f223(f909(x95441,a899)),x95442),x95443))+P1(f315(f315(f223(f909(x95441,a899)),f315(f315(f9(x95441,f909(x95441,a899),a899),f317(x95441)),x95442)),f315(f315(f9(x95441,f909(x95441,a899),a899),f317(x95441)),x95443)))
% 168.50/168.38 [9606]~P1(f315(f315(f317(f908(f909(x96061,a899),f909(x96061,a899))),f315(f315(f240(f909(x96061,a899),f909(x96061,a899)),x96062),x96063)),f302(x96061)))+P1(f315(f315(f224(f909(x96061,a899)),x96062),x96063))
% 168.50/168.38 [9634]P57(x96341,x96342,x96343)+~P1(f315(f315(f317(f908(x96341,x96341)),f315(f315(f240(x96341,x96341),f598(x96343,x96342,x96341)),f597(x96343,x96342,x96341))),x96343))
% 168.50/168.38 [9635]P57(x96351,x96352,x96353)+~P1(f315(f315(f317(f908(x96351,x96351)),f315(f315(f240(x96351,x96351),f597(x96353,x96352,x96351)),f598(x96353,x96352,x96351))),x96353))
% 168.50/168.38 [9672]~P1(f315(f315(f317(f908(f902(x96721),f902(x96721))),f315(f315(f240(f902(x96721),f902(x96721)),x96722),x96722)),f136(x96721,x96723)))+P1(f315(f315(f317(f908(x96721,x96721)),f315(f315(f240(x96721,x96721),f633(x96722,x96723,x96721)),f633(x96722,x96723,x96721))),x96723))
% 168.50/168.38 [9722]P1(f315(f315(f223(f909(x97221,a899)),x97222),x97223))+~P1(f315(f315(f223(f909(x97221,a899)),f315(f315(f9(x97221,f909(x97221,a899),a899),f317(x97221)),x97222)),f315(f315(f9(x97221,f909(x97221,a899),a899),f317(x97221)),x97223)))
% 168.50/168.38 [9803]E(f315(f315(f3(a901),f315(f315(f8(a901,a901),x98031),f315(f270(a901),x98032))),f315(f315(f8(a901,a901),x98033),f315(f270(a901),x98032))),f315(f315(f8(a901,a901),f315(f315(f20(a901,a901,a901),f315(f315(f10(a901,f909(a901,a901),a901),f3(a901)),x98031)),x98033)),f315(f270(a901),x98032)))+~P1(f315(f315(f223(a901),f315(x98033,f405(x98032,x98031,x98033))),f315(x98031,f405(x98032,x98031,x98033))))
% 168.50/168.38 [5725]~P76(x57251)+E(f315(f315(f3(x57251),f315(f315(f73(x57251),x57252),x57253)),x57253),x57252)
% 168.50/168.38 [5726]~P76(x57261)+E(f315(f315(f73(x57261),f315(f315(f3(x57261),x57262),x57263)),x57263),x57262)
% 168.50/168.38 [5960]~P76(x59601)+E(f315(f315(f73(x59601),x59602),f315(f315(f73(x59601),f315(f72(x59601),x59602)),x59603)),x59603)
% 168.50/168.38 [6048]~P84(x60481)+E(f315(f315(f74(x60481),f315(f315(f232(x60481),x60482),x60483)),x60482),f315(f315(f232(x60481),x60482),f315(a101,x60483)))
% 168.50/168.38 [6049]~P121(x60491)+E(f315(f315(f74(x60491),f315(f315(f232(x60491),x60492),x60493)),x60492),f315(f315(f232(x60491),x60492),f315(a101,x60493)))
% 168.50/168.38 [6275]~P114(x62751)+E(f315(f69(x62751),f315(f315(f232(x62751),f315(f72(x62751),x62752)),x62753)),f315(f69(x62751),f315(f315(f232(x62751),x62752),x62753)))
% 168.50/168.38 [6322]~P84(x63221)+E(f315(f315(f74(x63221),f315(f315(f232(x63221),x63222),x63223)),x63222),f315(f315(f74(x63221),x63222),f315(f315(f232(x63221),x63222),x63223)))
% 168.50/168.38 [6380]E(f315(f315(f3(a88),f315(f315(f73(a88),x63801),x63802)),x63803),f262(x63801,x63802,x63803))+~P1(f315(f315(f224(a88),x63802),x63803))
% 168.50/168.38 [6404]~E(f315(f315(f127(x64041),x64043),x64042),f102(x64041))+P1(f315(f315(f223(a901),f315(f178(f902(x64041)),x64042)),x64043))
% 168.50/168.38 [6545]E(f315(f315(f74(a901),f315(f92(a901),x65451)),f315(f315(f74(a901),f315(f92(a901),x65452)),x65453)),f2(a901))+~P1(f315(f315(f224(a1),x65451),a76))
% 168.50/168.38 [6562]~P65(x65621)+E(f315(f315(f232(x65621),f315(f315(f279(x65621),f71(x65621)),x65622)),x65623),f315(f315(f279(x65621),f71(x65621)),f315(f315(f232(x65621),x65622),x65623)))
% 168.50/168.38 [6643]E(f315(f315(f3(a901),f315(f315(f73(a901),x66431),x66432)),x66433),f315(f315(f3(a901),x66431),f315(f315(f3(a901),x66433),x66432)))+~P1(f315(f315(f223(a901),x66432),x66433))
% 168.50/168.38 [6645]E(f315(f315(f3(a901),f315(f315(f73(a901),x66451),x66452)),x66453),f315(f315(f73(a901),x66451),f315(f315(f3(a901),x66452),x66453)))+~P1(f315(f315(f223(a901),x66453),x66452))
% 168.50/168.38 [6684]~P80(x66841)+P1(f315(f315(f223(x66841),f315(f315(f90(x66841),x66842),x66843)),x66843))
% 168.50/168.38 [6685]~P104(x66851)+P1(f315(f315(f223(x66851),f315(f315(f90(x66851),x66852),x66853)),x66853))
% 168.50/168.38 [6686]~P80(x66861)+P1(f315(f315(f223(x66861),f315(f315(f90(x66861),x66862),x66863)),x66862))
% 168.50/168.38 [6687]~P104(x66871)+P1(f315(f315(f223(x66871),f315(f315(f90(x66871),x66872),x66873)),x66872))
% 168.50/168.38 [6688]~P110(x66881)+P1(f315(f315(f223(x66881),f315(f315(f221(x66881),x66882),x66883)),x66883))
% 168.50/168.38 [6689]~P110(x66891)+P1(f315(f315(f223(x66891),f315(f315(f221(x66891),x66892),x66893)),x66892))
% 168.50/168.38 [6703]E(f315(f315(f29(a1),f315(f315(f29(a1),x67031),x67032)),x67033),f315(f315(f29(a1),x67031),f315(f315(f74(a1),x67032),x67033)))+~P1(f315(f315(f224(a1),f2(a1)),x67033))
% 168.50/168.38 [6757]~P121(x67571)+E(f315(f315(f73(x67571),f315(f315(f74(x67571),x67572),x67573)),x67573),f315(f315(f74(x67571),f315(f315(f73(x67571),x67572),f71(x67571))),x67573))
% 168.50/168.38 [6758]~P97(x67581)+E(f315(f315(f74(x67581),f315(f72(x67581),f315(f92(x67581),x67582))),x67583),f315(f315(f74(x67581),f315(f92(x67581),f315(f72(a1),x67582))),x67583))
% 168.50/168.38 [6831]~P85(x68311)+E(f315(f154(x68311),f315(f315(f143(x68312,x68311),f315(f18(x68311,x68312),f2(x68311))),x68313)),f2(x68311))
% 168.50/168.38 [6849]E(f315(f315(f73(a901),f315(f92(a901),x68491)),f315(f315(f73(a901),f315(f92(a901),x68492)),x68493)),f315(f315(f73(a901),f315(f92(a901),x68492)),x68493))+~P1(f315(a182,f315(f92(a1),x68491)))
% 168.50/168.38 [6864]~P5(x68641)+E(f30(x68641,f315(f315(f297(x68641),x68642),f315(f315(f297(x68641),x68643),f177(f909(x68641,a899))))),f315(f315(f99(x68641),x68642),x68643))
% 168.50/168.38 [6865]~P5(x68651)+E(f31(x68651,f315(f315(f297(x68651),x68652),f315(f315(f297(x68651),x68653),f177(f909(x68651,a899))))),f315(f315(f90(x68651),x68652),x68653))
% 168.50/168.38 [6890]E(f315(f315(f164(x68901),x68902),x68903),x68903)+~P1(f315(f315(f223(a901),f315(f178(f902(x68901)),x68903)),x68902))
% 168.50/168.38 [6902]E(f315(f315(f127(x69021),x69022),x69023),f102(x69021))+~P1(f315(f315(f223(a901),f315(f178(f902(x69021)),x69023)),x69022))
% 168.50/168.38 [6913]E(f315(f315(f73(a901),f315(f315(f3(a901),x69131),x69132)),x69133),f315(f315(f3(a901),f315(f315(f73(a901),x69131),x69133)),x69132))+~P1(f315(f315(f223(a901),x69132),x69131))
% 168.50/168.38 [6927]~P1(f315(f315(f224(a901),x69271),x69273))+P1(f315(f315(f224(a901),f315(f315(f3(a901),x69271),x69272)),x69273))
% 168.50/168.38 [6954]~P110(x69541)+E(f159(x69541,x69542,f315(f315(f137(x69541,x69541,f7(x69541)),x69542),x69543)),x69543)
% 168.50/168.38 [7046]E(f315(f315(f3(a901),f315(f315(f73(a901),x70461),x70462)),f315(a101,x70463)),f315(f315(f3(a901),x70461),f315(a101,f315(f315(f3(a901),x70463),x70462))))+~P1(f315(f315(f223(a901),x70462),x70463))
% 168.50/168.38 [7047]~P114(x70471)+P1(f315(f315(f223(x70471),f2(x70471)),f315(f315(f232(x70471),f315(f69(x70471),x70472)),x70473)))
% 168.50/168.38 [7096]P14(x70961,x70962,x70963)+~P1(f315(f315(f223(f909(f900(x70961),a899)),x70963),x70962))
% 168.50/168.38 [7139]~P1(f315(f54(x71391),x71392))+P1(f315(f54(x71391),f315(f315(f3(f909(x71391,a899)),x71392),x71393)))
% 168.50/168.38 [7140]~P1(f315(f54(x71401),x71403))+P1(f315(f54(x71401),f315(f315(f90(f909(x71401,a899)),x71402),x71403)))
% 168.50/168.38 [7141]~P1(f315(f54(x71411),x71412))+P1(f315(f54(x71411),f315(f315(f90(f909(x71411,a899)),x71412),x71413)))
% 168.50/168.38 [7283]~P39(x72831,x72833)+P39(x72831,f315(f315(f90(f909(f908(x72831,x72831),a899)),x72832),x72833))
% 168.50/168.38 [7284]~P39(x72841,x72842)+P39(x72841,f315(f315(f90(f909(f908(x72841,x72841),a899)),x72842),x72843))
% 168.50/168.38 [7407]~P80(x74071)+E(f12(x74071,f315(f161(x74071),f315(f315(f140(x74071),x74072),x74073))),f315(f131(x74071,x74071,f99(x74071),x74072),x74073))
% 168.50/168.38 [7408]~P80(x74081)+E(f13(x74081,f315(f161(x74081),f315(f315(f140(x74081),x74082),x74083))),f315(f131(x74081,x74081,f90(x74081),x74082),x74083))
% 168.50/168.38 [7409]~P110(x74091)+E(f16(x74091,f315(f161(x74091),f315(f315(f140(x74091),x74092),x74093))),f315(f131(x74091,x74091,f221(x74091),x74092),x74093))
% 168.50/168.38 [7410]~P110(x74101)+E(f17(x74101,f315(f161(x74101),f315(f315(f140(x74101),x74102),x74103))),f315(f131(x74101,x74101,f222(x74101),x74102),x74103))
% 168.50/168.38 [7474]~P1(f315(f54(x74741),x74742))+P1(f315(f315(f223(a901),f315(f28(x74741),x74742)),f315(f28(x74741),f315(f315(f297(x74741),x74743),x74742))))
% 168.50/168.38 [7481]E(f315(f315(f99(f909(a901,a899)),f315(f290(a901,x74811),x74812)),f315(f290(a901,x74812),f315(f315(f73(a901),x74812),x74813))),f315(f290(a901,x74811),f315(f315(f73(a901),x74812),x74813)))+~P1(f315(f315(f223(a901),x74811),x74812))
% 168.50/168.38 [7490]P1(f315(f315(f223(a901),x74901),x74902))+~P1(f315(f315(f223(a901),f315(f315(f73(a901),x74903),x74901)),x74902))
% 168.50/168.38 [7491]P1(f315(f315(f223(a901),x74911),x74912))+~P1(f315(f315(f223(a901),f315(f315(f73(a901),x74911),x74913)),x74912))
% 168.50/168.38 [7492]P1(f315(f315(f224(a901),x74921),x74922))+~P1(f315(f315(f224(a901),f315(f315(f73(a901),x74921),x74923)),x74922))
% 168.50/168.38 [7532]~P110(x75321)+E(f14(x75321,f221(x75321),f315(f161(x75321),f315(f315(f140(x75321),x75322),x75323))),f315(f131(x75321,x75321,f221(x75321),x75322),x75323))
% 168.50/168.38 [7533]~P110(x75331)+E(f15(x75331,f222(x75331),f315(f161(x75331),f315(f315(f140(x75331),x75332),x75333))),f315(f131(x75331,x75331,f222(x75331),x75332),x75333))
% 168.50/168.38 [7537]~E(x75372,f177(f909(f908(x75371,x75371),a899)))+P1(f315(f315(f223(f909(f908(x75371,x75371),a899)),x75372),x75373))
% 168.50/168.38 [7638]E(f315(f315(f99(f909(x76381,a899)),x76382),f315(f315(f3(f909(x76381,a899)),x76383),x76382)),x76383)+~P1(f315(f315(f223(f909(x76381,a899)),x76382),x76383))
% 168.50/168.38 [7639]~P1(f315(f315(f223(a901),x76391),f315(f315(f73(a901),x76393),x76392)))+P1(f315(f315(f223(a901),f315(f315(f3(a901),x76391),x76392)),x76393))
% 168.50/168.38 [7640]~P1(f315(f315(f224(a901),x76401),f315(f315(f3(a901),x76403),x76402)))+P1(f315(f315(f224(a901),f315(f315(f73(a901),x76401),x76402)),x76403))
% 168.50/168.38 [7697]E(x76971,f102(x76972))+E(f315(f130(x76972),f315(f315(f315(f172(f902(x76972),f902(x76972)),x76973),f156(x76972)),x76971)),f315(f315(f153(x76972),x76971),f38(a901,x76973,f315(f178(f902(x76972)),x76971))))
% 168.50/168.38 [7706]E(f315(f315(f297(x77061),x77062),f315(f315(f3(f909(x77061,a899)),x77063),f315(f315(f297(x77061),x77062),f177(f909(x77061,a899))))),x77063)+~P1(f315(f315(f317(x77061),x77062),x77063))
% 168.50/168.38 [7868]P1(f315(f315(f223(a901),x78681),f315(f315(f73(a901),x78682),x78683)))+~P1(f315(f315(f223(a901),f315(f315(f3(a901),x78681),x78683)),x78682))
% 168.50/168.38 [7869]P1(f315(f315(f224(a901),x78691),f315(f315(f3(a901),x78692),x78693)))+~P1(f315(f315(f224(a901),f315(f315(f73(a901),x78691),x78693)),x78692))
% 168.50/168.38 [7894]P1(f315(f54(x78941),x78942))+~P1(f315(f54(x78941),f315(f315(f99(f909(x78941,a899)),x78943),x78942)))
% 168.50/168.38 [7895]P1(f315(f54(x78951),x78952))+~P1(f315(f54(x78951),f315(f315(f99(f909(x78951,a899)),x78952),x78953)))
% 168.50/168.38 [7969]~P48(x79691,x79693)+P1(f315(f315(f317(f908(x79691,x79691)),f315(f315(f240(x79691,x79691),x79692),x79692)),x79693))
% 168.50/168.38 [8103]E(f315(f315(f153(a901),f128(a901,f315(f290(a901,x81031),x81032))),x81033),f315(f315(f73(a901),x81031),x81033))+~P1(f315(f315(f224(a901),f315(f315(f73(a901),x81031),x81033)),x81032))
% 168.50/168.38 [8169]E(f315(f315(f164(a901),x81691),f128(a901,f315(f290(a901,x81692),x81693))),f128(a901,f315(f290(a901,x81692),f315(f315(f73(a901),x81692),x81691))))+~P1(f315(f315(f223(a901),f315(f315(f73(a901),x81692),x81691)),x81693))
% 168.50/168.38 [8227]~P97(x82271)+E(f315(f315(f232(x82271),x82272),f315(f92(a901),f315(f315(f73(a1),x82273),x82273))),f315(f315(f79(x82271,x82271),f315(f315(f232(x82271),x82272),f315(f92(a901),x82273))),f315(f315(f20(x82271,x82271,x82271),f74(x82271)),f7(x82271))))
% 168.50/168.38 [8493]E(f315(f315(f123(x84931),f315(f315(f164(x84931),x84932),x84933)),f315(f315(f140(x84931),f315(f315(f153(x84931),x84933),x84932)),f315(f315(f127(x84931),f315(a101,x84932)),x84933))),x84933)+~P1(f315(f315(f224(a901),x84932),f315(f178(f902(x84931)),x84933)))
% 168.50/168.38 [8500]P1(f315(f315(f223(f909(x85001,a899)),f303(x85001,x85002)),f303(x85001,x85003)))+~P1(f315(f315(f223(f909(x85001,f909(x85001,a899))),x85003),x85002))
% 168.50/168.38 [8501]~P57(x85011,x85012,x85013)+P57(x85011,x85012,f315(f315(f3(f909(f908(x85011,x85011),a899)),x85013),f295(x85011,f177(f909(f908(x85011,x85011),a899)))))
% 168.50/168.38 [8520]P1(f315(f315(f223(f909(x85201,a899)),f304(x85201,x85202)),f304(x85201,x85203)))+~P1(f315(f315(f223(f909(f908(x85201,x85201),a899)),x85203),x85202))
% 168.50/168.38 [8527]~P129(x85271)+P1(f315(f315(f223(x85271),f2(x85271)),f315(f315(f73(x85271),f315(f315(f74(x85271),x85272),x85272)),f315(f315(f74(x85271),x85273),x85273))))
% 168.50/168.38 [8561]P1(f315(f315(f223(f909(x85611,a899)),f315(f269(x85611),x85612)),f315(f269(x85611),x85613)))+~P1(f315(f315(f223(f909(f908(x85611,x85611),a899)),x85612),x85613))
% 168.50/168.38 [8590]~P55(x85901,x85902)+~P1(f315(f315(f317(f908(x85901,x85901)),f315(f315(f240(x85901,x85901),x85903),x85903)),x85902))
% 168.50/168.38 [8592]~P39(x85921,x85922)+~P1(f315(f315(f317(f908(x85921,x85921)),f315(f315(f240(x85921,x85921),x85923),x85923)),x85922))
% 168.50/168.38 [8650]P1(f315(f315(f223(f909(x86501,a899)),f30(f909(x86501,a899),x86502)),f30(f909(x86501,a899),x86503)))+~P1(f315(f315(f223(f909(f909(x86501,a899),a899)),x86502),x86503))
% 168.50/168.38 [8651]P1(f315(f315(f223(f909(x86511,a899)),f31(f909(x86511,a899),x86512)),f31(f909(x86511,a899),x86513)))+~P1(f315(f315(f223(f909(f909(x86511,a899),a899)),x86513),x86512))
% 168.50/168.38 [8705]~P8(x87051,x87053,x87052)+P1(f315(f315(f223(f909(f908(x87051,x87051),a899)),x87052),f315(f315(f242(x87051,x87051),x87053),f315(f18(f909(x87051,a899),x87051),x87053))))
% 168.50/168.38 [8706]~P54(x87061,x87063,x87062)+P1(f315(f315(f223(f909(f908(x87061,x87061),a899)),x87062),f315(f315(f242(x87061,x87061),x87063),f315(f18(f909(x87061,a899),x87061),x87063))))
% 168.50/168.38 [8755]~P89(x87551)+P1(f315(f315(f223(x87551),f315(f315(f3(x87551),f315(f69(x87551),x87552)),f315(f69(x87551),x87553))),f315(f69(x87551),f315(f315(f3(x87551),x87553),x87552))))
% 168.50/168.38 [8756]~P89(x87561)+P1(f315(f315(f223(x87561),f315(f315(f3(x87561),f315(f69(x87561),x87562)),f315(f69(x87561),x87563))),f315(f69(x87561),f315(f315(f3(x87561),x87562),x87563))))
% 168.50/168.38 [8788]P1(f315(f315(f223(f909(f908(x87881,x87881),a899)),f295(x87881,x87882)),f295(x87881,x87883)))+~P1(f315(f315(f223(f909(f908(x87881,x87881),a899)),x87882),x87883))
% 168.50/168.38 [8899]~P25(x88992,x88991,x88993,f230(f909(x88992,a899)))+E(f315(f66(x88991,x88992,x88992,f84(x88992,x88991,f230(f909(x88992,a899)),x88993)),x88993),f25(x88992))
% 168.50/168.38 [8959]P57(x89591,x89592,x89593)+~P57(x89591,x89592,f315(f315(f3(f909(f908(x89591,x89591),a899)),x89593),f295(x89591,f177(f909(f908(x89591,x89591),a899)))))
% 168.50/168.38 [8979]P1(f315(f315(f223(f909(f908(f902(x89791),f902(x89791)),a899)),f146(x89791,x89792)),f146(x89791,x89793)))+~P1(f315(f315(f223(f909(f908(x89791,x89791),a899)),x89792),x89793))
% 168.50/168.38 [8980]P1(f315(f315(f223(f909(f908(f902(x89801),f902(x89801)),a899)),f147(x89801,x89802)),f147(x89801,x89803)))+~P1(f315(f315(f223(f909(f908(x89801,x89801),a899)),x89802),x89803))
% 168.50/168.38 [9001]~P54(x90011,x90013,x90012)+P1(f315(f315(f223(f909(f908(x90011,x90011),a899)),x90012),f315(f315(f277(x90011,x90011,x90011),f315(f274(x90011,x90011),x90012)),x90012)))
% 168.50/168.38 [9054]~P1(f315(f126(x90541),x90542))+E(f315(f125(x90541,f315(f315(f9(x90541,f909(x90541,a899),a899),f317(x90541)),f315(f161(x90541),f165(x90541,x90542,x90543)))),x90542),f165(x90541,x90542,x90543))
% 168.50/168.38 [9107]E(x91071,x91072)+~P1(f315(f315(f317(f908(x91073,x91073)),f315(f315(f240(x91073,x91073),x91071),x91072)),f295(x91073,f177(f909(f908(x91073,x91073),a899)))))
% 168.50/168.38 [9189]P1(f315(f315(f317(x91891),x91892),f304(x91891,x91893)))+P1(f315(f315(f317(f908(x91891,x91891)),f315(f315(f240(x91891,x91891),f494(x91893,x91892,x91891)),x91892)),x91893))
% 168.50/168.38 [9190]P1(f315(f315(f317(x91901),x91902),f304(x91901,x91903)))+P1(f315(f315(f317(f908(x91901,x91901)),f315(f315(f240(x91901,x91901),f584(x91903,x91902,x91901)),x91902)),x91903))
% 168.50/168.38 [9191]P1(f315(f315(f317(x91911),x91912),f304(x91911,x91913)))+P1(f315(f315(f317(f908(x91911,x91911)),f315(f315(f240(x91911,x91911),f586(x91913,x91912,x91911)),x91912)),x91913))
% 168.50/168.38 [9227]P25(x92271,x92272,x92273,f230(f909(x92271,a899)))+~E(f315(f66(x92272,x92271,x92271,f84(x92271,x92272,f230(f909(x92271,a899)),x92273)),x92273),f25(x92271))
% 168.50/168.38 [9280]~P1(f315(f315(f317(f902(x92801)),x92803),f150(x92801,x92802)))+P1(f315(f149(x92801,f315(f315(f9(x92801,f909(x92801,a899),a899),f317(x92801)),x92802)),x92803))
% 168.50/168.38 [9303]P1(f315(x93033,x93032))+E(f315(f250(x93031),f315(f315(f20(x93031,a899,a899),f315(f315(f10(a899,f909(a899,a899),x93031),a313),f315(a312,x93032))),x93033)),f177(f909(x93031,a899)))
% 168.50/168.38 [9320]~P89(x93201)+P1(f315(f315(f223(x93201),f315(f69(x93201),f315(f315(f3(x93201),f315(f69(x93201),x93202)),f315(f69(x93201),x93203)))),f315(f69(x93201),f315(f315(f3(x93201),x93202),x93203))))
% 168.50/168.38 [9334]~P1(f315(x93343,x93342))+E(f315(f250(x93341),f315(f315(f20(x93341,a899,a899),f315(f315(f10(a899,f909(a899,a899),x93341),a313),f315(a312,x93342))),x93343)),f315(f315(f297(x93341),x93342),f177(f909(x93341,a899))))
% 168.50/168.38 [9343]~P1(f315(f315(f317(f909(x93431,a899)),x93433),f315(f296(x93431),x93432)))+P1(f315(f236(x93431,f315(f315(f9(x93431,f909(x93431,a899),a899),f317(x93431)),x93432)),x93433))
% 168.50/168.38 [9380]P39(x93801,x93802)+P1(f315(f315(f317(f908(x93801,x93801)),f315(f315(f240(x93801,x93801),f315(f552(x93802,x93801),f315(a101,x93803))),f315(f552(x93802,x93801),x93803))),x93802))
% 168.50/168.38 [9521]P1(f315(f315(f317(f902(x95211)),x95212),f150(x95211,x95213)))+~P1(f315(f149(x95211,f315(f315(f9(x95211,f909(x95211,a899),a899),f317(x95211)),x95213)),x95212))
% 168.50/168.38 [9536]P1(f315(f315(f317(f909(x95361,a899)),x95362),f315(f296(x95361),x95363)))+~P1(f315(f236(x95361,f315(f315(f9(x95361,f909(x95361,a899),a899),f317(x95361)),x95363)),x95362))
% 168.50/168.38 [9601]P1(f315(f315(f317(x96011),f315(f256(x96011,x96012),x96013)),f315(f161(x96011),f315(f315(f143(f908(a88,x96011),x96011),f244(a88,x96011)),x96012))))+~P1(f315(f315(f224(a88),x96013),f315(f154(a88),f315(f315(f143(f908(a88,x96011),a88),f239(a88,x96011)),x96012))))
% 168.50/168.38 [9651]P1(f315(f315(f223(f909(f908(f902(x96511),f902(x96511)),a899)),f147(x96511,x96512)),f315(f315(f242(f902(x96511),f902(x96511)),f150(x96511,x96513)),f315(f18(f909(f902(x96511),a899),f902(x96511)),f150(x96511,x96513)))))+~P1(f315(f315(f223(f909(f908(x96511,x96511),a899)),x96512),f315(f315(f242(x96511,x96511),x96513),f315(f18(f909(x96511,a899),x96511),x96513))))
% 168.50/168.38 [9675]P1(f315(f315(f317(x96751),f315(f239(x96751,f908(a88,a88)),f315(f254(x96751,x96752),x96753))),f315(f161(x96751),f315(f315(f143(f908(a88,x96751),x96751),f244(a88,x96751)),x96752))))+~P1(f315(f315(f224(a88),f2(a88)),f315(f154(a88),f315(f315(f143(f908(a88,x96751),a88),f239(a88,x96751)),x96752))))
% 168.50/168.38 [9690]~P1(f315(f315(f223(f909(f908(x96901,x96901),a899)),x96902),f315(f315(f242(x96901,x96901),x96903),f315(f18(f909(x96901,a899),x96901),x96903))))+P1(f315(f315(f223(f909(f908(x96901,x96901),a899)),f315(f315(f277(x96901,x96901,x96901),x96902),f295(x96901,x96902))),f315(f315(f242(x96901,x96901),x96903),f315(f18(f909(x96901,a899),x96901),x96903))))
% 168.50/168.38 [9988]~P39(x99881,x99882)+~P1(f315(f315(f317(f908(x99881,x99881)),f315(f315(f240(x99881,x99881),f315(x99883,f315(a101,f554(x99882,x99881,x99883)))),f315(x99883,f554(x99882,x99881,x99883)))),x99882))
% 168.50/168.38 [9989]~P39(x99891,x99892)+~P1(f315(f315(f317(f908(x99891,x99891)),f315(f315(f240(x99891,x99891),f315(x99893,f315(a101,f591(x99893,x99892,x99891)))),f315(x99893,f591(x99893,x99892,x99891)))),x99892))
% 168.50/168.38 [10243]P1(f315(f315(f223(f909(f908(f909(x102431,a899),f909(x102431,a899)),a899)),f315(f315(f277(f909(x102431,a899),f909(x102431,a899),f909(x102431,a899)),f308(x102431,x102432)),f315(f315(f99(f909(f908(f909(x102431,a899),f909(x102431,a899)),a899)),f308(x102431,x102433)),f315(f315(f297(f908(f909(x102431,a899),f909(x102431,a899))),f315(f315(f240(f909(x102431,a899),f909(x102431,a899)),f177(f909(x102431,a899))),f177(f909(x102431,a899)))),f177(f909(f908(f909(x102431,a899),f909(x102431,a899)),a899)))))),f308(x102431,x102432)))+~P1(f315(f315(f223(f909(f908(x102431,x102431),a899)),f315(f315(f277(x102431,x102431,x102431),x102432),x102433)),x102432))
% 168.50/168.38 [10244]P1(f315(f315(f223(f909(f908(f909(x102441,a899),f909(x102441,a899)),a899)),f315(f315(f277(f909(x102441,a899),f909(x102441,a899),f909(x102441,a899)),f306(x102441,x102442)),f315(f315(f99(f909(f908(f909(x102441,a899),f909(x102441,a899)),a899)),f306(x102441,x102443)),f315(f315(f297(f908(f909(x102441,a899),f909(x102441,a899))),f315(f315(f240(f909(x102441,a899),f909(x102441,a899)),f177(f909(x102441,a899))),f177(f909(x102441,a899)))),f177(f909(f908(f909(x102441,a899),f909(x102441,a899)),a899)))))),f306(x102441,x102442)))+~P1(f315(f315(f223(f909(f908(x102441,x102441),a899)),f315(f315(f277(x102441,x102441,x102441),x102442),x102443)),x102442))
% 168.50/168.38 [7406]~P1(f315(f315(f223(a901),x74062),x74061))+E(f315(f315(f3(a901),f315(a101,f315(f315(f3(a901),x74061),x74062))),x74063),f315(f315(f3(a901),f315(a101,x74061)),f315(f315(f73(a901),x74062),x74063)))
% 168.50/168.38 [7446]~P62(x74461)+E(f315(f315(f73(x74461),f38(x74461,x74462,x74463)),f315(f315(f74(x74461),f315(f315(f29(x74461),x74462),x74463)),x74463)),x74462)
% 168.50/168.38 [7644]E(f315(f315(f74(a901),f315(f92(a901),x76441)),f315(f315(f74(a901),f315(f92(a901),x76442)),x76443)),f315(f315(f74(a901),f315(f92(a901),f315(f315(f74(a1),x76441),x76442))),x76443))+P1(f315(f315(f224(a1),x76441),a76))
% 168.50/168.38 [8112]~P1(f315(f315(f223(a901),x81123),x81122))+P1(f315(f315(f223(a901),x81121),f315(f315(f3(a901),f315(f315(f73(a901),x81122),x81121)),x81123)))
% 168.50/168.38 [8314]~P1(f315(f315(f223(a901),x83141),x83142))+E(f315(f315(f123(a901),f128(a901,f315(f290(a901,x83141),x83142))),f128(a901,f315(f290(a901,x83142),f315(f315(f73(a901),x83142),x83143)))),f128(a901,f315(f290(a901,x83141),f315(f315(f73(a901),x83142),x83143))))
% 168.50/168.38 [8569]~P1(f315(f54(x85691),x85692))+E(f315(a101,f315(f28(x85691),f315(f315(f3(f909(x85691,a899)),x85692),f315(f315(f297(x85691),x85693),f177(f909(x85691,a899)))))),f315(f28(x85691),f315(f315(f297(x85691),x85693),x85692)))
% 168.50/168.38 [8608]~P1(f315(f54(x86081),x86082))+E(f315(f315(f73(a901),f71(a901)),f315(f28(x86081),f315(f315(f3(f909(x86081,a899)),x86082),f315(f315(f297(x86081),x86083),f177(f909(x86081,a899)))))),f315(f28(x86081),f315(f315(f297(x86081),x86083),x86082)))
% 168.50/168.38 [8797]E(f315(f315(f3(a901),f315(f28(x87971),x87972)),f315(f28(x87971),f315(f315(f90(f909(x87971,a899)),x87972),x87973))),f315(f28(x87971),f315(f315(f3(f909(x87971,a899)),x87972),x87973)))+~P1(f315(f54(x87971),f315(f315(f90(f909(x87971,a899)),x87972),x87973)))
% 168.50/168.38 [9049]~P6(f315(x90492,f389(x90492,x90493,x90491)))+E(f315(f89(a1),f315(f315(f8(x90491,a901),f315(f315(f10(a1,a901,x90491),a93),x90492)),x90493)),f315(f315(f8(x90491,a1),x90492),x90493))
% 168.50/168.38 [9050]~P6(f315(x90502,f385(x90502,x90503,x90501)))+E(f315(f89(a1),f315(f315(f11(x90501,a901),f315(f315(f10(a1,a901,x90501),a93),x90502)),x90503)),f315(f315(f11(x90501,a1),x90502),x90503))
% 168.50/168.38 [9090]~P1(f315(f54(x90901),x90903))+P1(f315(f315(f223(a901),f315(f315(f3(a901),f315(f28(x90901),x90902)),f315(f28(x90901),x90903))),f315(f28(x90901),f315(f315(f3(f909(x90901,a899)),x90902),x90903))))
% 168.50/168.38 [9117]P1(f315(f315(f317(x91171),f389(x91172,x91173,x91171)),x91173))+E(f315(f89(a1),f315(f315(f8(x91171,a901),f315(f315(f10(a1,a901,x91171),a93),x91172)),x91173)),f315(f315(f8(x91171,a1),x91172),x91173))
% 168.50/168.38 [9118]P1(f315(f315(f317(x91181),f385(x91182,x91183,x91181)),x91183))+E(f315(f89(a1),f315(f315(f11(x91181,a901),f315(f315(f10(a1,a901,x91181),a93),x91182)),x91183)),f315(f315(f11(x91181,a1),x91182),x91183))
% 168.50/168.38 [9181]E(f78(x91811,f315(f315(f9(x91811,f909(x91811,a899),a899),f317(x91811)),f315(f315(f3(f909(x91811,a899)),x91812),f315(f315(f297(x91811),x91813),f177(f909(x91811,a899)))))),f235(x91811,x91813,x91812))+P1(f315(f315(f223(f909(x91811,a899)),x91812),f315(f315(f297(x91811),x91813),f177(f909(x91811,a899)))))
% 168.50/168.38 [9537]E(f315(f315(f143(f902(x95371),x95371),f315(f315(f9(f902(x95371),a901,x95371),f153(x95371)),x95372)),f315(f125(f902(x95371),f315(f315(f10(a901,a899,f902(x95371)),f315(f224(a901),x95372)),f178(f902(x95371)))),x95373)),f315(f315(f153(f902(x95371)),f168(x95371,x95373)),x95372))+~P1(f315(f315(f224(a901),x95372),f315(f178(f902(f902(x95371))),f168(x95371,x95373))))
% 168.50/168.38 [9624]E(f315(f125(x96241,x96242),x96243),f166(x96241,x96242,x96243))+P1(f315(f315(f317(x96241),f704(x96243,x96242,x96241)),f315(f161(x96241),f315(f315(f127(x96241),f315(f178(f902(x96241)),f166(x96241,x96242,x96243))),x96243))))
% 168.50/168.38 [9763]E(f315(f315(f127(x97631),f315(f178(f902(x97631)),f166(x97631,x97632,x97633))),x97633),f102(x97631))+~P1(f315(x97632,f315(f130(x97631),f315(f315(f127(x97631),f315(f178(f902(x97631)),f166(x97631,x97632,x97633))),x97633))))
% 168.50/168.38 [9855]~P1(f315(f315(f317(f908(x98551,x98551)),x98552),f295(x98551,x98553)))+P1(f315(f315(f317(f908(x98551,x98551)),x98552),f315(f315(f33(a901,f909(f908(x98551,x98551),a899)),f230(f909(a901,a899))),f315(f315(f9(a901,f909(f908(x98551,x98551),a899),f909(f908(x98551,x98551),a899)),f172(f908(x98551,x98551),a899)),x98553))))
% 168.50/168.38 [9915]~P1(f315(f315(f223(f909(x99151,a899)),f315(f315(f33(a901,f909(x99151,a899)),f315(f290(a901,f2(a901)),f489(x99153,x99152,x99151))),x99152)),x99153))+P1(f315(f315(f223(f909(x99151,a899)),f315(f315(f33(a901,f909(x99151,a899)),f230(f909(a901,a899))),x99152)),x99153))
% 168.50/168.38 [9961]~P1(f315(f315(f224(a1),f2(a1)),x99613))+P1(f315(f315(f224(a1),x99611),f315(f315(f73(a1),x99612),f315(f315(f74(a1),f315(f315(f73(a1),f315(f69(a1),f315(f315(f3(a1),x99612),x99611))),f71(a1))),x99613))))
% 168.50/168.38 [9975]~P39(x99751,f315(f315(f99(f909(f908(x99751,x99751),a899)),x99752),x99753))+P39(x99751,f315(f315(f99(f909(f908(x99751,x99751),a899)),f315(f315(f99(f909(f908(x99751,x99751),a899)),f315(f315(f277(x99751,x99751,x99751),x99752),x99752)),f315(f315(f277(x99751,x99751,x99751),x99753),x99752))),x99753))
% 168.50/168.38 [10050]P39(x100501,f315(f315(f99(f909(f908(x100501,x100501),a899)),x100502),x100503))+~P39(x100501,f315(f315(f99(f909(f908(x100501,x100501),a899)),f315(f315(f99(f909(f908(x100501,x100501),a899)),f315(f315(f277(x100501,x100501,x100501),x100502),x100502)),f315(f315(f277(x100501,x100501,x100501),x100503),x100502))),x100503))
% 168.50/168.38 [9628]~P143(x96281)+E(f315(f91(x96281),f315(a82,f315(f273(f908(a901,a901),f908(a901,a901),a97),f315(f315(f297(f908(a901,a901)),f315(f315(f240(a901,a901),x96282),x96283)),f177(f909(f908(a901,a901),a899)))))),f315(f315(f3(x96281),f315(f89(x96281),x96282)),f315(f89(x96281),x96283)))
% 168.50/168.38 [9710]P1(f315(x97103,x97102))+E(f315(f250(x97101),f315(f315(f20(x97101,a899,a899),f315(f315(f10(a899,f909(a899,a899),x97101),a313),f315(f315(f9(x97101,x97101,a899),a312),x97102))),x97103)),f177(f909(x97101,a899)))
% 168.50/168.38 [9712]~P1(f315(x97123,x97122))+E(f315(f250(x97121),f315(f315(f20(x97121,a899,a899),f315(f315(f10(a899,f909(a899,a899),x97121),a313),f315(f315(f9(x97121,x97121,a899),a312),x97122))),x97123)),f315(f315(f297(x97121),x97122),f177(f909(x97121,a899))))
% 168.50/168.38 [9941]E(x99411,x99412)+P1(f315(f315(f231(x99413,x99413,f315(f315(f10(f909(x99413,a899),f909(x99413,a899),x99413),f315(f10(a899,a899,x99413),a310)),a312)),x99411),x99412))
% 168.50/168.38 [10030]~E(x100301,x100302)+~P1(f315(f315(f231(x100303,x100303,f315(f315(f10(f909(x100303,a899),f909(x100303,a899),x100303),f315(f10(a899,a899,x100303),a310)),a312)),x100301),x100302))
% 168.50/168.38 [10042]~P1(f315(f54(x100421),x100423))+E(f315(f315(f57(x100421,f909(x100421,a899),f315(f315(f10(f909(x100421,a899),f909(f909(x100421,a899),f909(x100421,a899)),x100421),f315(f9(f909(x100421,a899),f909(x100421,a899),f909(x100421,a899)),f3(f909(x100421,a899)))),f315(f315(f9(x100421,f909(x100421,a899),f909(x100421,a899)),f297(x100421)),f177(f909(x100421,a899))))),x100422),x100423),f315(f315(f3(f909(x100421,a899)),x100422),x100423))
% 168.50/168.38 [10072]~P1(f315(f315(f224(a1),f2(a1)),x100723))+P1(f315(f315(f224(a1),f315(f315(f3(a1),x100721),f315(f315(f74(a1),f315(f315(f73(a1),f315(f69(a1),f315(f315(f3(a1),x100721),x100722))),f71(a1))),x100723))),x100722))
% 168.50/168.38 [10333]~P1(f315(f315(f317(x103331),x103333),f304(x103331,x103332)))+P1(f315(f303(x103331,f315(f315(f9(x103331,f909(f908(x103331,x103331),a899),f909(x103331,a899)),f315(f315(f10(f909(x103331,f909(f909(f908(x103331,x103331),a899),a899)),f909(f909(f908(x103331,x103331),a899),f909(x103331,a899)),x103331),f9(x103331,f909(f908(x103331,x103331),a899),a899)),f315(f315(f10(f909(x103331,f908(x103331,x103331)),f909(x103331,f909(f909(f908(x103331,x103331),a899),a899)),x103331),f315(f10(f908(x103331,x103331),f909(f909(f908(x103331,x103331),a899),a899),x103331),f317(f908(x103331,x103331)))),f240(x103331,x103331)))),x103332)),x103333))
% 168.50/168.38 [10346]P1(f315(f315(f317(x103461),x103462),f304(x103461,x103463)))+~P1(f315(f303(x103461,f315(f315(f9(x103461,f909(f908(x103461,x103461),a899),f909(x103461,a899)),f315(f315(f10(f909(x103461,f909(f909(f908(x103461,x103461),a899),a899)),f909(f909(f908(x103461,x103461),a899),f909(x103461,a899)),x103461),f9(x103461,f909(f908(x103461,x103461),a899),a899)),f315(f315(f10(f909(x103461,f908(x103461,x103461)),f909(x103461,f909(f909(f908(x103461,x103461),a899),a899)),x103461),f315(f10(f908(x103461,x103461),f909(f909(f908(x103461,x103461),a899),a899),x103461),f317(f908(x103461,x103461)))),f240(x103461,x103461)))),x103463)),x103462))
% 168.50/168.38 [9913]~P1(f315(f54(x99131),f315(f250(x99131),x99133)))+P1(f315(f54(x99131),f315(f250(x99131),f315(f315(f20(x99131,a899,a899),f315(f315(f10(a899,f909(a899,a899),x99131),a313),x99132)),x99133))))
% 168.50/168.38 [9914]~P1(f315(f54(x99141),f315(f250(x99141),x99142)))+P1(f315(f54(x99141),f315(f250(x99141),f315(f315(f20(x99141,a899,a899),f315(f315(f10(a899,f909(a899,a899),x99141),a313),x99142)),x99143))))
% 168.50/168.38 [10009]P1(f315(f54(x100091),f315(f250(x100091),x100092)))+~P1(f315(f54(x100091),f315(f250(x100091),f315(f315(f20(x100091,a899,a899),f315(f315(f10(a899,f909(a899,a899),x100091),a314),x100093)),x100092))))
% 168.50/168.38 [10010]P1(f315(f54(x100101),f315(f250(x100101),x100102)))+~P1(f315(f54(x100101),f315(f250(x100101),f315(f315(f20(x100101,a899,a899),f315(f315(f10(a899,f909(a899,a899),x100101),a314),x100102)),x100103))))
% 168.50/168.38 [10312]~P1(f315(f54(x103121),x103122))+P1(f315(f54(f902(x103121)),f315(f250(f902(x103121)),f315(f315(f20(f902(x103121),a899,a899),f315(f315(f10(a899,f909(a899,a899),f902(x103121)),a313),f315(f315(f9(f902(x103121),f909(x103121,a899),a899),f315(f315(f10(f909(x103121,a899),f909(f909(x103121,a899),a899),f902(x103121)),f223(f909(x103121,a899))),f161(x103121))),x103122))),f315(f315(f9(f902(x103121),a901,a899),f315(f315(f10(a901,f909(a901,a899),f902(x103121)),a312),f178(f902(x103121)))),x103123)))))
% 168.50/168.38 [10313]~P1(f315(f54(x103131),x103132))+P1(f315(f54(f902(x103131)),f315(f250(f902(x103131)),f315(f315(f20(f902(x103131),a899,a899),f315(f315(f10(a899,f909(a899,a899),f902(x103131)),a313),f315(f315(f9(f902(x103131),f909(x103131,a899),a899),f315(f315(f10(f909(x103131,a899),f909(f909(x103131,a899),a899),f902(x103131)),f223(f909(x103131,a899))),f161(x103131))),x103132))),f315(f315(f9(f902(x103131),a901,a899),f315(f315(f10(a901,f909(a901,a899),f902(x103131)),f223(a901)),f178(f902(x103131)))),x103133)))))
% 168.50/168.38 [10023]~P121(x100231)+E(f315(f315(f232(x100231),x100232),f315(f315(f74(a901),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),x100233)),f315(f315(f74(x100231),f315(f315(f232(x100231),x100232),x100233)),f315(f315(f232(x100231),x100232),x100233)))
% 168.50/168.38 [10053]~P84(x100531)+E(f315(f315(f232(x100531),f315(f315(f232(x100531),x100532),x100533)),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),f315(f315(f232(x100531),x100532),f315(f315(f74(a901),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),x100533)))
% 168.50/168.38 [10109]~P143(x101091)+E(f315(f315(f232(x101091),f315(f72(x101091),x101092)),f315(f315(f74(a901),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),x101093)),f315(f315(f232(x101091),x101092),f315(f315(f74(a901),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),x101093)))
% 168.50/168.38 [10251]~P114(x102511)+P1(f315(f315(f223(x102511),f2(x102511)),f315(f315(f73(x102511),f315(f315(f232(x102511),x102512),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))))),f315(f315(f232(x102511),x102513),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))))))
% 168.50/168.38 [10119]~P121(x101191)+E(f315(f315(f232(x101191),x101192),f315(a101,f315(f315(f74(a901),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),x101193))),f315(f315(f74(x101191),x101192),f315(f315(f74(x101191),f315(f315(f232(x101191),x101192),x101193)),f315(f315(f232(x101191),x101192),x101193))))
% 168.50/168.38 [10169]~P84(x101691)+E(f315(f315(f74(x101691),x101692),f315(f315(f232(x101691),f315(f315(f232(x101691),x101692),x101693)),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))))),f315(f315(f232(x101691),x101692),f315(a101,f315(f315(f74(a901),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),x101693))))
% 168.50/168.38 [10208]~P114(x102081)+P1(f315(f315(f223(x102081),f2(x102081)),f315(f315(f232(x102081),x102082),f315(f315(f74(a901),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),x102083))))
% 168.50/168.38 [10288]~P97(x102881)+E(f315(f315(f3(x102881),f315(f315(f73(x102881),f315(f315(f232(x102881),x102882),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))))),f315(f315(f232(x102881),x102883),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))))),f315(f315(f74(x102881),f315(f315(f74(x102881),f315(f92(x102881),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),x102882)),x102883)),f315(f315(f232(x102881),f315(f315(f3(x102881),x102882),x102883)),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))))
% 168.50/168.38 [10289]~P97(x102891)+E(f315(f315(f73(x102891),f315(f315(f73(x102891),f315(f315(f232(x102891),x102892),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))))),f315(f315(f232(x102891),x102893),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))))),f315(f315(f74(x102891),f315(f315(f74(x102891),f315(f92(x102891),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),x102892)),x102893)),f315(f315(f232(x102891),f315(f315(f73(x102891),x102892),x102893)),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))))
% 168.50/168.38 [7911]P25(x79111,x79112,x79113,x79114)+~E(f471(x79114,x79113,x79112,x79111),f481(x79114,x79113,x79112,x79111))
% 168.50/168.38 [8204]P36(x82041,x82042,x82043,x82044,f102(x82042))+~E(x82044,f102(x82041))
% 168.50/168.38 [8205]P36(x82051,x82052,x82053,f102(x82051),x82054)+~E(x82054,f102(x82052))
% 168.50/168.38 [8745]~P36(x87452,x87453,x87454,x87451,f102(x87453))+E(x87451,f102(x87452))
% 168.50/168.38 [8746]~P36(x87463,x87462,x87464,f102(x87463),x87461)+E(x87461,f102(x87462))
% 168.50/168.38 [5140]~P18(x51403,x51401,x51404)+E(f315(f315(x51401,x51402),x51402),x51402)
% 168.50/168.38 [5388]P1(f315(x53882,x53884))+E(f315(f125(x53881,x53882),f158(x53881,x53883,x53884)),f102(x53881))
% 168.50/168.38 [5425]~E(x54254,f177(f909(x54251,a899)))+E(f315(f298(x54251,x54252,x54253),x54254),f177(f909(x54252,a899)))
% 168.50/168.38 [5673]~P1(f315(x56732,x56734))+E(f315(f125(x56731,x56732),f158(x56731,x56733,x56734)),f158(x56731,x56733,x56734))
% 168.50/168.38 [5704]~E(f315(f298(x57042,x57043,x57044),x57041),f177(f909(x57043,a899)))+E(x57041,f177(f909(x57042,a899)))
% 168.50/168.38 [5891]~P7(x58911,x58913)+E(f259(x58911,x58912,f258(x58911,x58913),x58914),x58914)
% 168.50/168.38 [6007]~P110(x60072)+E(f315(f315(f137(x60071,x60072,x60073),x60074),f102(x60071)),f315(f315(f140(x60071),x60074),f102(x60071)))
% 168.50/168.38 [6374]~E(x63741,f177(f909(x63742,a899)))+~P1(f315(f55(x63742,x63743,x63741),x63744))
% 168.50/168.38 [6396]~P60(x63961,x63963,x63964,x63962)+P1(f315(f54(x63961),x63962))
% 168.50/168.38 [6398]~P60(x63981,x63983,x63982,x63984)+P1(f315(f54(x63981),x63982))
% 168.50/168.38 [6406]~P60(x64062,x64063,x64064,x64061)+~E(x64061,f177(f909(x64062,a899)))
% 168.50/168.38 [6440]~P111(x64401)+E(f315(f315(f90(f909(x64401,a899)),f315(f290(x64401,x64402),x64403)),f291(x64401,x64403,x64404)),f177(f909(x64401,a899)))
% 168.50/168.38 [6468]~P1(f315(f315(x64683,x64684),x64682))+P1(f315(f315(f317(x64681),x64682),f282(x64681,x64683,x64684)))
% 168.50/168.38 [6469]~P1(f315(f315(x64693,x64694),x64692))+P1(f315(f315(f317(x64691),x64692),f283(x64691,x64693,x64694)))
% 168.50/168.38 [6470]~P1(f315(f315(x64703,x64702),x64704))+P1(f315(f315(f317(x64701),x64702),f284(x64701,x64703,x64704)))
% 168.50/168.38 [6471]~P1(f315(f315(x64713,x64712),x64714))+P1(f315(f315(f317(x64711),x64712),f286(x64711,x64713,x64714)))
% 168.50/168.38 [6618]~P111(x66181)+E(f315(f315(f90(f909(x66181,a899)),f291(x66181,x66182,x66183)),f294(x66181,x66183,x66184)),f177(f909(x66181,a899)))
% 168.50/168.38 [6619]~P111(x66191)+E(f315(f315(f90(f909(x66191,a899)),f291(x66191,x66192,x66193)),f293(x66191,x66193,x66194)),f177(f909(x66191,a899)))
% 168.50/168.38 [6620]~P111(x66201)+E(f315(f315(f90(f909(x66201,a899)),f294(x66201,x66202,x66203)),f291(x66201,x66203,x66204)),f177(f909(x66201,a899)))
% 168.50/168.38 [6621]~P111(x66211)+E(f315(f315(f90(f909(x66211,a899)),f293(x66211,x66212,x66213)),f294(x66211,x66213,x66214)),f177(f909(x66211,a899)))
% 168.50/168.38 [6622]~P111(x66221)+E(f315(f315(f90(f909(x66221,a899)),f293(x66221,x66222,x66223)),f293(x66221,x66223,x66224)),f177(f909(x66221,a899)))
% 168.50/168.38 [6660]P1(f315(f315(x66601,x66602),f551(x66602,x66601)))+~P1(f315(f237(x66603,x66604,x66601),x66602))
% 168.50/168.38 [6742]~P110(x67422)+E(f315(f161(x67421),f139(x67421,x67422,x67423,x67424)),f315(f161(x67421),x67424))
% 168.50/168.38 [6794]~P147(x67941)+E(f179(x67941,x67942,f315(a101,x67943),x67944),f179(x67941,x67942,x67943,f315(x67942,x67944)))
% 168.50/168.38 [6858]~P1(f315(f315(f317(x68584),x68583),f282(x68584,x68581,x68582)))+P1(f315(f315(x68581,x68582),x68583))
% 168.50/168.38 [6859]~P1(f315(f315(f317(x68594),x68593),f283(x68594,x68591,x68592)))+P1(f315(f315(x68591,x68592),x68593))
% 168.50/168.38 [6860]~P1(f315(f315(f317(x68604),x68602),f284(x68604,x68601,x68603)))+P1(f315(f315(x68601,x68602),x68603))
% 168.50/168.38 [6861]~P1(f315(f315(f317(x68614),x68612),f286(x68614,x68611,x68613)))+P1(f315(f315(x68611,x68612),x68613))
% 168.50/168.38 [6939]E(f315(f28(f907(x69391,x69392)),f301(x69391,x69392,x69393,x69394)),f2(a901))+P1(f315(f54(x69392),x69394))
% 168.50/168.38 [6940]E(f315(f28(f907(x69401,x69402)),f301(x69401,x69402,x69403,x69404)),f2(a901))+P1(f315(f54(x69401),x69403))
% 168.50/168.38 [7148]~P15(x71484,x71481,x71482)+E(f315(f66(x71481,x71481,x71481,f315(x71482,x71483)),f315(x71482,x71483)),f315(x71482,x71483))
% 168.50/168.38 [7391]E(f265(x73911,x73912,x73913,x73914),f315(f240(f909(a88,f909(a899,f905(f903(x73911)))),f908(a88,a88)),f34(x73911)))+~P1(f315(f315(f223(a88),x73913),f2(a88)))
% 168.50/168.38 [8034]~E(x80342,x80343)+P1(f315(f315(f317(f908(x80341,x80341)),f315(f315(f240(x80341,x80341),x80342),x80343)),f295(x80341,x80344)))
% 168.50/168.38 [8063]~P25(x80631,x80632,x80633,f230(f909(x80631,a899)))+E(f315(f70(x80631,x80632,f230(f909(x80631,a899)),x80633),f315(x80633,x80634)),x80634)
% 168.50/168.38 [8064]~P25(x80641,x80642,x80643,f230(f909(x80641,a899)))+E(f315(f84(x80641,x80642,f230(f909(x80641,a899)),x80643),f315(x80643,x80644)),x80644)
% 168.50/168.38 [8152]~P1(f315(f315(f317(f902(x81521)),f315(f315(f140(x81521),x81524),x81522)),f150(x81521,x81523)))+P1(f315(f315(f317(f902(x81521)),x81522),f150(x81521,x81523)))
% 168.50/168.38 [8153]~P1(f315(f315(f317(f902(x81531)),f315(f315(f123(x81531),x81534),x81532)),f150(x81531,x81533)))+P1(f315(f315(f317(f902(x81531)),x81532),f150(x81531,x81533)))
% 168.50/168.38 [8154]~P1(f315(f315(f317(f902(x81541)),f315(f315(f123(x81541),x81542),x81544)),f150(x81541,x81543)))+P1(f315(f315(f317(f902(x81541)),x81542),f150(x81541,x81543)))
% 168.50/168.38 [8165]~P110(x81651)+P13(x81651,f315(f315(f143(x81652,x81651),x81653),f139(x81652,x81651,x81653,x81654)))
% 168.50/168.38 [8272]P25(x82724,x82723,x82721,x82722)+E(f315(x82721,f471(x82722,x82721,x82723,x82724)),f315(x82721,f481(x82722,x82721,x82723,x82724)))
% 168.50/168.38 [8378]~P25(x83782,x83781,x83784,x83783)+P25(x83781,x83782,f70(x83782,x83781,x83783,x83784),f315(f298(x83782,x83781,x83784),x83783))
% 168.50/168.38 [8518]P39(f908(x85182,x85184),f268(x85182,x85184,x85181,x85183))+P1(f315(x85181,f557(x85182,x85183,x85184,x85181)))
% 168.50/168.38 [8633]E(x86331,x86332)+~P1(f315(f315(f317(f908(x86333,x86333)),f315(f315(f240(x86333,x86333),x86331),x86332)),f251(x86333,x86334)))
% 168.50/168.38 [8697]~P1(f315(f54(f907(x86973,x86971)),f301(x86973,x86971,x86974,x86972)))+P1(f315(f54(x86971),x86972))
% 168.50/168.38 [8698]~P1(f315(f54(f907(x86981,x86983)),f301(x86981,x86983,x86982,x86984)))+P1(f315(f54(x86981),x86982))
% 168.50/168.38 [8707]~P25(x87071,x87072,x87073,x87074)+P26(x87071,x87072,x87073,x87074,f315(f298(x87071,x87072,x87073),x87074))
% 168.50/168.38 [8708]P11(x87081,x87082,x87083,x87084)+~E(f315(x87084,f813(x87082,x87084,x87083,x87081)),f315(x87084,f814(x87082,x87084,x87083,x87081)))
% 168.50/168.38 [8798]~P26(x87982,x87983,x87984,x87981,f177(f909(x87983,a899)))+E(x87981,f177(f909(x87982,a899)))
% 168.50/168.38 [8799]~P26(x87993,x87992,x87994,f177(f909(x87993,a899)),x87991)+E(x87991,f177(f909(x87992,a899)))
% 168.50/168.38 [8891]P39(f908(x88911,x88912),f268(x88911,x88912,x88913,x88914))+~P39(x88912,f315(x88914,f557(x88911,x88914,x88912,x88913)))
% 168.50/168.38 [9457]E(f315(f315(f148(x94571,x94572),f652(x94573,x94574,x94572,x94571)),f653(x94573,x94574,x94572,x94571)),x94574)+~P1(f315(f315(f317(f908(f902(x94571),f902(x94571))),f315(f315(f240(f902(x94571),f902(x94571)),x94572),x94574)),f146(x94571,x94573)))
% 168.50/168.38 [9462]~P1(f315(f315(f317(f908(f902(x94621),f902(x94621))),f315(f315(f240(f902(x94621),f902(x94621)),x94622),x94623)),f134(x94621,x94624)))+P1(f315(f315(f317(f908(f902(x94621),f902(x94621))),f315(f315(f240(f902(x94621),f902(x94621)),x94622),x94623)),f136(x94621,x94624)))
% 168.50/168.38 [9574]P1(f315(f54(x95741),x95742))+~P1(f315(f315(f317(f908(f909(x95741,a899),f909(x95741,a899))),f315(f315(f240(f909(x95741,a899),f909(x95741,a899)),x95743),x95742)),f306(x95741,x95744)))
% 168.50/168.38 [9575]P1(f315(f54(x95751),x95752))+~P1(f315(f315(f317(f908(f909(x95751,a899),f909(x95751,a899))),f315(f315(f240(f909(x95751,a899),f909(x95751,a899)),x95752),x95753)),f306(x95751,x95754)))
% 168.50/168.38 [9578]~E(x95781,f177(f909(x95782,a899)))+~P1(f315(f315(f317(f908(f909(x95782,a899),f909(x95782,a899))),f315(f315(f240(f909(x95782,a899),f909(x95782,a899)),x95783),x95781)),f306(x95782,x95784)))
% 168.50/168.38 [10219]P11(x102191,x102192,x102193,x102194)+~P1(f315(f315(f245(x102191,x102191,a899),f315(f315(f9(x102191,f909(x102191,x102192),f909(x102191,a899)),f315(f315(f10(f909(x102192,a899),f909(f909(x102191,x102192),f909(x102191,a899)),x102191),f10(x102192,a899,x102191)),f315(f315(f10(x102192,f909(x102192,a899),x102191),a312),x102194))),x102194)),f474(x102194,x102193,x102192,x102191)))
% 168.50/168.38 [5038]~E(x50382,f102(x50381))+E(f315(f315(f148(x50381,x50382),x50383),x50384),f102(x50381))
% 168.50/168.38 [5039]~E(x50394,f102(x50391))+E(f315(f315(f143(x50391,x50392),x50393),x50394),f102(x50392))
% 168.50/168.38 [5273]E(x52731,f102(x52732))+~E(f315(f315(f143(x52732,x52733),x52734),x52731),f102(x52733))
% 168.50/168.38 [5274]E(x52741,f102(x52742))+~E(f315(f315(f148(x52742,x52741),x52743),x52744),f102(x52742))
% 168.50/168.38 [5312]E(x53121,x53122)+~E(f315(f315(f123(x53123),x53124),x53121),f315(f315(f123(x53123),x53124),x53122))
% 168.50/168.38 [5313]E(x53131,x53132)+~E(f315(f315(f123(x53133),x53131),x53134),f315(f315(f123(x53133),x53132),x53134))
% 168.50/168.38 [5462]P1(f315(x54623,x54622))+E(f159(x54621,x54622,f315(f125(x54621,x54623),x54624)),f315(f125(x54621,x54623),x54624))
% 168.50/168.38 [5464]~P1(f315(x54642,x54643))+P35(x54641,x54642,f315(f315(f140(x54641),x54643),x54644))
% 168.50/168.38 [5474]E(x54741,x54742)+~E(f128(a901,f315(f290(a901,x54741),x54743)),f315(f315(f140(a901),x54742),x54744))
% 168.50/168.38 [5523]~P27(x55232,x55233)+P27(x55231,f315(f315(f67(x55232,x55231),x55233),x55234))
% 168.50/168.38 [5524]~P39(x55242,x55243)+P39(x55241,f315(f315(f276(x55242,x55241),x55243),x55244))
% 168.50/168.38 [5525]~P40(x55252,x55253)+P40(x55251,f315(f315(f276(x55252,x55251),x55253),x55254))
% 168.50/168.38 [5526]~P53(x55262,x55263)+P53(x55261,f315(f315(f276(x55262,x55261),x55263),x55264))
% 168.50/168.38 [5657]~P35(x56571,x56572,x56574)+P35(x56571,x56572,f315(f315(f140(x56571),x56573),x56574))
% 168.50/168.38 [5658]~P35(x56581,x56582,x56584)+P35(x56581,x56582,f315(f315(f123(x56581),x56583),x56584))
% 168.50/168.38 [5659]~P35(x56591,x56592,x56593)+P35(x56591,x56592,f315(f315(f123(x56591),x56593),x56594))
% 168.50/168.38 [5747]~E(x57471,f102(x57472))+~E(f315(f315(f123(x57472),x57473),f315(f315(f140(x57472),x57474),f102(x57472))),x57471)
% 168.50/168.38 [5772]~P33(x57723,x57721,f315(f315(f140(x57723),x57722),x57724))+P1(f315(x57721,x57722))
% 168.50/168.38 [5782]E(f103(x57821,x57822),x57823)+~E(f315(f315(f123(x57821),x57823),f315(f315(f140(x57821),x57824),f102(x57821))),x57822)
% 168.50/168.38 [5783]E(f133(x57831,x57832),x57833)+~E(f315(f315(f123(x57831),x57834),f315(f315(f140(x57831),x57833),f102(x57831))),x57832)
% 168.50/168.38 [5893]~E(f128(a901,f315(f290(a901,x58931),x58932)),f315(f315(f140(a901),x58933),x58934))+P1(f315(f315(f224(a901),x58931),x58932))
% 168.50/168.38 [5911]P33(x59111,x59112,x59113)+~P33(x59111,x59112,f315(f315(f140(x59111),x59114),x59113))
% 168.50/168.38 [5912]P33(x59121,x59122,x59123)+~P33(x59121,x59122,f315(f315(f123(x59121),x59124),x59123))
% 168.50/168.38 [5913]P33(x59131,x59132,x59133)+~P33(x59131,x59132,f315(f315(f123(x59131),x59133),x59134))
% 168.50/168.38 [6112]E(x61121,f315(f315(f123(x61122),f315(f157(x61122),x61123)),f315(f315(f140(x61122),x61124),f102(x61122))))+~E(f315(f157(x61122),x61121),f315(f315(f140(x61122),x61124),x61123))
% 168.50/168.38 [6294]~P111(x62941)+E(f315(f315(f90(f909(x62941,a899)),f315(f290(x62941,x62942),x62943)),f315(f290(x62941,x62943),x62944)),f177(f909(x62941,a899)))
% 168.50/168.38 [6305]E(f315(f315(f153(x63051),f158(x63051,x63052,x63053)),x63054),x63053)+~P1(f315(f315(f224(a901),x63054),x63052))
% 168.50/168.38 [6332]~P72(x63321)+E(f315(f154(x63321),f315(f315(f143(a1,x63321),x63322),f167(x63323,x63324))),f315(f315(f8(a1,x63321),x63322),f315(f161(a1),f167(x63323,x63324))))
% 168.50/168.38 [6333]~P72(x63331)+E(f315(f315(f8(a1,x63331),x63332),f315(f161(a1),f167(x63333,x63334))),f315(f154(x63331),f315(f315(f143(a1,x63331),x63332),f167(x63333,x63334))))
% 168.50/168.38 [6481]~E(x64812,f315(f315(f123(x64811),f315(f157(x64811),x64814)),f315(f315(f140(x64811),x64813),f102(x64811))))+E(f315(f157(x64811),x64812),f315(f315(f140(x64811),x64813),x64814))
% 168.50/168.38 [6497]~P20(x64972,x64973,x64974,x64971)+E(f315(x64971,f177(f909(x64972,a899))),f25(x64973))
% 168.50/168.38 [6526]~P111(x65261)+E(f315(f315(f90(f909(x65261,a899)),f294(x65261,x65262,x65263)),f315(f290(x65261,x65263),x65264)),f177(f909(x65261,a899)))
% 168.50/168.38 [6745]E(x67451,f177(f909(x67452,a899)))+~E(f301(x67453,x67452,x67454,x67451),f177(f909(f907(x67453,x67452),a899)))
% 168.50/168.38 [6746]E(x67461,f177(f909(x67462,a899)))+~E(f301(x67462,x67463,x67461,x67464),f177(f909(f907(x67462,x67463),a899)))
% 168.50/168.38 [6815]~P110(x68152)+E(f315(f178(f902(x68151)),f139(x68151,x68152,x68153,x68154)),f315(f178(f902(x68151)),x68154))
% 168.50/168.38 [6826]~P1(f315(f238(x68263,x68264,x68261),x68262))+P1(f315(f315(x68261,f540(x68262,x68261)),x68262))
% 168.50/168.38 [6872]~P1(f315(f54(x68722),x68724))+P1(f315(f54(x68721),f315(f298(x68722,x68721,x68723),x68724)))
% 168.50/168.38 [7108]~P25(x71082,x71081,x71083,x71084)+E(f315(f28(x71081),f315(f298(x71082,x71081,x71083),x71084)),f315(f28(x71082),x71084))
% 168.50/168.38 [7126]E(f315(f298(x71261,x71262,x71263),f315(f299(x71261,x71262,x71263),x71264)),x71264)+~E(f315(f298(x71261,x71262,x71263),f230(f909(x71261,a899))),f230(f909(x71262,a899)))
% 168.50/168.38 [7545]~P25(x75451,x75452,x75453,f230(f909(x75451,a899)))+E(f315(f299(x75451,x75452,x75453),f315(f298(x75451,x75452,x75453),x75454)),x75454)
% 168.50/168.38 [7829]E(x78291,x78292)+~P1(f315(f315(f317(x78293),x78291),f315(f161(x78293),f158(x78293,x78294,x78292))))
% 168.50/168.38 [7838]~E(x78381,f2(a901))+~P1(f315(f315(f317(x78382),x78383),f315(f161(x78382),f158(x78382,x78381,x78384))))
% 168.50/168.38 [7871]P1(f315(x78711,x78712))+~P1(f315(f315(f317(x78713),x78712),f315(f161(x78713),f166(x78713,x78711,x78714))))
% 168.50/168.38 [7980]~P1(f315(f315(f317(f902(x79801)),f315(f315(f140(x79801),x79802),x79804)),f150(x79801,x79803)))+P1(f315(f315(f317(x79801),x79802),x79803))
% 168.50/168.38 [8109]~P1(f315(f315(f317(x81091),x81092),f315(f161(x81091),f165(x81091,x81093,x81094))))+P1(f315(f315(f317(x81091),x81092),f315(f161(x81091),x81093)))
% 168.50/168.38 [8110]~P1(f315(f315(f317(x81101),x81102),f315(f161(x81101),f159(x81101,x81104,x81103))))+P1(f315(f315(f317(x81101),x81102),f315(f161(x81101),x81103)))
% 168.50/168.38 [8111]~P1(f315(f315(f317(x81111),x81112),f315(f161(x81111),f166(x81111,x81114,x81113))))+P1(f315(f315(f317(x81111),x81112),f315(f161(x81111),x81113)))
% 168.50/168.38 [8121]E(f315(f178(f902(x81211)),x81212),x81213)+~P1(f315(f315(f317(f902(x81211)),x81212),f315(f161(f902(x81211)),f48(x81211,x81213,x81214))))
% 168.50/168.38 [8217]P1(f315(x82173,x82172))+E(f315(f125(x82171,f315(f315(f10(a899,a899,x82171),a310),f315(a312,x82172))),f315(f125(x82171,x82173),x82174)),f315(f125(x82171,x82173),x82174))
% 168.50/168.38 [8330]E(f315(f315(f153(x83301),f166(x83301,x83302,x83303)),x83304),f315(f315(f153(x83301),x83303),x83304))+~P1(f315(f315(f224(a901),x83304),f315(f178(f902(x83301)),f166(x83301,x83302,x83303))))
% 168.50/168.38 [8416]~P72(x84161)+E(f315(f315(f8(a901,x84161),f315(f315(f10(a901,x84161,a901),x84162),a101)),f315(f290(a901,x84163),x84164)),f315(f315(f8(a901,x84161),x84162),f315(f290(a901,f315(a101,x84163)),f315(a101,x84164))))
% 168.50/168.38 [8425]~P72(x84251)+E(f315(f315(f8(a901,x84251),f315(f315(f10(a901,x84251,a901),x84252),a101)),f291(a901,x84253,x84254)),f315(f315(f8(a901,x84251),x84252),f291(a901,f315(a101,x84253),f315(a101,x84254))))
% 168.50/168.38 [8554]~P25(x85541,x85543,x85544,f230(f909(x85541,a899)))+P25(x85541,f909(x85542,x85543),f315(f315(f10(x85543,f909(x85542,x85543),x85541),f18(x85543,x85542)),x85544),f230(f909(x85541,a899)))
% 168.50/168.38 [8639]~P25(x86392,x86391,x86394,x86393)+E(f315(f298(x86391,x86392,f70(x86392,x86391,x86393,x86394)),f315(f298(x86392,x86391,x86394),x86393)),x86393)
% 168.50/168.38 [8699]~P1(f315(f315(f317(f908(x86991,x86991)),f315(f315(f240(x86991,x86991),x86992),x86994)),f251(x86991,x86993)))+P1(f315(f315(f317(x86991),x86992),x86993))
% 168.50/168.38 [8822]~P25(x88222,x88221,x88223,f230(f909(x88222,a899)))+E(f315(f298(x88221,x88222,f84(x88222,x88221,f230(f909(x88222,a899)),x88223)),f315(f298(x88222,x88221,x88223),x88224)),x88224)
% 168.50/168.38 [8897]~P26(x88971,x88972,x88973,x88974,f230(f909(x88972,a899)))+E(f315(f298(x88971,x88972,x88973),f230(f909(x88971,a899))),f230(f909(x88972,a899)))
% 168.50/168.38 [8930]~E(f315(f315(f8(x89301,a901),x89304),x89303),f315(a101,x89302))+P1(f315(f315(f317(x89301),f879(x89302,x89303,x89304,x89301)),x89303))
% 168.50/168.38 [8951]~E(f315(f315(f8(x89514,a901),x89511),x89513),f315(a101,x89512))+P1(f315(f315(f224(a901),f2(a901)),f315(x89511,f879(x89512,x89513,x89511,x89514))))
% 168.50/168.38 [8962]~P1(f315(f54(x89622),x89624))+P1(f315(f315(f223(a901),f315(f28(x89621),f315(f298(x89622,x89621,x89623),x89624))),f315(f28(x89622),x89624)))
% 168.50/168.38 [8963]E(f315(f315(f240(x89631,x89632),f623(x89633,x89634,x89632,x89631)),f624(x89633,x89634,x89632,x89631)),x89634)+~P1(f315(f315(f317(f908(x89631,x89632)),x89634),f315(f274(x89632,x89631),x89633)))
% 168.50/168.38 [8971]P25(x89711,x89712,x89713,x89714)+P1(f315(f315(f317(x89711),f471(x89714,x89713,x89712,x89711)),x89714))
% 168.50/168.38 [8972]P25(x89721,x89722,x89723,x89724)+P1(f315(f315(f317(x89721),f481(x89724,x89723,x89722,x89721)),x89724))
% 168.50/168.38 [9041]P11(x90411,x90412,x90413,x90414)+P1(f315(f315(f317(f908(x90411,x90411)),f474(x90414,x90413,x90412,x90411)),x90413))
% 168.50/168.38 [9095]P1(f315(x90951,x90952))+~P1(f315(x90951,f315(f315(f240(x90953,x90954),f382(x90954,x90953,x90951)),f383(x90954,x90953,x90951))))
% 168.50/168.38 [9112]E(f315(f178(f902(x91121)),x91122),f315(f178(f902(x91121)),x91123))+~P1(f315(f315(f317(f908(f902(x91121),f902(x91121))),f315(f315(f240(f902(x91121),f902(x91121)),x91122),x91123)),f134(x91121,x91124)))
% 168.50/168.38 [9113]E(f315(f178(f902(x91131)),x91132),f315(f178(f902(x91131)),x91133))+~P1(f315(f315(f317(f908(f902(x91131),f902(x91131))),f315(f315(f240(f902(x91131),f902(x91131)),x91132),x91133)),f146(x91131,x91134)))
% 168.50/168.38 [9116]E(f315(f178(f902(x91161)),x91162),f315(f178(f902(x91161)),x91163))+~P1(f315(f315(f317(f908(f902(x91161),f902(x91161))),f315(f315(f240(f902(x91161),f902(x91161)),x91162),x91163)),f147(x91161,x91164)))
% 168.50/168.38 [9185]P1(f315(f315(f223(a901),f144(x91851,x91852,x91853)),f144(x91851,x91854,x91853)))+P1(f315(f315(f317(x91851),f651(x91854,x91852,x91853,x91851)),f315(f161(x91851),x91853)))
% 168.50/168.38 [9188]E(f315(f178(f902(x91881)),x91882),f315(f178(f902(x91881)),x91883))+~P1(f315(f315(f317(f908(f902(x91881),f902(x91881))),f315(f315(f240(f902(x91881),f902(x91881)),x91882),x91883)),f295(f902(x91881),f146(x91881,x91884))))
% 168.50/168.38 [9306]P1(f315(f315(f275(a901),x93061),x93062))+P1(f315(f315(f223(f909(a901,a899)),f278(a901,f275(a901),x93061,x93062)),f278(a901,f275(a901),x93063,x93064)))
% 168.50/168.38 [9428]~P25(x94281,x94282,x94283,x94284)+~P1(f315(f315(f224(a901),f315(f28(x94282),f315(f298(x94281,x94282,x94283),x94284))),f315(f28(x94281),x94284)))
% 168.50/168.38 [9475]~P1(f315(f315(f317(f908(f902(x94751),f902(x94751))),f315(f315(f240(f902(x94751),f902(x94751)),x94752),x94753)),f146(x94751,x94754)))+P1(f315(f315(f317(f908(f902(x94751),f902(x94751))),f315(f315(f240(f902(x94751),f902(x94751)),x94752),x94753)),f147(x94751,f295(x94751,x94754))))
% 168.50/168.38 [9479]~P1(f315(f315(f317(f908(f902(x94791),f902(x94791))),f315(f315(f240(f902(x94791),f902(x94791)),x94792),x94793)),f147(x94791,x94794)))+P1(f315(f315(f317(f908(f902(x94791),f902(x94791))),f315(f315(f240(f902(x94791),f902(x94791)),x94792),x94793)),f295(f902(x94791),f146(x94791,x94794))))
% 168.50/168.38 [9495]P1(f315(f315(f317(f908(x94951,x94951)),f315(f315(f240(x94951,x94951),x94952),x94953)),f295(x94951,x94954)))+~P1(f315(f315(f317(f908(x94951,x94951)),f315(f315(f240(x94951,x94951),x94952),x94953)),f315(f315(f277(x94951,x94951,x94951),x94954),f295(x94951,x94954))))
% 168.50/168.38 [9569]P1(f315(f315(f275(a901),x95691),x95692))+~P1(f315(f315(f224(f909(a901,a899)),f278(a901,f275(a901),x95693,x95694)),f278(a901,f275(a901),x95691,x95692)))
% 168.50/168.38 [9691]E(f315(f315(f123(x96911),f667(x96912,x96913,x96914,x96911)),f315(f315(f140(x96911),f666(x96912,x96913,x96914,x96911)),f669(x96912,x96913,x96914,x96911))),x96914)+~P1(f315(f315(f317(f908(f902(x96911),f902(x96911))),f315(f315(f240(f902(x96911),f902(x96911)),x96914),x96913)),f146(x96911,x96912)))
% 168.50/168.38 [9692]E(f315(f315(f123(x96921),f667(x96922,x96923,x96924,x96921)),f315(f315(f140(x96921),f668(x96922,x96923,x96924,x96921)),f669(x96922,x96923,x96924,x96921))),x96923)+~P1(f315(f315(f317(f908(f902(x96921),f902(x96921))),f315(f315(f240(f902(x96921),f902(x96921)),x96924),x96923)),f146(x96921,x96922)))
% 168.50/168.38 [9770]P1(f315(f315(f317(f908(x97701,x97701)),f315(f315(f240(x97701,x97701),x97702),f614(x97703,x97704,x97702,x97701))),f295(x97701,x97703)))+~P1(f315(f315(f317(f908(x97701,x97701)),f315(f315(f240(x97701,x97701),x97702),x97704)),f315(f315(f277(x97701,x97701,x97701),x97703),f295(x97701,x97703))))
% 168.50/168.38 [9838]P1(f315(f315(f223(a901),f144(x98381,x98382,x98383)),f144(x98381,x98384,x98383)))+~P1(f315(f315(f224(a901),f315(x98382,f651(x98384,x98382,x98383,x98381))),f315(x98384,f651(x98384,x98382,x98383,x98381))))
% 168.50/168.38 [9909]P1(f315(f315(f317(f908(x99091,x99091)),f315(f315(f240(x99091,x99091),f622(x99092,x99093,x99094,x99091)),x99093)),f295(x99091,x99092)))+~P1(f315(f315(f317(f908(x99091,x99091)),f315(f315(f240(x99091,x99091),x99094),x99093)),f315(f315(f277(x99091,x99091,x99091),x99092),f295(x99091,x99092))))
% 168.50/168.38 [5293]~E(x52932,x52933)+E(f159(x52931,x52932,f315(f315(f140(x52931),x52933),x52934)),x52934)
% 168.50/168.38 [5418]P1(f315(x54182,x54183))+E(f166(x54181,x54182,f315(f315(f140(x54181),x54183),x54184)),f102(x54181))
% 168.50/168.38 [5486]~P92(x54862)+E(f315(f315(f72(f909(x54861,x54862)),x54863),x54864),f315(f72(x54862),f315(x54863,x54864)))
% 168.50/168.38 [5499]~E(x54992,f2(a901))+E(f315(f315(f127(x54991),x54992),f315(f315(f140(x54991),x54993),x54994)),f315(f315(f140(x54991),x54993),x54994))
% 168.50/168.38 [5500]P1(f315(x55002,x55003))+E(f315(f125(x55001,x55002),f315(f315(f140(x55001),x55003),x55004)),f315(f125(x55001,x55002),x55004))
% 168.50/168.38 [5640]~E(x56402,x56404)+P1(f315(f315(f315(f297(x56401),x56402),x56403),x56404))
% 168.50/168.38 [5648]E(x56481,f102(x56482))+E(f133(x56483,f315(f315(f143(x56482,x56483),x56484),x56481)),f315(x56484,f133(x56482,x56481)))
% 168.50/168.38 [5662]~E(x56621,f56(x56622,x56624))+E(f315(x56621,f315(f315(f297(x56622),x56623),f177(f909(x56622,a899)))),x56623)
% 168.50/168.38 [5699]E(x56991,f102(x56992))+E(f315(f130(x56993),f315(f315(f143(x56992,x56993),x56994),x56991)),f315(x56994,f315(f130(x56992),x56991)))
% 168.50/168.38 [5802]~P1(f315(x58023,x58024))+P1(f315(f315(f315(f297(x58021),x58022),x58023),x58024))
% 168.50/168.38 [5930]~P19(x59302,x59304,x59301)+E(f315(x59301,f315(f315(f297(x59302),x59303),f177(f909(x59302,a899)))),x59303)
% 168.50/168.38 [5956]~E(x59562,x59563)+P1(f315(f315(f317(x59561),x59562),f315(f315(f297(x59561),x59563),x59564)))
% 168.50/168.38 [5961]~P80(x59611)+E(f315(f315(f99(x59611),x59612),f315(f315(f99(x59611),x59613),x59614)),f315(f315(f99(x59611),x59613),f315(f315(f99(x59611),x59612),x59614)))
% 168.50/168.38 [5963]~P103(x59631)+E(f315(f315(f99(x59631),x59632),f315(f315(f99(x59631),x59633),x59634)),f315(f315(f99(x59631),x59633),f315(f315(f99(x59631),x59632),x59634)))
% 168.50/168.38 [5964]~P121(x59641)+E(f315(f315(f74(x59641),x59642),f315(f315(f74(x59641),x59643),x59644)),f315(f315(f74(x59641),x59643),f315(f315(f74(x59641),x59642),x59644)))
% 168.50/168.38 [5965]~P80(x59651)+E(f315(f315(f90(x59651),x59652),f315(f315(f90(x59651),x59653),x59654)),f315(f315(f90(x59651),x59653),f315(f315(f90(x59651),x59652),x59654)))
% 168.50/168.38 [5967]~P104(x59671)+E(f315(f315(f90(x59671),x59672),f315(f315(f90(x59671),x59673),x59674)),f315(f315(f90(x59671),x59673),f315(f315(f90(x59671),x59672),x59674)))
% 168.50/168.38 [5968]~P121(x59681)+E(f315(f315(f73(x59681),x59682),f315(f315(f73(x59681),x59683),x59684)),f315(f315(f73(x59681),x59683),f315(f315(f73(x59681),x59682),x59684)))
% 168.50/168.38 [5970]~P110(x59701)+E(f315(f315(f221(x59701),x59702),f315(f315(f221(x59701),x59703),x59704)),f315(f315(f221(x59701),x59703),f315(f315(f221(x59701),x59702),x59704)))
% 168.50/168.38 [5972]~P110(x59721)+E(f315(f315(f222(x59721),x59722),f315(f315(f222(x59721),x59723),x59724)),f315(f315(f222(x59721),x59723),f315(f315(f222(x59721),x59722),x59724)))
% 168.50/168.38 [5979]E(x59791,x59792)+E(f159(x59793,x59791,f315(f315(f140(x59793),x59792),x59794)),f315(f315(f140(x59793),x59792),f159(x59793,x59791,x59794)))
% 168.50/168.38 [5994]~P1(f315(x59942,x59943))+E(f315(f125(x59941,x59942),f315(f315(f140(x59941),x59943),x59944)),f315(f315(f140(x59941),x59943),f315(f125(x59941,x59942),x59944)))
% 168.50/168.38 [6134]~P1(f315(x61342,x61343))+E(f166(x61341,x61342,f315(f315(f140(x61341),x61343),x61344)),f315(f315(f140(x61341),x61343),f166(x61341,x61342,x61344)))
% 168.50/168.38 [6183]P14(x61831,x61832,x61833)+~P14(x61831,x61832,f315(f315(f297(f900(x61831)),x61834),x61833))
% 168.50/168.38 [6199]E(x61991,f177(f909(x61992,a899)))+E(f315(f315(f32(x61992,f909(x61993,a899)),x61991),f315(f18(f909(x61993,a899),x61992),x61994)),x61994)
% 168.50/168.38 [6200]E(x62001,f177(f909(x62002,a899)))+E(f315(f315(f33(x62002,f909(x62003,a899)),x62001),f315(f18(f909(x62003,a899),x62002),x62004)),x62004)
% 168.50/168.38 [6209]~E(x62094,f177(f909(x62092,a899)))+E(f315(f315(f242(x62091,x62092),x62093),f315(f18(f909(x62092,a899),x62091),x62094)),f177(f909(f908(x62091,x62092),a899)))
% 168.50/168.38 [6210]~E(x62103,f177(f909(x62101,a899)))+E(f315(f315(f242(x62101,x62102),x62103),f315(f18(f909(x62102,a899),x62101),x62104)),f177(f909(f908(x62101,x62102),a899)))
% 168.50/168.38 [6266]E(x62661,f2(a901))+E(f315(f315(f127(x62662),x62661),f315(f315(f140(x62662),x62663),x62664)),f315(f315(f127(x62662),f315(f315(f3(a901),x62661),f71(a901))),x62664))
% 168.50/168.38 [6288]E(x62881,f177(f909(x62882,a899)))+E(f315(f298(x62882,x62883,f315(f18(x62883,x62882),x62884)),x62881),f315(f315(f297(x62883),x62884),f177(f909(x62883,a899))))
% 168.50/168.38 [6291]E(f315(f299(x62911,x62912,f315(f18(x62912,x62911),x62913)),x62914),f177(f909(x62911,a899)))+P1(f315(f315(f317(x62912),x62913),x62914))
% 168.50/168.38 [6357]~E(x63573,f177(f909(x63571,a899)))+E(f315(f315(f32(x63571,f909(x63572,a899)),x63573),f315(f18(f909(x63572,a899),x63571),x63574)),f230(f909(x63572,a899)))
% 168.50/168.38 [6358]~E(x63583,f177(f909(x63581,a899)))+E(f315(f315(f33(x63581,f909(x63582,a899)),x63583),f315(f18(f909(x63582,a899),x63581),x63584)),f177(f909(x63582,a899)))
% 168.50/168.38 [6360]~P62(x63601)+E(f38(x63601,f315(f315(f74(x63601),x63602),x63603),f315(f315(f74(x63601),x63602),x63604)),f315(f315(f74(x63601),x63602),f38(x63601,x63603,x63604)))
% 168.50/168.38 [6536]E(f315(f299(x65361,x65362,f315(f18(x65362,x65361),x65363)),x65364),f230(f909(x65361,a899)))+~P1(f315(f315(f317(x65362),x65363),x65364))
% 168.50/168.38 [6560]~P1(f315(f315(f317(x65601),x65602),x65604))+P1(f315(f315(f317(x65601),x65602),f315(f315(f297(x65601),x65603),x65604)))
% 168.50/168.38 [6565]P1(f315(x65651,x65652))+~P1(f315(f149(x65653,x65651),f315(f315(f140(x65653),x65652),x65654)))
% 168.50/168.38 [6574]~E(x65743,f315(f315(f3(a901),f315(f178(f902(x65741)),x65742)),f71(a901)))+E(f103(x65741,f315(f315(f148(x65741,x65742),x65743),x65744)),f103(x65741,x65742))
% 168.50/168.38 [6596]~P110(x65961)+E(f315(f315(f90(f909(x65961,a899)),f315(f289(x65961),x65962)),f291(x65961,x65963,x65964)),f291(x65961,x65963,f315(f315(f221(x65961),x65962),x65964)))
% 168.50/168.38 [6597]~P110(x65971)+E(f315(f315(f90(f909(x65971,a899)),f315(f271(x65971),x65972)),f291(x65971,x65973,x65974)),f291(x65971,f315(f315(f222(x65971),x65972),x65973),x65974))
% 168.50/168.38 [6613]E(f315(f315(f90(f909(x66131,a899)),x66132),f315(f315(f297(x66131),x66133),x66134)),f315(f315(f90(f909(x66131,a899)),x66132),x66134))+P1(f315(f315(f317(x66131),x66133),x66132))
% 168.50/168.38 [6625]E(f159(x66251,x66252,f315(f315(f123(x66251),x66253),x66254)),f315(f315(f123(x66251),x66253),f159(x66251,x66252,x66254)))+P1(f315(f315(f317(x66251),x66252),f315(f161(x66251),x66253)))
% 168.50/168.38 [6630]~P84(x66301)+E(f315(f315(f74(x66301),f315(f315(f232(x66301),x66302),x66303)),f315(f315(f232(x66301),x66302),x66304)),f315(f315(f232(x66301),x66302),f315(f315(f73(a901),x66303),x66304)))
% 168.50/168.38 [6631]~P121(x66311)+E(f315(f315(f74(x66311),f315(f315(f232(x66311),x66312),x66313)),f315(f315(f232(x66311),x66312),x66314)),f315(f315(f232(x66311),x66312),f315(f315(f73(a901),x66313),x66314)))
% 168.50/168.38 [6668]~P101(x66681)+E(f315(f315(f90(x66681),f315(f315(f99(x66681),x66682),x66683)),f315(f315(f99(x66681),x66682),x66684)),f315(f315(f99(x66681),x66682),f315(f315(f90(x66681),x66683),x66684)))
% 168.50/168.38 [6669]~P121(x66691)+E(f315(f315(f73(x66691),f315(f315(f74(x66691),x66692),x66693)),f315(f315(f74(x66691),x66692),x66694)),f315(f315(f74(x66691),x66692),f315(f315(f73(x66691),x66693),x66694)))
% 168.50/168.38 [6670]~P101(x66701)+E(f315(f315(f99(x66701),f315(f315(f90(x66701),x66702),x66703)),f315(f315(f90(x66701),x66702),x66704)),f315(f315(f90(x66701),x66702),f315(f315(f99(x66701),x66703),x66704)))
% 168.50/168.38 [6671]~P110(x66711)+E(f315(f315(f222(x66711),f315(f315(f221(x66711),x66712),x66713)),f315(f315(f221(x66711),x66712),x66714)),f315(f315(f221(x66711),x66712),f315(f315(f222(x66711),x66713),x66714)))
% 168.50/168.38 [6672]~P110(x66721)+E(f315(f315(f221(x66721),f315(f315(f222(x66721),x66722),x66723)),f315(f315(f222(x66721),x66722),x66724)),f315(f315(f222(x66721),x66722),f315(f315(f221(x66721),x66723),x66724)))
% 168.50/168.38 [6706]~P62(x67061)+E(f38(x67061,f315(f315(f74(x67061),x67062),x67063),f315(f315(f74(x67061),x67064),x67063)),f315(f315(f74(x67061),f38(x67061,x67062,x67064)),x67063))
% 168.50/168.38 [6709]~E(f315(f178(f902(x67091)),x67093),f315(f178(f902(x67092)),x67094))+E(f315(f315(f143(f908(x67091,x67092),x67092),f244(x67091,x67092)),f315(f315(f170(x67091,x67092),x67093),x67094)),x67094)
% 168.50/168.38 [6710]~E(f315(f178(f902(x67101)),x67103),f315(f178(f902(x67102)),x67104))+E(f315(f315(f143(f908(x67101,x67102),x67101),f239(x67101,x67102)),f315(f315(f170(x67101,x67102),x67103),x67104)),x67103)
% 168.50/168.38 [6715]P1(f315(f149(x67151,x67152),x67153))+~P1(f315(f149(x67151,x67152),f315(f315(f140(x67151),x67154),x67153)))
% 168.50/168.38 [6716]P1(f315(f149(x67161,x67162),x67163))+~P1(f315(f149(x67161,x67162),f315(f315(f123(x67161),x67164),x67163)))
% 168.50/168.38 [6717]P1(f315(f149(x67171,x67172),x67173))+~P1(f315(f149(x67171,x67172),f315(f315(f123(x67171),x67173),x67174)))
% 168.50/168.38 [6722]~P63(x67221)+E(f38(x67221,f315(f315(f3(x67221),x67222),f38(x67221,x67223,x67224)),x67224),f38(x67221,f315(f315(f3(x67221),x67222),x67223),x67224))
% 168.50/168.38 [6723]~P62(x67231)+E(f38(x67231,f315(f315(f74(x67231),x67232),f38(x67231,x67233,x67234)),x67234),f38(x67231,f315(f315(f74(x67231),x67232),x67233),x67234))
% 168.50/168.38 [6725]~P62(x67251)+E(f38(x67251,f315(f315(f73(x67251),x67252),f38(x67251,x67253,x67254)),x67254),f38(x67251,f315(f315(f73(x67251),x67252),x67253),x67254))
% 168.50/168.38 [6807]~P110(x68071)+E(f315(f315(f90(f909(x68071,a899)),f291(x68071,x68072,x68073)),f315(f289(x68071),x68074)),f291(x68071,x68072,f315(f315(f221(x68071),x68073),x68074)))
% 168.50/168.38 [6808]~P110(x68081)+E(f315(f315(f90(f909(x68081,a899)),f291(x68081,x68082,x68083)),f315(f271(x68081),x68084)),f291(x68081,f315(f315(f222(x68081),x68082),x68084),x68083))
% 168.50/168.38 [6811]~E(f315(f178(f902(x68111)),x68113),f315(f178(f902(x68112)),x68114))+E(f315(f315(f170(x68111,x68112),f315(f157(x68111),x68113)),f315(f157(x68112),x68114)),f315(f157(f908(x68111,x68112)),f315(f315(f170(x68111,x68112),x68113),x68114)))
% 168.50/168.38 [6823]E(x68231,f315(f315(f3(a901),f315(f178(f902(x68232)),x68233)),f71(a901)))+E(f103(x68232,f315(f315(f148(x68232,x68233),x68231),x68234)),f315(f315(f148(x68232,f103(x68232,x68233)),x68231),x68234))
% 168.50/168.38 [6838]~P1(f315(f126(x68382),x68384))+P1(f315(f126(f908(x68381,x68382)),f315(f315(f170(x68381,x68382),x68383),x68384)))
% 168.50/168.38 [6839]~P1(f315(f126(x68391),x68393))+P1(f315(f126(f908(x68391,x68392)),f315(f315(f170(x68391,x68392),x68393),x68394)))
% 168.50/168.38 [7111]E(f315(f315(f29(a901),x71111),x71112),x71113)+~P1(f315(f41(x71111,x71112),f315(f315(f240(a901,a901),x71113),x71114)))
% 168.50/168.38 [7135]E(f38(a901,x71351,x71352),x71353)+~P1(f315(f41(x71351,x71352),f315(f315(f240(a901,a901),x71354),x71353)))
% 168.50/168.38 [7138]P1(f315(f126(x71381),x71382))+~P1(f315(f126(x71383),f315(f315(f143(x71381,x71383),x71384),x71382)))
% 168.50/168.38 [7146]~P14(x71461,x71462,f315(f315(f297(f900(x71461)),x71463),x71464))+P14(x71461,x71462,f315(f315(f297(f900(x71461)),x71463),f177(f909(f900(x71461),a899))))
% 168.50/168.38 [7222]E(f159(x72221,x72222,f315(f315(f123(x72221),x72223),x72224)),f315(f315(f123(x72221),f159(x72221,x72222,x72223)),x72224))+~P1(f315(f315(f317(x72221),x72222),f315(f161(x72221),x72223)))
% 168.50/168.38 [7315]~P63(x73151)+E(f38(x73151,f315(f315(f3(x73151),f38(x73151,x73152,x73153)),x73154),x73153),f38(x73151,f315(f315(f3(x73151),x73152),x73154),x73153))
% 168.50/168.38 [7318]~P62(x73181)+E(f38(x73181,f315(f315(f74(x73181),f38(x73181,x73182,x73183)),x73184),x73183),f38(x73181,f315(f315(f74(x73181),x73182),x73184),x73183))
% 168.50/168.38 [7319]~P62(x73191)+E(f38(x73191,f315(f315(f73(x73191),f38(x73191,x73192,x73193)),x73194),x73193),f38(x73191,f315(f315(f73(x73191),x73192),x73194),x73193))
% 168.50/168.38 [7515]~E(x75151,f315(f315(f140(x75152),x75153),x75154))+~P1(f315(f315(f223(a901),f315(f178(f902(x75152)),x75151)),f315(f178(f902(x75152)),x75154)))
% 168.50/168.38 [7719]P25(x77191,x77192,x77193,f315(f161(x77191),x77194))+~P1(f315(f126(x77192),f315(f315(f143(x77191,x77192),x77193),x77194)))
% 168.50/168.38 [7794]~P1(f315(f315(f223(f909(x77941,a899)),x77942),x77944))+P1(f315(f315(f223(f909(x77941,a899)),x77942),f315(f315(f297(x77941),x77943),x77944)))
% 168.50/168.38 [7830]~P63(x78301)+E(f38(x78301,f315(f315(f3(x78301),f38(x78301,x78302,x78303)),f38(x78301,x78304,x78303)),x78303),f38(x78301,f315(f315(f3(x78301),x78302),x78304),x78303))
% 168.50/168.38 [7831]~P62(x78311)+E(f38(x78311,f315(f315(f74(x78311),f38(x78311,x78312,x78313)),f38(x78311,x78314,x78313)),x78313),f38(x78311,f315(f315(f74(x78311),x78312),x78314),x78313))
% 168.50/168.38 [7832]~P62(x78321)+E(f38(x78321,f315(f315(f73(x78321),f38(x78321,x78322,x78323)),f38(x78321,x78324,x78323)),x78323),f38(x78321,f315(f315(f73(x78321),x78322),x78324),x78323))
% 168.50/168.38 [7935]~E(f315(x79354,f400(x79354,x79353,x79351,x79352)),f177(f909(x79352,a899)))+E(f315(f315(f33(x79351,f909(x79352,a899)),x79353),x79354),f177(f909(x79352,a899)))
% 168.50/168.38 [7936]~E(f315(x79364,f410(x79364,x79363,x79361,x79362)),f230(f909(x79362,a899)))+E(f315(f315(f32(x79361,f909(x79362,a899)),x79363),x79364),f230(f909(x79362,a899)))
% 168.50/168.38 [7937]~E(f315(x79374,f416(x79374,x79373,x79372,x79371)),f230(f909(x79372,a899)))+E(f315(f315(f32(x79371,f909(x79372,a899)),x79373),x79374),f230(f909(x79372,a899)))
% 168.50/168.38 [7938]~E(f315(x79384,f401(x79384,x79383,x79382,x79381)),f177(f909(x79382,a899)))+E(f315(f315(f33(x79381,f909(x79382,a899)),x79383),x79384),f177(f909(x79382,a899)))
% 168.50/168.38 [8331]P1(f315(x83311,x83312))+~P1(f315(f315(f317(x83313),x83312),f315(f315(f90(f909(x83313,a899)),x83314),f315(f250(x83313),x83311))))
% 168.50/168.38 [8368]~P1(f315(f315(f223(f909(x83681,a899)),x83683),x83684))+P1(f315(f315(f223(f909(x83681,a899)),f315(f315(f297(x83681),x83682),x83683)),f315(f315(f297(x83681),x83682),x83684)))
% 168.50/168.38 [8547]P1(f315(x85472,x85473))+E(f315(f315(f127(x85471),f315(f178(f902(x85471)),f166(x85471,x85472,f315(f315(f140(x85471),x85473),x85474)))),f315(f315(f140(x85471),x85473),x85474)),f315(f315(f140(x85471),x85473),x85474))
% 168.50/168.38 [8653]~P1(f315(f315(f224(a901),f315(x86534,x86532)),f315(x86534,x86533)))+P1(f315(f315(f317(f908(x86531,x86531)),f315(f315(f240(x86531,x86531),x86532),x86533)),f315(f315(f276(a901,x86531),a228),x86534)))
% 168.50/168.38 [8749]~P1(f315(x87492,f723(x87494,x87492,x87493,x87491)))+E(f166(x87491,x87492,f315(f315(f123(x87491),x87493),x87494)),f315(f315(f123(x87491),x87493),f166(x87491,x87492,x87494)))
% 168.50/168.38 [8826]P25(f902(x88261),f902(x88262),f315(f143(x88261,x88262),x88263),x88264)+~P25(x88261,x88262,x88263,f30(f909(x88261,a899),f315(f298(f902(x88261),f909(x88261,a899),f161(x88261)),x88264)))
% 168.50/168.38 [8901]~P1(f315(x89012,x89013))+E(f315(f315(f127(x89011),f315(f178(f902(x89011)),f166(x89011,x89012,f315(f315(f140(x89011),x89013),x89014)))),f315(f315(f140(x89011),x89013),x89014)),f315(f315(f127(x89011),f315(f178(f902(x89011)),f166(x89011,x89012,x89014))),x89014))
% 168.50/168.38 [8942]~E(x89422,x89423)+E(f315(f125(x89421,f315(f315(f10(a899,a899,x89421),a310),f315(a312,x89422))),f315(f315(f140(x89421),x89423),x89424)),f315(f125(x89421,f315(f315(f10(a899,a899,x89421),a310),f315(a312,x89422))),x89424))
% 168.50/168.38 [8952]E(f315(f315(f33(x89521,f909(x89522,a899)),x89523),x89524),f177(f909(x89522,a899)))+P1(f315(f315(f317(x89521),f400(x89524,x89523,x89521,x89522)),x89523))
% 168.50/168.38 [8953]E(f315(f315(f32(x89531,f909(x89532,a899)),x89533),x89534),f230(f909(x89532,a899)))+P1(f315(f315(f317(x89531),f410(x89534,x89533,x89531,x89532)),x89533))
% 168.50/168.38 [8954]E(f315(f315(f32(x89541,f909(x89542,a899)),x89543),x89544),f230(f909(x89542,a899)))+P1(f315(f315(f317(x89541),f416(x89544,x89543,x89542,x89541)),x89543))
% 168.50/168.38 [8955]E(f315(f315(f33(x89551,f909(x89552,a899)),x89553),x89554),f177(f909(x89552,a899)))+P1(f315(f315(f317(x89551),f401(x89554,x89553,x89552,x89551)),x89553))
% 168.50/168.38 [8993]P1(f315(f315(f224(a901),f315(x89931,x89932)),f315(x89931,x89933)))+~P1(f315(f315(f317(f908(x89934,x89934)),f315(f315(f240(x89934,x89934),x89932),x89933)),f315(f315(f276(a901,x89934),a228),x89931)))
% 168.50/168.38 [9019]E(f166(x90191,x90192,f315(f315(f123(x90191),x90193),x90194)),f315(f315(f123(x90191),x90193),f166(x90191,x90192,x90194)))+P1(f315(f315(f317(x90191),f723(x90194,x90192,x90193,x90191)),f315(f161(x90191),x90193)))
% 168.50/168.38 [9071]~P26(x90711,x90712,x90713,f230(f909(x90711,a899)),f230(f909(x90712,a899)))+E(f315(f298(x90711,x90712,x90713),f315(f72(f909(x90711,a899)),x90714)),f315(f72(f909(x90712,a899)),f315(f298(x90711,x90712,x90713),x90714)))
% 168.50/168.38 [9174]P1(f315(f315(f317(x91741),f465(x91742,x91743,x91744,x91741)),x91743))+~P1(f315(f315(f317(f909(x91741,a899)),x91744),f315(f315(f53(x91741),x91743),x91742)))
% 168.50/168.38 [9177]E(x91771,x91772)+~P1(f315(f315(f317(f908(x91773,x91773)),f315(f315(f240(x91773,x91773),x91771),x91772)),f315(f315(f172(f908(x91773,x91773),a899),f2(a901)),x91774)))
% 168.50/168.38 [9258]E(f315(f273(x92581,x92581,x92582),f315(f315(f297(x92581),f465(x92582,x92583,x92584,x92581)),f177(f909(x92581,a899)))),x92584)+~P1(f315(f315(f317(f909(x92581,a899)),x92584),f315(f315(f53(x92581),x92583),x92582)))
% 168.50/168.38 [9263]~P1(f315(f315(f317(f908(x92631,x92631)),f315(f315(f240(x92631,x92631),x92633),x92632)),f295(x92631,x92634)))+P1(f315(f315(f317(f908(x92631,x92631)),f315(f315(f240(x92631,x92631),x92632),x92633)),f295(x92631,f315(f274(x92631,x92631),x92634))))
% 168.50/168.38 [9276]~P62(x92761)+E(f315(f315(f73(x92761),f315(f315(f73(x92761),f315(f315(f74(x92761),x92762),f315(f315(f29(x92761),x92763),x92762))),f38(x92761,x92763,x92762))),x92764),f315(f315(f73(x92761),x92763),x92764))
% 168.50/168.38 [9287]~P1(f315(f315(f317(x92871),x92873),x92874))+P1(f315(f315(f317(f909(x92871,a899)),f315(f273(x92871,x92871,x92872),f315(f315(f297(x92871),x92873),f177(f909(x92871,a899))))),f315(f315(f53(x92871),x92874),x92872)))
% 168.50/168.38 [9299]P1(f315(f315(f317(f908(x92991,x92991)),f315(f315(f240(x92991,x92991),x92992),x92993)),f295(x92991,x92994)))+~P1(f315(f315(f317(f908(x92991,x92991)),f315(f315(f240(x92991,x92991),x92993),x92992)),f295(x92991,f315(f274(x92991,x92991),x92994))))
% 168.50/168.38 [9387]E(f315(f315(f148(x93871,f315(f157(x93871),x93872)),f315(f315(f3(a901),f315(f315(f3(a901),f315(f178(f902(x93871)),x93872)),x93873)),f71(a901))),x93874),f315(f157(x93871),f315(f315(f148(x93871,x93872),x93873),x93874)))+~P1(f315(f315(f224(a901),x93873),f315(f178(f902(x93871)),x93872)))
% 168.50/168.38 [9390]~P1(f315(x93902,f717(x93904,x93902,x93903,x93901)))+E(f315(f315(f127(x93901),f315(f178(f902(x93901)),f166(x93901,x93902,f315(f315(f123(x93901),x93903),x93904)))),f315(f315(f123(x93901),x93903),x93904)),f315(f315(f127(x93901),f315(f178(f902(x93901)),f166(x93901,x93902,x93904))),x93904))
% 168.50/168.38 [9436]~P25(x94362,x94361,x94363,f230(f909(x94362,a899)))+P1(f315(f315(f223(f909(x94361,a899)),f315(f298(x94362,x94361,x94363),f315(f72(f909(x94362,a899)),x94364))),f315(f72(f909(x94361,a899)),f315(f298(x94362,x94361,x94363),x94364))))
% 168.50/168.38 [9448]~P5(x94481)+E(f315(f131(x94481,x94482,f315(f9(x94482,x94481,x94481),f315(f315(f10(x94481,f909(x94481,x94481),x94482),f90(x94481)),x94483)),f230(x94481)),x94484),f315(f315(f32(x94482,x94481),f315(f161(x94482),x94484)),x94483))
% 168.50/168.38 [9449]~P5(x94491)+E(f315(f131(x94491,x94492,f315(f9(x94492,x94491,x94491),f315(f315(f10(x94491,f909(x94491,x94491),x94492),f99(x94491)),x94493)),f177(x94491)),x94494),f315(f315(f33(x94492,x94491),f315(f161(x94492),x94494)),x94493))
% 168.50/168.38 [9459]E(f315(f315(f127(x94591),f315(f178(f902(x94591)),f166(x94591,x94592,f315(f315(f123(x94591),x94593),x94594)))),f315(f315(f123(x94591),x94593),x94594)),f315(f315(f127(x94591),f315(f178(f902(x94591)),f166(x94591,x94592,x94594))),x94594))+P1(f315(f315(f317(x94591),f717(x94594,x94592,x94593,x94591)),f315(f161(x94591),x94593)))
% 168.50/168.38 [9529]~P1(f315(f315(f317(f908(f902(x95294),f902(x95294))),f315(f315(f240(f902(x95294),f902(x95294)),x95293),x95292)),f146(x95294,x95291)))+P1(f315(f315(f224(a901),f652(x95291,x95292,x95293,x95294)),f315(f178(f902(x95294)),x95293)))
% 168.50/168.38 [9530]~P62(x95301)+E(f315(f315(f73(x95301),f315(f315(f73(x95301),f315(f315(f74(x95301),f315(f315(f29(x95301),x95302),x95303)),x95303)),f38(x95301,x95302,x95303))),x95304),f315(f315(f73(x95301),x95302),x95304))
% 168.50/168.38 [9559]~P1(f315(f315(f317(f908(f902(x95591),f902(x95591))),f315(f315(f240(f902(x95591),f902(x95591)),x95592),x95593)),f315(f274(f902(x95591),f902(x95591)),f146(x95591,x95594))))+P1(f315(f315(f317(f908(f902(x95591),f902(x95591))),f315(f315(f240(f902(x95591),f902(x95591)),x95592),x95593)),f146(x95591,f315(f274(x95591,x95591),x95594))))
% 168.50/168.38 [9560]P1(f315(f315(f317(f908(f902(x95601),f902(x95601))),f315(f315(f240(f902(x95601),f902(x95601)),x95602),x95603)),f315(f274(f902(x95601),f902(x95601)),f146(x95601,x95604))))+~P1(f315(f315(f317(f908(f902(x95601),f902(x95601))),f315(f315(f240(f902(x95601),f902(x95601)),x95602),x95603)),f146(x95601,f315(f274(x95601,x95601),x95604))))
% 168.50/168.38 [9604]~P1(f315(f315(f317(x96041),x96043),f315(f252(x96041,x96042),x96044)))+P1(f315(f315(f317(f908(x96041,x96042)),f315(f315(f240(x96041,x96042),x96043),f555(x96044,x96042,x96043,x96041))),x96044))
% 168.50/168.38 [9605]~P1(f315(f315(f317(x96051),x96053),f315(f252(x96051,x96052),x96054)))+P1(f315(f315(f317(f908(x96051,x96052)),f315(f315(f240(x96051,x96052),x96053),f556(x96054,x96052,x96053,x96051))),x96054))
% 168.50/168.38 [9765]~P1(f315(f315(f317(f908(x97651,x97651)),f315(f315(f240(x97651,x97651),x97652),x97654)),f315(f315(f277(x97651,x97651,x97651),x97653),f295(x97651,x97653))))+P1(f315(f315(f317(f908(x97651,x97651)),f315(f315(f240(x97651,x97651),x97652),f622(x97653,x97654,x97652,x97651))),x97653))
% 168.50/168.38 [9923]P11(x99231,x99232,x99233,x99234)+P1(f315(f315(f317(f908(x99231,x99231)),f315(f315(f240(x99231,x99231),f814(x99232,x99234,x99233,x99231)),f813(x99232,x99234,x99233,x99231))),x99233))
% 168.50/168.38 [9930]~P1(f315(f315(f317(f908(x99302,x99301)),x99304),f315(f274(x99301,x99302),x99303)))+P1(f315(f315(f317(f908(x99301,x99302)),f315(f315(f240(x99301,x99302),f624(x99303,x99304,x99301,x99302)),f623(x99303,x99304,x99301,x99302))),x99303))
% 168.50/168.38 [9954]~P1(f315(f315(f317(f908(f902(x99541),f902(x99541))),f315(f315(f240(f902(x99541),f902(x99541)),x99544),x99543)),f146(x99541,x99542)))+P1(f315(f315(f317(f908(x99541,x99541)),f315(f315(f240(x99541,x99541),f666(x99542,x99543,x99544,x99541)),f668(x99542,x99543,x99544,x99541))),x99542))
% 168.50/168.38 [10044]~P1(f315(f315(f317(f908(f902(x100441),f902(x100441))),f315(f315(f240(f902(x100441),f902(x100441)),x100442),x100444)),f146(x100441,x100443)))+P1(f315(f315(f317(f908(x100441,x100441)),f315(f315(f240(x100441,x100441),f315(f315(f153(x100441),x100442),f652(x100443,x100444,x100442,x100441))),f653(x100443,x100444,x100442,x100441))),x100443))
% 168.50/168.38 [10064]~P1(f315(f54(x100642),x100644))+E(f315(f315(f315(f58(f909(x100641,a899),x100642,f99(f909(x100641,a899))),f315(f315(f9(x100642,f909(x100641,a899),f909(x100641,a899)),f315(f315(f10(x100641,f909(f909(x100641,a899),f909(x100641,a899)),x100642),f297(x100641)),x100643)),f177(f909(x100641,a899)))),f177(f909(x100641,a899))),x100644),f315(f298(x100642,x100641,x100643),x100644))
% 168.50/168.38 [10174]~P25(x101741,x101742,x101743,f230(f909(x101741,a899)))+P1(f315(f315(f223(f909(x101741,a899)),f315(f299(x101741,x101742,x101743),f315(f315(f297(x101742),x101744),f177(f909(x101742,a899))))),f315(f315(f297(x101741),f78(x101741,f315(f315(f9(x101741,x101742,a899),f315(f315(f10(x101742,f909(x101742,a899),x101741),a312),x101743)),x101744))),f177(f909(x101741,a899)))))
% 168.50/168.38 [5710]~E(f315(f315(f123(x57101),x57102),x57104),x57103)+E(f315(f315(f164(x57101),f315(f178(f902(x57101)),x57102)),x57103),x57102)
% 168.50/168.38 [5711]~E(f315(f315(f123(x57112),x57113),x57111),x57114)+E(x57111,f315(f315(f127(x57112),f315(f178(f902(x57112)),x57113)),x57114))
% 168.50/168.38 [5722]~E(x57224,f2(a901))+E(f315(f315(f153(x57221),f315(f315(f140(x57221),x57222),x57223)),x57224),x57222)
% 168.50/168.38 [6279]~P121(x62791)+E(f315(f315(f232(x62791),f315(f315(f232(x62791),x62792),x62793)),x62794),f315(f315(f232(x62791),x62792),f315(f315(f74(a901),x62793),x62794)))
% 168.50/168.38 [6280]~P84(x62801)+E(f315(f315(f232(x62801),f315(f315(f232(x62801),x62802),x62803)),x62804),f315(f315(f232(x62801),x62802),f315(f315(f74(a901),x62803),x62804)))
% 168.50/168.38 [6289]E(x62891,f2(a901))+E(f315(f315(f153(x62892),f315(f315(f140(x62892),x62893),x62894)),x62891),f315(f315(f153(x62892),x62894),f315(f315(f3(a901),x62891),f71(a901))))
% 168.50/168.38 [6315]~P125(x63151)+E(f315(f315(f279(x63151),f315(f315(f74(x63151),x63152),x63153)),x63154),f315(f315(f74(x63151),x63152),f315(f315(f279(x63151),x63153),x63154)))
% 168.50/168.38 [6317]~P80(x63171)+E(f315(f315(f99(x63171),f315(f315(f99(x63171),x63172),x63173)),x63174),f315(f315(f99(x63171),x63172),f315(f315(f99(x63171),x63173),x63174)))
% 168.50/168.38 [6319]~P103(x63191)+E(f315(f315(f99(x63191),f315(f315(f99(x63191),x63192),x63193)),x63194),f315(f315(f99(x63191),x63192),f315(f315(f99(x63191),x63193),x63194)))
% 168.50/168.38 [6320]~P70(x63201)+E(f315(f315(f74(x63201),f315(f315(f74(x63201),x63202),x63203)),x63204),f315(f315(f74(x63201),x63202),f315(f315(f74(x63201),x63203),x63204)))
% 168.50/168.38 [6321]~P121(x63211)+E(f315(f315(f74(x63211),f315(f315(f74(x63211),x63212),x63213)),x63214),f315(f315(f74(x63211),x63212),f315(f315(f74(x63211),x63213),x63214)))
% 168.50/168.38 [6323]~P80(x63231)+E(f315(f315(f90(x63231),f315(f315(f90(x63231),x63232),x63233)),x63234),f315(f315(f90(x63231),x63232),f315(f315(f90(x63231),x63233),x63234)))
% 168.50/168.38 [6325]~P104(x63251)+E(f315(f315(f90(x63251),f315(f315(f90(x63251),x63252),x63253)),x63254),f315(f315(f90(x63251),x63252),f315(f315(f90(x63251),x63253),x63254)))
% 168.50/168.38 [6326]~P71(x63261)+E(f315(f315(f73(x63261),f315(f315(f73(x63261),x63262),x63263)),x63264),f315(f315(f73(x63261),x63262),f315(f315(f73(x63261),x63263),x63264)))
% 168.50/168.38 [6327]~P121(x63271)+E(f315(f315(f73(x63271),f315(f315(f73(x63271),x63272),x63273)),x63274),f315(f315(f73(x63271),x63272),f315(f315(f73(x63271),x63273),x63274)))
% 168.50/168.38 [6329]~P110(x63291)+E(f315(f315(f221(x63291),f315(f315(f221(x63291),x63292),x63293)),x63294),f315(f315(f221(x63291),x63292),f315(f315(f221(x63291),x63293),x63294)))
% 168.50/168.38 [6331]~P110(x63311)+E(f315(f315(f222(x63311),f315(f315(f222(x63311),x63312),x63313)),x63314),f315(f315(f222(x63311),x63312),f315(f315(f222(x63311),x63313),x63314)))
% 168.50/168.38 [6340]~P62(x63401)+E(f38(x63401,f315(f315(f73(x63401),x63402),f315(f315(f74(x63401),x63403),x63404)),x63404),f38(x63401,x63402,x63404))
% 168.50/168.38 [6341]~P62(x63411)+E(f38(x63411,f315(f315(f73(x63411),x63412),f315(f315(f74(x63411),x63413),x63414)),x63413),f38(x63411,x63412,x63413))
% 168.50/168.38 [6482]E(f315(f315(f153(x64821),f315(f315(f164(x64821),x64822),x64823)),x64824),f315(f315(f153(x64821),x64823),x64824))+~P1(f315(f315(f224(a901),x64824),x64822))
% 168.50/168.38 [6664]~E(x66642,x66644)+P1(f315(f315(f161(x66641),f315(f315(f140(x66641),x66642),x66643)),x66644))
% 168.50/168.38 [6666]~P121(x66661)+E(f315(f315(f74(x66661),f315(f315(f74(x66661),x66662),x66663)),x66664),f315(f315(f74(x66661),f315(f315(f74(x66661),x66662),x66664)),x66663))
% 168.50/168.38 [6667]~P121(x66671)+E(f315(f315(f73(x66671),f315(f315(f73(x66671),x66672),x66673)),x66674),f315(f315(f73(x66671),f315(f315(f73(x66671),x66672),x66674)),x66673))
% 168.50/168.38 [6728]~P147(x67282)+E(f315(f315(f8(x67281,x67282),f315(f18(x67282,x67281),x67283)),x67284),f315(f315(f74(x67282),f315(f89(x67282),f315(f28(x67281),x67284))),x67283))
% 168.50/168.38 [6905]E(f315(f315(f90(f909(x69051,a899)),f315(f315(f297(x69051),x69052),x69053)),x69054),f315(f315(f90(f909(x69051,a899)),x69053),x69054))+P1(f315(f315(f317(x69051),x69052),x69054))
% 168.50/168.38 [6974]~P101(x69741)+E(f315(f315(f90(x69741),f315(f315(f99(x69741),x69742),x69743)),f315(f315(f99(x69741),x69744),x69743)),f315(f315(f99(x69741),f315(f315(f90(x69741),x69742),x69744)),x69743))
% 168.50/168.38 [6975]~P82(x69751)+E(f315(f315(f221(x69751),f315(f315(f3(x69751),x69752),x69753)),f315(f315(f3(x69751),x69754),x69753)),f315(f315(f3(x69751),f315(f315(f221(x69751),x69752),x69754)),x69753))
% 168.50/168.38 [6976]~P82(x69761)+E(f315(f315(f222(x69761),f315(f315(f3(x69761),x69762),x69763)),f315(f315(f3(x69761),x69764),x69763)),f315(f315(f3(x69761),f315(f315(f222(x69761),x69762),x69764)),x69763))
% 168.50/168.38 [6977]~P115(x69771)+E(f315(f315(f73(x69771),f315(f315(f74(x69771),x69772),x69773)),f315(f315(f74(x69771),x69774),x69773)),f315(f315(f74(x69771),f315(f315(f73(x69771),x69772),x69774)),x69773))
% 168.50/168.38 [6979]~P101(x69791)+E(f315(f315(f99(x69791),f315(f315(f90(x69791),x69792),x69793)),f315(f315(f90(x69791),x69794),x69793)),f315(f315(f90(x69791),f315(f315(f99(x69791),x69792),x69794)),x69793))
% 168.50/168.38 [6980]~P87(x69801)+E(f315(f315(f221(x69801),f315(f315(f73(x69801),x69802),x69803)),f315(f315(f73(x69801),x69804),x69803)),f315(f315(f73(x69801),f315(f315(f221(x69801),x69802),x69804)),x69803))
% 168.50/168.38 [6981]~P87(x69811)+E(f315(f315(f222(x69811),f315(f315(f73(x69811),x69812),x69813)),f315(f315(f73(x69811),x69814),x69813)),f315(f315(f73(x69811),f315(f315(f222(x69811),x69812),x69814)),x69813))
% 168.50/168.38 [6982]~P125(x69821)+E(f315(f315(f3(x69821),f315(f315(f279(x69821),x69822),x69823)),f315(f315(f279(x69821),x69824),x69823)),f315(f315(f279(x69821),f315(f315(f3(x69821),x69822),x69824)),x69823))
% 168.50/168.38 [6983]~P125(x69831)+E(f315(f315(f73(x69831),f315(f315(f279(x69831),x69832),x69833)),f315(f315(f279(x69831),x69834),x69833)),f315(f315(f279(x69831),f315(f315(f73(x69831),x69832),x69834)),x69833))
% 168.50/168.38 [6984]~P110(x69841)+E(f315(f315(f222(x69841),f315(f315(f221(x69841),x69842),x69843)),f315(f315(f221(x69841),x69844),x69843)),f315(f315(f221(x69841),f315(f315(f222(x69841),x69842),x69844)),x69843))
% 168.50/168.38 [6985]~P77(x69851)+E(f315(f315(f74(x69851),f315(f315(f232(x69851),x69852),x69853)),f315(f315(f232(x69851),x69854),x69853)),f315(f315(f232(x69851),f315(f315(f74(x69851),x69852),x69854)),x69853))
% 168.50/168.38 [6986]~P121(x69861)+E(f315(f315(f74(x69861),f315(f315(f232(x69861),x69862),x69863)),f315(f315(f232(x69861),x69864),x69863)),f315(f315(f232(x69861),f315(f315(f74(x69861),x69862),x69864)),x69863))
% 168.50/168.38 [6987]~P65(x69871)+E(f315(f315(f279(x69871),f315(f315(f232(x69871),x69872),x69873)),f315(f315(f232(x69871),x69874),x69873)),f315(f315(f232(x69871),f315(f315(f279(x69871),x69872),x69874)),x69873))
% 168.50/168.38 [6988]~P110(x69881)+E(f315(f315(f221(x69881),f315(f315(f222(x69881),x69882),x69883)),f315(f315(f222(x69881),x69884),x69883)),f315(f315(f222(x69881),f315(f315(f221(x69881),x69882),x69884)),x69883))
% 168.50/168.38 [6989]~P121(x69891)+E(f315(f315(f73(x69891),f315(f315(f74(x69891),x69892),x69893)),f315(f315(f74(x69891),x69894),x69893)),f315(f315(f74(x69891),f315(f315(f73(x69891),x69892),x69894)),x69893))
% 168.50/168.38 [7021]E(f315(f315(f148(x70211,x70212),x70213),x70214),x70212)+~P1(f315(f315(f223(a901),f315(f178(f902(x70211)),x70212)),x70213))
% 168.50/168.38 [7049]~P1(f315(x70493,x70494))+P1(f315(f315(f315(f99(f909(x70491,a899)),x70492),x70493),x70494))
% 168.50/168.38 [7051]~P1(f315(x70512,x70514))+P1(f315(f315(f315(f99(f909(x70511,a899)),x70512),x70513),x70514))
% 168.50/168.38 [7071]E(f315(f315(f153(x70711),f315(f315(f123(x70711),x70712),x70713)),x70714),f315(f315(f153(x70711),x70712),x70714))+~P1(f315(f315(f224(a901),x70714),f315(f178(f902(x70711)),x70712)))
% 168.50/168.38 [7082]E(f315(f315(f3(f909(x70821,a899)),f315(f315(f297(x70821),x70822),x70823)),x70824),f315(f315(f3(f909(x70821,a899)),x70823),x70824))+~P1(f315(f315(f317(x70821),x70822),x70824))
% 168.50/168.38 [7124]~E(f128(a901,f315(f290(a901,x71241),x71242)),f315(f315(f140(a901),x71244),x71243))+E(f128(a901,f315(f290(a901,f315(f315(f73(a901),x71241),f71(a901))),x71242)),x71243)
% 168.50/168.38 [7147]~P1(f315(f315(f161(x71471),x71473),x71474))+P1(f315(f315(f161(x71471),f315(f315(f140(x71471),x71472),x71473)),x71474))
% 168.50/168.38 [7197]E(x71971,f2(a901))+E(f315(f315(f140(x71972),x71973),f315(f315(f164(x71972),f315(f315(f3(a901),x71971),f71(a901))),x71974)),f315(f315(f164(x71972),x71971),f315(f315(f140(x71972),x71973),x71974)))
% 168.50/168.38 [7299]E(f315(f315(f153(x72991),x72992),f315(f315(f3(a901),x72993),f315(f178(f902(x72991)),x72994))),f315(f315(f153(x72991),f315(f315(f123(x72991),x72994),x72992)),x72993))+P1(f315(f315(f224(a901),x72993),f315(f178(f902(x72991)),x72994)))
% 168.50/168.38 [7329]E(f315(f315(f90(f909(x73291,a899)),x73292),f315(f315(f297(x73291),x73293),x73294)),f315(f315(f297(x73291),x73293),f315(f315(f90(f909(x73291,a899)),x73292),x73294)))+~P1(f315(f315(f317(x73291),x73293),x73292))
% 168.50/168.38 [7367]E(f315(f315(f153(x73671),f315(f315(f148(x73671,x73672),x73673),x73674)),x73673),x73674)+~P1(f315(f315(f224(a901),x73673),f315(f178(f902(x73671)),x73672)))
% 168.50/168.38 [7389]E(x73891,f177(f909(x73892,a899)))+E(f315(f298(f908(x73893,x73892),x73893,f239(x73893,x73892)),f315(f315(f242(x73893,x73892),x73894),f315(f18(f909(x73892,a899),x73893),x73891))),x73894)
% 168.50/168.38 [7390]E(x73901,f177(f909(x73902,a899)))+E(f315(f298(f908(x73902,x73903),x73903,f244(x73902,x73903)),f315(f315(f242(x73902,x73903),x73901),f315(f18(f909(x73903,a899),x73902),x73904))),x73904)
% 168.50/168.38 [7465]E(f315(f315(f3(f909(x74651,a899)),f315(f315(f297(x74651),x74652),x74653)),x74654),f315(f315(f297(x74651),x74652),f315(f315(f3(f909(x74651,a899)),x74653),x74654)))+P1(f315(f315(f317(x74651),x74652),x74654))
% 168.50/168.38 [7501]~E(x75014,f177(f909(x75012,a899)))+E(f315(f298(f908(x75011,x75012),x75011,f239(x75011,x75012)),f315(f315(f242(x75011,x75012),x75013),f315(f18(f909(x75012,a899),x75011),x75014))),f177(f909(x75011,a899)))
% 168.50/168.38 [7502]~E(x75023,f177(f909(x75021,a899)))+E(f315(f298(f908(x75021,x75022),x75022,f244(x75021,x75022)),f315(f315(f242(x75021,x75022),x75023),f315(f18(f909(x75022,a899),x75021),x75024))),f177(f909(x75022,a899)))
% 168.50/168.38 [7554]~P1(f315(f315(f317(x75541),x75542),x75544))+P1(f315(f315(f317(x75541),x75542),f315(f315(f99(f909(x75541,a899)),x75543),x75544)))
% 168.50/168.38 [7557]~P1(f315(f315(f317(x75571),x75572),x75573))+P1(f315(f315(f317(x75571),x75572),f315(f315(f99(f909(x75571,a899)),x75573),x75574)))
% 168.50/168.38 [7575]E(f315(f315(f90(f909(x75751,a899)),f315(f315(f297(x75751),x75752),x75753)),x75754),f315(f315(f297(x75751),x75752),f315(f315(f90(f909(x75751,a899)),x75753),x75754)))+~P1(f315(f315(f317(x75751),x75752),x75754))
% 168.50/168.38 [7852]P1(f315(x78521,x78522))+~P1(f315(f315(f315(f90(f909(x78523,a899)),x78524),x78521),x78522))
% 168.50/168.38 [7853]P1(f315(x78531,x78532))+~P1(f315(f315(f315(f90(f909(x78533,a899)),x78531),x78534),x78532))
% 168.50/168.38 [7854]E(f315(f315(f8(x78541,a901),x78542),f315(f315(f3(f909(x78541,a899)),x78543),f315(f315(f297(x78541),x78544),f177(f909(x78541,a899))))),f315(f315(f8(x78541,a901),x78542),x78543))+P1(f315(f315(f317(x78541),x78544),x78543))
% 168.50/168.38 [7859]~P72(x78591)+E(f315(f154(x78591),f315(f315(f143(a901,x78591),x78592),f128(a901,f315(f290(a901,x78593),x78594)))),f315(f315(f8(a901,x78591),x78592),f315(f161(a901),f128(a901,f315(f290(a901,x78593),x78594)))))
% 168.50/168.38 [7860]~P72(x78601)+E(f315(f315(f8(a901,x78601),x78602),f315(f161(a901),f128(a901,f315(f290(a901,x78603),x78604)))),f315(f154(x78601),f315(f315(f143(a901,x78601),x78602),f128(a901,f315(f290(a901,x78603),x78604)))))
% 168.50/168.38 [7973]~E(x79733,x79734)+P1(f315(f55(x79731,x79732,f315(f315(f297(x79731),x79733),f177(f909(x79731,a899)))),x79734))
% 168.50/168.38 [8070]P1(f315(f315(f317(x80701),x80702),f315(f161(x80701),x80703)))+~P1(f315(f315(f317(x80701),x80702),f315(f161(x80701),f315(f315(f164(x80701),x80704),x80703))))
% 168.50/168.38 [8071]P1(f315(f315(f317(x80711),x80712),f315(f161(x80711),x80713)))+~P1(f315(f315(f317(x80711),x80712),f315(f161(x80711),f315(f315(f127(x80711),x80714),x80713))))
% 168.50/168.38 [8142]P1(f315(f315(f317(x81421),x81422),x81423))+~P1(f315(f315(f317(x81421),x81422),f315(f315(f3(f909(x81421,a899)),x81423),x81424)))
% 168.50/168.38 [8144]P1(f315(f315(f317(x81441),x81442),x81443))+~P1(f315(f315(f317(x81441),x81442),f315(f315(f90(f909(x81441,a899)),x81444),x81443)))
% 168.50/168.38 [8147]P1(f315(f315(f317(x81471),x81472),x81473))+~P1(f315(f315(f317(x81471),x81472),f315(f315(f90(f909(x81471,a899)),x81473),x81474)))
% 168.50/168.38 [8162]E(f315(f315(f123(x81621),f315(f315(f164(x81621),x81622),x81623)),f315(f315(f140(x81621),x81624),f315(f315(f127(x81621),f315(a101,x81622)),x81623))),f315(f315(f148(x81621,x81623),x81622),x81624))+~P1(f315(f315(f224(a901),x81622),f315(f178(f902(x81621)),x81623)))
% 168.50/168.38 [8186]P1(f315(f315(f317(x81861),x81862),x81863))+~P1(f315(f315(f223(f909(x81861,a899)),f315(f315(f297(x81861),x81862),x81864)),x81863))
% 168.50/168.38 [8223]~P1(f315(f315(f317(x82231),x82232),x82233))+~P1(f315(f315(f317(x82231),x82232),f315(f315(f3(f909(x82231,a899)),x82234),x82233)))
% 168.50/168.38 [8257]~P1(f315(f315(f224(a901),x82574),f315(f178(f902(x82571)),x82573)))+P1(f315(f315(f317(x82571),x82572),f315(f161(x82571),f315(f315(f148(x82571,x82573),x82574),x82572))))
% 168.50/168.38 [8310]E(f315(f315(f153(x83101),f315(f315(f127(x83101),x83102),x83103)),x83104),f315(f315(f153(x83101),x83103),f315(f315(f73(a901),x83102),x83104)))+~P1(f315(f315(f223(a901),f315(f315(f73(a901),x83102),x83104)),f315(f178(f902(x83101)),x83103)))
% 168.50/168.38 [8319]~P147(x83192)+E(f315(f315(f8(x83191,x83192),f315(f315(f10(a901,x83192,x83191),f89(x83192)),x83193)),x83194),f315(f89(x83192),f315(f315(f8(x83191,a901),x83193),x83194)))
% 168.50/168.38 [8320]~P143(x83202)+E(f315(f315(f8(x83201,x83202),f315(f315(f10(a1,x83202,x83201),f91(x83202)),x83203)),x83204),f315(f91(x83202),f315(f315(f8(x83201,a1),x83203),x83204)))
% 168.50/168.38 [8370]~P68(x83702)+E(f315(f315(f11(x83701,x83702),f315(f315(f10(x83702,x83702,x83701),f69(x83702)),x83703)),x83704),f315(f69(x83702),f315(f315(f11(x83701,x83702),x83703),x83704)))
% 168.50/168.38 [8371]~P69(x83712)+E(f315(f315(f8(x83711,x83712),f315(f315(f10(x83712,x83712,x83711),f72(x83712)),x83713)),x83714),f315(f72(x83712),f315(f315(f8(x83711,x83712),x83713),x83714)))
% 168.50/168.38 [8373]E(f315(f315(f8(x83731,a901),x83732),f315(f315(f3(f909(x83731,a899)),x83733),f315(f315(f297(x83731),x83734),f177(f909(x83731,a899))))),f315(f315(f3(a901),f315(f315(f8(x83731,a901),x83732),x83733)),f315(x83732,x83734)))+~P1(f315(f315(f317(x83731),x83734),x83733))
% 168.50/168.38 [8392]P1(f315(f315(f223(f909(x83921,a899)),x83922),x83923))+~P1(f315(f315(f223(f909(x83921,a899)),f315(f315(f297(x83921),x83924),x83922)),x83923))
% 168.50/168.38 [8516]~E(f315(f298(x85162,x85163,x85161),f230(f909(x85162,a899))),f230(f909(x85163,a899)))+E(f315(x85161,f315(f84(x85162,x85163,f230(f909(x85162,a899)),x85161),x85164)),x85164)
% 168.50/168.38 [8599]P39(x85991,x85992)+~P39(x85991,f315(f315(f297(f908(x85991,x85991)),f315(f315(f240(x85991,x85991),x85993),x85994)),x85992))
% 168.50/168.38 [8600]P59(x86001,x86002)+~P59(x86001,f315(f315(f297(f908(x86001,x86001)),f315(f315(f240(x86001,x86001),x86003),x86004)),x86002))
% 168.50/168.38 [8605]~P110(x86051)+E(f315(f315(f137(x86051,x86051,f7(x86051)),x86052),f315(f315(f137(x86051,x86051,f7(x86051)),x86053),x86054)),f315(f315(f137(x86051,x86051,f7(x86051)),x86053),f315(f315(f137(x86051,x86051,f7(x86051)),x86052),x86054)))
% 168.50/168.38 [8620]E(x86201,x86202)+~P1(f315(f55(x86203,x86204,f315(f315(f297(x86203),x86201),f177(f909(x86203,a899)))),x86202))
% 168.50/168.38 [8629]E(f315(f315(f123(x86291),f315(f315(f164(x86291),x86292),x86293)),f315(f315(f164(x86291),x86294),f315(f315(f127(x86291),x86292),x86293))),f315(f315(f164(x86291),f315(f315(f73(a901),x86292),x86294)),x86293))+~P1(f315(f315(f223(a901),f315(f315(f73(a901),x86292),x86294)),f315(f178(f902(x86291)),x86293)))
% 168.50/168.38 [8669]P1(f315(f54(x86691),x86692))+~E(x86692,f315(f298(a901,x86691,x86693),f315(f250(a901),f315(f315(f9(a901,a901,a899),f224(a901)),x86694))))
% 168.50/168.38 [8689]~P94(x86891)+E(f315(f131(x86891,x86891,f73(x86891),f315(f315(f73(x86891),x86892),x86893)),x86894),f315(f315(f73(x86891),x86892),f315(f131(x86891,x86891,f73(x86891),x86893),x86894)))
% 168.50/168.38 [8725]P1(f315(f315(f223(f909(x87251,a899)),f315(f252(x87251,x87252),x87253)),f315(f252(x87251,x87252),x87254)))+~P1(f315(f315(f223(f909(f908(x87251,x87252),a899)),x87253),x87254))
% 168.50/168.38 [8737]~P1(f315(f315(f223(a901),x87372),x87374))+P1(f315(f315(f223(f909(x87371,a899)),f315(f161(x87371),f315(f315(f164(x87371),x87372),x87373))),f315(f161(x87371),f315(f315(f164(x87371),x87374),x87373))))
% 168.50/168.38 [8738]~P1(f315(f315(f223(a901),x87384),x87382))+P1(f315(f315(f223(f909(x87381,a899)),f315(f161(x87381),f315(f315(f127(x87381),x87382),x87383))),f315(f161(x87381),f315(f315(f127(x87381),x87384),x87383))))
% 168.50/168.38 [8795]~P1(f315(f54(x87951),f315(f315(f3(f909(x87951,a899)),x87952),x87954)))+P1(f315(f54(x87951),f315(f315(f3(f909(x87951,a899)),x87952),f315(f315(f297(x87951),x87953),x87954))))
% 168.50/168.38 [8837]P1(f315(f315(f317(f908(x88371,x88371)),x88372),f295(x88371,x88373)))+~P1(f315(f315(f317(f908(x88371,x88371)),x88372),f315(f315(f172(f908(x88371,x88371),a899),x88374),x88373)))
% 168.50/168.38 [8923]~P1(f315(f54(x89231),f315(f315(f3(f909(x89231,a899)),x89232),f315(f315(f297(x89231),x89234),x89233))))+P1(f315(f54(x89231),f315(f315(f3(f909(x89231,a899)),x89232),x89233)))
% 168.50/168.38 [9135]~P80(x91351)+P1(f315(f315(f223(x91351),f315(f315(f99(x91351),x91352),f315(f315(f90(x91351),x91353),x91354))),f315(f315(f90(x91351),f315(f315(f99(x91351),x91352),x91353)),f315(f315(f99(x91351),x91352),x91354))))
% 168.50/168.38 [9136]~P110(x91361)+P1(f315(f315(f223(x91361),f315(f315(f222(x91361),x91362),f315(f315(f221(x91361),x91363),x91364))),f315(f315(f221(x91361),f315(f315(f222(x91361),x91362),x91363)),f315(f315(f222(x91361),x91362),x91364))))
% 168.50/168.38 [9283]E(x92831,x92832)+~P1(f315(f315(f317(f908(x92833,x92833)),f315(f315(f240(x92833,x92833),x92831),x92832)),f315(f161(f908(x92833,x92833)),f315(f315(f170(x92833,x92833),x92834),x92834))))
% 168.50/168.38 [9314]~P1(f315(f315(f317(f908(x93141,x93141)),f315(f315(f240(x93141,x93141),x93143),x93142)),f295(x93141,x93144)))+~P39(x93141,f315(f315(f297(f908(x93141,x93141)),f315(f315(f240(x93141,x93141),x93142),x93143)),x93144))
% 168.50/168.38 [9315]~P1(f315(f315(f317(f908(x93151,x93151)),f315(f315(f240(x93151,x93151),x93153),x93152)),f295(x93151,x93154)))+~P59(x93151,f315(f315(f297(f908(x93151,x93151)),f315(f315(f240(x93151,x93151),x93152),x93153)),x93154))
% 168.50/168.38 [9319]E(x93191,x93192)+E(f315(f125(x93193,f315(f315(f10(a899,a899,x93193),a310),f315(a312,x93191))),f315(f315(f140(x93193),x93192),x93194)),f315(f315(f140(x93193),x93192),f315(f125(x93193,f315(f315(f10(a899,a899,x93193),a310),f315(a312,x93191))),x93194)))
% 168.50/168.38 [9350]~P26(x93502,x93501,x93503,f230(f909(x93502,a899)),f230(f909(x93501,a899)))+E(f315(f298(x93501,x93502,f84(x93502,x93501,f230(f909(x93502,a899)),x93503)),x93504),f315(f299(x93502,x93501,x93503),x93504))
% 168.50/168.38 [9366]~P80(x93661)+P1(f315(f315(f223(x93661),f315(f315(f99(x93661),f315(f315(f90(x93661),x93662),x93663)),f315(f315(f90(x93661),x93662),x93664))),f315(f315(f90(x93661),x93662),f315(f315(f99(x93661),x93663),x93664))))
% 168.50/168.38 [9367]~P110(x93671)+P1(f315(f315(f223(x93671),f315(f315(f222(x93671),f315(f315(f221(x93671),x93672),x93673)),f315(f315(f221(x93671),x93672),x93674))),f315(f315(f221(x93671),x93672),f315(f315(f222(x93671),x93673),x93674))))
% 168.50/168.38 [9430]~P26(x94302,x94301,x94304,f230(f909(x94302,a899)),f230(f909(x94301,a899)))+E(f315(f250(x94301),f315(f315(f10(x94302,a899,x94301),x94303),f84(x94302,x94301,f230(f909(x94302,a899)),x94304))),f315(f298(x94302,x94301,x94304),f315(f250(x94302),x94303)))
% 168.50/168.38 [9444]~E(f315(f298(x94442,x94441,x94443),f230(f909(x94442,a899))),f230(f909(x94441,a899)))+P1(f315(f315(f223(f909(x94441,a899)),f315(f72(f909(x94441,a899)),f315(f298(x94442,x94441,x94443),x94444))),f315(f298(x94442,x94441,x94443),f315(f72(f909(x94442,a899)),x94444))))
% 168.50/168.38 [9778]P1(f315(f315(f317(f908(x97781,x97781)),f315(f315(f240(x97781,x97781),x97782),x97783)),f315(f274(x97781,x97781),f315(f315(f277(x97781,x97781,x97781),x97784),f295(x97781,x97784)))))+~P1(f315(f315(f317(f908(x97781,x97781)),f315(f315(f240(x97781,x97781),x97782),x97783)),f315(f315(f277(x97781,x97781,x97781),f315(f274(x97781,x97781),x97784)),f295(x97781,f315(f274(x97781,x97781),x97784)))))
% 168.50/168.38 [9779]~P1(f315(f315(f317(f908(x97791,x97791)),f315(f315(f240(x97791,x97791),x97792),x97793)),f315(f274(x97791,x97791),f315(f315(f277(x97791,x97791,x97791),x97794),f295(x97791,x97794)))))+P1(f315(f315(f317(f908(x97791,x97791)),f315(f315(f240(x97791,x97791),x97792),x97793)),f315(f315(f277(x97791,x97791,x97791),f315(f274(x97791,x97791),x97794)),f295(x97791,f315(f274(x97791,x97791),x97794)))))
% 168.50/168.38 [9800]~P1(f315(f315(f317(x98002),x98004),f315(f272(x98001,x98002),x98003)))+P1(f315(f315(f317(f908(x98001,x98002)),f315(f315(f240(x98001,x98002),f548(x98003,x98001,x98004,x98002)),x98004)),x98003))
% 168.50/168.38 [9801]~P1(f315(f315(f317(x98012),x98014),f315(f272(x98011,x98012),x98013)))+P1(f315(f315(f317(f908(x98011,x98012)),f315(f315(f240(x98011,x98012),f549(x98013,x98011,x98014,x98012)),x98014)),x98013))
% 168.50/168.38 [9826]~P1(f315(f315(f317(x98261),x98264),f315(f315(f99(f909(x98261,a899)),x98262),x98263)))+P1(f315(f315(f315(f99(f909(x98261,a899)),f315(f315(f9(x98261,f909(x98261,a899),a899),f317(x98261)),x98262)),f315(f315(f9(x98261,f909(x98261,a899),a899),f317(x98261)),x98263)),x98264))
% 168.50/168.38 [9827]~P1(f315(f315(f317(x98271),x98274),f315(f315(f90(f909(x98271,a899)),x98272),x98273)))+P1(f315(f315(f315(f90(f909(x98271,a899)),f315(f315(f9(x98271,f909(x98271,a899),a899),f317(x98271)),x98272)),f315(f315(f9(x98271,f909(x98271,a899),a899),f317(x98271)),x98273)),x98274))
% 168.50/168.38 [9907]~P1(f315(f315(f317(f908(x99071,x99071)),f315(f315(f240(x99071,x99071),x99074),x99073)),f315(f315(f277(x99071,x99071,x99071),x99072),f295(x99071,x99072))))+P1(f315(f315(f317(f908(x99071,x99071)),f315(f315(f240(x99071,x99071),f614(x99072,x99073,x99074,x99071)),x99073)),x99072))
% 168.50/168.38 [9942]P1(f315(f315(f317(x99421),x99422),f315(f315(f99(f909(x99421,a899)),x99423),x99424)))+~P1(f315(f315(f315(f99(f909(x99421,a899)),f315(f315(f9(x99421,f909(x99421,a899),a899),f317(x99421)),x99423)),f315(f315(f9(x99421,f909(x99421,a899),a899),f317(x99421)),x99424)),x99422))
% 168.50/168.38 [9943]P1(f315(f315(f317(x99431),x99432),f315(f315(f90(f909(x99431,a899)),x99433),x99434)))+~P1(f315(f315(f315(f90(f909(x99431,a899)),f315(f315(f9(x99431,f909(x99431,a899),a899),f317(x99431)),x99433)),f315(f315(f9(x99431,f909(x99431,a899),a899),f317(x99431)),x99434)),x99432))
% 168.50/168.38 [10224]P34(x102241,f315(f315(f9(x102241,f909(f908(x102241,x102241),a899),f909(x102241,a899)),f315(f315(f10(f909(x102241,f909(f909(f908(x102241,x102241),a899),a899)),f909(f909(f908(x102241,x102241),a899),f909(x102241,a899)),x102241),f9(x102241,f909(f908(x102241,x102241),a899),a899)),f315(f315(f10(f909(x102241,f908(x102241,x102241)),f909(x102241,f909(f909(f908(x102241,x102241),a899),a899)),x102241),f315(f10(f908(x102241,x102241),f909(f909(f908(x102241,x102241),a899),a899),x102241),f317(f908(x102241,x102241)))),f240(x102241,x102241)))),x102242),x102243,x102244)+~P1(f315(f315(f317(f908(f902(x102241),f902(x102241))),f315(f315(f240(f902(x102241),f902(x102241)),x102243),x102244)),f147(x102241,x102242)))
% 168.50/168.38 [10228]P60(x102281,f315(f315(f9(x102281,f909(f908(x102281,x102281),a899),f909(x102281,a899)),f315(f315(f10(f909(x102281,f909(f909(f908(x102281,x102281),a899),a899)),f909(f909(f908(x102281,x102281),a899),f909(x102281,a899)),x102281),f9(x102281,f909(f908(x102281,x102281),a899),a899)),f315(f315(f10(f909(x102281,f908(x102281,x102281)),f909(x102281,f909(f909(f908(x102281,x102281),a899),a899)),x102281),f315(f10(f908(x102281,x102281),f909(f909(f908(x102281,x102281),a899),a899),x102281),f317(f908(x102281,x102281)))),f240(x102281,x102281)))),x102282),x102283,x102284)+~P1(f315(f315(f317(f908(f909(x102281,a899),f909(x102281,a899))),f315(f315(f240(f909(x102281,a899),f909(x102281,a899)),x102283),x102284)),f306(x102281,x102282)))
% 168.50/168.38 [10263]E(x102631,x102632)+~E(f315(f315(f9(x102633,f909(f908(x102633,x102634),a899),f909(x102634,a899)),f315(f315(f10(f909(x102634,f909(f909(f908(x102633,x102634),a899),a899)),f909(f909(f908(x102633,x102634),a899),f909(x102634,a899)),x102633),f9(x102634,f909(f908(x102633,x102634),a899),a899)),f315(f315(f10(f909(x102634,f908(x102633,x102634)),f909(x102634,f909(f909(f908(x102633,x102634),a899),a899)),x102633),f315(f10(f908(x102633,x102634),f909(f909(f908(x102633,x102634),a899),a899),x102634),f317(f908(x102633,x102634)))),f240(x102633,x102634)))),x102631),f315(f315(f9(x102633,f909(f908(x102633,x102634),a899),f909(x102634,a899)),f315(f315(f10(f909(x102634,f909(f909(f908(x102633,x102634),a899),a899)),f909(f909(f908(x102633,x102634),a899),f909(x102634,a899)),x102633),f9(x102634,f909(f908(x102633,x102634),a899),a899)),f315(f315(f10(f909(x102634,f908(x102633,x102634)),f909(x102634,f909(f909(f908(x102633,x102634),a899),a899)),x102633),f315(f10(f908(x102633,x102634),f909(f909(f908(x102633,x102634),a899),a899),x102634),f317(f908(x102633,x102634)))),f240(x102633,x102634)))),x102632))
% 168.50/168.38 [10266]~P34(x102661,f315(f315(f9(x102661,f909(f908(x102661,x102661),a899),f909(x102661,a899)),f315(f315(f10(f909(x102661,f909(f909(f908(x102661,x102661),a899),a899)),f909(f909(f908(x102661,x102661),a899),f909(x102661,a899)),x102661),f9(x102661,f909(f908(x102661,x102661),a899),a899)),f315(f315(f10(f909(x102661,f908(x102661,x102661)),f909(x102661,f909(f909(f908(x102661,x102661),a899),a899)),x102661),f315(f10(f908(x102661,x102661),f909(f909(f908(x102661,x102661),a899),a899),x102661),f317(f908(x102661,x102661)))),f240(x102661,x102661)))),x102664),x102662,x102663)+P1(f315(f315(f317(f908(f902(x102661),f902(x102661))),f315(f315(f240(f902(x102661),f902(x102661)),x102662),x102663)),f147(x102661,x102664)))
% 168.50/168.38 [10267]~P60(x102671,f315(f315(f9(x102671,f909(f908(x102671,x102671),a899),f909(x102671,a899)),f315(f315(f10(f909(x102671,f909(f909(f908(x102671,x102671),a899),a899)),f909(f909(f908(x102671,x102671),a899),f909(x102671,a899)),x102671),f9(x102671,f909(f908(x102671,x102671),a899),a899)),f315(f315(f10(f909(x102671,f908(x102671,x102671)),f909(x102671,f909(f909(f908(x102671,x102671),a899),a899)),x102671),f315(f10(f908(x102671,x102671),f909(f909(f908(x102671,x102671),a899),a899),x102671),f317(f908(x102671,x102671)))),f240(x102671,x102671)))),x102674),x102672,x102673)+P1(f315(f315(f317(f908(f909(x102671,a899),f909(x102671,a899))),f315(f315(f240(f909(x102671,a899),f909(x102671,a899)),x102672),x102673)),f306(x102671,x102674)))
% 168.50/168.38 [7625]~P97(x76251)+E(f315(f315(f74(x76251),f315(f92(x76251),x76252)),f315(f315(f74(x76251),f315(f92(x76251),x76253)),x76254)),f315(f315(f74(x76251),f315(f92(x76251),f315(f315(f74(a1),x76252),x76253))),x76254))
% 168.50/168.38 [7626]~P97(x76261)+E(f315(f315(f73(x76261),f315(f92(x76261),x76262)),f315(f315(f3(x76261),f315(f92(x76261),x76263)),x76264)),f315(f315(f3(x76261),f315(f92(x76261),f315(f315(f73(a1),x76262),x76263))),x76264))
% 168.50/168.38 [7627]~P97(x76271)+E(f315(f315(f73(x76271),f315(f92(x76271),x76272)),f315(f315(f73(x76271),f315(f92(x76271),x76273)),x76274)),f315(f315(f73(x76271),f315(f92(x76271),f315(f315(f73(a1),x76272),x76273))),x76274))
% 168.50/168.38 [7669]~P147(x76691)+E(f315(f154(x76691),f315(f315(f143(x76692,x76691),f315(f18(x76691,x76692),x76693)),x76694)),f315(f315(f74(x76691),f315(f89(x76691),f315(f178(f902(x76692)),x76694))),x76693))
% 168.50/168.38 [7908]E(f315(f256(x79081,f315(f315(f140(f908(a88,x79081)),x79082),x79083)),x79084),f315(f244(a88,x79081),x79082))+~P1(f315(f315(f224(a88),x79084),f315(f239(a88,x79081),x79082)))
% 168.50/168.38 [7949]~P97(x79491)+E(f315(f315(f73(x79491),f315(f92(x79491),x79492)),f315(f315(f3(x79491),x79493),f315(f92(x79491),x79494))),f315(f315(f73(x79491),f315(f92(x79491),f315(f315(f73(a1),x79492),f315(f72(a1),x79494)))),x79493))
% 168.50/168.38 [8083]E(f315(f256(x80831,x80832),f315(f315(f3(a88),x80833),f315(f239(a88,x80831),x80834))),f315(f256(x80831,f315(f315(f140(f908(a88,x80831)),x80834),x80832)),x80833))+P1(f315(f315(f224(a88),x80833),f315(f239(a88,x80831),x80834)))
% 168.50/168.38 [8522]~P1(f315(f315(f317(x85221),x85222),f315(f161(x85221),f103(x85221,x85224))))+P1(f315(f315(f317(x85221),x85222),f315(f161(x85221),f103(x85221,f315(f315(f123(x85221),x85223),x85224)))))
% 168.50/168.38 [8523]~P1(f315(f315(f317(x85231),x85232),f315(f161(x85231),f103(x85231,x85233))))+P1(f315(f315(f317(x85231),x85232),f315(f161(x85231),f103(x85231,f315(f315(f123(x85231),x85233),x85234)))))
% 168.50/168.38 [8542]E(f315(f315(f99(f909(x85421,a899)),f315(f315(f90(f909(x85421,a899)),x85422),x85423)),x85424),f315(f315(f90(f909(x85421,a899)),x85422),f315(f315(f99(f909(x85421,a899)),x85423),x85424)))+~P1(f315(f315(f223(f909(x85421,a899)),x85424),x85422))
% 168.50/168.38 [8851]~E(f315(f315(f99(f909(x88511,a899)),f315(f315(f90(f909(x88511,a899)),x88513),x88514)),x88512),f315(f315(f90(f909(x88511,a899)),x88513),f315(f315(f99(f909(x88511,a899)),x88514),x88512)))+P1(f315(f315(f223(f909(x88511,a899)),x88512),x88513))
% 168.50/168.38 [9140]~P1(f315(f315(f223(f909(x91401,a899)),x91402),f315(f315(f99(f909(x91401,a899)),x91403),x91404)))+P1(f315(f315(f223(f909(x91401,a899)),f315(f315(f3(f909(x91401,a899)),x91402),x91403)),x91404))
% 168.50/168.38 [9255]~E(f315(f298(x92551,x92552,x92553),f230(f909(x92551,a899))),f230(f909(x92552,a899)))+E(f315(f298(x92551,x92552,x92553),f315(f298(x92552,x92551,f84(x92551,x92552,f230(f909(x92551,a899)),x92553)),x92554)),x92554)
% 168.50/168.38 [9260]P1(f315(f315(f223(f909(x92601,a899)),x92602),f315(f315(f99(f909(x92601,a899)),x92603),x92604)))+~P1(f315(f315(f223(f909(x92601,a899)),f315(f315(f3(f909(x92601,a899)),x92602),x92603)),x92604))
% 168.50/168.38 [9345]~P89(x93451)+E(f315(f69(x93451),f315(f315(f8(x93452,x93451),f315(f315(f10(x93451,x93451,x93452),f69(x93451)),x93453)),x93454)),f315(f315(f8(x93452,x93451),f315(f315(f10(x93451,x93451,x93452),f69(x93451)),x93453)),x93454))
% 168.50/168.38 [9520]~P89(x95201)+P1(f315(f315(f223(x95201),f2(x95201)),f315(f315(f8(x95202,x95201),f315(f315(f10(x95201,x95201,x95202),f69(x95201)),x95203)),x95204)))
% 168.50/168.38 [9524]~P69(x95241)+E(f315(f154(x95241),f315(f315(f143(x95242,x95241),f315(f66(x95241,x95241,x95242,f72(x95241)),x95243)),x95244)),f315(f72(x95241),f315(f154(x95241),f315(f315(f143(x95242,x95241),x95243),x95244))))
% 168.50/168.38 [9674]~P89(x96741)+P1(f315(f315(f223(x96741),f315(f69(x96741),f315(f315(f8(x96742,x96741),x96743),x96744))),f315(f315(f8(x96742,x96741),f315(f315(f10(x96741,x96741,x96742),f69(x96741)),x96743)),x96744)))
% 168.50/168.38 [9703]~E(f315(f315(f73(a901),x97031),x97034),f315(f315(f73(a901),x97033),x97032))+P1(f315(f315(f317(f908(f908(a901,a901),f908(a901,a901))),f315(f315(f240(f908(a901,a901),f908(a901,a901)),f315(f315(f240(a901,a901),x97031),x97032)),f315(f315(f240(a901,a901),x97033),x97034))),a97))
% 168.50/168.38 [9704]~P1(f315(f315(f224(a901),x97041),x97043))+P1(f315(f315(f317(f908(f908(a901,a901),f908(a901,a901))),f315(f315(f240(f908(a901,a901),f908(a901,a901)),f315(f315(f240(a901,a901),x97041),x97042)),f315(f315(f240(a901,a901),x97043),x97044))),a26))
% 168.50/168.38 [9705]~P1(f315(f315(f224(a901),x97051),x97053))+P1(f315(f315(f317(f908(f908(a901,a901),f908(a901,a901))),f315(f315(f240(f908(a901,a901),f908(a901,a901)),f315(f315(f240(a901,a901),x97051),x97052)),f315(f315(f240(a901,a901),x97053),x97054))),a64))
% 168.50/168.38 [9851]E(f315(f315(f73(a901),x98511),x98512),f315(f315(f73(a901),x98513),x98514))+~P1(f315(f315(f317(f908(f908(a901,a901),f908(a901,a901))),f315(f315(f240(f908(a901,a901),f908(a901,a901)),f315(f315(f240(a901,a901),x98511),x98514)),f315(f315(f240(a901,a901),x98513),x98512))),a97))
% 168.50/168.38 [9882]E(f315(f315(f153(x98821),f315(f315(f127(x98821),f315(f178(f902(x98821)),f166(x98821,x98822,x98823))),x98823)),x98824),f315(f315(f153(x98821),x98823),f315(f315(f73(a901),x98824),f315(f178(f902(x98821)),f166(x98821,x98822,x98823)))))+~P1(f315(f315(f224(a901),x98824),f315(f178(f902(x98821)),f315(f315(f127(x98821),f315(f178(f902(x98821)),f166(x98821,x98822,x98823))),x98823))))
% 168.50/168.38 [9898]~P1(f315(f315(f317(x98982),x98984),f315(f315(f32(x98981,f909(x98982,a899)),f230(f909(x98981,a899))),x98983)))+P1(f315(f315(f315(f32(x98981,f909(x98982,a899)),f230(f909(x98981,a899))),f315(f315(f10(f909(x98982,a899),f909(x98982,a899),x98981),f315(f9(x98982,f909(x98982,a899),a899),f317(x98982))),x98983)),x98984))
% 168.50/168.38 [9899]~P1(f315(f315(f317(x98992),x98994),f315(f315(f33(x98991,f909(x98992,a899)),f230(f909(x98991,a899))),x98993)))+P1(f315(f315(f315(f33(x98991,f909(x98992,a899)),f230(f909(x98991,a899))),f315(f315(f10(f909(x98992,a899),f909(x98992,a899),x98991),f315(f9(x98992,f909(x98992,a899),a899),f317(x98992))),x98993)),x98994))
% 168.50/168.38 [9968]~P1(f315(f42(x99681,x99682),f315(f315(f240(a1,a1),x99684),x99683)))+P1(f315(f42(f315(f72(a1),x99681),x99682),f315(f315(f240(a1,a1),f315(f315(f315(f85(a1),f315(f315(a312,x99683),f2(a1))),f315(f72(a1),x99684)),f315(f315(f3(a1),f315(f72(a1),x99684)),f71(a1)))),f315(f315(f315(f85(a1),f315(f315(a312,x99683),f2(a1))),f2(a1)),f315(f315(f3(a1),x99682),x99683)))))
% 168.50/168.38 [9980]P1(f315(f315(f317(x99801),x99802),f315(f315(f32(x99803,f909(x99801,a899)),f230(f909(x99803,a899))),x99804)))+~P1(f315(f315(f315(f32(x99803,f909(x99801,a899)),f230(f909(x99803,a899))),f315(f315(f10(f909(x99801,a899),f909(x99801,a899),x99803),f315(f9(x99801,f909(x99801,a899),a899),f317(x99801))),x99804)),x99802))
% 168.50/168.38 [9981]P1(f315(f315(f317(x99811),x99812),f315(f315(f33(x99813,f909(x99811,a899)),f230(f909(x99813,a899))),x99814)))+~P1(f315(f315(f315(f33(x99813,f909(x99811,a899)),f230(f909(x99813,a899))),f315(f315(f10(f909(x99811,a899),f909(x99811,a899),x99813),f315(f9(x99811,f909(x99811,a899),a899),f317(x99811))),x99814)),x99812))
% 168.50/168.38 [9993]E(f315(f315(f33(a901,f909(x99931,a899)),f230(f909(a901,a899))),x99932),f315(f315(f33(a901,f909(x99931,a899)),f230(f909(a901,a899))),x99933))+~E(f315(f315(f33(a901,f909(x99931,a899)),f315(f290(a901,f2(a901)),f487(x99932,x99934,x99933,x99931))),x99933),f315(f315(f33(a901,f909(x99931,a899)),f315(f290(a901,f2(a901)),f315(f315(f73(a901),f487(x99932,x99934,x99933,x99931)),x99934))),x99932))
% 168.50/168.38 [10344]~P1(f315(f315(f223(f909(f908(x103441,x103442),a899)),x103443),x103444))+P1(f315(f315(f223(f909(x103441,f909(x103442,a899))),f315(f315(f9(x103441,f909(f908(x103441,x103442),a899),f909(x103442,a899)),f315(f315(f10(f909(x103442,f909(f909(f908(x103441,x103442),a899),a899)),f909(f909(f908(x103441,x103442),a899),f909(x103442,a899)),x103441),f9(x103442,f909(f908(x103441,x103442),a899),a899)),f315(f315(f10(f909(x103442,f908(x103441,x103442)),f909(x103442,f909(f909(f908(x103441,x103442),a899),a899)),x103441),f315(f10(f908(x103441,x103442),f909(f909(f908(x103441,x103442),a899),a899),x103442),f317(f908(x103441,x103442)))),f240(x103441,x103442)))),x103443)),f315(f315(f9(x103441,f909(f908(x103441,x103442),a899),f909(x103442,a899)),f315(f315(f10(f909(x103442,f909(f909(f908(x103441,x103442),a899),a899)),f909(f909(f908(x103441,x103442),a899),f909(x103442,a899)),x103441),f9(x103442,f909(f908(x103441,x103442),a899),a899)),f315(f315(f10(f909(x103442,f908(x103441,x103442)),f909(x103442,f909(f909(f908(x103441,x103442),a899),a899)),x103441),f315(f10(f908(x103441,x103442),f909(f909(f908(x103441,x103442),a899),a899),x103442),f317(f908(x103441,x103442)))),f240(x103441,x103442)))),x103444)))
% 168.50/168.38 [10360]P1(f315(f315(f223(f909(f908(x103601,x103602),a899)),x103603),x103604))+~P1(f315(f315(f223(f909(x103601,f909(x103602,a899))),f315(f315(f9(x103601,f909(f908(x103601,x103602),a899),f909(x103602,a899)),f315(f315(f10(f909(x103602,f909(f909(f908(x103601,x103602),a899),a899)),f909(f909(f908(x103601,x103602),a899),f909(x103602,a899)),x103601),f9(x103602,f909(f908(x103601,x103602),a899),a899)),f315(f315(f10(f909(x103602,f908(x103601,x103602)),f909(x103602,f909(f909(f908(x103601,x103602),a899),a899)),x103601),f315(f10(f908(x103601,x103602),f909(f909(f908(x103601,x103602),a899),a899),x103602),f317(f908(x103601,x103602)))),f240(x103601,x103602)))),x103603)),f315(f315(f9(x103601,f909(f908(x103601,x103602),a899),f909(x103602,a899)),f315(f315(f10(f909(x103602,f909(f909(f908(x103601,x103602),a899),a899)),f909(f909(f908(x103601,x103602),a899),f909(x103602,a899)),x103601),f9(x103602,f909(f908(x103601,x103602),a899),a899)),f315(f315(f10(f909(x103602,f908(x103601,x103602)),f909(x103602,f909(f909(f908(x103601,x103602),a899),a899)),x103601),f315(f10(f908(x103601,x103602),f909(f909(f908(x103601,x103602),a899),a899),x103602),f317(f908(x103601,x103602)))),f240(x103601,x103602)))),x103604)))
% 168.50/168.38 [9393]~P1(f315(f315(f317(f908(x93931,x93931)),x93932),f295(x93931,x93934)))+P1(f315(f315(f317(f908(x93931,x93931)),x93932),f295(x93931,f315(f315(f99(f909(f908(x93931,x93931),a899)),x93933),x93934))))
% 168.50/168.38 [9394]~P1(f315(f315(f317(f908(x93941,x93941)),x93942),f295(x93941,x93943)))+P1(f315(f315(f317(f908(x93941,x93941)),x93942),f295(x93941,f315(f315(f99(f909(f908(x93941,x93941),a899)),x93943),x93944))))
% 168.50/168.38 [10079]~P1(f315(f315(f223(a901),f315(f315(f73(a901),x100791),x100794)),f315(f315(f73(a901),x100793),x100792)))+P1(f315(f315(f223(a1),f315(a82,f315(f273(f908(a901,a901),f908(a901,a901),a97),f315(f315(f297(f908(a901,a901)),f315(f315(f240(a901,a901),x100791),x100792)),f177(f909(f908(a901,a901),a899)))))),f315(a82,f315(f273(f908(a901,a901),f908(a901,a901),a97),f315(f315(f297(f908(a901,a901)),f315(f315(f240(a901,a901),x100793),x100794)),f177(f909(f908(a901,a901),a899)))))))
% 168.50/168.38 [10080]~P1(f315(f315(f224(a901),f315(f315(f73(a901),x100801),x100804)),f315(f315(f73(a901),x100803),x100802)))+P1(f315(f315(f224(a1),f315(a82,f315(f273(f908(a901,a901),f908(a901,a901),a97),f315(f315(f297(f908(a901,a901)),f315(f315(f240(a901,a901),x100801),x100802)),f177(f909(f908(a901,a901),a899)))))),f315(a82,f315(f273(f908(a901,a901),f908(a901,a901),a97),f315(f315(f297(f908(a901,a901)),f315(f315(f240(a901,a901),x100803),x100804)),f177(f909(f908(a901,a901),a899)))))))
% 168.50/168.38 [10167]P1(f315(f315(f223(a901),f315(f315(f73(a901),x101671),x101672)),f315(f315(f73(a901),x101673),x101674)))+~P1(f315(f315(f223(a1),f315(a82,f315(f273(f908(a901,a901),f908(a901,a901),a97),f315(f315(f297(f908(a901,a901)),f315(f315(f240(a901,a901),x101671),x101674)),f177(f909(f908(a901,a901),a899)))))),f315(a82,f315(f273(f908(a901,a901),f908(a901,a901),a97),f315(f315(f297(f908(a901,a901)),f315(f315(f240(a901,a901),x101673),x101672)),f177(f909(f908(a901,a901),a899)))))))
% 168.50/168.38 [10168]P1(f315(f315(f224(a901),f315(f315(f73(a901),x101681),x101682)),f315(f315(f73(a901),x101683),x101684)))+~P1(f315(f315(f224(a1),f315(a82,f315(f273(f908(a901,a901),f908(a901,a901),a97),f315(f315(f297(f908(a901,a901)),f315(f315(f240(a901,a901),x101681),x101684)),f177(f909(f908(a901,a901),a899)))))),f315(a82,f315(f273(f908(a901,a901),f908(a901,a901),a97),f315(f315(f297(f908(a901,a901)),f315(f315(f240(a901,a901),x101683),x101682)),f177(f909(f908(a901,a901),a899)))))))
% 168.50/168.38 [10210]P1(f315(f315(f223(f909(x102101,a899)),f315(f315(f33(a901,f909(x102101,a899)),f230(f909(a901,a899))),x102102)),f315(f315(f33(a901,f909(x102101,a899)),f230(f909(a901,a899))),x102103)))+~P1(f315(f315(f223(f909(x102101,a899)),f315(f315(f33(a901,f909(x102101,a899)),f315(f290(a901,f2(a901)),f488(x102103,x102104,x102102,x102101))),x102102)),f315(f315(f33(a901,f909(x102101,a899)),f315(f290(a901,f2(a901)),f315(f315(f73(a901),f488(x102103,x102104,x102102,x102101)),x102104))),x102103)))
% 168.50/168.38 [10270]P1(f315(f315(f223(a88),x102704),f2(a88)))+E(f315(f315(f247(f908(a88,a88),f908(x102701,f909(a904,a311)),f908(a88,a88),f908(f909(a88,f909(a899,f905(f903(x102701)))),f908(a88,a88))),f315(x102702,x102703)),f315(f315(f10(f909(f909(a88,f909(a899,f905(f903(x102701)))),f909(f908(a88,a88),f908(f909(a88,f909(a899,f905(f903(x102701)))),f908(a88,a88)))),f909(f908(a88,a88),f908(f909(a88,f909(a899,f905(f903(x102701)))),f908(a88,a88))),f908(x102701,f909(a904,a311))),f315(f247(f908(a88,a88),f909(a88,f909(a899,f905(f903(x102701)))),f908(a88,a88),f908(f909(a88,f909(a899,f905(f903(x102701)))),f908(a88,a88))),f265(x102701,x102702,f315(f315(f3(a88),x102704),f71(a88)),x102703))),f315(f315(f10(f909(f909(a88,f909(a899,f905(f903(x102701)))),f909(a88,f909(a899,f905(f903(x102701))))),f909(f909(a88,f909(a899,f905(f903(x102701)))),f909(f908(a88,a88),f908(f909(a88,f909(a899,f905(f903(x102701)))),f908(a88,a88)))),f908(x102701,f909(a904,a311))),f315(f10(f909(a88,f909(a899,f905(f903(x102701)))),f909(f908(a88,a88),f908(f909(a88,f909(a899,f905(f903(x102701)))),f908(a88,a88))),f909(a88,f909(a899,f905(f903(x102701))))),f240(f909(a88,f909(a899,f905(f903(x102701)))),f908(a88,a88)))),f315(f315(f10(f909(a88,f909(a899,f905(f903(x102701)))),f909(f909(a88,f909(a899,f905(f903(x102701)))),f909(a88,f909(a899,f905(f903(x102701))))),f908(x102701,f909(a904,a311))),f37(x102701)),f315(f315(f10(x102701,f909(a88,f909(a899,f905(f903(x102701)))),f908(x102701,f909(a904,a311))),f35(x102701)),f239(x102701,f909(a904,a311))))))),f265(x102701,x102702,x102704,x102703))
% 168.50/168.38 [10334]~P1(f315(f315(f317(x103342),x103344),f315(f272(x103341,x103342),x103343)))+P1(f315(f238(x103341,x103342,f315(f315(f9(x103341,f909(f908(x103341,x103342),a899),f909(x103342,a899)),f315(f315(f10(f909(x103342,f909(f909(f908(x103341,x103342),a899),a899)),f909(f909(f908(x103341,x103342),a899),f909(x103342,a899)),x103341),f9(x103342,f909(f908(x103341,x103342),a899),a899)),f315(f315(f10(f909(x103342,f908(x103341,x103342)),f909(x103342,f909(f909(f908(x103341,x103342),a899),a899)),x103341),f315(f10(f908(x103341,x103342),f909(f909(f908(x103341,x103342),a899),a899),x103342),f317(f908(x103341,x103342)))),f240(x103341,x103342)))),x103343)),x103344))
% 168.50/168.38 [10335]~P1(f315(f315(f317(x103351),x103354),f315(f252(x103351,x103352),x103353)))+P1(f315(f237(x103351,x103352,f315(f315(f9(x103351,f909(f908(x103351,x103352),a899),f909(x103352,a899)),f315(f315(f10(f909(x103352,f909(f909(f908(x103351,x103352),a899),a899)),f909(f909(f908(x103351,x103352),a899),f909(x103352,a899)),x103351),f9(x103352,f909(f908(x103351,x103352),a899),a899)),f315(f315(f10(f909(x103352,f908(x103351,x103352)),f909(x103352,f909(f909(f908(x103351,x103352),a899),a899)),x103351),f315(f10(f908(x103351,x103352),f909(f909(f908(x103351,x103352),a899),a899),x103352),f317(f908(x103351,x103352)))),f240(x103351,x103352)))),x103353)),x103354))
% 168.50/168.38 [10347]P1(f315(f315(f317(x103471),x103472),f315(f272(x103473,x103471),x103474)))+~P1(f315(f238(x103473,x103471,f315(f315(f9(x103473,f909(f908(x103473,x103471),a899),f909(x103471,a899)),f315(f315(f10(f909(x103471,f909(f909(f908(x103473,x103471),a899),a899)),f909(f909(f908(x103473,x103471),a899),f909(x103471,a899)),x103473),f9(x103471,f909(f908(x103473,x103471),a899),a899)),f315(f315(f10(f909(x103471,f908(x103473,x103471)),f909(x103471,f909(f909(f908(x103473,x103471),a899),a899)),x103473),f315(f10(f908(x103473,x103471),f909(f909(f908(x103473,x103471),a899),a899),x103471),f317(f908(x103473,x103471)))),f240(x103473,x103471)))),x103474)),x103472))
% 168.50/168.38 [10348]P1(f315(f315(f317(x103481),x103482),f315(f252(x103481,x103483),x103484)))+~P1(f315(f237(x103481,x103483,f315(f315(f9(x103481,f909(f908(x103481,x103483),a899),f909(x103483,a899)),f315(f315(f10(f909(x103483,f909(f909(f908(x103481,x103483),a899),a899)),f909(f909(f908(x103481,x103483),a899),f909(x103483,a899)),x103481),f9(x103483,f909(f908(x103481,x103483),a899),a899)),f315(f315(f10(f909(x103483,f908(x103481,x103483)),f909(x103483,f909(f909(f908(x103481,x103483),a899),a899)),x103481),f315(f10(f908(x103481,x103483),f909(f909(f908(x103481,x103483),a899),a899),x103483),f317(f908(x103481,x103483)))),f240(x103481,x103483)))),x103484)),x103482))
% 168.50/168.38 [10004]P1(f315(f149(x100041,x100042),x100043))+~P1(f315(f149(x100041,f315(f315(f20(x100041,a899,a899),f315(f315(f10(a899,f909(a899,a899),x100041),a313),x100044)),x100042)),x100043))
% 168.50/168.38 [10005]P1(f315(f149(x100051,x100052),x100053))+~P1(f315(f149(x100051,f315(f315(f20(x100051,a899,a899),f315(f315(f10(a899,f909(a899,a899),x100051),a313),x100052)),x100054)),x100053))
% 168.50/168.38 [10091]~P121(x100911)+E(f315(f315(f74(x100911),f315(f315(f73(x100911),f71(x100911)),f71(x100911))),f315(f315(f8(a901,x100911),f315(f315(f10(x100911,x100911,a901),f315(f73(x100911),x100912)),f315(f315(f9(a901,x100911,x100911),f315(f315(f10(x100911,f909(x100911,x100911),a901),f74(x100911)),f89(x100911))),x100913))),f315(f270(a901),x100914))),f315(f315(f74(x100911),f315(f89(x100911),x100914)),f315(f315(f73(x100911),x100912),f315(f315(f73(x100911),x100912),f315(f315(f74(x100911),f315(f89(x100911),f315(f315(f3(a901),x100914),f71(a901)))),x100913)))))
% 168.50/168.38 [10231]P1(f315(x102311,f558(x102312,x102313,x102314,x102311)))+P39(x102312,f315(f250(f908(x102312,x102312)),f315(f245(x102312,x102312,a899),f315(f315(f10(f909(x102312,a899),f909(x102312,a899),x102312),f315(f20(x102312,a899,a899),f315(f315(f10(a899,f909(a899,a899),x102312),a313),x102311))),f315(f315(f9(x102312,f909(x102312,x102312),f909(x102312,a899)),f315(f315(f10(f909(x102312,a899),f909(f909(x102312,x102312),f909(x102312,a899)),x102312),f10(x102312,a899,x102312)),a312)),x102313)))))
% 168.50/168.38 [10245]~P1(f315(f315(f224(a901),f315(x102454,f315(x102453,f558(x102451,x102453,x102454,x102452)))),f315(x102454,f558(x102451,x102453,x102454,x102452))))+P39(x102451,f315(f250(f908(x102451,x102451)),f315(f245(x102451,x102451,a899),f315(f315(f10(f909(x102451,a899),f909(x102451,a899),x102451),f315(f20(x102451,a899,a899),f315(f315(f10(a899,f909(a899,a899),x102451),a313),x102452))),f315(f315(f9(x102451,f909(x102451,x102451),f909(x102451,a899)),f315(f315(f10(f909(x102451,a899),f909(f909(x102451,x102451),f909(x102451,a899)),x102451),f10(x102451,a899,x102451)),a312)),x102453)))))
% 168.50/168.38 [10321]~P5(x103211)+E(f30(x103211,f315(f250(x103211),f315(f315(f10(f909(f909(x103212,x103211),a899),a899,x103211),f80(f909(x103212,x103211))),f315(f315(f10(f909(f909(x103212,x103211),a899),f909(f909(x103212,x103211),a899),x103211),f315(f20(f909(x103212,x103211),a899,a899),f315(f315(f10(a899,f909(a899,a899),f909(x103212,x103211)),a313),f315(f315(f9(f909(x103212,x103211),f909(f909(x103212,x103211),a899),a899),f317(f909(x103212,x103211))),x103213)))),f315(f315(f9(x103211,f909(f909(x103212,x103211),x103211),f909(f909(x103212,x103211),a899)),f315(f315(f10(f909(x103211,a899),f909(f909(f909(x103212,x103211),x103211),f909(f909(x103212,x103211),a899)),x103211),f10(x103211,a899,f909(x103212,x103211))),a312)),f315(f315(f9(f909(x103212,x103211),x103212,x103211),f7(f909(x103212,x103211))),x103214)))))),f315(f30(f909(x103212,x103211),x103213),x103214))
% 168.50/168.38 [10322]~P5(x103221)+E(f30(x103221,f315(f250(x103221),f315(f315(f10(f909(f909(x103222,x103221),a899),a899,x103221),f80(f909(x103222,x103221))),f315(f315(f10(f909(f909(x103222,x103221),a899),f909(f909(x103222,x103221),a899),x103221),f315(f20(f909(x103222,x103221),a899,a899),f315(f315(f10(a899,f909(a899,a899),f909(x103222,x103221)),a313),f315(f315(f9(f909(x103222,x103221),f909(f909(x103222,x103221),a899),a899),f317(f909(x103222,x103221))),x103223)))),f315(f315(f9(x103221,f909(f909(x103222,x103221),x103221),f909(f909(x103222,x103221),a899)),f315(f315(f10(f909(x103221,a899),f909(f909(f909(x103222,x103221),x103221),f909(f909(x103222,x103221),a899)),x103221),f10(x103221,a899,f909(x103222,x103221))),a312)),f315(f315(f9(f909(x103222,x103221),x103222,x103221),f7(f909(x103222,x103221))),x103224)))))),f315(f30(f909(x103222,x103221),x103223),x103224))
% 168.50/168.38 [10323]~P5(x103231)+E(f31(x103231,f315(f250(x103231),f315(f315(f10(f909(f909(x103232,x103231),a899),a899,x103231),f80(f909(x103232,x103231))),f315(f315(f10(f909(f909(x103232,x103231),a899),f909(f909(x103232,x103231),a899),x103231),f315(f20(f909(x103232,x103231),a899,a899),f315(f315(f10(a899,f909(a899,a899),f909(x103232,x103231)),a313),f315(f315(f9(f909(x103232,x103231),f909(f909(x103232,x103231),a899),a899),f317(f909(x103232,x103231))),x103233)))),f315(f315(f9(x103231,f909(f909(x103232,x103231),x103231),f909(f909(x103232,x103231),a899)),f315(f315(f10(f909(x103231,a899),f909(f909(f909(x103232,x103231),x103231),f909(f909(x103232,x103231),a899)),x103231),f10(x103231,a899,f909(x103232,x103231))),a312)),f315(f315(f9(f909(x103232,x103231),x103232,x103231),f7(f909(x103232,x103231))),x103234)))))),f315(f31(f909(x103232,x103231),x103233),x103234))
% 168.50/168.38 [10324]~P5(x103241)+E(f31(x103241,f315(f250(x103241),f315(f315(f10(f909(f909(x103242,x103241),a899),a899,x103241),f80(f909(x103242,x103241))),f315(f315(f10(f909(f909(x103242,x103241),a899),f909(f909(x103242,x103241),a899),x103241),f315(f20(f909(x103242,x103241),a899,a899),f315(f315(f10(a899,f909(a899,a899),f909(x103242,x103241)),a313),f315(f315(f9(f909(x103242,x103241),f909(f909(x103242,x103241),a899),a899),f317(f909(x103242,x103241))),x103243)))),f315(f315(f9(x103241,f909(f909(x103242,x103241),x103241),f909(f909(x103242,x103241),a899)),f315(f315(f10(f909(x103241,a899),f909(f909(f909(x103242,x103241),x103241),f909(f909(x103242,x103241),a899)),x103241),f10(x103241,a899,f909(x103242,x103241))),a312)),f315(f315(f9(f909(x103242,x103241),x103242,x103241),f7(f909(x103242,x103241))),x103244)))))),f315(f31(f909(x103242,x103241),x103243),x103244))
% 168.50/168.38 [10373]~P1(f315(f315(f317(f908(x103731,x103731)),f315(f315(f240(x103731,x103731),x103733),x103734)),f315(f315(f99(f909(f908(x103731,x103731),a899)),x103732),f295(x103731,f177(f909(f908(x103731,x103731),a899))))))+P1(f315(f315(f315(f315(f99(f909(x103731,f909(x103731,a899))),f315(f315(f9(x103731,f909(f908(x103731,x103731),a899),f909(x103731,a899)),f315(f315(f10(f909(x103731,f909(f909(f908(x103731,x103731),a899),a899)),f909(f909(f908(x103731,x103731),a899),f909(x103731,a899)),x103731),f9(x103731,f909(f908(x103731,x103731),a899),a899)),f315(f315(f10(f909(x103731,f908(x103731,x103731)),f909(x103731,f909(f909(f908(x103731,x103731),a899),a899)),x103731),f315(f10(f908(x103731,x103731),f909(f909(f908(x103731,x103731),a899),a899),x103731),f317(f908(x103731,x103731)))),f240(x103731,x103731)))),x103732)),a312),x103733),x103734))
% 168.50/168.38 [10383]P1(f315(f315(f317(f908(x103831,x103831)),f315(f315(f240(x103831,x103831),x103832),x103833)),f315(f315(f99(f909(f908(x103831,x103831),a899)),x103834),f295(x103831,f177(f909(f908(x103831,x103831),a899))))))+~P1(f315(f315(f315(f315(f99(f909(x103831,f909(x103831,a899))),f315(f315(f9(x103831,f909(f908(x103831,x103831),a899),f909(x103831,a899)),f315(f315(f10(f909(x103831,f909(f909(f908(x103831,x103831),a899),a899)),f909(f909(f908(x103831,x103831),a899),f909(x103831,a899)),x103831),f9(x103831,f909(f908(x103831,x103831),a899),a899)),f315(f315(f10(f909(x103831,f908(x103831,x103831)),f909(x103831,f909(f909(f908(x103831,x103831),a899),a899)),x103831),f315(f10(f908(x103831,x103831),f909(f909(f908(x103831,x103831),a899),a899),x103831),f317(f908(x103831,x103831)))),f240(x103831,x103831)))),x103834)),a312),x103832),x103833))
% 168.50/168.38 [10331]E(f315(f315(f140(f902(x103311)),f315(f315(f140(x103311),x103312),f315(f131(f902(x103311),f902(x103311),f123(x103311),f102(x103311)),f315(f315(f143(f902(x103311),f902(x103311)),f145(f902(x103311),x103311,f102(x103311),f315(f315(f10(f902(x103311),f909(f902(x103311),f902(x103311)),x103311),f18(f902(x103311),f902(x103311))),f315(f315(f9(x103311,f902(x103311),f902(x103311)),f140(x103311)),f102(x103311))))),x103313)))),f168(x103311,f315(f315(f140(f902(x103311)),x103314),f315(f131(f902(f902(x103311)),f902(f902(x103311)),f123(f902(x103311)),f102(f902(x103311))),f315(f315(f143(f902(x103311),f902(f902(x103311))),f145(f902(f902(x103311)),x103311,f102(f902(x103311)),f315(f18(f909(f902(x103311),f902(f902(x103311))),x103311),f315(f315(f9(f902(x103311),f902(f902(x103311)),f902(f902(x103311))),f140(f902(x103311))),f102(f902(x103311)))))),x103313))))),f168(x103311,f315(f315(f140(f902(x103311)),f315(f315(f140(x103311),x103312),x103314)),x103313)))+~P1(f315(f303(f902(f902(x103311)),f169(x103311)),f315(f315(f140(f902(x103311)),f315(f315(f140(x103311),x103312),x103314)),x103313)))
% 168.50/168.38 [10372]~P1(f315(f54(x103722),f315(f250(x103722),x103724)))+P1(f315(f54(x103721),f315(f250(x103721),f315(f315(f10(f909(x103722,a899),a899,x103721),f80(x103722)),f315(f315(f9(x103721,f909(x103722,a899),f909(x103722,a899)),f315(f315(f10(f909(x103722,f909(a899,a899)),f909(f909(x103722,a899),f909(x103722,a899)),x103721),f20(x103722,a899,a899)),f315(f315(f10(f909(x103722,a899),f909(x103722,f909(a899,a899)),x103721),f315(f10(a899,f909(a899,a899),x103722),a313)),f315(f315(f9(x103721,f909(x103722,x103721),f909(x103722,a899)),f315(f315(f10(f909(x103721,a899),f909(f909(x103722,x103721),f909(x103722,a899)),x103721),f10(x103721,a899,x103722)),a312)),x103723)))),x103724)))))
% 168.50/168.38 [8889]P25(x88891,x88892,x88893,x88894)+~P26(x88891,x88892,x88893,x88894,x88895)
% 168.50/168.38 [5340]E(x53401,x53402)+~E(f158(x53403,x53401,x53404),f158(x53403,x53402,x53405))
% 168.50/168.38 [5341]E(x53411,x53412)+~E(f115(x53413,x53414,x53411),f115(x53413,x53415,x53412))
% 168.50/168.38 [5342]E(x53421,x53422)+~E(f115(x53423,x53421,x53424),f115(x53423,x53422,x53425))
% 168.50/168.38 [8216]~E(f315(x82163,x82164),x82165)+E(f68(x82161,x82162,x82163,x82164,x82165),x82163)
% 168.50/168.38 [8747]~E(f68(x87474,x87475,x87471,x87472,x87473),x87471)+E(f315(x87471,x87472),x87473)
% 168.50/168.38 [9364]~P26(x93642,x93641,x93644,x93643,x93645)+P26(x93641,x93642,f70(x93642,x93641,x93643,x93644),x93645,x93643)
% 168.50/168.38 [9365]~P26(x93652,x93651,x93654,x93653,x93655)+P26(x93651,x93652,f84(x93652,x93651,x93653,x93654),x93655,x93653)
% 168.50/168.38 [6164]P1(f315(f238(x61641,x61642,x61643),x61644))+~P1(f315(f315(x61643,x61645),x61644))
% 168.50/168.38 [6166]P1(f315(f237(x61661,x61662,x61663),x61664))+~P1(f315(f315(x61663,x61664),x61665))
% 168.50/168.38 [6655]~E(x66555,f2(a88))+E(f315(f185(x66551,x66552,x66553,x66554),x66555),f113(x66552))
% 168.50/168.38 [6656]~E(x66565,f2(a88))+E(f315(f187(x66561,x66562,x66563,x66564),x66565),f104(x66562))
% 168.50/168.38 [6796]~E(x67963,f2(a88))+E(f315(f261(x67961,x67962,x67963,x67964),x67965),f315(f240(x67961,x67962),x67965))
% 168.50/168.38 [7864]~P21(x78644,x78641,x78642,x78645)+E(f315(f66(x78641,x78641,x78641,f315(x78642,x78643)),f315(x78642,x78643)),f315(x78642,x78643))
% 168.50/168.38 [8258]~P17(x82585,x82581,x82582)+E(f315(f66(x82581,x82581,x82581,f315(x82582,x82583)),f315(x82582,x82584)),f315(f66(x82581,x82581,x82581,f315(x82582,x82584)),f315(x82582,x82583)))
% 168.50/168.38 [8582]P1(f315(f315(f317(f908(x85821,x85821)),f315(f315(f240(x85821,x85821),x85822),x85823)),f309(x85821,x85824,x85825)))+~P1(f315(f315(f224(a901),f315(x85824,x85822)),f315(x85824,x85823)))
% 168.50/168.38 [8675]~P1(f315(f315(f317(x86754),x86753),f287(x86754,x86751,x86752,x86755)))+P1(f315(f315(x86751,x86752),x86753))
% 168.50/168.38 [8676]~P1(f315(f315(f317(x86764),x86763),f278(x86764,x86761,x86762,x86765)))+P1(f315(f315(x86761,x86762),x86763))
% 168.50/168.38 [8677]~P1(f315(f315(f317(x86774),x86772),f287(x86774,x86771,x86775,x86773)))+P1(f315(f315(x86771,x86772),x86773))
% 168.50/168.38 [8678]~P1(f315(f315(f317(x86784),x86782),f278(x86784,x86781,x86785,x86783)))+P1(f315(f315(x86781,x86782),x86783))
% 168.50/168.38 [8759]~P26(x87591,x87593,x87595,x87592,x87594)+E(f315(f28(x87591),x87592),f315(f28(x87593),x87594))
% 168.50/168.38 [8807]~P26(x88071,x88072,x88073,x88074,x88075)+E(f315(f298(x88071,x88072,x88073),x88074),x88075)
% 168.50/168.38 [8827]~P58(x88272,x88271,x88275,x88273,x88274)+E(f315(f298(x88271,x88272,x88273),x88274),f230(f909(x88272,a899)))
% 168.50/168.38 [9272]~P36(x92721,x92722,x92723,x92724,x92725)+P36(x92721,x92722,x92723,f315(f157(x92721),x92724),f315(f157(x92722),x92725))
% 168.50/168.38 [9274]~P36(x92741,x92742,x92743,f315(f157(x92741),x92744),x92745)+P36(x92741,x92742,x92743,x92744,f315(f157(x92742),x92745))
% 168.50/168.38 [9275]~P36(x92751,x92752,x92753,x92754,f315(f157(x92752),x92755))+P36(x92751,x92752,x92753,f315(f157(x92751),x92754),x92755)
% 168.50/168.38 [9281]P36(x92811,x92812,x92813,x92814,x92815)+~P36(x92811,x92812,x92813,f315(f157(x92811),x92814),f315(f157(x92812),x92815))
% 168.50/168.38 [9693]P1(f315(f315(f317(f908(f902(x96931),f902(x96931))),f315(f315(f240(f902(x96931),f902(x96931)),f315(f315(f140(x96931),x96932),x96933)),f315(f315(f140(x96931),x96932),x96934))),f146(x96931,x96935)))+~P1(f315(f315(f317(f908(f902(x96931),f902(x96931))),f315(f315(f240(f902(x96931),f902(x96931)),x96933),x96934)),f146(x96931,x96935)))
% 168.50/168.38 [9694]P1(f315(f315(f317(f908(f902(x96941),f902(x96941))),f315(f315(f240(f902(x96941),f902(x96941)),f315(f315(f123(x96941),x96942),x96943)),f315(f315(f123(x96941),x96942),x96944))),f136(x96941,x96945)))+~P1(f315(f315(f317(f908(f902(x96941),f902(x96941))),f315(f315(f240(f902(x96941),f902(x96941)),x96943),x96944)),f136(x96941,x96945)))
% 168.50/168.38 [9889]E(f315(f315(f140(x98891),f634(x98892,x98893,x98894,x98895,x98891)),f635(x98892,x98893,x98894,x98895,x98891)),x98895)+~P1(f315(f315(f317(f908(f902(x98891),f902(x98891))),f315(f315(f240(f902(x98891),f902(x98891)),x98895),f315(f315(f140(x98891),x98894),x98893))),f147(x98891,x98892)))
% 168.50/168.38 [9910]E(f315(f315(f140(x99101),f636(x99102,x99103,x99104,x99105,x99101)),f637(x99102,x99103,x99104,x99105,x99101)),x99103)+~P1(f315(f315(f317(f908(f902(x99101),f902(x99101))),f315(f315(f240(f902(x99101),f902(x99101)),f315(f315(f140(x99101),x99105),x99104)),x99103)),f147(x99101,x99102)))
% 168.50/168.38 [10054]~P1(f315(f315(f317(f908(f902(x100541),f902(x100541))),f315(f315(f240(f902(x100541),f902(x100541)),f315(f315(f140(x100541),x100545),x100542)),x100544)),f147(x100541,x100543)))+P1(f315(f315(f317(f908(f902(x100541),f902(x100541))),f315(f315(f240(f902(x100541),f902(x100541)),x100542),f637(x100543,x100544,x100542,x100545,x100541))),f147(x100541,x100543)))
% 168.50/168.38 [10134]~P1(f315(f315(f317(f908(f902(x101341),f902(x101341))),f315(f315(f240(f902(x101341),f902(x101341)),x101345),f315(f315(f140(x101341),x101344),x101343))),f147(x101341,x101342)))+P1(f315(f315(f317(f908(f902(x101341),f902(x101341))),f315(f315(f240(f902(x101341),f902(x101341)),f635(x101342,x101343,x101344,x101345,x101341)),x101343)),f147(x101341,x101342)))
% 168.50/168.38 [10325]P1(f315(f315(f317(f908(x103251,x103251)),f315(f315(f240(x103251,x103251),f315(x103252,f315(f315(f73(a901),x103253),x103254))),f315(x103252,x103253))),f295(x103251,x103255)))+~P1(f315(f315(f317(f908(x103251,x103251)),f315(f315(f240(x103251,x103251),f315(x103252,f315(a101,f599(x103254,x103253,x103255,x103252,x103251)))),f315(x103252,f599(x103254,x103253,x103255,x103252,x103251)))),f295(x103251,x103255)))
% 168.50/168.38 [5314]E(x53141,x53142)+~E(f315(f315(f140(x53143),x53144),x53141),f315(f315(f140(x53143),x53145),x53142))
% 168.50/168.38 [5315]E(x53151,x53152)+~E(f315(f315(f140(x53153),x53151),x53154),f315(f315(f140(x53153),x53152),x53155))
% 168.50/168.38 [5357]P1(f315(x53571,x53572))+~E(f315(f125(x53573,x53571),x53574),f315(f315(f140(x53573),x53572),x53575))
% 168.50/168.38 [5358]P1(f315(x53581,x53582))+~E(f315(f315(f140(x53583),x53582),x53584),f315(f125(x53583,x53581),x53585))
% 168.50/168.38 [5519]~E(f315(f315(f127(x55191),x55193),x55192),f315(f315(f140(x55191),x55194),x55195))+E(f315(f315(f153(x55191),x55192),x55193),x55194)
% 168.50/168.38 [5661]~P15(x56614,x56615,x56611)+E(f315(f315(x56611,x56612),f315(f315(x56611,x56612),x56613)),f315(f315(x56611,x56612),x56613))
% 168.50/168.38 [6224]~E(x62244,f2(a88))+E(f315(f315(f106(x62241,x62242,x62243),x62244),x62245),f315(f315(f240(f902(x62242),x62241),f102(x62242)),x62245))
% 168.50/168.38 [6298]~P110(x62982)+~E(f315(f315(f137(x62981,x62982,x62983),x62984),x62985),f102(x62981))
% 168.50/168.38 [6696]E(x66961,x66962)+~E(f315(f315(f123(x66963),x66964),f315(f315(f140(x66963),x66961),f102(x66963))),f315(f315(f123(x66963),x66965),f315(f315(f140(x66963),x66962),f102(x66963))))
% 168.50/168.38 [6697]E(x66971,x66972)+~E(f315(f315(f123(x66973),x66971),f315(f315(f140(x66973),x66974),f102(x66973))),f315(f315(f123(x66973),x66972),f315(f315(f140(x66973),x66975),f102(x66973))))
% 168.50/168.38 [7019]E(f315(f315(f297(x70191),f315(x70192,x70193)),f315(f298(x70194,x70191,x70192),x70195)),f315(f298(x70194,x70191,x70192),x70195))+~P1(f315(f315(f317(x70194),x70193),x70195))
% 168.50/168.38 [7027]~P1(f315(x70274,f315(x70273,x70275)))+P1(f315(f315(f299(x70271,x70272,x70273),x70274),x70275))
% 168.50/168.38 [7030]~P1(f315(f315(x70303,x70305),x70304))+P1(f315(f315(f231(x70301,x70302,x70303),x70304),x70305))
% 168.50/168.38 [7128]~E(f315(f298(x71281,x71282,x71283),x71284),x71285)+E(f315(f298(f909(x71281,a899),f909(x71282,a899),f298(x71281,x71282,x71283)),f315(f296(x71281),x71284)),f315(f296(x71282),x71285))
% 168.50/168.38 [7157]E(f315(f259(x71571,x71572,x71573,x71574),x71575),f315(x71574,x71575))+~P1(f315(f315(f317(x71571),x71575),x71573))
% 168.50/168.38 [7473]P25(x74731,x74732,x74733,x74734)+~P25(x74731,x74732,x74733,f315(f315(f297(x74731),x74735),x74734))
% 168.50/168.38 [7579]~P1(f315(f315(f317(x75794),x75793),x75795))+P1(f315(f315(f317(x75791),f315(x75792,x75793)),f315(f298(x75794,x75791,x75792),x75795)))
% 168.50/168.38 [7600]~P110(x76002)+E(f139(x76001,x76002,x76003,f315(f125(x76001,x76004),x76005)),f315(f125(x76001,x76004),f139(x76001,x76002,x76003,x76005)))
% 168.50/168.38 [7632]P1(f315(x76321,f315(x76322,x76323)))+~P1(f315(f315(f299(x76324,x76325,x76322),x76321),x76323))
% 168.50/168.38 [7635]P1(f315(f315(x76351,x76352),x76353))+~P1(f315(f315(f231(x76354,x76355,x76351),x76353),x76352))
% 168.50/168.38 [7699]~P1(f315(f315(f317(x76993),f315(x76994,x76992)),x76995))+P1(f315(f315(f317(x76991),x76992),f315(f299(x76991,x76993,x76994),x76995)))
% 168.50/168.38 [8096]~P1(f315(f315(f317(x80965),x80963),f315(f299(x80965,x80961,x80962),x80964)))+P1(f315(f315(f317(x80961),f315(x80962,x80963)),x80964))
% 168.50/168.38 [8397]~P17(x83972,x83971,x83973)+E(f315(f131(x83971,x83972,f315(f9(x83972,x83971,x83971),x83973),x83974),f141(x83972,x83975)),f315(f315(f57(x83972,x83971,x83973),x83974),f315(f161(x83972),x83975)))
% 168.50/168.38 [8419]E(f315(x84191,f485(x84192,x84191,x84193,x84194)),x84194)+~P1(f315(f315(f317(x84195),x84194),f315(f298(x84193,x84195,x84191),x84192)))
% 168.50/168.38 [8722]~E(x87222,f315(f315(f140(x87221),x87224),x87225))+P1(f315(f315(f317(f908(f902(x87221),f902(x87221))),f315(f315(f240(f902(x87221),f902(x87221)),f102(x87221)),x87222)),f136(x87221,x87223)))
% 168.50/168.38 [8768]E(f315(x87681,f315(f84(x87682,x87683,x87684,x87681),x87685)),x87685)+~P1(f315(f315(f317(x87683),x87685),f315(f298(x87682,x87683,x87681),x87684)))
% 168.50/168.38 [8771]P25(x87711,x87712,f84(x87712,x87711,x87713,x87714),x87715)+~P1(f315(f315(f223(f909(x87711,a899)),x87715),f315(f298(x87712,x87711,x87714),x87713)))
% 168.50/168.38 [8778]~P36(x87781,x87783,x87785,x87782,x87784)+E(f315(f178(f902(x87781)),x87782),f315(f178(f902(x87783)),x87784))
% 168.50/168.38 [8789]P1(f315(f315(f223(f909(x87891,a899)),f315(f315(f32(x87892,f909(x87891,a899)),x87893),x87894)),f315(x87894,x87895)))+~P1(f315(f315(f317(x87892),x87895),x87893))
% 168.50/168.38 [8843]~P58(x88431,x88432,x88433,x88435,x88434)+E(f315(f298(x88431,x88432,x88433),f230(f909(x88431,a899))),x88434)
% 168.50/168.38 [9069]E(f315(f125(x90691,x90692),f724(x90693,x90694,x90695,x90692,x90691)),x90693)+~E(f315(f125(x90691,x90692),x90695),f315(f315(f140(x90691),x90694),x90693))
% 168.50/168.38 [9070]E(f315(f125(x90701,x90702),f725(x90703,x90702,x90704,x90705,x90701)),x90704)+~E(f315(f315(f140(x90701),x90705),x90704),f315(f125(x90701,x90702),x90703))
% 168.50/168.38 [9161]E(f315(f178(f902(x91611)),x91612),x91613)+~P1(f315(f315(f317(f908(f902(x91611),f902(x91611))),f315(f315(f240(f902(x91611),f902(x91611)),x91614),x91612)),f315(f132(x91611,x91615),x91613)))
% 168.50/168.38 [9162]E(f315(f178(f902(x91621)),x91622),x91623)+~P1(f315(f315(f317(f908(f902(x91621),f902(x91621))),f315(f315(f240(f902(x91621),f902(x91621)),x91622),x91624)),f315(f132(x91621,x91625),x91623)))
% 168.50/168.38 [9231]P1(f315(f315(f317(x92311),f485(x92312,x92313,x92311,x92314)),x92312))+~P1(f315(f315(f317(x92315),x92314),f315(f298(x92311,x92315,x92313),x92312)))
% 168.50/168.38 [9391]E(f315(f298(x93911,x93912,x93913),f491(x93914,x93913,x93911,x93915,x93912)),x93915)+~P1(f315(f315(f223(f909(x93912,a899)),x93915),f315(f298(x93911,x93912,x93913),x93914)))
% 168.50/168.38 [9711]P1(f315(f315(f317(f908(f902(x97111),f902(x97111))),f315(f315(f240(f902(x97111),f902(x97111)),f315(f315(f140(x97111),x97112),x97113)),f315(f315(f140(x97111),x97112),x97114))),f295(f902(x97111),f146(x97111,x97115))))+~P1(f315(f315(f317(f908(f902(x97111),f902(x97111))),f315(f315(f240(f902(x97111),f902(x97111)),x97113),x97114)),f295(f902(x97111),f146(x97111,x97115))))
% 168.50/168.38 [9742]~E(f315(x97423,f675(x97425,x97424,x97423,x97422,x97421)),f315(x97425,f675(x97425,x97424,x97423,x97422,x97421)))+E(f315(f315(f143(x97421,x97422),x97423),x97424),f315(f315(f143(x97421,x97422),x97425),x97424))
% 168.50/168.38 [9817]~E(f315(f125(x98171,x98175),x98174),f315(f315(f140(x98171),x98173),x98172))+E(f315(f315(f123(x98171),f728(x98172,x98173,x98174,x98175,x98171)),f315(f315(f140(x98171),x98173),f724(x98172,x98173,x98174,x98175,x98171))),x98174)
% 168.50/168.38 [9818]~E(f315(f315(f140(x98181),x98185),x98184),f315(f125(x98181,x98183),x98182))+E(f315(f315(f123(x98181),f726(x98182,x98183,x98184,x98185,x98181)),f315(f315(f140(x98181),x98185),f725(x98182,x98183,x98184,x98185,x98181))),x98182)
% 168.50/168.38 [9822]E(f315(f315(f143(x98221,x98222),x98223),x98224),f315(f315(f143(x98221,x98222),x98225),x98224))+P1(f315(f315(f317(x98221),f675(x98223,x98224,x98225,x98222,x98221)),f315(f161(x98221),x98224)))
% 168.50/168.38 [9852]~P1(f315(f315(f317(x98525),x98524),f315(f273(x98521,x98525,x98523),x98522)))+P1(f315(f315(f317(x98521),f386(x98522,x98523,x98521,x98524,x98525)),x98522))
% 168.50/168.38 [9853]~P1(f315(f315(f317(x98535),x98534),f315(f273(x98531,x98535,x98533),x98532)))+P1(f315(f315(f317(x98531),f482(x98532,x98533,x98531,x98534,x98535)),x98532))
% 168.50/168.38 [9883]~P1(f315(f315(f223(f909(x98835,a899)),x98834),f315(f298(x98831,x98835,x98833),x98832)))+P1(f315(f315(f223(f909(x98831,a899)),f491(x98832,x98833,x98831,x98834,x98835)),x98832))
% 168.50/168.38 [10326]E(x103261,f2(a88))+E(f212(f908(f902(x103262),x103263),f908(x103262,x103263),f315(f315(f240(f902(x103262),x103263),f102(x103262)),x103264),f315(f245(x103262,x103263,f908(f902(x103262),x103263)),f315(f315(f9(x103262,f909(x103263,f908(f902(x103262),x103263)),f909(x103263,f908(f902(x103262),x103263))),f315(f315(f10(f909(f908(f902(x103262),x103263),f908(f902(x103262),x103263)),f909(f909(x103263,f908(f902(x103262),x103263)),f909(x103263,f908(f902(x103262),x103263))),x103262),f10(f908(f902(x103262),x103263),f908(f902(x103262),x103263),x103263)),f315(f315(f10(f909(f902(x103262),f909(x103263,f908(f902(x103262),x103263))),f909(f908(f902(x103262),x103263),f908(f902(x103262),x103263)),x103262),f245(f902(x103262),x103263,f908(f902(x103262),x103263))),f315(f315(f10(f909(f902(x103262),f902(x103262)),f909(f902(x103262),f909(x103263,f908(f902(x103262),x103263))),x103262),f315(f10(f902(x103262),f909(x103263,f908(f902(x103262),x103263)),f902(x103262)),f240(f902(x103262),x103263))),f140(x103262))))),f315(f106(x103263,x103262,x103265),f315(f315(f3(a88),x103261),f71(a88))))),f315(x103265,x103264)),f315(f315(f106(x103263,x103262,x103265),x103261),x103264))
% 168.50/168.38 [6101]E(x61011,x61012)+~E(f315(f244(x61013,x61014),f315(f315(f240(x61013,x61014),x61015),x61011)),x61012)
% 168.50/168.38 [6102]E(x61021,x61022)+~E(f315(f239(x61023,x61024),f315(f315(f240(x61023,x61024),x61021),x61025)),x61022)
% 168.50/168.38 [6373]~E(x63733,f315(f315(f123(x63731),x63734),f315(f315(f140(x63731),x63732),x63735)))+P1(f315(f315(f317(x63731),x63732),f315(f161(x63731),x63733)))
% 168.50/168.38 [6783]E(f315(f298(x67831,x67832,f315(f18(x67832,x67831),x67833)),x67834),f315(f315(f297(x67832),x67833),f177(f909(x67832,a899))))+~P1(f315(f315(f317(x67831),x67835),x67834))
% 168.50/168.38 [6857]E(f315(f315(f99(f909(x68571,a899)),f315(f161(x68571),x68572)),f315(f161(x68571),x68573)),f315(f161(x68571),x68574))+~E(f155(x68571,x68575,x68574),f315(f315(f240(f902(x68571),f902(x68571)),x68572),x68573))
% 168.50/168.38 [6959]~P110(x69592)+E(f315(f178(f902(x69591)),f315(f315(f137(x69591,x69592,x69593),x69594),x69595)),f315(a101,f315(f178(f902(x69591)),x69595)))
% 168.50/168.38 [6973]~P110(x69732)+E(f315(f161(x69731),f315(f315(f137(x69731,x69732,x69733),x69734),x69735)),f315(f315(f297(x69731),x69734),f315(f161(x69731),x69735)))
% 168.50/168.38 [7251]~P121(x72511)+E(f315(f315(f74(x72511),f315(f315(f74(x72511),x72512),x72513)),f315(f315(f74(x72511),x72514),x72515)),f315(f315(f74(x72511),f315(f315(f74(x72511),x72512),x72514)),f315(f315(f74(x72511),x72513),x72515)))
% 168.50/168.38 [7252]~P121(x72521)+E(f315(f315(f73(x72521),f315(f315(f73(x72521),x72522),x72523)),f315(f315(f73(x72521),x72524),x72525)),f315(f315(f73(x72521),f315(f315(f73(x72521),x72522),x72524)),f315(f315(f73(x72521),x72523),x72525)))
% 168.50/168.38 [7253]~P65(x72531)+E(f315(f315(f279(x72531),f315(f315(f74(x72531),x72532),x72533)),f315(f315(f74(x72531),x72534),x72535)),f315(f315(f74(x72531),f315(f315(f279(x72531),x72532),x72534)),f315(f315(f279(x72531),x72533),x72535)))
% 168.50/168.38 [7267]~P110(x72671)+E(f291(x72671,f315(f315(f222(x72671),x72672),x72673),f315(f315(f221(x72671),x72674),x72675)),f315(f315(f90(f909(x72671,a899)),f291(x72671,x72672,x72674)),f291(x72671,x72673,x72675)))
% 168.50/168.38 [7268]~P110(x72681)+E(f294(x72681,f315(f315(f222(x72681),x72682),x72683),f315(f315(f221(x72681),x72684),x72685)),f315(f315(f90(f909(x72681,a899)),f294(x72681,x72682,x72684)),f294(x72681,x72683,x72685)))
% 168.50/168.38 [7269]~P110(x72691)+E(f293(x72691,f315(f315(f222(x72691),x72692),x72693),f315(f315(f221(x72691),x72694),x72695)),f315(f315(f90(f909(x72691,a899)),f293(x72691,x72692,x72694)),f293(x72691,x72693,x72695)))
% 168.50/168.38 [7270]~P110(x72701)+E(f315(f315(f90(f909(x72701,a899)),f315(f290(x72701,x72702),x72703)),f315(f290(x72701,x72704),x72705)),f315(f290(x72701,f315(f315(f222(x72701),x72702),x72704)),f315(f315(f221(x72701),x72703),x72705)))
% 168.50/168.38 [7392]~P1(f315(x73921,f379(x73923,x73922,x73921)))+P1(f315(x73921,f315(f315(f240(x73922,x73923),x73924),x73925)))
% 168.50/168.38 [7504]~E(x75042,f315(x75044,x75045))+P1(f315(f315(f317(x75041),x75042),f315(f298(x75043,x75041,x75044),f230(f909(x75043,a899)))))
% 168.50/168.38 [7576]~P17(x75763,x75762,x75764)+P17(x75761,x75762,f315(f315(f10(x75763,f909(x75762,x75762),x75761),x75764),x75765))
% 168.50/168.38 [7577]~P15(x75773,x75772,x75774)+P15(x75771,x75772,f315(f315(f10(x75773,f909(x75772,x75772),x75771),x75774),x75775))
% 168.50/168.38 [7716]~P25(x77161,x77162,x77163,x77164)+P25(x77161,x77162,x77163,f315(f315(f3(f909(x77161,a899)),x77164),x77165))
% 168.50/168.38 [7873]~P1(f315(f315(x78733,x78734),x78735))+P1(f315(f315(f245(x78731,x78732,a899),x78733),f315(f315(f240(x78731,x78732),x78734),x78735)))
% 168.50/168.38 [7986]~P1(f315(x79862,x79864))+~E(f315(f315(f127(x79861),f315(f178(f902(x79861)),f166(x79861,x79862,x79863))),x79863),f315(f315(f140(x79861),x79864),x79865))
% 168.50/168.38 [8006]P25(x80061,x80062,x80063,x80064)+~P25(x80061,x80062,x80063,f315(f315(f99(f909(x80061,a899)),x80065),x80064))
% 168.50/168.38 [8007]P25(x80071,x80072,x80073,x80074)+~P25(x80071,x80072,x80073,f315(f315(f99(f909(x80071,a899)),x80074),x80075))
% 168.50/168.38 [8054]~P110(x80542)+E(f315(f315(f137(x80541,x80542,x80543),x80544),f139(x80541,x80542,x80543,x80545)),f139(x80541,x80542,x80543,f315(f315(f140(x80541),x80544),x80545)))
% 168.50/168.38 [8374]~P15(x83742,x83741,x83743)+E(f315(f131(x83741,x83742,f315(f9(x83742,x83741,x83741),x83743),x83744),x83745),f315(f315(f57(x83742,x83741,x83743),x83744),f315(f161(x83742),x83745)))
% 168.50/168.38 [8402]~E(f315(f315(f127(x84021),f315(f178(f902(x84021)),f166(x84021,x84022,x84023))),x84023),f315(f315(f140(x84021),x84024),x84025))+E(f315(f315(f123(x84021),f166(x84021,x84022,x84023)),f315(f315(f140(x84021),x84024),x84025)),x84023)
% 168.50/168.38 [8429]P1(f315(f315(x84291,x84292),x84293))+~P1(f315(f315(f245(x84294,x84295,a899),x84291),f315(f315(f240(x84294,x84295),x84292),x84293)))
% 168.50/168.38 [8906]P1(f315(f315(f223(f909(x89061,a899)),f315(f298(x89062,x89061,x89063),x89064)),f315(f298(x89062,x89061,x89063),x89065)))+~P1(f315(f315(f223(f909(x89062,a899)),x89064),x89065))
% 168.50/168.38 [8907]P1(f315(f315(f223(f909(x89071,a899)),f315(f299(x89071,x89072,x89073),x89074)),f315(f299(x89071,x89072,x89073),x89075)))+~P1(f315(f315(f223(f909(x89072,a899)),x89074),x89075))
% 168.50/168.38 [8986]E(x89861,f2(a88))+E(f315(f315(f247(x89862,x89863,x89862,f908(x89863,x89862)),f315(x89864,x89865)),f261(x89863,x89862,f315(f315(f3(a88),x89861),f71(a88)),x89864)),f315(f261(x89863,x89862,x89861,x89864),x89865))
% 168.50/168.38 [9094]P1(f315(f315(f243(x90941,x90942,a899,x90943),x90944),x90945))+~P1(f315(x90943,f315(f315(f240(x90941,x90942),x90944),x90945)))
% 168.50/168.38 [9370]~P1(f315(f315(f243(x93702,x93703,a899,x93701),x93704),x93705))+P1(f315(x93701,f315(f315(f240(x93702,x93703),x93704),x93705)))
% 168.50/168.38 [9554]~P1(f315(f315(f317(x95542),x95545),f315(f298(x95541,x95542,x95544),x95543)))+P1(f315(f315(f317(x95541),f315(f84(x95541,x95542,x95543,x95544),x95545)),x95543))
% 168.50/168.38 [9653]~P1(f315(f54(x96533),f315(f298(x96532,x96533,x96535),f230(f909(x96532,a899)))))+P1(f315(f54(x96531),f315(f298(x96532,x96531,f315(f315(f10(x96533,x96531,x96532),x96534),x96535)),f230(f909(x96532,a899)))))
% 168.50/168.38 [9678]P1(f315(f315(f223(f909(f909(x96781,a899),a899)),f315(f298(f909(x96782,a899),f909(x96781,a899),f298(x96782,x96781,x96783)),f315(f296(x96782),x96784))),f315(f296(x96781),x96785)))+~P1(f315(f315(f223(f909(x96781,a899)),f315(f298(x96782,x96781,x96783),x96784)),x96785))
% 168.50/168.38 [9750]E(x97501,x97502)+~P1(f315(f59(x97503,x97504,x97505,x97501,f177(f909(x97503,a899))),x97502))
% 168.50/168.38 [9766]E(f315(f315(f240(x97661,x97662),f533(x97663,x97664,x97665,x97662,x97661)),f534(x97663,x97664,x97665,x97662,x97661)),x97665)+~P1(f315(f315(f317(f908(x97661,x97662)),x97665),f315(f315(f242(x97661,x97662),x97664),x97663)))
% 168.50/168.38 [9858]P1(f315(f315(f317(x98581),f533(x98582,x98583,x98584,x98585,x98581)),x98583))+~P1(f315(f315(f317(f908(x98581,x98585)),x98584),f315(f315(f242(x98581,x98585),x98583),x98582)))
% 168.50/168.38 [10013]P1(f315(f315(f317(x100131),f534(x100132,x100133,x100134,x100131,x100135)),f315(x100132,f533(x100132,x100133,x100134,x100131,x100135))))+~P1(f315(f315(f317(f908(x100135,x100131)),x100134),f315(f315(f242(x100135,x100131),x100133),x100132)))
% 168.50/168.38 [10033]P1(f315(f315(f317(f908(x100331,x100331)),f315(f315(f240(x100331,x100331),x100332),f619(x100333,x100334,x100335,x100332,x100331))),x100333))+~P1(f315(f315(f317(f908(x100331,x100331)),f315(f315(f240(x100331,x100331),x100332),x100335)),f315(f315(f172(f908(x100331,x100331),a899),f315(a101,x100334)),x100333)))
% 168.50/168.38 [10034]P1(f315(f315(f317(f908(x100341,x100341)),f315(f315(f240(x100341,x100341),x100342),f621(x100343,x100344,x100345,x100342,x100341))),x100343))+~P1(f315(f315(f317(f908(x100341,x100341)),f315(f315(f240(x100341,x100341),x100342),x100345)),f315(f315(f172(f908(x100341,x100341),a899),f315(a101,x100344)),x100343)))
% 168.50/168.38 [10051]~P1(f315(f315(f317(f908(f902(x100511),f902(x100511))),f315(f315(f240(f902(x100511),f902(x100511)),f315(f315(f140(x100511),x100512),x100515)),x100514)),f147(x100511,x100513)))+P1(f315(f315(f317(f908(x100511,x100511)),f315(f315(f240(x100511,x100511),x100512),f636(x100513,x100514,x100515,x100512,x100511))),x100513))
% 168.50/168.38 [6453]P1(f315(x64532,x64534))+E(f166(x64531,x64532,f315(f315(f123(x64531),x64533),f315(f315(f140(x64531),x64534),x64535))),f166(x64531,x64532,x64533))
% 168.50/168.38 [6502]~P80(x65022)+E(f315(f315(f315(f99(f909(x65021,x65022)),x65023),x65024),x65025),f315(f315(f99(x65022),f315(x65023,x65025)),f315(x65024,x65025)))
% 168.50/168.38 [6504]~P3(x65042)+E(f315(f315(f315(f3(f909(x65041,x65042)),x65043),x65044),x65045),f315(f315(f3(x65042),f315(x65043,x65045)),f315(x65044,x65045)))
% 168.50/168.38 [6506]~P80(x65062)+E(f315(f315(f315(f90(f909(x65061,x65062)),x65063),x65064),x65065),f315(f315(f90(x65062),f315(x65063,x65065)),f315(x65064,x65065)))
% 168.50/168.38 [6527]E(x65271,x65272)+E(f315(f315(f153(x65273),f315(f315(f148(x65273,x65274),x65271),x65275)),x65272),f315(f315(f153(x65273),x65274),x65272))
% 168.50/168.38 [6801]~E(x68014,f177(f909(x68013,a899)))+E(f315(f315(f99(f909(x68011,a899)),x68012),f315(f315(f33(x68013,f909(x68011,a899)),x68014),x68015)),x68012)
% 168.50/168.38 [6802]~E(x68024,f177(f909(x68023,a899)))+E(f315(f315(f3(f909(x68021,a899)),x68022),f315(f315(f33(x68023,f909(x68021,a899)),x68024),x68025)),x68022)
% 168.50/168.38 [6803]~E(x68034,f177(f909(x68033,a899)))+E(f315(f315(f90(f909(x68031,a899)),x68032),f315(f315(f32(x68033,f909(x68031,a899)),x68034),x68035)),x68032)
% 168.50/168.38 [6819]~E(x68194,f177(f909(x68193,a899)))+E(f315(f315(f297(x68191),x68192),f315(f315(f33(x68193,f909(x68191,a899)),x68194),x68195)),f315(f315(f297(x68191),x68192),f177(f909(x68191,a899))))
% 168.50/168.38 [7623]E(f315(f315(f153(x76231),f315(f315(f143(x76232,x76231),x76233),x76234)),x76235),f315(x76233,f315(f315(f153(x76232),x76234),x76235)))+~P1(f315(f315(f224(a901),x76235),f315(f178(f902(x76232)),x76234)))
% 168.50/168.38 [7687]E(f315(f315(f99(f909(x76871,a899)),f315(x76872,x76873)),f315(f315(f33(x76874,f909(x76871,a899)),x76875),x76872)),f315(f315(f33(x76874,f909(x76871,a899)),x76875),x76872))+~P1(f315(f315(f317(x76874),x76873),x76875))
% 168.50/168.38 [7688]E(f315(f315(f90(f909(x76881,a899)),f315(x76882,x76883)),f315(f315(f32(x76884,f909(x76881,a899)),x76885),x76882)),f315(f315(f32(x76884,f909(x76881,a899)),x76885),x76882))+~P1(f315(f315(f317(x76884),x76883),x76885))
% 168.50/168.38 [8297]~E(x82973,f177(f909(x82971,a899)))+E(f315(f315(f33(x82971,f909(x82972,a899)),x82973),f315(f315(f10(f909(x82972,a899),f909(x82972,a899),x82971),f315(f297(x82972),x82974)),x82975)),f177(f909(x82972,a899)))
% 168.50/168.38 [8302]~P1(f315(f315(f317(x83024),x83023),x83025))+P1(f315(f315(f223(f909(x83021,a899)),f315(x83022,x83023)),f315(f315(f33(x83024,f909(x83021,a899)),x83025),x83022)))
% 168.50/168.38 [8428]~E(f315(x84284,x84282),x84285)+P1(f315(f315(f317(x84281),x84282),f315(f299(x84281,x84283,x84284),f315(f315(f297(x84283),x84285),f177(f909(x84283,a899))))))
% 168.50/168.38 [8475]~P56(x84751,x84752,f315(f274(x84752,x84751),x84753))+E(f315(f315(f90(f909(x84751,a899)),f315(f273(x84752,x84751,x84753),x84754)),f315(f273(x84752,x84751,x84753),x84755)),f315(f273(x84752,x84751,x84753),f315(f315(f90(f909(x84752,a899)),x84754),x84755)))
% 168.50/168.38 [8551]E(x85511,f2(a88))+E(f315(f107(x85512,x85513,f315(x85514,f315(f315(f3(a88),x85511),f71(a88)))),f315(f315(f9(x85512,a88,f903(x85513)),x85515),x85511)),f315(f187(x85512,x85513,x85514,x85515),x85511))
% 168.50/168.38 [8589]E(x85891,f177(f909(x85892,a899)))+E(f315(f315(f33(x85892,f909(x85893,a899)),x85891),f315(f315(f10(f909(x85893,a899),f909(x85893,a899),x85892),f315(f297(x85893),x85894)),x85895)),f315(f315(f297(x85893),x85894),f315(f315(f33(x85892,f909(x85893,a899)),x85891),x85895)))
% 168.50/168.38 [8640]~P25(x86402,x86401,x86403,f230(f909(x86402,a899)))+E(f315(f315(f3(f909(x86401,a899)),f315(f298(x86402,x86401,x86403),x86404)),f315(f298(x86402,x86401,x86403),x86405)),f315(f298(x86402,x86401,x86403),f315(f315(f3(f909(x86402,a899)),x86404),x86405)))
% 168.50/168.38 [8641]~P25(x86412,x86411,x86413,f230(f909(x86412,a899)))+E(f315(f315(f90(f909(x86411,a899)),f315(f298(x86412,x86411,x86413),x86414)),f315(f298(x86412,x86411,x86413),x86415)),f315(f298(x86412,x86411,x86413),f315(f315(f90(f909(x86412,a899)),x86414),x86415)))
% 168.50/168.38 [8709]~P1(f315(f315(f60(x87091,x87092,x87095),x87093),x87094))+P1(f315(f315(f317(f908(x87091,x87092)),f315(f315(f240(x87091,x87092),x87093),x87094)),x87095))
% 168.50/168.38 [8741]P1(f315(f315(f317(x87411),x87412),f315(f272(x87413,x87411),x87414)))+~P1(f315(f315(f317(f908(x87413,x87411)),f315(f315(f240(x87413,x87411),x87415),x87412)),x87414))
% 168.50/168.38 [8743]P1(f315(f315(f317(x87431),x87432),f315(f252(x87431,x87433),x87434)))+~P1(f315(f315(f317(f908(x87431,x87433)),f315(f315(f240(x87431,x87433),x87432),x87435)),x87434))
% 168.50/168.38 [8890]P1(f315(f315(f60(x88901,x88902,x88903),x88904),x88905))+~P1(f315(f315(f317(f908(x88901,x88902)),f315(f315(f240(x88901,x88902),x88904),x88905)),x88903))
% 168.50/168.38 [8929]E(f315(x89291,x89292),x89293)+~P1(f315(f315(f317(x89294),x89292),f315(f299(x89294,x89295,x89291),f315(f315(f297(x89295),x89293),f177(f909(x89295,a899))))))
% 168.50/168.38 [9158]P1(f315(f315(f317(f908(x91581,x91582)),f315(f315(f240(x91581,x91582),x91583),x91584)),f315(f274(x91582,x91581),x91585)))+~P1(f315(f315(f317(f908(x91582,x91581)),f315(f315(f240(x91582,x91581),x91584),x91583)),x91585))
% 168.50/168.38 [9176]~P1(f315(f315(x91761,x91765),x91764))+P1(f315(f315(x91761,f315(f244(x91762,x91763),f315(f315(f240(x91762,x91763),x91764),x91765))),f315(f239(x91762,x91763),f315(f315(f240(x91762,x91763),x91764),x91765))))
% 168.50/168.38 [9206]~P1(f315(f315(f317(f908(x92062,x92061)),f315(f315(f240(x92062,x92061),x92064),x92063)),f315(f274(x92061,x92062),x92065)))+P1(f315(f315(f317(f908(x92061,x92062)),f315(f315(f240(x92061,x92062),x92063),x92064)),x92065))
% 168.50/168.38 [9238]~P1(f315(f315(f317(f908(x92383,x92381)),f315(f315(f240(x92383,x92381),x92385),x92382)),x92384))+P1(f315(f315(f317(x92381),x92382),f315(f273(x92383,x92381,x92384),f315(f315(f297(x92383),x92385),f177(f909(x92383,a899))))))
% 168.50/168.38 [9285]P1(f315(f315(f317(f908(x92851,x92852)),f315(f315(f240(x92851,x92852),x92853),x92854)),x92855))+~P1(f315(f315(f317(x92852),x92854),f315(f273(x92851,x92852,x92855),f315(f315(f297(x92851),x92853),f177(f909(x92851,a899))))))
% 168.50/168.38 [9377]~P72(x93771)+E(f315(f315(f8(a901,x93771),x93772),f291(a901,f315(f315(f73(a901),x93773),x93774),f315(f315(f73(a901),x93775),x93774))),f315(f315(f8(a901,x93771),f315(f315(f10(a901,x93771,a901),x93772),f315(f315(f9(a901,a901,a901),f73(a901)),x93774))),f291(a901,x93773,x93775)))
% 168.50/168.38 [9396]~P72(x93961)+E(f315(f315(f8(a901,x93961),x93962),f315(f290(a901,f315(f315(f73(a901),x93963),x93964)),f315(f315(f73(a901),x93965),x93964))),f315(f315(f8(a901,x93961),f315(f315(f10(a901,x93961,a901),x93962),f315(f315(f9(a901,a901,a901),f73(a901)),x93964))),f315(f290(a901,x93963),x93965)))
% 168.50/168.38 [9454]~P25(x94541,x94542,x94543,f230(f909(x94541,a899)))+E(f315(f315(f143(x94541,x94542),x94543),f315(f125(x94541,f315(f315(f10(a899,a899,x94541),a310),f315(a312,x94544))),x94545)),f315(f125(x94542,f315(f315(f10(a899,a899,x94542),a310),f315(a312,f315(x94543,x94544)))),f315(f315(f143(x94541,x94542),x94543),x94545)))
% 168.50/168.38 [9472]~P25(x94721,x94722,x94723,f315(f315(f297(x94721),x94724),f315(f161(x94721),x94725)))+E(f315(f315(f143(x94721,x94722),x94723),f315(f125(x94721,f315(f315(f10(a899,a899,x94721),a310),f315(a312,x94724))),x94725)),f315(f125(x94722,f315(f315(f10(a899,a899,x94722),a310),f315(a312,f315(x94723,x94724)))),f315(f315(f143(x94721,x94722),x94723),x94725)))
% 168.50/168.38 [9641]P1(f315(f315(f317(f908(f902(x96411),f902(x96411))),f315(f315(f240(f902(x96411),f902(x96411)),f315(f315(f140(x96411),x96412),x96413)),f315(f315(f140(x96411),x96414),x96413))),f146(x96411,x96415)))+~P1(f315(f315(f317(f908(x96411,x96411)),f315(f315(f240(x96411,x96411),x96412),x96414)),x96415))
% 168.50/168.38 [9761]E(f315(f315(f297(x97611),f520(x97612,x97613,x97614,x97615,x97611)),f529(x97612,x97613,x97614,x97615,x97611)),f315(f315(f297(x97611),x97614),x97613))+~P1(f315(f55(x97611,x97615,f315(f315(f297(x97611),x97614),x97613)),x97612))
% 168.50/168.38 [9762]E(f315(f315(f297(x97621),f542(x97622,x97623,x97624,x97625,x97621)),f553(x97622,x97623,x97624,x97625,x97621)),f315(f315(f297(x97621),x97624),x97623))+~P1(f315(f55(x97621,x97625,f315(f315(f297(x97621),x97624),x97623)),x97622))
% 168.50/168.38 [9843]P1(f315(f315(f317(x98431),f426(x98432,x98433,x98434,x98435,x98431)),x98434))+P1(f315(f315(f315(f32(x98431,f909(x98435,a899)),x98434),x98433),x98432))
% 168.50/168.38 [9848]P1(f315(f315(f317(x98481),f411(x98482,x98483,x98481,x98484,x98485)),x98483))+P1(f315(f315(f317(x98485),x98484),f315(f315(f32(x98481,f909(x98485,a899)),x98483),x98482)))
% 168.50/168.38 [9856]P1(f315(f315(f317(x98561),f414(x98562,x98563,x98561,x98564,x98565)),x98563))+P1(f315(f315(f223(f909(x98565,a899)),x98564),f315(f315(f32(x98561,f909(x98565,a899)),x98563),x98562)))
% 168.50/168.38 [9857]P1(f315(f315(f317(x98571),f818(x98572,x98573,x98574,x98575,x98571)),x98575))+P1(f315(f315(f223(f909(x98574,a899)),x98573),f315(f315(f32(x98571,f909(x98574,a899)),x98575),x98572)))
% 168.50/168.38 [9859]P1(f315(f315(x98591,f427(x98592,x98591,x98593,x98594,x98595)),x98592))+~P1(f315(f315(f315(f33(x98595,f909(x98594,a899)),x98593),x98591),x98592))
% 168.50/168.38 [9863]P1(f315(f315(f317(x98631),f427(x98632,x98633,x98634,x98635,x98631)),x98634))+~P1(f315(f315(f315(f33(x98631,f909(x98635,a899)),x98634),x98633),x98632))
% 168.50/168.38 [9864]P54(x98644,f315(f315(f32(x98641,f909(x98644,a899)),x98645),x98643),f315(f315(f32(x98641,f909(f908(x98644,x98644),a899)),x98645),x98642))+P1(f315(f315(f317(x98641),f756(x98642,x98643,x98644,x98645,x98641)),x98645))
% 168.50/168.38 [9865]P54(x98654,f315(f315(f33(x98651,f909(x98654,a899)),x98655),x98653),f315(f315(f33(x98651,f909(f908(x98654,x98654),a899)),x98655),x98652))+P1(f315(f315(f317(x98651),f810(x98652,x98653,x98654,x98655,x98651)),x98655))
% 168.50/168.38 [9875]P1(f315(f315(f317(x98751),f412(x98752,x98753,x98751,x98754,x98755)),x98753))+~P1(f315(f315(f317(x98755),x98754),f315(f315(f33(x98751,f909(x98755,a899)),x98753),x98752)))
% 168.50/168.38 [9881]P1(f315(f315(f317(x98811),x98812),f315(x98813,f412(x98813,x98814,x98815,x98812,x98811))))+~P1(f315(f315(f317(x98811),x98812),f315(f315(f33(x98815,f909(x98811,a899)),x98814),x98813)))
% 168.50/168.38 [9962]~P1(f315(f315(x99624,f426(x99625,x99624,x99623,x99622,x99621)),x99625))+P1(f315(f315(f315(f32(x99621,f909(x99622,a899)),x99623),x99624),x99625))
% 168.50/168.38 [9965]~P1(f315(f315(f317(x99651),x99652),f315(x99655,f411(x99655,x99654,x99653,x99652,x99651))))+P1(f315(f315(f317(x99651),x99652),f315(f315(f32(x99653,f909(x99651,a899)),x99654),x99655)))
% 168.50/168.38 [9969]~P54(x99691,f315(x99694,f756(x99695,x99694,x99691,x99693,x99692)),f315(x99695,f756(x99695,x99694,x99691,x99693,x99692)))+P54(x99691,f315(f315(f32(x99692,f909(x99691,a899)),x99693),x99694),f315(f315(f32(x99692,f909(f908(x99691,x99691),a899)),x99693),x99695))
% 168.50/168.38 [9970]~P54(x99701,f315(x99704,f810(x99705,x99704,x99701,x99703,x99702)),f315(x99705,f810(x99705,x99704,x99701,x99703,x99702)))+P54(x99701,f315(f315(f33(x99702,f909(x99701,a899)),x99703),x99704),f315(f315(f33(x99702,f909(f908(x99701,x99701),a899)),x99703),x99705))
% 168.50/168.38 [9971]~P1(f315(f315(f223(f909(x99711,a899)),x99712),f315(x99715,f414(x99715,x99714,x99713,x99712,x99711))))+P1(f315(f315(f223(f909(x99711,a899)),x99712),f315(f315(f32(x99713,f909(x99711,a899)),x99714),x99715)))
% 168.50/168.38 [9972]~P1(f315(f315(f223(f909(x99721,a899)),x99722),f315(x99725,f818(x99725,x99722,x99721,x99724,x99723))))+P1(f315(f315(f223(f909(x99721,a899)),x99722),f315(f315(f32(x99723,f909(x99721,a899)),x99724),x99725)))
% 168.50/168.38 [10037]~P1(f315(f315(f317(x100371),f520(x100375,x100374,x100373,x100372,x100371)),f529(x100375,x100374,x100373,x100372,x100371)))+~P1(f315(f55(x100371,x100372,f315(f315(f297(x100371),x100373),x100374)),x100375))
% 168.50/168.38 [10038]~P1(f315(f315(f317(x100381),f542(x100385,x100384,x100383,x100382,x100381)),f553(x100385,x100384,x100383,x100382,x100381)))+~P1(f315(f55(x100381,x100382,f315(f315(f297(x100381),x100383),x100384)),x100385))
% 168.50/168.38 [10039]~P1(f315(f315(f317(f908(x100391,x100391)),f315(f315(f240(x100391,x100391),x100392),x100395)),f315(f315(f172(f908(x100391,x100391),a899),f315(a101,x100394)),x100393)))+P1(f315(f315(f317(f908(x100391,x100391)),f315(f315(f240(x100391,x100391),x100392),f620(x100393,x100394,x100395,x100392,x100391))),f315(f315(f172(f908(x100391,x100391),a899),x100394),x100393)))
% 168.50/168.38 [10045]P1(f315(f59(x100451,x100451,x100452,f520(x100453,x100454,x100455,x100452,x100451),f529(x100453,x100454,x100455,x100452,x100451)),x100453))+~P1(f315(f55(x100451,x100452,f315(f315(f297(x100451),x100455),x100454)),x100453))
% 168.50/168.38 [10046]P1(f315(f59(x100461,x100461,x100462,f542(x100463,x100464,x100465,x100462,x100461),f553(x100463,x100464,x100465,x100462,x100461)),x100463))+~P1(f315(f55(x100461,x100462,f315(f315(f297(x100461),x100465),x100464)),x100463))
% 168.50/168.38 [10056]~P110(x100561)+P13(x100561,f315(f315(f143(x100562,x100561),x100563),f315(f125(x100562,f315(f315(f9(x100562,x100561,a899),f315(f315(f10(x100561,f909(x100561,a899),x100562),a312),x100563)),f315(x100564,x100565))),x100565)))
% 168.50/168.38 [10106]~P1(f315(f315(f317(x101062),x101065),f315(f273(x101061,x101062,x101064),x101063)))+P1(f315(f315(f317(f908(x101061,x101062)),f315(f315(f240(x101061,x101062),f386(x101063,x101064,x101061,x101065,x101062)),x101065)),x101064))
% 168.50/168.38 [10107]~P1(f315(f315(f317(x101072),x101075),f315(f273(x101071,x101072,x101074),x101073)))+P1(f315(f315(f317(f908(x101071,x101072)),f315(f315(f240(x101071,x101072),f482(x101073,x101074,x101071,x101075,x101072)),x101075)),x101074))
% 168.50/168.38 [10127]~P1(f315(f315(f317(f908(x101271,x101271)),f315(f315(f240(x101271,x101271),x101275),x101274)),f315(f315(f172(f908(x101271,x101271),a899),f315(a101,x101273)),x101272)))+P1(f315(f315(f317(f908(x101271,x101271)),f315(f315(f240(x101271,x101271),f620(x101272,x101273,x101274,x101275,x101271)),x101274)),x101272))
% 168.50/168.38 [10130]~P1(f315(f315(f317(f908(x101301,x101301)),f315(f315(f240(x101301,x101301),x101305),x101304)),f315(f315(f172(f908(x101301,x101301),a899),f315(a101,x101303)),x101302)))+P1(f315(f315(f317(f908(x101301,x101301)),f315(f315(f240(x101301,x101301),f619(x101302,x101303,x101304,x101305,x101301)),x101304)),f315(f315(f172(f908(x101301,x101301),a899),x101303),x101302)))
% 168.50/168.38 [10131]~P1(f315(f315(f317(f908(x101311,x101311)),f315(f315(f240(x101311,x101311),x101315),x101314)),f315(f315(f172(f908(x101311,x101311),a899),f315(a101,x101313)),x101312)))+P1(f315(f315(f317(f908(x101311,x101311)),f315(f315(f240(x101311,x101311),f621(x101312,x101313,x101314,x101315,x101311)),x101314)),f315(f315(f172(f908(x101311,x101311),a899),x101313),x101312)))
% 168.50/168.38 [10132]~P1(f315(f315(f317(f908(f902(x101321),f902(x101321))),f315(f315(f240(f902(x101321),f902(x101321)),x101325),f315(f315(f140(x101321),x101324),x101323))),f147(x101321,x101322)))+P1(f315(f315(f317(f908(x101321,x101321)),f315(f315(f240(x101321,x101321),f634(x101322,x101323,x101324,x101325,x101321)),x101324)),x101322))
% 168.50/168.38 [7708]~E(x77083,f177(f909(x77082,a899)))+E(f315(f315(f99(f909(x77081,a899)),f315(f315(f33(x77082,f909(x77081,a899)),x77083),x77084)),x77085),x77085)
% 168.50/168.38 [7709]~E(x77093,f177(f909(x77092,a899)))+E(f315(f315(f90(f909(x77091,a899)),f315(f315(f32(x77092,f909(x77091,a899)),x77093),x77094)),x77095),x77095)
% 168.50/168.38 [8136]~E(x81363,f177(f909(x81362,a899)))+E(f315(f315(f3(f909(x81361,a899)),f315(f315(f32(x81362,f909(x81361,a899)),x81363),x81364)),x81365),f315(f315(f3(f909(x81361,a899)),f230(f909(x81361,a899))),x81365))
% 168.50/168.38 [8271]E(f315(f315(f148(x82711,f315(f315(f123(x82711),x82712),x82713)),x82714),x82715),f315(f315(f123(x82711),f315(f315(f148(x82711,x82712),x82714),x82715)),x82713))+~P1(f315(f315(f224(a901),x82714),f315(f178(f902(x82711)),x82712)))
% 168.50/168.38 [8541]E(f315(f315(f153(x85411),f315(f315(f143(a901,x85411),x85412),f128(a901,f315(f290(a901,x85413),x85414)))),x85415),f315(x85412,f315(f315(f73(a901),x85413),x85415)))+~P1(f315(f315(f224(a901),x85415),f315(f315(f3(a901),x85414),x85413)))
% 168.50/168.38 [8555]E(x85551,f2(a88))+E(f111(x85552,x85553,f315(x85554,f315(f315(f3(a88),x85551),f71(a88))),f315(f315(f9(x85552,a88,f903(f905(x85553))),x85555),x85551)),f315(f185(x85552,x85553,x85554,x85555),x85551))
% 168.50/168.38 [8579]~E(x85793,f177(f909(x85791,a899)))+E(f315(f315(f32(x85791,f909(x85792,a899)),x85793),f315(f315(f10(f909(x85792,a899),f909(x85792,a899),x85791),f315(f3(f909(x85792,a899)),x85794)),x85795)),f230(f909(x85792,a899)))
% 168.50/168.38 [8580]~E(x85803,f177(f909(x85801,a899)))+E(f315(f315(f32(x85801,f909(x85802,a899)),x85803),f315(f315(f10(f909(x85802,a899),f909(x85802,a899),x85801),f315(f90(f909(x85802,a899)),x85804)),x85805)),f230(f909(x85802,a899)))
% 168.50/168.38 [8581]~E(x85813,f177(f909(x85811,a899)))+E(f315(f315(f33(x85811,f909(x85812,a899)),x85813),f315(f315(f10(f909(x85812,a899),f909(x85812,a899),x85811),f315(f99(f909(x85812,a899)),x85814)),x85815)),f177(f909(x85812,a899)))
% 168.50/168.38 [8583]~P148(x85832)+E(f315(f315(f8(x85831,x85832),f315(f315(f10(x85832,x85832,x85831),f315(f74(x85832),x85833)),x85834)),x85835),f315(f315(f74(x85832),x85833),f315(f315(f8(x85831,x85832),x85834),x85835)))
% 168.50/168.38 [8874]E(x88741,f177(f909(x88742,a899)))+E(f315(f315(f32(x88742,f909(x88743,a899)),x88741),f315(f315(f10(f909(x88743,a899),f909(x88743,a899),x88742),f315(f3(f909(x88743,a899)),x88744)),x88745)),f315(f315(f3(f909(x88743,a899)),x88744),f315(f315(f33(x88742,f909(x88743,a899)),x88741),x88745)))
% 168.50/168.38 [8875]E(x88751,f177(f909(x88752,a899)))+E(f315(f315(f32(x88752,f909(x88753,a899)),x88751),f315(f315(f10(f909(x88753,a899),f909(x88753,a899),x88752),f315(f90(f909(x88753,a899)),x88754)),x88755)),f315(f315(f90(f909(x88753,a899)),x88754),f315(f315(f32(x88752,f909(x88753,a899)),x88751),x88755)))
% 168.50/168.38 [8876]E(x88761,f177(f909(x88762,a899)))+E(f315(f315(f33(x88762,f909(x88763,a899)),x88761),f315(f315(f10(f909(x88763,a899),f909(x88763,a899),x88762),f315(f99(f909(x88763,a899)),x88764)),x88765)),f315(f315(f99(f909(x88763,a899)),x88764),f315(f315(f33(x88762,f909(x88763,a899)),x88761),x88765)))
% 168.50/168.38 [9076]~P1(f315(f315(f224(a901),f315(x90764,x90762)),f315(x90764,x90763)))+P1(f315(f315(f317(f908(x90761,x90761)),f315(f315(f240(x90761,x90761),x90762),x90763)),f142(x90761,f315(f315(f140(f909(x90761,a901)),x90764),x90765))))
% 168.50/168.38 [9341]~P25(x93412,x93411,x93413,f315(f315(f99(f909(x93412,a899)),x93414),x93415))+E(f315(f315(f90(f909(x93411,a899)),f315(f298(x93412,x93411,x93413),f315(f315(f3(f909(x93412,a899)),x93414),x93415))),f315(f298(x93412,x93411,x93413),f315(f315(f3(f909(x93412,a899)),x93415),x93414))),f177(f909(x93411,a899)))
% 168.50/168.38 [9603]~P25(x96033,x96031,x96035,f230(f909(x96033,a899)))+E(f315(f66(x96031,x96032,x96033,f315(f66(x96033,x96032,x96031,x96034),f84(x96033,x96031,f230(f909(x96033,a899)),x96035))),x96035),x96034)
% 168.50/168.38 [9637]~P1(f315(f315(f223(f909(x96373,a899)),f315(f273(x96371,x96373,x96374),x96372)),x96375))+P1(f315(f315(f223(f909(x96371,a899)),x96372),f315(f72(f909(x96371,a899)),f315(f273(x96373,x96371,f315(f274(x96371,x96373),x96374)),f315(f72(f909(x96373,a899)),x96375)))))
% 168.50/168.38 [9662]~P25(x96621,x96622,x96623,f315(f315(f297(x96621),x96624),x96625))+~P1(f315(f315(f317(x96622),f315(x96623,x96624)),f315(f298(x96621,x96622,x96623),f315(f315(f3(f909(x96621,a899)),x96625),f315(f315(f297(x96621),x96624),f177(f909(x96621,a899)))))))
% 168.50/168.38 [9715]P1(f315(f315(f223(f909(x97151,a899)),f315(f273(x97152,x97151,x97153),x97154)),x97155))+~P1(f315(f315(f223(f909(x97152,a899)),x97154),f315(f72(f909(x97152,a899)),f315(f273(x97151,x97152,f315(f274(x97152,x97151),x97153)),f315(f72(f909(x97151,a899)),x97155)))))
% 168.50/168.38 [9788]~P89(x97881)+P1(f315(f315(f223(x97881),f315(f69(x97881),f315(f315(f3(x97881),f315(f315(f73(x97881),x97882),x97883)),f315(f315(f73(x97881),x97884),x97885)))),f315(f315(f73(x97881),f315(f69(x97881),f315(f315(f3(x97881),x97882),x97884))),f315(f69(x97881),f315(f315(f3(x97881),x97883),x97885)))))
% 168.50/168.38 [9896]P1(f315(f315(f317(x98961),f415(x98962,x98963,x98964,x98961,x98965)),x98964))+P1(f315(f315(f223(f909(x98965,a899)),f315(f315(f33(x98961,f909(x98965,a899)),x98964),x98963)),x98962))
% 168.50/168.38 [10074]~P1(f315(f315(f223(f909(x100741,a899)),f315(x100744,f415(x100745,x100744,x100743,x100742,x100741))),x100745))+P1(f315(f315(f223(f909(x100741,a899)),f315(f315(f33(x100742,f909(x100741,a899)),x100743),x100744)),x100745))
% 168.50/168.38 [8688]E(f315(f315(f123(x86881),x86882),f315(f315(f148(x86881,x86883),f315(f315(f3(a901),x86884),f315(f178(f902(x86881)),x86882))),x86885)),f315(f315(f148(x86881,f315(f315(f123(x86881),x86882),x86883)),x86884),x86885))+P1(f315(f315(f224(a901),x86884),f315(f178(f902(x86881)),x86882)))
% 168.50/168.38 [8716]~P141(x87161)+E(f315(f315(f73(x87161),f315(f315(f74(x87161),x87162),x87163)),f315(f315(f73(x87161),f315(f315(f74(x87161),x87164),x87163)),x87165)),f315(f315(f73(x87161),f315(f315(f74(x87161),f315(f315(f73(x87161),x87162),x87164)),x87163)),x87165))
% 168.50/168.38 [9294]~P148(x92941)+E(f315(f154(x92941),f315(f315(f143(x92942,x92941),f315(f315(f10(x92941,x92941,x92942),f315(f74(x92941),x92943)),x92944)),x92945)),f315(f315(f74(x92941),x92943),f315(f154(x92941),f315(f315(f143(x92942,x92941),x92944),x92945))))
% 168.50/168.38 [9471]E(f315(f178(f902(x94711)),f315(f315(f164(x94711),f315(f315(f221(a901),f315(f178(f902(x94711)),x94712)),f315(f178(f902(x94713)),x94714))),x94712)),f315(f178(f902(x94713)),f315(f315(f164(x94713),f315(f315(f221(a901),f315(f178(f902(x94711)),x94712)),f315(f178(f902(x94713)),x94714))),x94714)))+P1(f315(x94715,f315(f315(f170(x94711,x94713),x94712),x94714)))
% 168.50/168.38 [9725]~P148(x97252)+E(f315(f315(f8(x97251,x97252),f315(f315(f9(x97251,x97252,x97252),f315(f315(f10(x97252,f909(x97252,x97252),x97251),f74(x97252)),x97253)),x97254)),x97255),f315(f315(f74(x97252),f315(f315(f8(x97251,x97252),x97253),x97255)),x97254))
% 168.50/168.38 [9726]~P66(x97262)+E(f315(f315(f8(x97261,x97262),f315(f315(f9(x97261,x97262,x97262),f315(f315(f10(x97262,f909(x97262,x97262),x97261),f279(x97262)),x97263)),x97264)),x97265),f315(f315(f279(x97262),f315(f315(f8(x97261,x97262),x97263),x97265)),x97264))
% 168.50/168.38 [9733]~P69(x97332)+E(f315(f315(f8(x97331,x97332),f315(f315(f20(x97331,x97332,x97332),f315(f315(f10(x97332,f909(x97332,x97332),x97331),f3(x97332)),x97333)),x97334)),x97335),f315(f315(f3(x97332),f315(f315(f8(x97331,x97332),x97333),x97335)),f315(f315(f8(x97331,x97332),x97334),x97335)))
% 168.50/168.38 [9734]~P72(x97342)+E(f315(f315(f8(x97341,x97342),f315(f315(f20(x97341,x97342,x97342),f315(f315(f10(x97342,f909(x97342,x97342),x97341),f73(x97342)),x97343)),x97344)),x97345),f315(f315(f73(x97342),f315(f315(f8(x97341,x97342),x97343),x97345)),f315(f315(f8(x97341,x97342),x97344),x97345)))
% 168.50/168.38 [9735]~P77(x97352)+E(f315(f315(f11(x97351,x97352),f315(f315(f20(x97351,x97352,x97352),f315(f315(f10(x97352,f909(x97352,x97352),x97351),f74(x97352)),x97353)),x97354)),x97355),f315(f315(f74(x97352),f315(f315(f11(x97351,x97352),x97353),x97355)),f315(f315(f11(x97351,x97352),x97354),x97355)))
% 168.50/168.38 [9773]~E(x97733,f177(f909(x97731,a899)))+E(f315(f315(f32(x97731,f909(x97732,a899)),x97733),f315(f315(f9(x97731,f909(x97732,a899),f909(x97732,a899)),f315(f315(f10(f909(x97732,a899),f909(f909(x97732,a899),f909(x97732,a899)),x97731),f3(f909(x97732,a899))),x97734)),x97735)),f230(f909(x97732,a899)))
% 168.50/168.38 [9774]~E(x97743,f177(f909(x97741,a899)))+E(f315(f315(f32(x97741,f909(x97742,a899)),x97743),f315(f315(f9(x97741,f909(x97742,a899),f909(x97742,a899)),f315(f315(f10(f909(x97742,a899),f909(f909(x97742,a899),f909(x97742,a899)),x97741),f90(f909(x97742,a899))),x97744)),x97745)),f230(f909(x97742,a899)))
% 168.50/168.38 [9775]~E(x97753,f177(f909(x97751,a899)))+E(f315(f315(f33(x97751,f909(x97752,a899)),x97753),f315(f315(f9(x97751,f909(x97752,a899),f909(x97752,a899)),f315(f315(f10(f909(x97752,a899),f909(f909(x97752,a899),f909(x97752,a899)),x97751),f99(f909(x97752,a899))),x97754)),x97755)),f177(f909(x97752,a899)))
% 168.50/168.38 [9796]E(x97961,f177(f909(x97962,a899)))+E(f315(f315(f32(x97962,f909(x97963,a899)),x97961),f315(f315(f9(x97962,f909(x97963,a899),f909(x97963,a899)),f315(f315(f10(f909(x97963,a899),f909(f909(x97963,a899),f909(x97963,a899)),x97962),f3(f909(x97963,a899))),x97964)),x97965)),f315(f315(f3(f909(x97963,a899)),f315(f315(f32(x97962,f909(x97963,a899)),x97961),x97964)),x97965))
% 168.50/168.38 [9797]E(x97971,f177(f909(x97972,a899)))+E(f315(f315(f32(x97972,f909(x97973,a899)),x97971),f315(f315(f9(x97972,f909(x97973,a899),f909(x97973,a899)),f315(f315(f10(f909(x97973,a899),f909(f909(x97973,a899),f909(x97973,a899)),x97972),f90(f909(x97973,a899))),x97974)),x97975)),f315(f315(f90(f909(x97973,a899)),f315(f315(f32(x97972,f909(x97973,a899)),x97971),x97974)),x97975))
% 168.50/168.38 [9798]E(x97981,f177(f909(x97982,a899)))+E(f315(f315(f33(x97982,f909(x97983,a899)),x97981),f315(f315(f9(x97982,f909(x97983,a899),f909(x97983,a899)),f315(f315(f10(f909(x97983,a899),f909(f909(x97983,a899),f909(x97983,a899)),x97982),f99(f909(x97983,a899))),x97984)),x97985)),f315(f315(f99(f909(x97983,a899)),f315(f315(f33(x97982,f909(x97983,a899)),x97981),x97984)),x97985))
% 168.50/168.38 [9346]~P1(f315(f315(f223(a901),x93461),x93464))+E(f315(f315(f3(a901),f315(f315(f73(a901),f315(f315(f74(a901),x93461),x93462)),x93463)),f315(f315(f73(a901),f315(f315(f74(a901),x93464),x93462)),x93465)),f315(f315(f3(a901),x93463),f315(f315(f73(a901),f315(f315(f74(a901),f315(f315(f3(a901),x93464),x93461)),x93462)),x93465)))
% 168.50/168.38 [9945]~P148(x99451)+E(f315(f154(x99451),f315(f315(f143(x99452,x99451),f315(f315(f9(x99452,x99451,x99451),f315(f315(f10(x99451,f909(x99451,x99451),x99452),f74(x99451)),x99453)),x99454)),x99455)),f315(f315(f74(x99451),f315(f154(x99451),f315(f315(f143(x99452,x99451),x99453),x99455))),x99454))
% 168.50/168.38 [9951]~P69(x99511)+E(f315(f154(x99511),f315(f315(f143(x99512,x99511),f315(f315(f20(x99512,x99511,x99511),f315(f315(f10(x99511,f909(x99511,x99511),x99512),f3(x99511)),x99513)),x99514)),x99515)),f315(f315(f3(x99511),f315(f154(x99511),f315(f315(f143(x99512,x99511),x99513),x99515))),f315(f154(x99511),f315(f315(f143(x99512,x99511),x99514),x99515))))
% 168.50/168.38 [9952]~P72(x99521)+E(f315(f154(x99521),f315(f315(f143(x99522,x99521),f315(f315(f20(x99522,x99521,x99521),f315(f315(f10(x99521,f909(x99521,x99521),x99522),f73(x99521)),x99523)),x99524)),x99525)),f315(f315(f73(x99521),f315(f154(x99521),f315(f315(f143(x99522,x99521),x99523),x99525))),f315(f154(x99521),f315(f315(f143(x99522,x99521),x99524),x99525))))
% 168.50/168.38 [10098]P1(f315(x100981,f315(f315(f170(x100982,x100983),x100984),x100985)))+~P1(f315(x100981,f315(f315(f170(x100982,x100983),f315(f315(f164(x100982),f315(f315(f221(a901),f315(f178(f902(x100982)),x100984)),f315(f178(f902(x100983)),x100985))),x100984)),f315(f315(f164(x100983),f315(f315(f221(a901),f315(f178(f902(x100982)),x100984)),f315(f178(f902(x100983)),x100985))),x100985))))
% 168.50/168.38 [10359]~P1(f315(f315(f317(f908(x103592,x103591)),f315(f315(f240(x103592,x103591),x103594),x103595)),f315(f274(x103591,x103592),x103593)))+P1(f315(f315(f231(x103591,x103592,f315(f315(f9(x103591,f909(f908(x103591,x103592),a899),f909(x103592,a899)),f315(f315(f10(f909(x103592,f909(f909(f908(x103591,x103592),a899),a899)),f909(f909(f908(x103591,x103592),a899),f909(x103592,a899)),x103591),f9(x103592,f909(f908(x103591,x103592),a899),a899)),f315(f315(f10(f909(x103592,f908(x103591,x103592)),f909(x103592,f909(f909(f908(x103591,x103592),a899),a899)),x103591),f315(f10(f908(x103591,x103592),f909(f909(f908(x103591,x103592),a899),a899),x103592),f317(f908(x103591,x103592)))),f240(x103591,x103592)))),x103593)),x103594),x103595))
% 168.50/168.38 [10369]P1(f315(f315(f317(f908(x103691,x103692)),f315(f315(f240(x103691,x103692),x103693),x103694)),f315(f274(x103692,x103691),x103695)))+~P1(f315(f315(f231(x103692,x103691,f315(f315(f9(x103692,f909(f908(x103692,x103691),a899),f909(x103691,a899)),f315(f315(f10(f909(x103691,f909(f909(f908(x103692,x103691),a899),a899)),f909(f909(f908(x103692,x103691),a899),f909(x103691,a899)),x103692),f9(x103691,f909(f908(x103692,x103691),a899),a899)),f315(f315(f10(f909(x103691,f908(x103692,x103691)),f909(x103691,f909(f909(f908(x103692,x103691),a899),a899)),x103692),f315(f10(f908(x103692,x103691),f909(f909(f908(x103692,x103691),a899),a899),x103691),f317(f908(x103692,x103691)))),f240(x103692,x103691)))),x103695)),x103693),x103694))
% 168.50/168.38 [9602]~P1(f315(f315(f223(a901),x96024),x96021))+E(f315(f315(f3(a901),f315(f315(f73(a901),f315(f315(f74(a901),x96021),x96022)),x96023)),f315(f315(f73(a901),f315(f315(f74(a901),x96024),x96022)),x96025)),f315(f315(f3(a901),f315(f315(f73(a901),f315(f315(f74(a901),f315(f315(f3(a901),x96021),x96024)),x96022)),x96023)),x96025))
% 168.50/168.38 [7400]E(x74001,x74002)+~E(f209(x74003,x74004,x74005,x74001),f209(x74003,x74004,x74006,x74002))
% 168.50/168.38 [7401]E(x74011,x74012)+~E(f209(x74013,x74014,x74011,x74015),f209(x74013,x74014,x74012,x74016))
% 168.50/168.38 [8525]~P20(x85255,x85251,x85252,x85256)+E(f315(f66(x85251,x85251,x85251,f315(x85252,x85253)),f315(x85252,x85254)),f315(f66(x85251,x85251,x85251,f315(x85252,x85254)),f315(x85252,x85253)))
% 168.50/168.38 [8760]~P58(x87604,x87605,x87602,x87601,x87606)+E(f315(x87601,f315(x87602,x87603)),x87603)
% 168.50/168.38 [8927]P25(x89271,x89272,x89273,x89274)+~P25(x89271,x89275,f315(f66(x89272,x89275,x89271,x89276),x89273),x89274)
% 168.50/168.38 [9000]~E(x90006,x90004)+E(f315(f68(x90001,x90002,x90003,x90004,x90005),x90006),x90005)
% 168.50/168.38 [9006]E(x90061,x90062)+E(f315(f68(x90063,x90064,x90065,x90062,x90066),x90061),f315(x90065,x90061))
% 168.50/168.38 [9018]~P25(x90184,x90182,f315(f66(x90181,x90182,x90184,x90183),x90185),x90186)+P25(x90181,x90182,x90183,f315(f298(x90184,x90181,x90185),x90186))
% 168.50/168.38 [9736]P1(f315(f54(x97361),x97362))+~P1(f315(f59(x97361,x97363,x97364,x97365,x97362),x97366))
% 168.50/168.38 [9745]~P1(f315(f315(f317(x97454),x97453),f288(x97454,x97455,x97451,x97452,x97456)))+P1(f315(f315(x97451,x97452),x97453))
% 168.50/168.38 [9746]~P1(f315(f315(f317(x97464),x97463),f285(x97464,x97461,x97465,x97462,x97466)))+P1(f315(f315(x97461,x97462),x97463))
% 168.50/168.38 [9747]~P1(f315(f315(f317(x97474),x97472),f288(x97474,x97471,x97475,x97476,x97473)))+P1(f315(f315(x97471,x97472),x97473))
% 168.50/168.38 [9748]~P1(f315(f315(f317(x97484),x97482),f285(x97484,x97485,x97481,x97486,x97483)))+P1(f315(f315(x97481,x97482),x97483))
% 168.50/168.38 [10246]P12(x102461,x102462,x102463,x102464,x102465,x102466)+~E(f315(f315(x102466,f833(x102463,x102466,x102465,x102462,x102464,x102461)),f835(x102463,x102466,x102465,x102462,x102464,x102461)),f315(f315(x102466,f834(x102463,x102466,x102465,x102462,x102464,x102461)),f836(x102463,x102466,x102465,x102462,x102464,x102461)))
% 168.50/168.38 [5853]E(x58531,x58532)+~E(f315(f315(f240(x58533,x58534),x58535),x58531),f315(f315(f240(x58533,x58534),x58536),x58532))
% 168.50/168.38 [5855]E(x58551,x58552)+~E(f315(f315(f240(x58553,x58554),x58551),x58555),f315(f315(f240(x58553,x58554),x58552),x58556))
% 168.50/168.38 [6000]~P17(x60005,x60006,x60001)+E(f315(f315(x60001,x60002),f315(f315(x60001,x60003),x60004)),f315(f315(x60001,x60003),f315(f315(x60001,x60002),x60004)))
% 168.50/168.38 [7467]~P34(x74674,x74671,f315(f315(f140(x74674),x74672),x74675),f315(f315(f140(x74674),x74673),x74676))+P1(f315(f315(x74671,x74672),x74673))
% 168.50/168.38 [7826]P34(x78261,x78262,x78263,x78264)+~P34(x78261,x78262,f315(f315(f140(x78261),x78265),x78263),f315(f315(f140(x78261),x78266),x78264))
% 168.50/168.38 [8864]~P58(x88645,x88641,x88642,x88646,x88644)+P1(f315(f315(f317(x88641),f315(x88642,x88643)),x88644))
% 168.50/168.39 [9067]~E(x90673,f315(f315(f140(x90671),x90675),x90676))+P1(f315(f315(f317(f908(f902(x90671),f902(x90671))),f315(f315(f240(f902(x90671),f902(x90671)),x90672),f315(f315(f123(x90671),x90672),x90673))),f136(x90671,x90674)))
% 168.50/168.39 [9300]~P36(x93001,x93002,x93003,x93005,x93006)+P36(x93001,x93002,x93003,f315(f315(f164(x93001),x93004),x93005),f315(f315(f164(x93002),x93004),x93006))
% 168.50/168.39 [9301]~P36(x93011,x93012,x93013,x93015,x93016)+P36(x93011,x93012,x93013,f315(f315(f127(x93011),x93014),x93015),f315(f315(f127(x93012),x93014),x93016))
% 168.50/168.39 [9564]E(f315(f298(x95641,x95642,f68(x95641,x95642,x95643,x95644,x95645)),x95646),f315(f298(x95641,x95642,x95643),x95646))+P1(f315(f315(f317(x95641),x95644),x95646))
% 168.50/168.39 [9567]E(f315(f315(f143(x95671,x95672),f68(x95671,x95672,x95673,x95674,x95675)),x95676),f315(f315(f143(x95671,x95672),x95673),x95676))+P1(f315(f315(f317(x95671),x95674),f315(f161(x95671),x95676)))
% 168.50/168.39 [9808]~P24(x98084,x98082,x98085,x98083,x98086,x98081)+E(f315(x98081,f177(f909(x98082,a899))),x98083)
% 168.50/168.39 [10040]~E(f315(x100404,f315(f239(x100401,x100403),x100405)),f315(x100406,f315(f239(x100401,x100403),x100405)))+E(f315(f246(x100401,x100402,x100403,x100403,x100404,f25(x100403)),x100405),f315(f246(x100401,x100402,x100403,x100403,x100406,f25(x100403)),x100405))
% 168.50/168.39 [10041]~E(f315(x100414,f315(f244(x100411,x100412),x100415)),f315(x100416,f315(f244(x100411,x100412),x100415)))+E(f315(f246(x100411,x100411,x100412,x100413,f25(x100411),x100414),x100415),f315(f246(x100411,x100411,x100412,x100413,f25(x100411),x100416),x100415))
% 168.50/168.39 [10094]~E(f315(f246(x100942,x100946,x100943,x100943,x100941,f25(x100943)),x100944),f315(f246(x100942,x100946,x100943,x100943,x100945,f25(x100943)),x100944))+E(f315(x100941,f315(f239(x100942,x100943),x100944)),f315(x100945,f315(f239(x100942,x100943),x100944)))
% 168.50/168.39 [10095]~E(f315(f246(x100952,x100952,x100953,x100956,f25(x100952),x100951),x100954),f315(f246(x100952,x100952,x100953,x100956,f25(x100952),x100955),x100954))+E(f315(x100951,f315(f244(x100952,x100953),x100954)),f315(x100955,f315(f244(x100952,x100953),x100954)))
% 168.50/168.39 [8967]P1(f315(f315(f317(x89671),x89672),x89673))+~P1(f315(f315(f317(f908(x89671,x89674)),f315(f315(f240(x89671,x89674),x89672),x89675)),f315(f315(f242(x89671,x89674),x89673),x89676)))
% 168.50/168.39 [8983]P1(f315(f315(f317(x89831),x89832),f315(x89833,x89834)))+~P1(f315(f315(f317(f908(x89835,x89831)),f315(f315(f240(x89835,x89831),x89834),x89832)),f315(f315(f242(x89835,x89831),x89836),x89833)))
% 168.50/168.39 [9421]P1(f315(f315(f317(f908(x94211,x94211)),f315(f315(f240(x94211,x94211),f315(x94212,x94213)),f315(x94212,x94214))),x94215))+~P1(f315(f315(f317(f908(x94216,x94216)),f315(f315(f240(x94216,x94216),x94213),x94214)),f315(f315(f276(x94211,x94216),x94215),x94212)))
% 168.50/168.39 [9441]~P1(f315(f315(f317(f908(x94414,x94414)),f315(f315(f240(x94414,x94414),f315(x94416,x94412)),f315(x94416,x94413))),x94415))+P1(f315(f315(f317(f908(x94411,x94411)),f315(f315(f240(x94411,x94411),x94412),x94413)),f315(f315(f276(x94414,x94411),x94415),x94416)))
% 168.50/168.39 [10097]E(f315(f315(f240(x100971,x100972),f627(x100973,x100974,x100975,x100976,x100972,x100971)),f628(x100973,x100974,x100975,x100976,x100972,x100971)),x100976)+~P1(f315(f315(f317(f908(x100971,x100972)),x100976),f315(f315(f277(x100971,x100975,x100972),x100974),x100973)))
% 168.50/168.39 [10317]~P1(f315(f315(f317(f908(x103171,x103176)),x103175),f315(f315(f277(x103171,x103172,x103176),x103174),x103173)))+P1(f315(f315(f317(f908(x103171,x103172)),f315(f315(f240(x103171,x103172),f627(x103173,x103174,x103172,x103175,x103176,x103171)),f629(x103173,x103174,x103172,x103175,x103176,x103171))),x103174))
% 168.50/168.39 [10318]~P1(f315(f315(f317(f908(x103186,x103182)),x103185),f315(f315(f277(x103186,x103181,x103182),x103184),x103183)))+P1(f315(f315(f317(f908(x103181,x103182)),f315(f315(f240(x103181,x103182),f629(x103183,x103184,x103181,x103185,x103182,x103186)),f628(x103183,x103184,x103181,x103185,x103182,x103186))),x103183))
% 168.50/168.39 [10319]P12(x103191,x103192,x103193,x103194,x103195,x103196)+P1(f315(f315(f317(f908(x103192,x103192)),f315(f315(f240(x103192,x103192),f836(x103193,x103196,x103195,x103192,x103194,x103191)),f835(x103193,x103196,x103195,x103192,x103194,x103191))),x103195))
% 168.50/168.39 [10320]P12(x103201,x103202,x103203,x103204,x103205,x103206)+P1(f315(f315(f317(f908(x103201,x103201)),f315(f315(f240(x103201,x103201),f834(x103203,x103206,x103205,x103202,x103204,x103201)),f833(x103203,x103206,x103205,x103202,x103204,x103201))),x103204))
% 168.50/168.39 [7896]~P5(x78962)+E(f315(f315(f32(x78961,x78962),x78963),f315(f315(f9(x78961,x78964,x78962),x78965),x78966)),f315(f315(f315(f32(x78961,f909(x78964,x78962)),x78963),x78965),x78966))
% 168.50/168.39 [7897]~P5(x78972)+E(f315(f315(f33(x78971,x78972),x78973),f315(f315(f9(x78971,x78974,x78972),x78975),x78976)),f315(f315(f315(f33(x78971,f909(x78974,x78972)),x78973),x78975),x78976))
% 168.50/168.39 [8671]E(f315(f315(f33(x86711,f909(x86712,a899)),x86713),f315(f315(f10(f909(x86712,a899),f909(x86712,a899),x86711),f315(f297(x86712),x86714)),x86715)),f315(f315(f297(x86712),x86714),f315(f315(f33(x86711,f909(x86712,a899)),x86713),x86715)))+~P1(f315(f315(f317(x86711),x86716),x86713))
% 168.50/168.39 [9120]~P5(x91202)+E(f315(f315(f32(x91201,x91202),x91203),f315(f315(f10(f909(x91204,x91202),x91202,x91201),f315(f32(x91204,x91202),x91205)),f315(f9(x91204,x91201,x91202),x91206))),f315(f315(f32(x91204,x91202),x91205),f315(f315(f10(f909(x91201,x91202),x91202,x91204),f315(f32(x91201,x91202),x91203)),x91206)))
% 168.50/168.39 [9121]~P5(x91212)+E(f315(f315(f33(x91211,x91212),x91213),f315(f315(f10(f909(x91214,x91212),x91212,x91211),f315(f33(x91214,x91212),x91215)),f315(f9(x91214,x91211,x91212),x91216))),f315(f315(f33(x91214,x91212),x91215),f315(f315(f10(f909(x91211,x91212),x91212,x91214),f315(f33(x91211,x91212),x91213)),x91216)))
% 168.50/168.39 [9326]P1(f315(f315(f317(x93261),x93262),f315(f161(x93261),x93263)))+~P1(f315(f315(f317(f908(x93264,x93261)),f315(f315(f240(x93264,x93261),x93265),x93262)),f315(f161(f908(x93264,x93261)),f315(f315(f170(x93264,x93261),x93266),x93263))))
% 168.50/168.39 [9327]P1(f315(f315(f317(x93271),x93272),f315(f161(x93271),x93273)))+~P1(f315(f315(f317(f908(x93271,x93274)),f315(f315(f240(x93271,x93274),x93272),x93275)),f315(f161(f908(x93271,x93274)),f315(f315(f170(x93271,x93274),x93273),x93276))))
% 168.50/168.39 [9437]P1(f315(f315(f223(f909(x94371,a899)),f315(f273(x94372,x94371,x94373),x94374)),x94375))+~P1(f315(f315(f223(f909(f908(x94372,x94371),a899)),x94373),f315(f315(f242(x94372,x94371),x94376),f315(f18(f909(x94371,a899),x94372),x94375))))
% 168.50/168.39 [9442]~P26(x94424,x94422,x94425,f230(f909(x94424,a899)),f230(f909(x94422,a899)))+E(f315(f315(f32(x94421,f909(x94422,a899)),x94423),f315(f315(f10(f909(x94424,a899),f909(x94422,a899),x94421),f298(x94424,x94422,x94425)),x94426)),f315(f298(x94424,x94422,x94425),f315(f315(f32(x94421,f909(x94424,a899)),x94423),x94426)))
% 168.50/168.39 [9640]P1(f315(f315(f317(f908(f902(x96401),f902(x96401))),f315(f315(f240(f902(x96401),f902(x96401)),f315(f315(f140(x96401),x96402),x96403)),f315(f315(f140(x96401),x96404),x96405))),f136(x96401,x96406)))+~P1(f315(f315(f317(f908(x96401,x96401)),f315(f315(f240(x96401,x96401),x96402),x96404)),x96406))
% 168.50/168.39 [10093]E(f315(f315(f240(x100931,x100932),f571(x100933,x100934,x100935,x100932,x100931,x100936)),f574(x100933,x100934,x100935,x100932,x100931,x100936)),x100936)+P1(f315(f315(f317(x100935),x100934),f315(f315(f245(x100931,x100932,f909(x100935,a899)),x100933),x100936)))
% 168.50/168.39 [10099]E(f315(f315(f240(x100991,x100992),f572(x100993,x100994,x100992,x100991,x100995,x100996)),f573(x100993,x100994,x100992,x100991,x100995,x100996)),x100993)+~P1(f315(f315(f317(x100996),x100995),f315(f315(f245(x100991,x100992,f909(x100996,a899)),x100994),x100993)))
% 168.50/168.39 [10261]P1(f315(f315(f317(x102611),x102612),f315(f315(x102613,f572(x102614,x102613,x102615,x102616,x102612,x102611)),f573(x102614,x102613,x102615,x102616,x102612,x102611))))+~P1(f315(f315(f317(x102611),x102612),f315(f315(f245(x102616,x102615,f909(x102611,a899)),x102613),x102614)))
% 168.50/168.39 [10290]~P1(f315(f315(f317(x102901),x102902),f315(f315(x102905,f571(x102905,x102902,x102901,x102904,x102903,x102906)),f574(x102905,x102902,x102901,x102904,x102903,x102906))))+P1(f315(f315(f317(x102901),x102902),f315(f315(f245(x102903,x102904,f909(x102901,a899)),x102905),x102906)))
% 168.50/168.39 [8571]E(x85711,x85712)+E(f315(f315(f148(x85713,f315(f315(f148(x85713,x85714),x85711),x85715)),x85712),x85716),f315(f315(f148(x85713,f315(f315(f148(x85713,x85714),x85712),x85716)),x85711),x85715))
% 168.50/168.39 [9700]~P1(f315(f315(f317(x97003),x97006),x97005))+E(f315(f315(f297(x97001),x97002),f315(f298(x97003,x97001,x97004),f315(f315(f3(f909(x97003,a899)),x97005),f315(f315(f297(x97003),x97006),f177(f909(x97003,a899)))))),f315(f298(x97003,x97001,f68(x97003,x97001,x97004,x97006,x97002)),x97005))
% 168.50/168.39 [9199]~P1(f315(f315(x91994,x91995),x91996))+P1(f315(f315(f315(f315(f99(f909(x91991,f909(x91992,a899))),x91993),x91994),x91995),x91996))
% 168.50/168.39 [9201]~P1(f315(f315(x92013,x92015),x92016))+P1(f315(f315(f315(f315(f99(f909(x92011,f909(x92012,a899))),x92013),x92014),x92015),x92016))
% 168.50/168.39 [9492]P1(f315(f315(x94921,x94922),x94923))+~P1(f315(f315(f315(f315(f90(f909(x94924,f909(x94925,a899))),x94926),x94921),x94922),x94923))
% 168.50/168.39 [9493]P1(f315(f315(x94931,x94932),x94933))+~P1(f315(f315(f315(f315(f90(f909(x94934,f909(x94935,a899))),x94931),x94936),x94932),x94933))
% 168.50/168.39 [9933]~P72(x99332)+E(f315(f315(f8(x99331,x99332),f315(f315(f9(x99331,f909(x99333,a899),x99332),f315(f315(f10(f909(x99333,x99332),f909(f909(x99333,a899),x99332),x99331),f8(x99333,x99332)),x99334)),x99335)),x99336),f315(f315(f8(f908(x99331,x99333),x99332),f315(f245(x99331,x99333,x99332),x99334)),f315(f315(f242(x99331,x99333),x99336),f315(f18(f909(x99333,a899),x99331),x99335))))
% 168.50/168.39 [9934]~P77(x99342)+E(f315(f315(f11(x99341,x99342),f315(f315(f9(x99341,f909(x99343,a899),x99342),f315(f315(f10(f909(x99343,x99342),f909(f909(x99343,a899),x99342),x99341),f11(x99343,x99342)),x99344)),x99345)),x99346),f315(f315(f11(f908(x99341,x99343),x99342),f315(f245(x99341,x99343,x99342),x99344)),f315(f315(f242(x99341,x99343),x99346),f315(f18(f909(x99343,a899),x99341),x99345))))
% 168.50/168.39 [10065]~P72(x100652)+E(f315(f315(f8(x100651,x100652),f315(f315(f9(x100651,f909(x100653,a899),x100652),f315(f315(f10(f909(x100653,x100652),f909(f909(x100653,a899),x100652),x100651),f8(x100653,x100652)),f315(f9(x100653,x100651,x100652),x100654))),x100655)),x100656),f315(f315(f8(x100653,x100652),f315(f315(f9(x100653,f909(x100651,a899),x100652),f315(f315(f10(f909(x100651,x100652),f909(f909(x100651,a899),x100652),x100653),f8(x100651,x100652)),x100654)),x100656)),x100655))
% 168.50/168.39 [10381]~P1(f315(f315(f317(f908(x103811,x103812)),f315(f315(f240(x103811,x103812),x103815),x103816)),f315(f315(f99(f909(f908(x103811,x103812),a899)),x103813),x103814)))+P1(f315(f315(f315(f315(f99(f909(x103811,f909(x103812,a899))),f315(f315(f9(x103811,f909(f908(x103811,x103812),a899),f909(x103812,a899)),f315(f315(f10(f909(x103812,f909(f909(f908(x103811,x103812),a899),a899)),f909(f909(f908(x103811,x103812),a899),f909(x103812,a899)),x103811),f9(x103812,f909(f908(x103811,x103812),a899),a899)),f315(f315(f10(f909(x103812,f908(x103811,x103812)),f909(x103812,f909(f909(f908(x103811,x103812),a899),a899)),x103811),f315(f10(f908(x103811,x103812),f909(f909(f908(x103811,x103812),a899),a899),x103812),f317(f908(x103811,x103812)))),f240(x103811,x103812)))),x103813)),f315(f315(f9(x103811,f909(f908(x103811,x103812),a899),f909(x103812,a899)),f315(f315(f10(f909(x103812,f909(f909(f908(x103811,x103812),a899),a899)),f909(f909(f908(x103811,x103812),a899),f909(x103812,a899)),x103811),f9(x103812,f909(f908(x103811,x103812),a899),a899)),f315(f315(f10(f909(x103812,f908(x103811,x103812)),f909(x103812,f909(f909(f908(x103811,x103812),a899),a899)),x103811),f315(f10(f908(x103811,x103812),f909(f909(f908(x103811,x103812),a899),a899),x103812),f317(f908(x103811,x103812)))),f240(x103811,x103812)))),x103814)),x103815),x103816))
% 168.50/168.39 [10382]~P1(f315(f315(f317(f908(x103821,x103822)),f315(f315(f240(x103821,x103822),x103825),x103826)),f315(f315(f90(f909(f908(x103821,x103822),a899)),x103823),x103824)))+P1(f315(f315(f315(f315(f90(f909(x103821,f909(x103822,a899))),f315(f315(f9(x103821,f909(f908(x103821,x103822),a899),f909(x103822,a899)),f315(f315(f10(f909(x103822,f909(f909(f908(x103821,x103822),a899),a899)),f909(f909(f908(x103821,x103822),a899),f909(x103822,a899)),x103821),f9(x103822,f909(f908(x103821,x103822),a899),a899)),f315(f315(f10(f909(x103822,f908(x103821,x103822)),f909(x103822,f909(f909(f908(x103821,x103822),a899),a899)),x103821),f315(f10(f908(x103821,x103822),f909(f909(f908(x103821,x103822),a899),a899),x103822),f317(f908(x103821,x103822)))),f240(x103821,x103822)))),x103823)),f315(f315(f9(x103821,f909(f908(x103821,x103822),a899),f909(x103822,a899)),f315(f315(f10(f909(x103822,f909(f909(f908(x103821,x103822),a899),a899)),f909(f909(f908(x103821,x103822),a899),f909(x103822,a899)),x103821),f9(x103822,f909(f908(x103821,x103822),a899),a899)),f315(f315(f10(f909(x103822,f908(x103821,x103822)),f909(x103822,f909(f909(f908(x103821,x103822),a899),a899)),x103821),f315(f10(f908(x103821,x103822),f909(f909(f908(x103821,x103822),a899),a899),x103822),f317(f908(x103821,x103822)))),f240(x103821,x103822)))),x103824)),x103825),x103826))
% 168.50/168.39 [10391]P1(f315(f315(f317(f908(x103911,x103912)),f315(f315(f240(x103911,x103912),x103913),x103914)),f315(f315(f99(f909(f908(x103911,x103912),a899)),x103915),x103916)))+~P1(f315(f315(f315(f315(f99(f909(x103911,f909(x103912,a899))),f315(f315(f9(x103911,f909(f908(x103911,x103912),a899),f909(x103912,a899)),f315(f315(f10(f909(x103912,f909(f909(f908(x103911,x103912),a899),a899)),f909(f909(f908(x103911,x103912),a899),f909(x103912,a899)),x103911),f9(x103912,f909(f908(x103911,x103912),a899),a899)),f315(f315(f10(f909(x103912,f908(x103911,x103912)),f909(x103912,f909(f909(f908(x103911,x103912),a899),a899)),x103911),f315(f10(f908(x103911,x103912),f909(f909(f908(x103911,x103912),a899),a899),x103912),f317(f908(x103911,x103912)))),f240(x103911,x103912)))),x103915)),f315(f315(f9(x103911,f909(f908(x103911,x103912),a899),f909(x103912,a899)),f315(f315(f10(f909(x103912,f909(f909(f908(x103911,x103912),a899),a899)),f909(f909(f908(x103911,x103912),a899),f909(x103912,a899)),x103911),f9(x103912,f909(f908(x103911,x103912),a899),a899)),f315(f315(f10(f909(x103912,f908(x103911,x103912)),f909(x103912,f909(f909(f908(x103911,x103912),a899),a899)),x103911),f315(f10(f908(x103911,x103912),f909(f909(f908(x103911,x103912),a899),a899),x103912),f317(f908(x103911,x103912)))),f240(x103911,x103912)))),x103916)),x103913),x103914))
% 168.50/168.39 [10392]P1(f315(f315(f317(f908(x103921,x103922)),f315(f315(f240(x103921,x103922),x103923),x103924)),f315(f315(f90(f909(f908(x103921,x103922),a899)),x103925),x103926)))+~P1(f315(f315(f315(f315(f90(f909(x103921,f909(x103922,a899))),f315(f315(f9(x103921,f909(f908(x103921,x103922),a899),f909(x103922,a899)),f315(f315(f10(f909(x103922,f909(f909(f908(x103921,x103922),a899),a899)),f909(f909(f908(x103921,x103922),a899),f909(x103922,a899)),x103921),f9(x103922,f909(f908(x103921,x103922),a899),a899)),f315(f315(f10(f909(x103922,f908(x103921,x103922)),f909(x103922,f909(f909(f908(x103921,x103922),a899),a899)),x103921),f315(f10(f908(x103921,x103922),f909(f909(f908(x103921,x103922),a899),a899),x103922),f317(f908(x103921,x103922)))),f240(x103921,x103922)))),x103925)),f315(f315(f9(x103921,f909(f908(x103921,x103922),a899),f909(x103922,a899)),f315(f315(f10(f909(x103922,f909(f909(f908(x103921,x103922),a899),a899)),f909(f909(f908(x103921,x103922),a899),f909(x103922,a899)),x103921),f9(x103922,f909(f908(x103921,x103922),a899),a899)),f315(f315(f10(f909(x103922,f908(x103921,x103922)),f909(x103922,f909(f909(f908(x103921,x103922),a899),a899)),x103921),f315(f10(f908(x103921,x103922),f909(f909(f908(x103921,x103922),a899),a899),x103922),f317(f908(x103921,x103922)))),f240(x103921,x103922)))),x103926)),x103923),x103924))
% 168.50/168.39 [10375]~P1(f315(f315(f317(f908(x103752,x103753)),f315(f315(f240(x103752,x103753),x103755),x103756)),f315(f315(f32(x103751,f909(f908(x103752,x103753),a899)),f230(f909(x103751,a899))),x103754)))+P1(f315(f315(f315(f315(f32(x103751,f909(x103752,f909(x103753,a899))),f230(f909(x103751,a899))),f315(f315(f10(f909(f908(x103752,x103753),a899),f909(x103752,f909(x103753,a899)),x103751),f315(f9(x103752,f909(f908(x103752,x103753),a899),f909(x103753,a899)),f315(f315(f10(f909(x103753,f909(f909(f908(x103752,x103753),a899),a899)),f909(f909(f908(x103752,x103753),a899),f909(x103753,a899)),x103752),f9(x103753,f909(f908(x103752,x103753),a899),a899)),f315(f315(f10(f909(x103753,f908(x103752,x103753)),f909(x103753,f909(f909(f908(x103752,x103753),a899),a899)),x103752),f315(f10(f908(x103752,x103753),f909(f909(f908(x103752,x103753),a899),a899),x103753),f317(f908(x103752,x103753)))),f240(x103752,x103753))))),x103754)),x103755),x103756))
% 168.50/168.39 [10376]~P1(f315(f315(f317(f908(x103762,x103763)),f315(f315(f240(x103762,x103763),x103765),x103766)),f315(f315(f33(x103761,f909(f908(x103762,x103763),a899)),f230(f909(x103761,a899))),x103764)))+P1(f315(f315(f315(f315(f33(x103761,f909(x103762,f909(x103763,a899))),f230(f909(x103761,a899))),f315(f315(f10(f909(f908(x103762,x103763),a899),f909(x103762,f909(x103763,a899)),x103761),f315(f9(x103762,f909(f908(x103762,x103763),a899),f909(x103763,a899)),f315(f315(f10(f909(x103763,f909(f909(f908(x103762,x103763),a899),a899)),f909(f909(f908(x103762,x103763),a899),f909(x103763,a899)),x103762),f9(x103763,f909(f908(x103762,x103763),a899),a899)),f315(f315(f10(f909(x103763,f908(x103762,x103763)),f909(x103763,f909(f909(f908(x103762,x103763),a899),a899)),x103762),f315(f10(f908(x103762,x103763),f909(f909(f908(x103762,x103763),a899),a899),x103763),f317(f908(x103762,x103763)))),f240(x103762,x103763))))),x103764)),x103765),x103766))
% 168.50/168.39 [10385]P1(f315(f315(f317(f908(x103851,x103852)),f315(f315(f240(x103851,x103852),x103853),x103854)),f315(f315(f32(x103855,f909(f908(x103851,x103852),a899)),f230(f909(x103855,a899))),x103856)))+~P1(f315(f315(f315(f315(f32(x103855,f909(x103851,f909(x103852,a899))),f230(f909(x103855,a899))),f315(f315(f10(f909(f908(x103851,x103852),a899),f909(x103851,f909(x103852,a899)),x103855),f315(f9(x103851,f909(f908(x103851,x103852),a899),f909(x103852,a899)),f315(f315(f10(f909(x103852,f909(f909(f908(x103851,x103852),a899),a899)),f909(f909(f908(x103851,x103852),a899),f909(x103852,a899)),x103851),f9(x103852,f909(f908(x103851,x103852),a899),a899)),f315(f315(f10(f909(x103852,f908(x103851,x103852)),f909(x103852,f909(f909(f908(x103851,x103852),a899),a899)),x103851),f315(f10(f908(x103851,x103852),f909(f909(f908(x103851,x103852),a899),a899),x103852),f317(f908(x103851,x103852)))),f240(x103851,x103852))))),x103856)),x103853),x103854))
% 168.50/168.39 [10386]P1(f315(f315(f317(f908(x103861,x103862)),f315(f315(f240(x103861,x103862),x103863),x103864)),f315(f315(f33(x103865,f909(f908(x103861,x103862),a899)),f230(f909(x103865,a899))),x103866)))+~P1(f315(f315(f315(f315(f33(x103865,f909(x103861,f909(x103862,a899))),f230(f909(x103865,a899))),f315(f315(f10(f909(f908(x103861,x103862),a899),f909(x103861,f909(x103862,a899)),x103865),f315(f9(x103861,f909(f908(x103861,x103862),a899),f909(x103862,a899)),f315(f315(f10(f909(x103862,f909(f909(f908(x103861,x103862),a899),a899)),f909(f909(f908(x103861,x103862),a899),f909(x103862,a899)),x103861),f9(x103862,f909(f908(x103861,x103862),a899),a899)),f315(f315(f10(f909(x103862,f908(x103861,x103862)),f909(x103862,f909(f909(f908(x103861,x103862),a899),a899)),x103861),f315(f10(f908(x103861,x103862),f909(f909(f908(x103861,x103862),a899),a899),x103862),f317(f908(x103861,x103862)))),f240(x103861,x103862))))),x103866)),x103863),x103864))
% 168.50/168.39 [7572]E(f315(x75721,f315(x75722,x75723)),f315(x75724,x75723))+~E(f315(f66(x75725,x75726,x75727,x75721),x75722),x75724)
% 168.50/168.39 [9716]E(x97161,x97162)+E(f68(x97163,x97164,f68(x97163,x97164,x97165,x97161,x97166),x97162,x97167),f68(x97163,x97164,f68(x97163,x97164,x97165,x97162,x97167),x97161,x97166))
% 168.50/168.39 [9807]~P23(x98073,x98074,x98071,x98075,x98076,x98077)+E(f315(f315(x98071,x98072),x98072),x98072)
% 168.50/168.39 [6103]~E(f315(f315(f143(x61031,x61035),x61036),x61032),f315(f315(f143(x61033,x61035),x61037),x61034))+E(f315(f178(f902(x61031)),x61032),f315(f178(f902(x61033)),x61034))
% 168.50/168.39 [8602]E(f315(x86021,f315(x86022,x86023)),f315(x86024,x86023))+~E(f315(f66(x86025,x86026,x86027,x86021),x86022),f315(f66(x86026,x86026,x86027,f25(x86026)),x86024))
% 168.50/168.39 [8956]~P36(x89564,x89565,x89561,f315(f315(f140(x89564),x89562),x89566),f315(f315(f140(x89565),x89563),x89567))+P1(f315(f315(x89561,x89562),x89563))
% 168.50/168.39 [9333]P36(x93331,x93332,x93333,x93334,x93335)+~P36(x93331,x93332,x93333,f315(f315(f140(x93331),x93336),x93334),f315(f315(f140(x93332),x93337),x93335))
% 168.50/168.39 [9966]P1(f315(f315(x99661,x99662),f550(x99663,x99662,x99664,x99661)))+~P1(f315(f315(f241(x99665,x99666,x99667,x99661,x99664),x99662),x99663))
% 168.50/168.39 [9990]P1(f315(f315(x99901,f550(x99902,x99903,x99901,x99904)),x99902))+~P1(f315(f315(f241(x99905,x99906,x99907,x99904,x99901),x99903),x99902))
% 168.50/168.39 [9074]~P21(x90746,x90741,x90743,x90747)+E(f315(f66(x90741,x90741,x90742,f315(x90743,x90744)),f315(f66(x90741,x90741,x90742,f315(x90743,x90744)),x90745)),f315(f66(x90741,x90741,x90742,f315(x90743,x90744)),x90745))
% 168.50/168.39 [9445]~P36(x94453,x94452,x94454,f315(f315(f143(x94451,x94453),x94455),x94456),x94457)+P36(x94451,x94452,f315(f315(f10(x94453,f909(x94452,a899),x94451),x94454),x94455),x94456,x94457)
% 168.50/168.39 [9468]P36(x94681,x94682,x94683,f315(f315(f143(x94684,x94681),x94685),x94686),x94687)+~P36(x94684,x94682,f315(f315(f10(x94681,f909(x94682,a899),x94684),x94683),x94685),x94686,x94687)
% 168.50/168.39 [9073]~P1(f315(f315(f317(x90731),x90732),f315(f315(x90735,x90736),x90737)))+P1(f315(f315(f317(x90731),x90732),f315(f315(f245(x90733,x90734,f909(x90731,a899)),x90735),f315(f315(f240(x90733,x90734),x90736),x90737))))
% 168.50/168.39 [9359]P1(f315(f315(f315(x93591,x93592),x93593),x93594))+~P1(f315(f315(f315(f245(x93595,x93596,f909(x93597,a899)),x93591),f315(f315(f240(x93595,x93596),x93592),x93593)),x93594))
% 168.50/168.39 [9507]P1(f315(f315(f317(x95071),f315(f315(x95072,x95073),x95074)),f315(f298(f908(x95075,x95076),x95071,f315(f245(x95075,x95076,x95071),x95072)),x95077)))+~P1(f315(f315(f317(f908(x95075,x95076)),f315(f315(f240(x95075,x95076),x95073),x95074)),x95077))
% 168.50/168.39 [9854]P1(f315(f315(f317(f908(f902(x98541),f902(x98541))),f315(f315(f240(f902(x98541),f902(x98541)),f315(f315(f123(x98541),x98542),f315(f315(f140(x98541),x98543),x98544))),f315(f315(f123(x98541),x98542),f315(f315(f140(x98541),x98545),x98546)))),f136(x98541,x98547)))+~P1(f315(f315(f317(f908(x98541,x98541)),f315(f315(f240(x98541,x98541),x98543),x98545)),x98547))
% 168.50/168.39 [9918]~P36(x99181,x99183,x99184,x99186,f315(f315(f143(x99182,x99183),x99185),x99187))+P36(x99181,x99182,f315(f315(f9(x99181,f909(x99182,x99183),f909(x99182,a899)),f315(f315(f10(f909(x99183,a899),f909(f909(x99182,x99183),f909(x99182,a899)),x99181),f10(x99183,a899,x99182)),x99184)),x99185),x99186,x99187)
% 168.50/168.39 [9994]P36(x99941,x99942,x99943,x99944,f315(f315(f143(x99945,x99942),x99946),x99947))+~P36(x99941,x99945,f315(f315(f9(x99941,f909(x99945,x99942),f909(x99945,a899)),f315(f315(f10(f909(x99942,a899),f909(f909(x99945,x99942),f909(x99945,a899)),x99941),f10(x99942,a899,x99945)),x99943)),x99946),x99944,x99947)
% 168.50/168.39 [10304]P1(f315(f315(f317(x103041),f428(x103042,x103043,x103044,x103045,x103046,x103047,x103041)),x103045))+P1(f315(f315(f315(f315(f32(x103041,f909(x103047,f909(x103046,a899))),x103045),x103044),x103043),x103042))
% 168.50/168.39 [10305]P1(f315(f315(f317(x103051),f769(x103052,x103053,x103054,x103055,x103056,x103057,x103051)),x103057))+P1(f315(f315(f315(f315(f32(x103051,f909(x103053,f909(x103052,a899))),x103057),x103056),x103055),x103054))
% 168.50/168.39 [10306]P1(f315(f315(f317(x103061),f429(x103062,x103063,x103064,x103065,x103066,x103067,x103061)),x103065))+~P1(f315(f315(f315(f315(f33(x103061,f909(x103067,f909(x103066,a899))),x103065),x103064),x103063),x103062))
% 168.50/168.39 [10307]P1(f315(f315(f317(x103071),f764(x103072,x103073,x103074,x103075,x103076,x103077,x103071)),x103075))+~P1(f315(f315(f315(f315(f33(x103071,f909(x103077,f909(x103076,a899))),x103075),x103074),x103073),x103072))
% 168.50/168.39 [10340]P1(f315(f315(f315(x103401,f429(x103402,x103403,x103401,x103404,x103405,x103406,x103407)),x103403),x103402))+~P1(f315(f315(f315(f315(f33(x103407,f909(x103406,f909(x103405,a899))),x103404),x103401),x103403),x103402))
% 168.50/168.39 [10341]P1(f315(f315(f315(x103411,f764(x103412,x103413,x103411,x103414,x103415,x103416,x103417)),x103413),x103412))+~P1(f315(f315(f315(f315(f33(x103417,f909(x103416,f909(x103415,a899))),x103414),x103411),x103413),x103412))
% 168.50/168.39 [10356]~P1(f315(f315(f315(x103565,f428(x103567,x103566,x103565,x103564,x103563,x103562,x103561)),x103566),x103567))+P1(f315(f315(f315(f315(f32(x103561,f909(x103562,f909(x103563,a899))),x103564),x103565),x103566),x103567))
% 168.50/168.39 [10357]~P1(f315(f315(f315(x103575,f769(x103573,x103572,x103577,x103576,x103575,x103574,x103571)),x103576),x103577))+P1(f315(f315(f315(f315(f32(x103571,f909(x103572,f909(x103573,a899))),x103574),x103575),x103576),x103577))
% 168.50/168.39 [10374]~P1(f315(f315(f317(f908(x103741,x103743)),f315(f315(f240(x103741,x103743),x103746),x103747)),f315(f315(f277(x103741,x103742,x103743),x103744),x103745)))+P1(f315(f315(f241(x103741,x103742,x103743,f315(f315(f9(x103741,f909(f908(x103741,x103742),a899),f909(x103742,a899)),f315(f315(f10(f909(x103742,f909(f909(f908(x103741,x103742),a899),a899)),f909(f909(f908(x103741,x103742),a899),f909(x103742,a899)),x103741),f9(x103742,f909(f908(x103741,x103742),a899),a899)),f315(f315(f10(f909(x103742,f908(x103741,x103742)),f909(x103742,f909(f909(f908(x103741,x103742),a899),a899)),x103741),f315(f10(f908(x103741,x103742),f909(f909(f908(x103741,x103742),a899),a899),x103742),f317(f908(x103741,x103742)))),f240(x103741,x103742)))),x103744),f315(f315(f9(x103742,f909(f908(x103742,x103743),a899),f909(x103743,a899)),f315(f315(f10(f909(x103743,f909(f909(f908(x103742,x103743),a899),a899)),f909(f909(f908(x103742,x103743),a899),f909(x103743,a899)),x103742),f9(x103743,f909(f908(x103742,x103743),a899),a899)),f315(f315(f10(f909(x103743,f908(x103742,x103743)),f909(x103743,f909(f909(f908(x103742,x103743),a899),a899)),x103742),f315(f10(f908(x103742,x103743),f909(f909(f908(x103742,x103743),a899),a899),x103743),f317(f908(x103742,x103743)))),f240(x103742,x103743)))),x103745)),x103746),x103747))
% 168.50/168.39 [10384]P1(f315(f315(f317(f908(x103841,x103842)),f315(f315(f240(x103841,x103842),x103843),x103844)),f315(f315(f277(x103841,x103845,x103842),x103846),x103847)))+~P1(f315(f315(f241(x103841,x103845,x103842,f315(f315(f9(x103841,f909(f908(x103841,x103845),a899),f909(x103845,a899)),f315(f315(f10(f909(x103845,f909(f909(f908(x103841,x103845),a899),a899)),f909(f909(f908(x103841,x103845),a899),f909(x103845,a899)),x103841),f9(x103845,f909(f908(x103841,x103845),a899),a899)),f315(f315(f10(f909(x103845,f908(x103841,x103845)),f909(x103845,f909(f909(f908(x103841,x103845),a899),a899)),x103841),f315(f10(f908(x103841,x103845),f909(f909(f908(x103841,x103845),a899),a899),x103845),f317(f908(x103841,x103845)))),f240(x103841,x103845)))),x103846),f315(f315(f9(x103845,f909(f908(x103845,x103842),a899),f909(x103842,a899)),f315(f315(f10(f909(x103842,f909(f909(f908(x103845,x103842),a899),a899)),f909(f909(f908(x103845,x103842),a899),f909(x103842,a899)),x103845),f9(x103842,f909(f908(x103845,x103842),a899),a899)),f315(f315(f10(f909(x103842,f908(x103845,x103842)),f909(x103842,f909(f909(f908(x103845,x103842),a899),a899)),x103845),f315(f10(f908(x103845,x103842),f909(f909(f908(x103845,x103842),a899),a899),x103842),f317(f908(x103845,x103842)))),f240(x103845,x103842)))),x103847)),x103843),x103844))
% 168.50/168.39 [10316]~P148(x103162)+E(f315(f315(f8(x103161,x103162),f315(f315(f9(x103161,f909(x103163,a899),x103162),f315(f315(f10(f909(x103163,x103162),f909(f909(x103163,a899),x103162),x103161),f8(x103163,x103162)),f315(f315(f9(x103161,f909(x103163,x103162),f909(x103163,x103162)),f315(f315(f10(f909(x103162,x103162),f909(f909(x103163,x103162),f909(x103163,x103162)),x103161),f10(x103162,x103162,x103163)),f315(f315(f10(x103162,f909(x103162,x103162),x103161),f74(x103162)),x103164))),x103165))),x103166)),x103167),f315(f315(f74(x103162),f315(f315(f8(x103161,x103162),x103164),x103167)),f315(f315(f8(x103163,x103162),x103165),x103166)))
% 168.50/168.39 [9392]~P20(x93927,x93921,x93923,x93928)+E(f315(f66(x93921,x93921,x93922,f315(x93923,x93924)),f315(f66(x93921,x93921,x93922,f315(x93923,x93925)),x93926)),f315(f66(x93921,x93921,x93922,f315(x93923,x93925)),f315(f66(x93921,x93921,x93922,f315(x93923,x93924)),x93926)))
% 168.50/168.39 [10379]E(f315(f315(f240(x103791,x103792),f315(x103793,f535(x103794,x103795,x103793,x103796,x103797,x103798,x103792,x103791))),f315(x103795,f536(x103794,x103795,x103793,x103796,x103797,x103798,x103792,x103791))),x103798)+~P1(f315(f315(f317(f908(x103791,x103792)),x103798),f315(f298(f908(x103797,x103796),f908(x103791,x103792),f246(x103797,x103791,x103796,x103792,x103793,x103795)),x103794)))
% 168.50/168.39 [10397]~P1(f315(f315(f317(f908(x103978,x103977)),x103976),f315(f298(f908(x103971,x103972),f908(x103978,x103977),f246(x103971,x103978,x103972,x103977,x103975,x103974)),x103973)))+P1(f315(f315(f317(f908(x103971,x103972)),f315(f315(f240(x103971,x103972),f535(x103973,x103974,x103975,x103972,x103971,x103976,x103977,x103978)),f536(x103973,x103974,x103975,x103972,x103971,x103976,x103977,x103978))),x103973))
% 168.50/168.39 [9844]P1(f315(f315(f317(f908(f908(x98441,x98442),f908(x98441,x98442))),f315(f315(f240(f908(x98441,x98442),f908(x98441,x98442)),f315(f315(f240(x98441,x98442),x98443),x98444)),f315(f315(f240(x98441,x98442),x98445),x98446))),f307(x98441,x98442,x98447,x98448)))+~P1(f315(f315(f317(f908(x98441,x98441)),f315(f315(f240(x98441,x98441),x98443),x98445)),x98447))
% 168.50/168.39 [10368]E(f315(f131(x103681,x103682,f315(f9(x103682,x103681,x103681),x103683),f315(x103684,x103685)),x103686),f315(x103684,f315(f131(x103687,x103682,f315(f9(x103682,x103687,x103687),x103688),x103685),x103686)))+P1(f315(f315(f317(x103682),f715(x103685,x103688,x103684,x103683,x103687,x103681,x103686,x103682)),f315(f161(x103682),x103686)))
% 168.50/168.39 [10387]~E(f315(f66(x103871,x103871,x103877,f315(x103873,f715(x103875,x103878,x103874,x103873,x103877,x103871,x103876,x103872))),x103874),f315(f66(x103877,x103871,x103877,x103874),f315(x103878,f715(x103875,x103878,x103874,x103873,x103877,x103871,x103876,x103872))))+E(f315(f131(x103871,x103872,f315(f9(x103872,x103871,x103871),x103873),f315(x103874,x103875)),x103876),f315(x103874,f315(f131(x103877,x103872,f315(f9(x103872,x103877,x103877),x103878),x103875),x103876)))
% 168.50/168.39 [8607]E(f315(x86071,f315(x86072,x86073)),f315(x86074,f315(x86075,x86073)))+~E(f315(f66(x86076,x86077,x86078,x86071),x86072),f315(f66(x86079,x86077,x86078,x86074),x86075))
% 168.50/168.39 [10225]P1(f315(f315(f317(f908(x102251,x102252)),f315(f315(f240(x102251,x102252),f315(x102253,x102254)),f315(x102255,x102256))),f315(f298(f908(x102257,x102258),f908(x102251,x102252),f246(x102257,x102251,x102258,x102252,x102253,x102255)),x102259)))+~P1(f315(f315(f317(f908(x102257,x102258)),f315(f315(f240(x102257,x102258),x102254),x102256)),x102259))
% 168.50/168.39 [8902]~E(f315(x89024,f315(x89025,x89026)),f315(x89029,f315(x890210,x890211)))+E(f315(f315(f66(x89021,x89022,x89023,x89024),x89025),x89026),f315(f315(f66(x89027,x89022,x89028,x89029),x890210),x890211))
% 168.50/168.39 [4658]~P110(x46581)+~P104(x46581)+E(f90(x46581),f221(x46581))
% 168.50/168.39 [4659]~P110(x46591)+~P103(x46591)+E(f99(x46591),f222(x46591))
% 168.50/168.39 [4904]~P114(x49041)+~P97(x49041)+E(f315(f69(x49041),f315(f92(x49041),a86)),f71(x49041))
% 168.50/168.39 [5197]E(x51971,f2(a1))+E(f75(a1,x51971),f315(f72(a1),f71(a1)))+P1(f315(f315(f224(a1),f2(a1)),x51971))
% 168.50/168.39 [5403]E(x54031,f2(a1))+E(f75(a1,x54031),f71(a1))+~P1(f315(f315(f224(a1),f2(a1)),x54031))
% 168.50/168.39 [7471]~P42(x74711)+P1(f315(f54(a1),x74711))+~P1(f315(f54(a901),f315(f298(a1,a901,a93),x74711)))
% 168.50/168.39 [9806]E(x98061,f177(f909(f908(a901,a901),a899)))+~P1(f315(f54(f908(a901,a901)),x98061))+P1(f315(f315(f317(f908(f909(f908(a901,a901),a899),f909(f908(a901,a901),a899))),f315(f315(f240(f909(f908(a901,a901),a899),f909(f908(a901,a901),a899)),f177(f909(f908(a901,a901),a899))),x98061)),a27))
% 168.50/168.39 [9967]E(x99671,f2(a901))+E(x99671,f315(a101,f2(a901)))+~P1(f315(f315(f224(a901),x99671),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))))
% 168.50/168.39 [10254]E(x102541,f2(a88))+E(f315(f315(f73(a1),f315(f315(f74(a1),f315(f92(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),f315(a24,f315(f315(f29(a88),x102541),f315(f92(a88),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))))))),f71(a1)),f315(a24,x102541))+E(f38(a88,x102541,f315(f92(a88),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),f2(a88))
% 168.50/168.39 [10103]E(x101031,f2(a88))+~E(f38(a88,x101031,f315(f92(a88),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),f2(a88))+E(f315(f315(f74(a1),f315(f92(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),f315(a24,f315(f315(f29(a88),x101031),f315(f92(a88),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))))),f315(a24,x101031))
% 168.50/168.39 [4739]~P59(x47391,x47392)+P46(x47391,x47392)+~P47(a899)
% 168.50/168.39 [4668]~P147(x46681)+P30(x46681,x46682)+~E(x46682,f2(x46681))
% 168.50/168.39 [4669]~P110(x46691)+P13(x46691,x46692)+~E(x46692,f102(x46691))
% 168.50/168.39 [4678]~P114(x46781)+~E(x46782,f2(x46781))+E(f75(x46781,x46782),f2(x46781))
% 168.50/168.39 [4679]~P93(x46791)+~E(x46792,f2(x46791))+E(f75(x46791,x46792),f2(x46791))
% 168.50/168.39 [4687]~P147(x46872)+~P30(x46872,x46871)+E(x46871,f2(x46872))
% 168.50/168.39 [4732]~P114(x47322)+~E(f75(x47322,x47321),f2(x47322))+E(x47321,f2(x47322))
% 168.50/168.39 [4746]~P4(x47462)+~P4(x47461)+P4(f909(x47461,x47462))
% 168.50/168.39 [4747]~P4(x47472)+~P4(x47471)+P4(f907(x47471,x47472))
% 168.50/168.39 [4748]~P4(x47482)+~P4(x47481)+P4(f908(x47481,x47482))
% 168.50/168.39 [4749]~P6(x47492)+~P6(x47491)+P6(f183(x47491,x47492))
% 168.50/168.39 [4750]~P64(x47502)+~P64(x47501)+P64(f909(x47501,x47502))
% 168.50/168.39 [4751]~P64(x47512)+~P64(x47511)+P64(f907(x47511,x47512))
% 168.50/168.39 [4752]~P64(x47522)+~P64(x47521)+P64(f908(x47521,x47522))
% 168.50/168.39 [4753]~P106(x47532)+~P106(x47531)+P106(f908(x47531,x47532))
% 168.50/168.39 [4876]~P110(x48761)+~P13(x48761,x48762)+P13(x48761,f141(x48761,x48762))
% 168.50/168.39 [5124]~P6(x51242)+~P6(x51241)+P6(f38(a1,x51241,x51242))
% 168.50/168.39 [4689]~P78(x46891)+~E(x46892,f2(x46891))+E(f315(f72(x46891),x46892),x46892)
% 168.50/168.39 [4704]~P143(x47041)+~E(x47042,f2(a1))+E(f315(f91(x47041),x47042),f2(x47041))
% 168.50/168.39 [4705]~P95(x47051)+~E(x47052,f2(a1))+E(f315(f91(x47051),x47052),f2(x47051))
% 168.50/168.39 [4729]~P76(x47291)+~E(f2(x47291),x47292)+E(f315(f72(x47291),x47292),f2(x47291))
% 168.50/168.39 [4730]~P89(x47301)+~E(x47302,f2(x47301))+E(f315(f69(x47301),x47302),f2(x47301))
% 168.50/168.39 [4731]~P76(x47311)+~E(x47312,f2(x47311))+E(f315(f72(x47311),x47312),f2(x47311))
% 168.50/168.39 [4755]~P78(x47552)+E(x47551,f2(x47552))+~E(f315(f72(x47552),x47551),x47551)
% 168.50/168.39 [4757]E(x47571,f315(a93,x47572))+~E(x47571,f2(a901))+~E(x47572,f315(f89(a1),x47571))
% 168.50/168.39 [4758]E(f315(a93,x47581),x47582)+~E(x47582,f2(a901))+~E(x47581,f315(f89(a1),x47582))
% 168.50/168.39 [4762]~P95(x47622)+E(x47621,f2(a1))+~E(f315(f91(x47622),x47621),f2(x47622))
% 168.50/168.39 [4766]~P89(x47662)+E(x47661,f2(x47662))+~E(f315(f69(x47662),x47661),f2(x47662))
% 168.50/168.39 [4767]~P76(x47672)+E(x47671,f2(x47672))+~E(f315(f72(x47672),x47671),f2(x47672))
% 168.50/168.39 [4768]~P76(x47681)+E(f2(x47681),x47682)+~E(f315(f72(x47681),x47682),f2(x47681))
% 168.50/168.39 [4951]~P110(x49511)+~P13(x49511,x49512)+P13(x49511,f315(f160(x49511),x49512))
% 168.50/168.39 [4978]~P1(x49782)+~P1(x49781)+P1(f315(f315(a313,x49781),x49782))
% 168.50/168.39 [5016]~E(f71(a901),f2(a901))+E(f315(f28(x50161),x50162),f2(a901))+~P1(f315(f54(x50161),x50162))
% 168.50/168.39 [5052]~P117(x50521)+~P148(x50521)+E(f315(f315(f232(x50521),f2(x50521)),f315(a101,x50522)),f2(x50521))
% 168.50/168.39 [5092]~P110(x50921)+P13(x50921,f128(x50921,x50922))+~P1(f315(f54(x50921),x50922))
% 168.50/168.39 [5093]~P110(x50931)+P13(x50931,f707(x50932,x50931))+~P1(f315(f54(x50931),x50932))
% 168.50/168.39 [5116]~P110(x51161)+E(f315(f161(x51161),f128(x51161,x51162)),x51162)+~P1(f315(f54(x51161),x51162))
% 168.50/168.39 [5117]~P110(x51171)+E(f315(f161(x51171),f707(x51172,x51171)),x51172)+~P1(f315(f54(x51171),x51172))
% 168.50/168.39 [5146]P1(x51461)+P1(x51462)+~P1(f315(f315(a314,x51462),x51461))
% 168.50/168.39 [5159]E(x51591,f177(f909(x51592,a899)))+~E(f315(f28(x51592),x51591),f2(a901))+~P1(f315(f54(x51592),x51591))
% 168.50/168.39 [5164]P1(x51641)+~P1(x51642)+~P1(f315(f315(a318,x51642),x51641))
% 168.50/168.39 [5215]~P75(x52151)+E(f315(f69(x52151),x52152),x52152)+P1(f315(f315(f224(x52151),x52152),f2(x52151)))
% 168.50/168.39 [5275]~P64(x52752)+~P1(f315(f49(x52752),x52751))+P1(f315(x52751,f708(x52751,x52752)))
% 168.50/168.39 [5276]~P64(x52762)+~P1(f315(f49(x52762),x52761))+P1(f315(x52761,f716(x52761,x52762)))
% 168.50/168.39 [5318]E(x53181,f102(x53182))+P1(f315(f126(x53182),f103(x53182,x53181)))+~P1(f315(f126(x53182),x53181))
% 168.50/168.39 [5323]~P110(x53231)+~P1(f315(f54(x53231),x53232))+P1(f315(f126(x53231),f128(x53231,x53232)))
% 168.50/168.39 [5324]~P110(x53241)+~P1(f315(f54(x53241),x53242))+P1(f315(f126(x53241),f707(x53242,x53241)))
% 168.50/168.39 [5329]~P143(x53291)+E(f315(f89(x53291),f315(a93,x53292)),f315(f91(x53291),x53292))+P1(f315(f315(f224(a1),x53292),f2(a1)))
% 168.50/168.39 [5350]P7(x53502,x53501)+E(f315(x53501,f432(x53501)),f315(x53501,f466(x53501)))+P1(f315(f315(x53501,f432(x53501)),f466(x53501)))
% 168.50/168.39 [5364]E(f315(f89(a1),f348(x53641,x53642)),x53641)+P1(f315(x53642,f315(a93,x53641)))+~P1(f315(x53642,f2(a901)))
% 168.50/168.39 [5377]~P64(x53771)+~P1(f315(x53772,f721(x53772,x53771)))+P1(f315(f50(x53771),x53772))
% 168.50/168.39 [5378]~P64(x53781)+~P1(f315(x53782,f731(x53782,x53781)))+P1(f315(f50(x53781),x53782))
% 168.50/168.39 [5413]~P114(x54131)+~E(f75(x54131,x54132),f315(f72(x54131),f71(x54131)))+P1(f315(f315(f224(x54131),x54132),f2(x54131)))
% 168.50/168.39 [5488]~E(x54882,f2(a1))+E(f204(x54881,x54882),f315(f315(f240(a1,a1),f2(a1)),f71(a1)))+P1(f315(f315(f224(a1),x54882),f2(a1)))
% 168.50/168.39 [5489]~E(x54891,f2(a1))+E(f204(x54891,x54892),f315(f315(f240(a1,a1),f2(a1)),f71(a1)))+P1(f315(f315(f224(a1),x54892),f2(a1)))
% 168.50/168.39 [5542]E(f315(f89(a1),f348(x55421,x55422)),x55421)+P1(f315(x55422,f315(a93,x55421)))+P1(f315(f315(f224(a1),x55421),f2(a1)))
% 168.50/168.39 [5611]~P114(x56111)+E(f75(x56111,x56112),f315(f72(x56111),f71(x56111)))+~P1(f315(f315(f224(x56111),x56112),f2(x56111)))
% 168.50/168.39 [5612]~P89(x56121)+E(f315(f69(x56121),x56122),f315(f72(x56121),x56122))+~P1(f315(f315(f223(x56121),x56122),f2(x56121)))
% 168.50/168.39 [5613]~P89(x56131)+E(f315(f69(x56131),x56132),f315(f72(x56131),x56132))+~P1(f315(f315(f224(x56131),x56132),f2(x56131)))
% 168.50/168.39 [5614]~P75(x56141)+E(f315(f69(x56141),x56142),f315(f72(x56141),x56142))+~P1(f315(f315(f224(x56141),x56142),f2(x56141)))
% 168.50/168.39 [5716]~P1(f315(x57161,f348(x57162,x57161)))+P1(f315(x57161,f315(a93,x57162)))+~P1(f315(x57161,f2(a901)))
% 168.50/168.39 [5723]E(x57231,f2(a901))+E(f315(a101,f691(x57232,x57231)),x57231)+~P1(f315(f315(f224(a901),x57231),f315(a101,x57232)))
% 168.50/168.39 [5727]P7(x57271,x57272)+~E(f315(x57272,f432(x57272)),f315(x57272,f466(x57272)))+~P1(f315(f315(x57272,f432(x57272)),f466(x57272)))
% 168.50/168.39 [5745]~P110(x57451)+P13(x57451,x57452)+P1(f315(f315(f223(a901),f692(x57452,x57451)),f693(x57452,x57451)))
% 168.50/168.39 [5746]~P110(x57461)+P13(x57461,x57462)+P1(f315(f315(f223(a901),f699(x57462,x57461)),f703(x57462,x57461)))
% 168.50/168.39 [5832]~P89(x58321)+~E(x58322,f2(x58321))+P1(f315(f315(f223(x58321),f315(f69(x58321),x58322)),f2(x58321)))
% 168.50/168.39 [5929]~P1(f315(x59291,f348(x59292,x59291)))+P1(f315(x59291,f315(a93,x59292)))+P1(f315(f315(f224(a1),x59292),f2(a1)))
% 168.50/168.39 [5954]~P1(f315(x59541,f315(a93,x59542)))+P1(f315(x59541,f2(a901)))+~P1(f315(f315(f224(a1),x59542),f2(a1)))
% 168.50/168.39 [6308]~P114(x63081)+~P1(f315(f315(f224(x63081),x63082),f2(x63081)))+P1(f315(f315(f224(x63081),f75(x63081,x63082)),f2(x63081)))
% 168.50/168.39 [6426]~P114(x64261)+P1(f315(f315(f223(x64261),f315(f91(x64261),x64262)),f2(x64261)))+~P1(f315(f315(f223(a1),x64262),f2(a1)))
% 168.50/168.39 [6427]~P114(x64271)+P1(f315(f315(f224(x64271),f315(f91(x64271),x64272)),f2(x64271)))+~P1(f315(f315(f224(a1),x64272),f2(a1)))
% 168.50/168.39 [6436]~P89(x64362)+E(x64361,f2(x64362))+~P1(f315(f315(f223(x64362),f315(f69(x64362),x64361)),f2(x64362)))
% 168.50/168.39 [6516]~P143(x65161)+~P1(f315(f315(f317(x65161),x65162),f98(x65161)))+P1(f315(f315(f317(x65161),f315(f72(x65161),x65162)),f98(x65161)))
% 168.50/168.39 [6548]~P114(x65481)+~P1(f315(f315(f224(x65481),f75(x65481,x65482)),f2(x65481)))+P1(f315(f315(f224(x65481),x65482),f2(x65481)))
% 168.50/168.39 [6726]~P114(x67262)+~P1(f315(f315(f223(x67262),f315(f91(x67262),x67261)),f2(x67262)))+P1(f315(f315(f223(a1),x67261),f2(a1)))
% 168.50/168.39 [6727]~P114(x67272)+~P1(f315(f315(f224(x67272),f315(f91(x67272),x67271)),f2(x67272)))+P1(f315(f315(f224(a1),x67271),f2(a1)))
% 168.50/168.39 [7244]~P78(x72441)+~P1(f315(f315(f223(x72441),x72442),f2(x72441)))+P1(f315(f315(f223(x72441),f315(f315(f73(x72441),x72442),x72442)),f2(x72441)))
% 168.50/168.39 [7245]~P114(x72451)+~P1(f315(f315(f224(x72451),x72452),f2(x72451)))+P1(f315(f315(f224(x72451),f315(f315(f73(x72451),x72452),x72452)),f2(x72451)))
% 168.50/168.39 [7246]~P78(x72461)+~P1(f315(f315(f224(x72461),x72462),f2(x72461)))+P1(f315(f315(f224(x72461),f315(f315(f73(x72461),x72462),x72462)),f2(x72461)))
% 168.50/168.39 [7819]~P78(x78191)+~P1(f315(f315(f223(x78191),f315(f315(f73(x78191),x78192),x78192)),f2(x78191)))+P1(f315(f315(f223(x78191),x78192),f2(x78191)))
% 168.50/168.39 [7820]~P114(x78201)+~P1(f315(f315(f224(x78201),f315(f315(f73(x78201),x78202),x78202)),f2(x78201)))+P1(f315(f315(f224(x78201),x78202),f2(x78201)))
% 168.50/168.39 [7821]~P78(x78211)+~P1(f315(f315(f224(x78211),f315(f315(f73(x78211),x78212),x78212)),f2(x78211)))+P1(f315(f315(f224(x78211),x78212),f2(x78211)))
% 168.50/168.39 [4803]~E(x48032,f71(a901))+~E(x48031,f71(a901))+E(f315(f315(f74(a901),x48031),x48032),f71(a901))
% 168.50/168.39 [4804]~E(x48042,f71(a1))+~E(x48041,f71(a1))+E(f315(f315(f74(a1),x48041),x48042),f71(a1))
% 168.50/168.39 [4805]~E(x48052,f2(a901))+~E(x48051,f2(a901))+E(f315(f315(f73(a901),x48051),x48052),f2(a901))
% 168.50/168.39 [4860]~P125(x48602)+E(x48601,f2(x48602))+E(f315(f315(f279(x48602),x48601),x48601),f71(x48602))
% 168.50/168.39 [4861]~P62(x48612)+E(x48611,f2(x48612))+E(f315(f315(f29(x48612),x48611),x48611),f71(x48612))
% 168.50/168.39 [4862]~P126(x48622)+E(x48621,f2(x48622))+E(f315(f315(f279(x48622),x48621),x48621),f71(x48622))
% 168.50/168.39 [4882]~P144(x48821)+~E(x48822,f71(x48821))+E(f315(f315(f74(x48821),x48822),x48822),f71(x48821))
% 168.50/168.39 [4883]~P78(x48831)+~E(x48832,f2(x48831))+E(f315(f315(f73(x48831),x48832),x48832),f2(x48831))
% 168.50/168.39 [4884]~P126(x48841)+~E(x48842,f2(x48841))+E(f315(f315(f279(x48841),x48842),x48842),f2(x48841))
% 168.50/168.39 [4929]~E(x49292,f2(a901))+~E(x49291,f2(a901))+E(f315(f72(a1),f315(f89(a1),x49291)),f315(f89(a1),x49292))
% 168.50/168.39 [4948]E(x49481,f71(a901))+E(x49482,f2(a901))+~E(f315(f315(f74(a901),x49482),x49481),x49482)
% 168.50/168.39 [4960]E(x49601,f2(a901))+E(x49602,f2(a901))+~E(f315(f315(f74(a901),x49602),x49601),f2(a901))
% 168.50/168.39 [4987]~E(x49872,f2(a901))+~E(x49871,f315(a101,f2(a901)))+E(f315(f315(f73(a901),x49871),x49872),f315(a101,f2(a901)))
% 168.50/168.39 [4988]~E(x49881,f2(a901))+~E(x49882,f315(a101,f2(a901)))+E(f315(f315(f73(a901),x49881),x49882),f315(a101,f2(a901)))
% 168.50/168.39 [4995]E(x49951,f71(a1))+E(x49952,f315(f92(a1),a86))+~E(f315(f315(f74(a1),x49951),x49952),f71(a1))
% 168.50/168.39 [4996]E(x49961,f71(a1))+E(x49962,f315(f92(a1),a86))+~E(f315(f315(f74(a1),x49962),x49961),f71(a1))
% 168.50/168.39 [4997]E(x49971,f71(a1))+E(x49971,f315(f92(a1),a86))+~E(f315(f315(f74(a1),x49972),x49971),f71(a1))
% 168.50/168.39 [4999]E(x49991,f71(a1))+E(x49991,f315(f92(a1),a86))+~E(f315(f315(f74(a1),x49991),x49992),f71(a1))
% 168.50/168.39 [5024]~P78(x50242)+E(x50241,f2(x50242))+~E(f315(f315(f73(x50242),x50241),x50241),f2(x50242))
% 168.50/168.39 [5030]~E(x50301,f315(f92(a1),a86))+~E(x50302,f315(f92(a1),a86))+E(f315(f315(f74(a1),x50301),x50302),f71(a1))
% 168.50/168.39 [5041]E(x50411,f2(a901))+E(x50412,f2(a901))+~E(f315(f315(f73(a901),x50412),x50411),f315(a101,f2(a901)))
% 168.50/168.39 [5051]~P65(x50511)+~P97(x50511)+E(f315(f315(f279(x50511),x50512),f315(f92(x50511),a76)),f2(x50511))
% 168.50/168.39 [5058]~P144(x50581)+~E(x50582,f315(f72(x50581),f71(x50581)))+E(f315(f315(f74(x50581),x50582),x50582),f71(x50581))
% 168.50/168.39 [5063]~P6(x50632)+~P6(x50631)+P6(f315(f315(f74(a1),x50631),x50632))
% 168.50/168.39 [5064]~P6(x50642)+~P6(x50641)+P6(f315(f315(f73(a1),x50641),x50642))
% 168.50/168.39 [5065]~P6(x50652)+~P6(x50651)+P6(f315(f315(f29(a1),x50651),x50652))
% 168.50/168.39 [5067]~E(x50672,f2(a1))+E(x50671,f2(a1))+E(f39(x50671,x50672),f315(f315(f240(a1,a1),f2(a1)),x50671))
% 168.50/168.39 [5090]~E(x50902,f315(a101,f2(a901)))+~E(x50901,f315(a101,f2(a901)))+E(f315(f315(f74(a901),x50901),x50902),f315(a101,f2(a901)))
% 168.50/168.39 [5107]E(x51071,f2(a901))+E(x51072,f315(a101,f2(a901)))+~E(f315(f315(f232(a901),x51072),x51071),f315(a101,f2(a901)))
% 168.50/168.39 [5108]E(x51081,f2(a901))+E(x51081,f315(a101,f2(a901)))+~E(f315(f315(f73(a901),x51082),x51081),f315(a101,f2(a901)))
% 168.50/168.39 [5109]E(x51091,f2(a901))+E(x51091,f315(a101,f2(a901)))+~E(f315(f315(f73(a901),x51091),x51092),f315(a101,f2(a901)))
% 168.50/168.39 [5118]~P65(x51181)+~P97(x51181)+E(f315(f315(f279(x51181),x51182),f315(f92(x51181),a86)),f315(f72(x51181),x51182))
% 168.50/168.39 [5138]E(x51381,f315(a93,x51382))+~E(x51381,f2(a901))+P1(f315(f315(f223(a1),f2(a1)),x51382))
% 168.50/168.39 [5139]E(f315(a93,x51391),x51392)+~E(x51392,f2(a901))+P1(f315(f315(f223(a1),f2(a1)),x51391))
% 168.50/168.39 [5155]E(x51551,f315(a101,f2(a901)))+E(x51552,f315(a101,f2(a901)))+~E(f315(f315(f73(a901),x51551),x51552),f315(a101,f2(a901)))
% 168.50/168.39 [5166]~E(x51661,f315(a93,x51662))+E(x51661,f2(a901))+P1(f315(f315(f223(a1),f2(a1)),x51662))
% 168.50/168.39 [5167]~E(f315(a93,x51672),x51671)+E(x51671,f2(a901))+P1(f315(f315(f223(a1),f2(a1)),x51672))
% 168.50/168.39 [5190]~P80(x51901)+E(f315(f56(x51901,f99(x51901)),x51902),f12(x51901,x51902))+~P1(f315(f54(x51901),x51902))
% 168.50/168.39 [5191]~P80(x51911)+E(f315(f56(x51911,f90(x51911)),x51912),f13(x51911,x51912))+~P1(f315(f54(x51911),x51912))
% 168.50/168.39 [5192]~P110(x51921)+E(f315(f56(x51921,f221(x51921)),x51922),f16(x51921,x51922))+~P1(f315(f54(x51921),x51922))
% 168.50/168.39 [5193]~P110(x51931)+E(f315(f56(x51931,f222(x51931)),x51932),f17(x51931,x51932))+~P1(f315(f54(x51931),x51932))
% 168.50/168.39 [5270]E(x52701,x52702)+~E(f315(f315(f3(a901),x52702),x52701),f2(a901))+~E(f315(f315(f3(a901),x52701),x52702),f2(a901))
% 168.50/168.39 [5288]P6(x52881)+~P42(x52882)+~P1(f315(f315(f317(a1),x52881),x52882))
% 168.50/168.39 [5319]~P114(x53191)+~E(f75(x53191,x53192),f71(x53191))+P1(f315(f315(f224(x53191),f2(x53191)),x53192))
% 168.50/168.39 [5330]~P97(x53301)+E(f315(f89(x53301),f315(f92(a901),x53302)),f315(f92(x53301),x53302))+P1(f315(a182,f315(f92(a1),x53302)))
% 168.50/168.39 [5335]~P46(x53351,x53352)+P47(a899)+P1(f315(f54(f908(x53351,x53351)),x53352))
% 168.50/168.39 [5405]~P110(x54051)+E(f315(f56(x54051,f221(x54051)),x54052),f14(x54051,f221(x54051),x54052))+~P1(f315(f54(x54051),x54052))
% 168.50/168.39 [5406]~P110(x54061)+E(f315(f56(x54061,f222(x54061)),x54062),f15(x54061,f222(x54061),x54062))+~P1(f315(f54(x54061),x54062))
% 168.50/168.39 [5420]E(x54201,x54202)+P1(f315(f315(f224(a901),x54202),x54201))+P1(f315(f315(f224(a901),x54201),x54202))
% 168.50/168.39 [5421]E(x54211,x54212)+P1(f315(f315(f224(a1),x54212),x54211))+P1(f315(f315(f224(a1),x54211),x54212))
% 168.50/168.39 [5475]~P97(x54751)+E(f315(f89(x54751),f315(f92(a901),x54752)),f2(x54751))+~P1(f315(a182,f315(f92(a1),x54752)))
% 168.50/168.39 [5478]~E(x54782,f315(a93,x54781))+E(x54781,f315(f89(a1),x54782))+~P1(f315(f315(f223(a1),f2(a1)),x54781))
% 168.50/168.39 [5479]~E(f315(a93,x54791),x54792)+E(x54791,f315(f89(a1),x54792))+~P1(f315(f315(f223(a1),f2(a1)),x54791))
% 168.50/168.39 [5480]~E(x54801,f315(a93,x54802))+E(f315(f89(a1),x54801),x54802)+~P1(f315(f315(f223(a1),f2(a1)),x54802))
% 168.50/168.39 [5490]E(x54901,f315(a93,x54902))+~E(x54902,f315(f89(a1),x54901))+~P1(f315(f315(f223(a1),f2(a1)),x54902))
% 168.50/168.39 [5491]E(f315(a93,x54911),x54912)+~E(x54911,f315(f89(a1),x54912))+~P1(f315(f315(f223(a1),f2(a1)),x54911))
% 168.50/168.39 [5522]~P121(x55222)+E(x55221,f2(x55222))+~P1(f315(f315(f275(x55222),f2(x55222)),x55221))
% 168.50/168.39 [5533]~P89(x55332)+E(x55331,f2(x55332))+P1(f315(f315(f224(x55332),f2(x55332)),f315(f69(x55332),x55331)))
% 168.50/168.39 [5598]~P114(x55981)+E(f75(x55981,x55982),f71(x55981))+~P1(f315(f315(f224(x55981),f2(x55981)),x55982))
% 168.50/168.39 [5604]~P97(x56041)+E(f315(f89(x56041),f315(f92(a901),x56042)),f2(x56041))+P1(f315(f315(f223(a1),f2(a1)),f315(f92(a1),x56042)))
% 168.50/168.39 [5615]~P89(x56151)+E(f315(f69(x56151),x56152),x56152)+~P1(f315(f315(f223(x56151),f2(x56151)),x56152))
% 168.50/168.39 [5616]~P89(x56161)+E(f315(f69(x56161),x56162),x56162)+~P1(f315(f315(f224(x56161),f2(x56161)),x56162))
% 168.50/168.39 [5625]E(x56251,f2(a901))+~E(f128(a901,f315(f290(a901,x56252),x56251)),f102(a901))+P1(f315(f315(f223(a901),x56251),x56252))
% 168.50/168.39 [5636]~P72(x56361)+E(f315(f315(f8(x56361,x56361),f7(x56361)),f315(f161(x56361),x56362)),f315(f154(x56361),x56362))+~P1(f315(f126(x56361),x56362))
% 168.50/168.39 [5639]~P143(x56391)+E(f315(f89(x56391),f315(a93,x56392)),f315(f91(x56391),x56392))+~P1(f315(f315(f223(a1),f2(a1)),x56392))
% 168.50/168.39 [5666]E(x56661,x56662)+P1(f315(f315(f224(a901),x56661),x56662))+~P1(f315(f315(f223(a901),x56661),x56662))
% 168.50/168.39 [5667]E(x56671,x56672)+P1(f315(f315(f224(a1),x56671),x56672))+~P1(f315(f315(f223(a1),x56671),x56672))
% 168.50/168.39 [5670]E(x56701,f71(a1))+~E(f315(f315(f74(a1),x56702),x56701),f71(a1))+~P1(f315(f315(f224(a1),f2(a1)),x56702))
% 168.50/168.39 [5671]E(x56711,f71(a1))+~E(f315(f315(f74(a1),x56711),x56712),f71(a1))+~P1(f315(f315(f224(a1),f2(a1)),x56711))
% 168.50/168.39 [5713]~P42(x57132)+P1(f315(f315(f223(a1),f2(a1)),x57131))+~P1(f315(f315(f317(a1),x57131),x57132))
% 168.50/168.39 [5732]~P59(x57321,x57322)+P39(x57321,x57322)+~P1(f315(f54(f908(x57321,x57321)),x57322))
% 168.50/168.39 [5734]~P59(x57341,x57342)+P46(x57341,x57342)+~P1(f315(f54(f908(x57341,x57341)),x57342))
% 168.50/168.39 [5776]E(x57761,f177(f909(x57762,a899)))+~P1(f315(f54(x57762),x57761))+P1(f315(f315(f224(a901),f2(a901)),f315(f28(x57762),x57761)))
% 168.50/168.39 [5803]~P1(f315(x58031,x58032))+P1(f315(x58031,f2(a901)))+P1(f315(f315(f224(a901),f858(x58032,x58031)),x58032))
% 168.50/168.39 [5826]E(x58261,f2(a901))+~E(f315(f154(a901),x58262),f2(a901))+~P1(f315(f315(f317(a901),x58261),f315(f161(a901),x58262)))
% 168.50/168.39 [5894]E(x58941,x58942)+~P1(f315(f315(f223(a901),x58942),x58941))+~P1(f315(f315(f223(a901),x58941),x58942))
% 168.50/168.39 [5895]E(x58951,x58952)+~P1(f315(f315(f223(a1),x58952),x58951))+~P1(f315(f315(f223(a1),x58951),x58952))
% 168.50/168.39 [5904]E(x59041,x59042)+~P1(f315(f315(f275(a901),x59042),x59041))+~P1(f315(f315(f275(a901),x59041),x59042))
% 168.50/168.39 [5906]E(f315(f28(x59061),x59062),f2(a901))+~P1(f315(f54(x59061),x59062))+P1(f315(f315(f317(x59061),f860(x59062,x59061)),x59062))
% 168.50/168.39 [5915]E(f43(x59151,x59152),f39(x59151,x59152))+P1(f315(f315(f223(a1),f2(a1)),x59151))+~P1(f315(f315(f224(a1),f2(a1)),x59152))
% 168.50/168.39 [5941]~P1(f315(x59411,f343(x59411)))+P1(f315(x59411,f315(a93,x59412)))+~P1(f315(f315(f223(a1),f2(a1)),x59412))
% 168.50/168.39 [5944]P1(f315(f315(f223(a901),x59441),f398(x59442)))+~P1(f315(f54(a901),x59442))+~P1(f315(f315(f317(a901),x59441),x59442))
% 168.50/168.39 [5945]P1(f315(f315(f224(a901),x59451),f396(x59452)))+~P1(f315(f54(a901),x59452))+~P1(f315(f315(f317(a901),x59451),x59452))
% 168.50/168.39 [5976]E(x59761,x59762)+~P1(f315(f315(f224(a901),x59761),f315(a101,x59762)))+P1(f315(f315(f224(a901),x59761),x59762))
% 168.50/168.39 [6012]E(x60121,f315(a101,x60122))+~P1(f315(f315(f223(a901),x60121),f315(a101,x60122)))+P1(f315(f315(f223(a901),x60121),x60122))
% 168.50/168.39 [6028]P1(f315(x60281,f344(x60281)))+~P1(f315(x60281,f315(a93,x60282)))+~P1(f315(f315(f223(a1),f2(a1)),x60282))
% 168.50/168.39 [6044]~P1(f315(x60441,x60442))+~P1(f315(f315(f223(a1),f2(a1)),x60442))+P1(f315(x60441,f315(f89(a1),f325(x60441))))
% 168.50/168.39 [6055]~P89(x60552)+~E(x60551,f2(x60552))+~P1(f315(f315(f224(x60552),f2(x60552)),f315(f69(x60552),x60551)))
% 168.50/168.39 [6080]~P59(x60801,x60802)+P39(x60801,f315(f274(x60801,x60801),x60802))+~P1(f315(f54(f908(x60801,x60801)),x60802))
% 168.50/168.39 [6089]~P97(x60891)+E(f315(f89(x60891),f315(f92(a901),x60892)),f315(f92(x60891),x60892))+~P1(f315(f315(f223(a1),f2(a1)),f315(f92(a1),x60892)))
% 168.50/168.39 [6093]E(f315(a101,x60931),x60932)+~P1(f315(f315(f224(a901),x60931),x60932))+P1(f315(f315(f224(a901),f315(a101,x60931)),x60932))
% 168.50/168.39 [6109]E(f315(f315(f29(a1),x61091),x61092),f2(a1))+~P1(f315(f315(f223(a1),x61091),f2(a1)))+~P1(f315(f315(f224(a1),x61092),x61091))
% 168.50/168.39 [6121]E(f38(a1,x61211,x61212),x61211)+~P1(f315(f315(f223(a1),x61211),f2(a1)))+~P1(f315(f315(f224(a1),x61212),x61211))
% 168.50/168.39 [6135]E(f40(x61351,x61352),f39(x61351,x61352))+~P1(f315(f315(f223(a1),f2(a1)),x61351))+~P1(f315(f315(f223(a1),f2(a1)),x61352))
% 168.50/168.39 [6145]E(f315(f315(f29(a1),x61451),x61452),f2(a1))+~P1(f315(f315(f223(a1),f2(a1)),x61451))+~P1(f315(f315(f224(a1),x61451),x61452))
% 168.50/168.39 [6156]E(f38(a901,f315(f92(a901),x61561),f315(f92(a901),x61562)),f315(f92(a901),x61561))+P1(f315(a182,f315(f92(a1),x61561)))+~P1(f315(a182,f315(f92(a1),x61562)))
% 168.50/168.39 [6158]E(f38(a1,x61581,x61582),x61581)+~P1(f315(f315(f223(a1),f2(a1)),x61581))+~P1(f315(f315(f224(a1),x61581),x61582))
% 168.50/168.39 [6159]E(x61591,x61592)+~P1(f315(f315(f224(a901),x61591),f315(a101,x61592)))+~P1(f315(f315(f223(a901),x61592),x61591))
% 168.50/168.39 [6173]~P78(x61731)+~P1(f315(f315(f223(x61731),x61732),f2(x61731)))+P1(f315(f315(f223(x61731),x61732),f315(f72(x61731),x61732)))
% 168.50/168.39 [6174]~P114(x61741)+~P1(f315(f315(f224(x61741),x61742),f2(x61741)))+P1(f315(f315(f224(x61741),x61742),f315(f72(x61741),x61742)))
% 168.50/168.39 [6184]~P5(x61841)+E(f315(f315(f57(x61841,x61841,f99(x61841)),f177(x61841)),x61842),f30(x61841,x61842))+~P1(f315(f54(x61841),x61842))
% 168.50/168.39 [6185]~P5(x61851)+E(f315(f315(f57(x61851,x61851,f90(x61851)),f230(x61851)),x61852),f31(x61851,x61852))+~P1(f315(f54(x61851),x61852))
% 168.50/168.39 [6202]~P114(x62021)+~P1(f315(f315(f223(a1),f2(a1)),x62022))+P1(f315(f315(f223(x62021),f2(x62021)),f315(f91(x62021),x62022)))
% 168.50/168.39 [6203]~P128(x62031)+~P1(f315(f315(f224(a901),f2(a901)),x62032))+P1(f315(f315(f224(x62031),f2(x62031)),f315(f89(x62031),x62032)))
% 168.50/168.39 [6204]~P114(x62041)+~P1(f315(f315(f224(a1),f2(a1)),x62042))+P1(f315(f315(f224(x62041),f2(x62041)),f315(f91(x62041),x62042)))
% 168.50/168.39 [6207]~P6(x62072)+~P6(x62071)+E(f315(f298(a901,a1,f89(a1)),f291(a901,f315(a93,x62071),f315(a93,x62072))),f291(a1,x62071,x62072))
% 168.50/168.39 [6213]P1(f315(x62131,x62132))+~P1(f315(f315(f223(a1),f2(a1)),x62132))+~P1(f315(x62131,f315(f89(a1),f330(x62131))))
% 168.50/168.39 [6245]E(f315(f315(f73(a901),f315(f92(a901),x62451)),f315(f92(a901),x62452)),f315(f92(a901),x62451))+P1(f315(f315(f224(a1),x62451),a76))+~P1(f315(f315(f224(a1),x62452),a76))
% 168.50/168.39 [6249]~P114(x62491)+P1(f315(f315(f224(x62491),f2(x62491)),f75(x62491,x62492)))+~P1(f315(f315(f224(x62491),f2(x62491)),x62492))
% 168.50/168.39 [6263]~P82(x62631)+~P1(f315(f315(f223(x62631),x62632),f2(x62631)))+P1(f315(f315(f223(x62631),f2(x62631)),f315(f72(x62631),x62632)))
% 168.50/168.39 [6264]~P82(x62641)+~P1(f315(f315(f224(x62641),x62642),f2(x62641)))+P1(f315(f315(f224(x62641),f2(x62641)),f315(f72(x62641),x62642)))
% 168.50/168.39 [6267]E(x62671,f230(f909(x62672,a899)))+~E(f315(f28(x62672),x62671),f315(f28(x62672),f230(f909(x62672,a899))))+~P1(f315(f54(x62672),f230(f909(x62672,a899))))
% 168.50/168.39 [6300]~P78(x63001)+P1(f315(f315(f223(x63001),x63002),f2(x63001)))+~P1(f315(f315(f223(x63001),x63002),f315(f72(x63001),x63002)))
% 168.50/168.39 [6301]~P114(x63011)+P1(f315(f315(f224(x63011),x63012),f2(x63011)))+~P1(f315(f315(f224(x63011),x63012),f315(f72(x63011),x63012)))
% 168.50/168.39 [6310]~P97(x63101)+P1(f315(f315(f317(x63101),f315(f92(x63101),x63102)),f175(x63101)))+~P1(f315(f315(f223(a1),a76),x63102))
% 168.50/168.39 [6339]E(x63391,f2(a901))+~P1(f315(f315(f224(a901),x63391),f315(a101,x63392)))+P1(f315(f315(f224(a901),f691(x63392,x63391)),x63392))
% 168.50/168.39 [6363]~P114(x63631)+~P1(f315(f315(f224(x63631),f2(x63631)),f75(x63631,x63632)))+P1(f315(f315(f224(x63631),f2(x63631)),x63632))
% 168.50/168.39 [6365]~E(f315(f92(a901),x63652),f315(f92(a901),x63651))+P1(f315(f315(f223(a1),f315(f92(a1),x63651)),f2(a1)))+~P1(f315(a182,f315(f92(a1),x63652)))
% 168.50/168.39 [6394]E(f315(f239(a1,a1),f43(x63941,x63942)),f315(f315(f29(a1),x63941),x63942))+~P1(f315(f315(f224(a1),x63941),f2(a1)))+~P1(f315(f315(f224(a1),f2(a1)),x63942))
% 168.50/168.39 [6434]E(f315(f244(a1,a1),f43(x64341,x64342)),f38(a1,x64341,x64342))+~P1(f315(f315(f224(a1),x64341),f2(a1)))+~P1(f315(f315(f224(a1),f2(a1)),x64342))
% 168.50/168.39 [6437]~P114(x64372)+~P1(f315(f315(f223(x64372),f2(x64372)),f315(f91(x64372),x64371)))+P1(f315(f315(f223(a1),f2(a1)),x64371))
% 168.50/168.39 [6438]~P128(x64382)+~P1(f315(f315(f224(x64382),f2(x64382)),f315(f89(x64382),x64381)))+P1(f315(f315(f224(a901),f2(a901)),x64381))
% 168.50/168.39 [6439]~P114(x64392)+~P1(f315(f315(f224(x64392),f2(x64392)),f315(f91(x64392),x64391)))+P1(f315(f315(f224(a1),f2(a1)),x64391))
% 168.50/168.39 [6443]E(f315(f239(a1,a1),f40(x64431,x64432)),f315(f315(f29(a1),x64431),x64432))+~P1(f315(f315(f223(a1),f2(a1)),x64432))+~P1(f315(f315(f224(a1),f2(a1)),x64431))
% 168.50/168.39 [6457]E(f315(f244(a1,a1),f40(x64571,x64572)),f38(a1,x64571,x64572))+~P1(f315(f315(f223(a1),f2(a1)),x64572))+~P1(f315(f315(f224(a1),f2(a1)),x64571))
% 168.50/168.39 [6473]~P82(x64731)+P1(f315(f315(f223(x64731),x64732),f2(x64731)))+~P1(f315(f315(f223(x64731),f2(x64731)),f315(f72(x64731),x64732)))
% 168.50/168.39 [6474]~P82(x64741)+P1(f315(f315(f224(x64741),x64742),f2(x64741)))+~P1(f315(f315(f224(x64741),f2(x64741)),f315(f72(x64741),x64742)))
% 168.50/168.39 [6500]P1(f315(f42(x65001,x65002),f43(x65001,x65002)))+~P1(f315(f315(f224(a1),x65001),f2(a1)))+~P1(f315(f315(f224(a1),f2(a1)),x65002))
% 168.50/168.39 [6515]~P1(f315(f315(f224(a901),f2(a901)),x65151))+~P1(f315(f315(f275(a901),x65152),x65151))+~P1(f315(f315(f224(a901),x65151),x65152))
% 168.50/168.39 [6528]P1(f315(f42(x65281,x65282),f40(x65281,x65282)))+~P1(f315(f315(f223(a1),f2(a1)),x65281))+~P1(f315(f315(f224(a1),f2(a1)),x65282))
% 168.50/168.39 [6572]~P82(x65721)+P1(f315(f315(f223(x65721),f315(f72(x65721),x65722)),f2(x65721)))+~P1(f315(f315(f223(x65721),f2(x65721)),x65722))
% 168.50/168.39 [6573]~P82(x65731)+P1(f315(f315(f224(x65731),f315(f72(x65731),x65732)),f2(x65731)))+~P1(f315(f315(f224(x65731),f2(x65731)),x65732))
% 168.50/168.39 [6593]E(f315(f315(f3(a901),f315(a93,x65931)),f315(a93,x65932)),f315(a93,f183(x65931,x65932)))+~P1(f315(f315(f223(a1),f2(a1)),x65932))+~P1(f315(f315(f223(a1),f2(a1)),x65931))
% 168.50/168.39 [6611]P1(f315(f315(f223(a1),f2(a1)),f183(x66111,x66112)))+~P1(f315(f315(f223(a1),f2(a1)),x66112))+~P1(f315(f315(f223(a1),f2(a1)),x66111))
% 168.50/168.39 [6648]~P1(f315(x66481,x66482))+P1(f315(x66481,f2(a901)))+P1(f315(x66481,f315(f315(f73(a901),f858(x66482,x66481)),f71(a901))))
% 168.50/168.39 [6733]E(f315(f92(a901),x67331),f315(f92(a901),x67332))+~P1(f315(f315(f223(a1),f315(f92(a1),x67332)),f2(a1)))+~P1(f315(a182,f315(f92(a1),x67331)))
% 168.50/168.39 [6747]~E(x67471,f2(a901))+~E(f657(x67472,x67471),f2(a901))+E(f315(f131(a901,a901,f73(a901),x67471),x67472),f2(a901))
% 168.50/168.39 [6771]~P1(f315(f54(x67711),f862(x67712,x67711)))+~P1(f315(f54(f909(x67711,a899)),x67712))+P1(f315(f54(x67711),f30(f909(x67711,a899),x67712)))
% 168.50/168.39 [6777]E(x67771,x67772)+P1(f315(f315(f224(a1),x67771),x67772))+~P1(f315(f315(f224(a1),x67771),f315(f315(f73(a1),x67772),f71(a1))))
% 168.50/168.39 [6778]P1(f315(f315(f223(a901),f315(a93,x67781)),f315(a93,x67782)))+~P1(f315(f315(f223(a1),f2(a1)),x67782))+~P1(f315(f315(f223(a1),x67781),x67782))
% 168.50/168.39 [6779]P1(f315(f315(f223(a901),f315(a93,x67791)),f315(a93,x67792)))+~P1(f315(f315(f224(a1),f2(a1)),x67791))+~P1(f315(f315(f223(a1),x67791),x67792))
% 168.50/168.39 [6781]P1(f315(f315(f224(a901),f315(a93,x67811)),f315(a93,x67812)))+~P1(f315(f315(f223(a1),f2(a1)),x67811))+~P1(f315(f315(f224(a1),x67811),x67812))
% 168.50/168.39 [6782]P1(f315(f315(f224(a901),f315(a93,x67821)),f315(a93,x67822)))+~P1(f315(f315(f224(a1),f2(a1)),x67822))+~P1(f315(f315(f224(a1),x67821),x67822))
% 168.50/168.39 [6793]E(f38(a901,f315(a93,x67931),f315(a93,x67932)),f315(a93,f38(a1,x67931,x67932)))+~P1(f315(f315(f223(a1),f2(a1)),x67932))+~P1(f315(f315(f223(a1),f2(a1)),x67931))
% 168.50/168.39 [6817]~P82(x68171)+~P1(f315(f315(f223(x68171),f315(f72(x68171),x68172)),f2(x68171)))+P1(f315(f315(f223(x68171),f2(x68171)),x68172))
% 168.50/168.39 [6818]~P82(x68181)+~P1(f315(f315(f224(x68181),f315(f72(x68181),x68182)),f2(x68181)))+P1(f315(f315(f224(x68181),f2(x68181)),x68182))
% 168.50/168.39 [6833]~P1(f315(f315(f224(a1),a76),x68332))+~P1(f315(f315(f224(a1),x68331),x68332))+P1(f315(f315(f224(a901),f315(f92(a901),x68331)),f315(f92(a901),x68332)))
% 168.50/168.39 [6928]~P1(f315(f315(f223(a1),f2(a1)),x69281))+P1(f315(f315(f224(a901),f315(a93,x69281)),x69282))+~P1(f315(f315(f224(a1),x69281),f315(f89(a1),x69282)))
% 168.50/168.39 [6933]P1(f315(x69331,x69332))+~P1(f315(x69331,f315(a22,f791(x69331,x69332))))+~P1(f315(f315(f317(a901),x69332),f230(f909(a901,a899))))
% 168.50/168.39 [6944]E(x69441,f2(a1))+E(f38(a1,x69442,x69441),f2(a1))+E(f315(f315(f3(a1),f315(f72(a1),f315(f315(f29(a1),x69442),x69441))),f71(a1)),f315(f315(f29(a1),x69442),f315(f72(a1),x69441)))
% 168.50/168.39 [6958]~P1(f315(f315(f223(a1),f2(a1)),x69581))+~P1(f315(f315(f224(a901),f315(a93,x69581)),x69582))+P1(f315(f315(f224(a1),x69581),f315(f89(a1),x69582)))
% 168.50/168.39 [6994]~P1(f315(f315(f223(a901),f315(a93,x69941)),f315(a93,x69942)))+~P1(f315(f315(f223(a1),f2(a1)),x69942))+P1(f315(f315(f223(a1),x69941),x69942))
% 168.50/168.39 [6995]~P1(f315(f315(f223(a901),f315(a93,x69951)),f315(a93,x69952)))+~P1(f315(f315(f224(a1),f2(a1)),x69951))+P1(f315(f315(f223(a1),x69951),x69952))
% 168.50/168.39 [7025]P1(f315(f315(f223(a1),x70251),x70252))+~P1(f315(f315(f223(a901),f315(f92(a901),x70251)),f315(f92(a901),x70252)))+P1(f315(f315(f223(a1),x70251),a76))
% 168.50/168.39 [7052]P1(f315(f315(f223(a1),f2(a1)),f38(a1,x70521,x70522)))+~P1(f315(f315(f223(a1),f2(a1)),x70522))+~P1(f315(f315(f223(a1),f2(a1)),x70521))
% 168.50/168.39 [7152]P1(f315(f315(f224(a1),a76),x71521))+~P1(f315(f315(f224(a1),x71522),x71521))+~P1(f315(f315(f224(a901),f315(f92(a901),x71522)),f315(f92(a901),x71521)))
% 168.50/168.39 [7206]E(f315(f315(f240(a1,a1),f315(f315(f29(a1),x72061),x72062)),f38(a1,x72061,x72062)),f43(x72061,x72062))+~P1(f315(f315(f224(a1),x72061),f2(a1)))+~P1(f315(f315(f224(a1),f2(a1)),x72062))
% 168.50/168.39 [7226]E(f315(f315(f240(a1,a1),f315(f315(f29(a1),x72261),x72262)),f38(a1,x72261,x72262)),f40(x72261,x72262))+~P1(f315(f315(f223(a1),f2(a1)),x72262))+~P1(f315(f315(f223(a1),f2(a1)),x72261))
% 168.50/168.39 [7280]~P99(x72802)+E(x72801,f102(x72802))+E(f315(f131(x72802,x72802,f74(x72802),f315(f130(x72802),x72801)),f315(f160(x72802),x72801)),f315(f56(x72802,f74(x72802)),f315(f161(x72802),x72801)))
% 168.50/168.39 [7397]~E(x73971,f2(a901))+E(f315(f131(a901,a901,f73(a901),x73971),x73972),f2(a901))+P1(f315(f315(f317(a901),f657(x73972,x73971)),f315(f161(a901),x73972)))
% 168.50/168.39 [7450]~P1(f315(f315(f223(a1),x74501),f2(a1)))+P1(f315(f315(f223(a1),f315(f315(f29(a1),x74501),x74502)),f2(a1)))+~P1(f315(f315(f224(a1),f2(a1)),x74502))
% 168.50/168.39 [7451]~P1(f315(f315(f224(a1),x74512),f2(a1)))+P1(f315(f315(f223(a1),f315(f315(f29(a1),x74511),x74512)),f2(a1)))+~P1(f315(f315(f223(a1),f2(a1)),x74511))
% 168.50/168.39 [7452]~P1(f315(f315(f224(a1),x74522),f2(a1)))+P1(f315(f315(f224(a1),f315(f315(f29(a1),x74521),x74522)),f2(a1)))+~P1(f315(f315(f224(a1),f2(a1)),x74521))
% 168.50/168.39 [7454]~P1(f315(f315(f224(a1),x74541),f2(a1)))+P1(f315(f315(f224(a1),f315(f315(f29(a1),x74541),x74542)),f2(a1)))+~P1(f315(f315(f224(a1),f2(a1)),x74542))
% 168.50/168.39 [7461]P1(f315(f315(f317(f909(x74611,a899)),f862(x74612,x74611)),x74612))+~P1(f315(f54(f909(x74611,a899)),x74612))+P1(f315(f54(x74611),f30(f909(x74611,a899),x74612)))
% 168.50/168.39 [7551]P25(x75511,x75511,x75512,f230(f909(x75511,a899)))+~E(f315(f298(x75511,x75511,x75512),f230(f909(x75511,a899))),f230(f909(x75511,a899)))+~P1(f315(f54(x75511),f230(f909(x75511,a899))))
% 168.50/168.39 [7673]~P25(x76731,x76731,x76732,f230(f909(x76731,a899)))+E(f315(f298(x76731,x76731,x76732),f230(f909(x76731,a899))),f230(f909(x76731,a899)))+~P1(f315(f54(x76731),f230(f909(x76731,a899))))
% 168.50/168.39 [7813]E(f315(f315(f29(a1),x78131),x78132),f315(f92(a1),a86))+~P1(f315(f315(f223(a1),f315(f315(f73(a1),x78131),x78132)),f2(a1)))+~P1(f315(f315(f224(a1),f2(a1)),x78131))
% 168.50/168.39 [7870]~P1(f315(f315(f224(a1),x78702),f2(a1)))+~P1(f315(f315(f224(a1),f315(f315(f29(a1),x78701),x78702)),f2(a1)))+P1(f315(f315(f224(a1),f2(a1)),x78701))
% 168.50/168.39 [7875]E(f315(f315(f73(a1),x78751),x78752),f38(a1,x78751,x78752))+~P1(f315(f315(f223(a1),f315(f315(f73(a1),x78751),x78752)),f2(a1)))+~P1(f315(f315(f224(a1),f2(a1)),x78751))
% 168.50/168.39 [7878]P1(f315(f315(f224(a1),x78781),f2(a1)))+~P1(f315(f315(f224(a1),f315(f315(f29(a1),x78781),x78782)),f2(a1)))+~P1(f315(f315(f224(a1),f2(a1)),x78782))
% 168.50/168.39 [8576]~P110(x85761)+P13(x85761,x85762)+~P1(f315(f315(f223(x85761),f315(f315(f153(x85761),x85762),f692(x85762,x85761))),f315(f315(f153(x85761),x85762),f693(x85762,x85761))))
% 168.50/168.39 [8577]~P110(x85771)+P13(x85771,x85772)+~P1(f315(f315(f223(x85771),f315(f315(f153(x85771),x85772),f699(x85772,x85771))),f315(f315(f153(x85771),x85772),f703(x85772,x85771))))
% 168.50/168.39 [5769]E(x57691,f2(a1))+~E(f38(a1,x57692,x57691),f2(a1))+E(f315(f315(f29(a1),x57692),f315(f72(a1),x57691)),f315(f72(a1),f315(f315(f29(a1),x57692),x57691)))
% 168.50/168.39 [5787]~P42(x57872)+~P42(x57871)+P42(f315(f315(f99(f909(a1,a899)),x57871),x57872))
% 168.50/168.39 [5788]~P42(x57882)+~P42(x57881)+P42(f315(f315(f90(f909(a1,a899)),x57881),x57882))
% 168.50/168.39 [5806]~P65(x58061)+~P97(x58061)+E(f315(f72(x58061),f315(f315(f279(x58061),f71(x58061)),x58062)),f315(f315(f279(x58061),f315(f92(x58061),a86)),x58062))
% 168.50/168.39 [5933]E(x59331,f2(a1))+~E(f38(a1,x59332,x59331),f2(a1))+E(f315(f315(f29(a1),f315(f72(a1),x59332)),x59331),f315(f72(a1),f315(f315(f29(a1),x59332),x59331)))
% 168.50/168.39 [6074]~P110(x60741)+P13(x60741,x60742)+P1(f315(f315(f224(a901),f693(x60742,x60741)),f315(f178(f902(x60741)),x60742)))
% 168.50/168.39 [6075]~P110(x60751)+P13(x60751,x60752)+P1(f315(f315(f224(a901),f703(x60752,x60751)),f315(f178(f902(x60751)),x60752)))
% 168.50/168.39 [6092]P28(a898,x60921,x60922)+~P28(a898,x60921,f811(x60921))+~P1(f315(f315(f317(f900(a898)),x60922),a911))
% 168.50/168.39 [6239]~P97(x62391)+~E(f315(f92(x62391),x62392),f2(x62391))+P30(x62391,f315(f92(x62391),f315(f315(f73(a1),x62392),f315(f72(a1),a76))))
% 168.50/168.39 [6240]~P97(x62401)+~E(f315(f92(x62401),x62402),f2(x62401))+P30(x62401,f315(f92(x62401),f315(f315(f73(a1),a76),f315(f72(a1),x62402))))
% 168.50/168.39 [6242]E(f315(a44,f40(f315(f72(a1),x62421),f315(f72(a1),x62422))),f39(x62421,x62422))+P1(f315(f315(f223(a1),f2(a1)),x62421))+P1(f315(f315(f224(a1),f2(a1)),x62422))
% 168.50/168.39 [6282]P28(a898,x62821,x62822)+P1(f315(f315(f317(f900(a898)),f811(x62821)),a910))+~P1(f315(f315(f317(f900(a898)),x62822),a911))
% 168.50/168.39 [6371]~E(x63712,f2(a901))+~E(x63711,f2(a901))+P1(f315(f315(f223(a1),f315(f89(a1),x63711)),f315(f72(a1),f315(f89(a1),x63712))))
% 168.50/168.39 [6400]E(f315(f315(f73(a901),f315(f92(a901),x64001)),f315(f92(a901),x64002)),f315(f92(a901),f315(f315(f73(a1),x64001),x64002)))+P1(f315(f315(f224(a1),x64001),a76))+P1(f315(f315(f224(a1),x64002),a76))
% 168.50/168.39 [6537]~P78(x65371)+~P1(f315(f315(f223(x65371),f2(x65371)),x65372))+P1(f315(f315(f223(x65371),f315(f72(x65371),x65372)),x65372))
% 168.50/168.39 [6538]~P78(x65381)+~P1(f315(f315(f224(x65381),f2(x65381)),x65382))+P1(f315(f315(f224(x65381),f315(f72(x65381),x65382)),x65382))
% 168.50/168.39 [6719]E(f315(f315(f3(a901),f315(a93,x67191)),f315(a93,x67192)),f315(a93,f315(f315(f3(a1),x67191),x67192)))+~P1(f315(f315(f223(a1),f2(a1)),x67192))+~P1(f315(f315(f223(a1),x67192),x67191))
% 168.50/168.39 [6755]E(f315(a93,f38(a1,f315(f92(a1),x67551),f315(f92(a1),x67552))),f38(a901,f315(f92(a901),x67551),f315(f92(a901),x67552)))+P1(f315(a182,f315(f92(a1),x67551)))+P1(f315(a182,f315(f92(a1),x67552)))
% 168.50/168.39 [6772]~P78(x67721)+P1(f315(f315(f223(x67721),f2(x67721)),x67722))+~P1(f315(f315(f223(x67721),f315(f72(x67721),x67722)),x67722))
% 168.50/168.39 [6773]~P78(x67731)+P1(f315(f315(f224(x67731),f2(x67731)),x67732))+~P1(f315(f315(f224(x67731),f315(f72(x67731),x67732)),x67732))
% 168.50/168.39 [6785]~P78(x67851)+~P1(f315(f315(f223(x67851),f2(x67851)),x67852))+P1(f315(f315(f223(x67851),f2(x67851)),f315(f315(f73(x67851),x67852),x67852)))
% 168.50/168.39 [6787]~P78(x67871)+~P1(f315(f315(f224(x67871),f2(x67871)),x67872))+P1(f315(f315(f224(x67871),f2(x67871)),f315(f315(f73(x67871),x67872),x67872)))
% 168.50/168.39 [6799]E(f315(f315(f73(a901),f315(a93,x67991)),f315(a93,x67992)),f315(a93,f315(f315(f73(a1),x67991),x67992)))+~P1(f315(f315(f223(a1),f2(a1)),x67992))+~P1(f315(f315(f223(a1),f2(a1)),x67991))
% 168.50/168.39 [6810]E(x68101,f2(a901))+P1(f315(f315(f224(a901),f2(a901)),x68102))+~P1(f315(f315(f224(a901),f2(a901)),f315(f315(f232(a901),x68102),x68101)))
% 168.50/168.39 [6845]~P97(x68451)+E(f315(f92(x68451),x68452),f2(x68451))+~P30(x68451,f315(f92(x68451),f315(f315(f73(a1),a76),f315(f72(a1),x68452))))
% 168.50/168.39 [6846]~P97(x68461)+E(f315(f92(x68461),x68462),f2(x68461))+~P30(x68461,f315(f92(x68461),f315(f315(f73(a1),x68462),f315(f72(a1),a76))))
% 168.50/168.39 [6906]~P1(f315(f54(x69061),x69062))+~P1(f315(f54(x69061),f230(f909(x69061,a899))))+P1(f315(f54(x69061),f315(f72(f909(x69061,a899)),x69062)))
% 168.50/168.39 [6929]~P1(f315(f315(f224(a1),f2(a1)),x69292))+~P1(f315(f315(f223(a1),x69292),x69291))+P1(f315(f315(f224(a1),f2(a1)),f315(f315(f29(a1),x69291),x69292)))
% 168.50/168.39 [6930]~P1(f315(f315(f223(a1),x69301),f2(a1)))+~P1(f315(f315(f224(a1),x69302),f2(a1)))+P1(f315(f315(f223(a1),f2(a1)),f315(f315(f29(a1),x69301),x69302)))
% 168.50/168.39 [6968]~P1(f315(f315(f223(a1),f2(a1)),x69682))+~P1(f315(f315(f223(a1),f2(a1)),x69681))+P1(f315(f315(f223(a1),f2(a1)),f315(f315(f74(a1),x69681),x69682)))
% 168.50/168.39 [6969]~P1(f315(f315(f223(a1),f2(a1)),x69692))+~P1(f315(f315(f223(a1),f2(a1)),x69691))+P1(f315(f315(f223(a1),f2(a1)),f315(f315(f73(a1),x69691),x69692)))
% 168.50/168.39 [6970]~P1(f315(f315(f223(a1),f2(a1)),x69702))+~P1(f315(f315(f223(a1),f2(a1)),x69701))+P1(f315(f315(f223(a1),f2(a1)),f315(f315(f29(a1),x69701),x69702)))
% 168.50/168.39 [6971]~P1(f315(f315(f223(a1),f2(a1)),x69711))+~P1(f315(f315(f224(a1),f2(a1)),x69712))+P1(f315(f315(f223(a1),f2(a1)),f315(f315(f29(a1),x69711),x69712)))
% 168.50/168.39 [6972]~P1(f315(f315(f224(a901),f2(a901)),x69722))+~P1(f315(f315(f224(a901),f2(a901)),x69721))+P1(f315(f315(f224(a901),f2(a901)),f315(f315(f74(a901),x69721),x69722)))
% 168.50/168.39 [7039]E(x70391,f2(a1))+E(f38(a1,x70392,x70391),f2(a1))+E(f315(f315(f3(a1),f315(f72(a1),f315(f315(f29(a1),x70392),x70391))),f71(a1)),f315(f315(f29(a1),f315(f72(a1),x70392)),x70391))
% 168.50/168.39 [7097]P1(f315(f315(f224(a901),f2(a901)),x70971))+P1(f315(f315(f224(a901),f2(a901)),x70972))+~P1(f315(f315(f224(a901),f2(a901)),f315(f315(f73(a901),x70972),x70971)))
% 168.50/168.39 [7101]~P78(x71011)+P1(f315(f315(f223(x71011),f2(x71011)),x71012))+~P1(f315(f315(f223(x71011),f2(x71011)),f315(f315(f73(x71011),x71012),x71012)))
% 168.50/168.39 [7102]~P78(x71021)+P1(f315(f315(f224(x71021),f2(x71021)),x71022))+~P1(f315(f315(f224(x71021),f2(x71021)),f315(f315(f73(x71021),x71022),x71022)))
% 168.50/168.39 [7153]~P1(f315(f54(x71531),x71532))+P1(f315(f54(x71531),f230(f909(x71531,a899))))+~P1(f315(f54(x71531),f315(f72(f909(x71531,a899)),x71532)))
% 168.50/168.39 [7218]P1(f315(f315(f223(a1),x72181),f2(a1)))+~P1(f315(f315(f224(a1),x72182),f2(a1)))+~P1(f315(f315(f223(a1),f2(a1)),f315(f315(f29(a1),x72181),x72182)))
% 168.50/168.39 [7224]~P1(f315(f315(f224(a1),f2(a1)),x72241))+P1(f315(f315(f223(a1),x72241),x72242))+~P1(f315(f315(f224(a1),f2(a1)),f315(f315(f29(a1),x72242),x72241)))
% 168.50/168.39 [7225]~P1(f315(f315(f223(a1),f2(a1)),x72252))+P1(f315(f315(f223(a1),x72251),x72252))+~P1(f315(f315(f224(a1),f2(a1)),f315(f315(f29(a1),x72252),x72251)))
% 168.50/168.39 [7255]P1(f315(f315(f223(a1),f2(a1)),x72551))+~P1(f315(f315(f224(a1),f2(a1)),x72552))+~P1(f315(f315(f223(a1),f2(a1)),f315(f315(f29(a1),x72551),x72552)))
% 168.50/168.39 [7256]P1(f315(f315(f224(a1),f2(a1)),x72561))+~P1(f315(f315(f223(a1),f2(a1)),x72562))+~P1(f315(f315(f224(a1),f2(a1)),f315(f315(f29(a1),x72562),x72561)))
% 168.50/168.39 [7704]~P1(f315(f54(x77042),f230(f909(x77042,a899))))+~P1(f315(f54(x77041),f230(f909(x77041,a899))))+P1(f315(f54(f907(x77041,x77042)),f230(f909(f907(x77041,x77042),a899))))
% 168.50/168.39 [7705]~P1(f315(f54(x77052),f230(f909(x77052,a899))))+~P1(f315(f54(x77051),f230(f909(x77051,a899))))+P1(f315(f54(f908(x77051,x77052)),f230(f909(f908(x77051,x77052),a899))))
% 168.50/168.39 [7777]~P1(f315(f315(f224(a901),f315(a101,f2(a901))),x77771))+~P1(f315(f315(f224(a901),f315(a101,f2(a901))),x77772))+P1(f315(f315(f224(a901),x77771),f315(f315(f74(a901),x77772),x77771)))
% 168.50/168.39 [7778]~P1(f315(f315(f224(a901),f315(a101,f2(a901))),x77781))+~P1(f315(f315(f224(a901),f315(a101,f2(a901))),x77782))+P1(f315(f315(f224(a901),x77781),f315(f315(f74(a901),x77781),x77782)))
% 168.50/168.39 [7812]E(f315(f28(x78121),f230(f909(x78121,a899))),f315(a101,f2(a901)))+P1(f315(f54(x78122),f230(f909(x78122,a899))))+~P1(f315(f54(f909(x78122,x78121)),f230(f909(f909(x78122,x78121),a899))))
% 168.50/168.39 [7939]~P1(f315(f315(f223(a901),f315(a101,f2(a901))),x79391))+~P1(f315(f315(f223(a901),f315(a101,f2(a901))),x79392))+P1(f315(f315(f223(a901),f315(a101,f2(a901))),f315(f315(f74(a901),x79391),x79392)))
% 168.50/168.39 [7940]~P1(f315(f315(f224(a901),f315(a101,f2(a901))),x79402))+~P1(f315(f315(f224(a901),f315(a101,f2(a901))),x79401))+P1(f315(f315(f224(a901),f315(a101,f2(a901))),f315(f315(f74(a901),x79401),x79402)))
% 168.50/168.39 [8623]E(x86231,f102(x86232))+~P1(f315(f126(x86232),x86231))+E(f166(x86232,f315(f315(f10(a899,a899,x86232),a310),f315(f315(f9(x86232,x86232,a899),a312),f133(x86232,x86231))),x86231),f103(x86232,x86231))
% 168.50/168.39 [8718]~P42(x87182)+~P42(x87181)+E(f315(f298(a901,a1,f89(a1)),f315(f315(f99(f909(a901,a899)),f315(f298(a1,a901,a93),x87181)),f315(f298(a1,a901,a93),x87182))),f315(f315(f99(f909(a1,a899)),x87181),x87182))
% 168.50/168.39 [8719]~P42(x87192)+~P42(x87191)+E(f315(f298(a901,a1,f89(a1)),f315(f315(f90(f909(a901,a899)),f315(f298(a1,a901,a93),x87191)),f315(f298(a1,a901,a93),x87192))),f315(f315(f90(f909(a1,a899)),x87191),x87192))
% 168.50/168.39 [9386]~P97(x93861)+~E(f315(f92(x93861),x93862),f71(x93861))+P30(x93861,f315(f92(x93861),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f72(a1),x93862))))
% 168.50/168.39 [9638]~P97(x96381)+E(f315(f92(x96381),x96382),f71(x96381))+~P30(x96381,f315(f92(x96381),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f72(a1),x96382))))
% 168.50/168.39 [10394]E(x103941,f2(a1))+E(x103942,f2(a1))+E(f315(f246(a1,a1,a1,a1,f25(a1),f315(f74(a1),f75(a1,x103942))),f315(f315(f315(f85(f908(a1,a1)),f315(f315(a312,f75(a1,x103941)),f75(a1,x103942))),f46(x103941,x103942)),f315(f315(f245(a1,a1,f908(a1,a1)),f315(f315(f20(a1,f909(a1,f908(a1,a1)),f909(a1,f908(a1,a1))),f315(f315(f10(f909(a1,f909(f908(a1,a1),f908(a1,a1))),f909(f909(a1,f908(a1,a1)),f909(a1,f908(a1,a1))),a1),f20(a1,f908(a1,a1),f908(a1,a1))),f315(f315(f10(f908(a1,a1),f909(a1,f909(f908(a1,a1),f908(a1,a1))),a1),f315(f9(a1,f908(a1,a1),f909(f908(a1,a1),f908(a1,a1))),f315(f315(f10(a899,f909(f908(a1,a1),f909(f908(a1,a1),f908(a1,a1))),a1),f85(f908(a1,a1))),f315(f315(f9(a1,a1,a899),a312),f2(a1))))),f315(f315(f9(a1,a1,f908(a1,a1)),f315(f315(f10(a1,f909(a1,f908(a1,a1)),a1),f240(a1,a1)),f72(a1))),f2(a1))))),f315(f315(f9(a1,f909(a1,a1),f909(a1,f908(a1,a1))),f315(f315(f10(f909(a1,f908(a1,a1)),f909(f909(a1,a1),f909(a1,f908(a1,a1))),a1),f10(a1,f908(a1,a1),a1)),f315(f315(f10(a1,f909(a1,f908(a1,a1)),a1),f240(a1,a1)),f315(f315(f9(a1,a1,a1),f315(f315(f10(a1,f909(a1,a1),a1),f3(a1)),f72(a1))),f71(a1))))),f315(f3(a1),f315(f69(a1),x103942))))),f46(x103941,x103942)))),f39(x103941,x103942))
% 168.50/168.39 [10395]E(x103951,f2(a1))+E(x103952,f2(a1))+E(f315(f246(a1,a1,a1,a1,f25(a1),f315(f74(a1),f75(a1,x103952))),f315(f315(f315(f85(f908(a1,a1)),f315(f315(a314,f315(f315(a313,f315(f315(f224(a1),f2(a1)),x103952)),f315(f315(f223(a1),f2(a1)),x103951))),f315(f315(a313,f315(f315(f224(a1),x103952),f2(a1))),f315(f315(f224(a1),x103951),f2(a1))))),f46(x103951,x103952)),f315(f315(f245(a1,a1,f908(a1,a1)),f315(f315(f20(a1,f909(a1,f908(a1,a1)),f909(a1,f908(a1,a1))),f315(f315(f10(f909(a1,f909(f908(a1,a1),f908(a1,a1))),f909(f909(a1,f908(a1,a1)),f909(a1,f908(a1,a1))),a1),f20(a1,f908(a1,a1),f908(a1,a1))),f315(f315(f10(f908(a1,a1),f909(a1,f909(f908(a1,a1),f908(a1,a1))),a1),f315(f9(a1,f908(a1,a1),f909(f908(a1,a1),f908(a1,a1))),f315(f315(f10(a899,f909(f908(a1,a1),f909(f908(a1,a1),f908(a1,a1))),a1),f85(f908(a1,a1))),f315(f315(f9(a1,a1,a899),a312),f2(a1))))),f315(f315(f9(a1,a1,f908(a1,a1)),f315(f315(f10(a1,f909(a1,f908(a1,a1)),a1),f240(a1,a1)),f72(a1))),f2(a1))))),f315(f315(f9(a1,f909(a1,a1),f909(a1,f908(a1,a1))),f315(f315(f10(f909(a1,f908(a1,a1)),f909(f909(a1,a1),f909(a1,f908(a1,a1))),a1),f10(a1,f908(a1,a1),a1)),f315(f315(f10(a1,f909(a1,f908(a1,a1)),a1),f240(a1,a1)),f315(f315(f9(a1,a1,a1),f315(f315(f10(a1,f909(a1,a1),a1),f3(a1)),f72(a1))),f71(a1))))),f315(f3(a1),f315(f69(a1),x103952))))),f46(x103951,x103952)))),f39(x103951,x103952))
% 168.50/168.39 [5795]~P114(x57951)+~P97(x57951)+E(f315(f69(x57951),f315(f315(f232(x57951),f315(f92(x57951),a86)),x57952)),f71(x57951))
% 168.50/168.39 [6311]~P143(x63111)+~P1(f315(f315(f224(a1),x63112),f2(a1)))+E(f315(f72(x63111),f315(f89(x63111),f315(a93,f315(f72(a1),x63112)))),f315(f91(x63111),x63112))
% 168.50/168.39 [6521]P1(f315(f315(f223(a88),x65211),f71(a88)))+E(f315(f315(f73(a88),f71(a88)),f260(x65211,f315(f315(f29(a88),x65212),x65211))),f260(x65211,x65212))+P1(f315(f315(f224(a88),x65212),x65211))
% 168.50/168.39 [7142]~P95(x71421)+~P1(f315(f315(f317(x71421),x71422),f98(x71421)))+~E(f315(f315(f73(x71421),f315(f315(f73(x71421),f71(x71421)),x71422)),x71422),f2(x71421))
% 168.50/168.39 [7257]~P1(f315(f315(f223(a1),x72572),f2(a1)))+~P1(f315(f315(f224(a1),x72571),f2(a1)))+E(f315(f239(a1,a1),f315(a44,f40(f315(f72(a1),x72571),f315(f72(a1),x72572)))),f315(f315(f29(a1),x72571),x72572))
% 168.50/168.39 [7274]~P1(f315(f315(f223(a1),x72742),f2(a1)))+~P1(f315(f315(f224(a1),x72741),f2(a1)))+E(f315(f244(a1,a1),f315(a44,f40(f315(f72(a1),x72741),f315(f72(a1),x72742)))),f38(a1,x72741,x72742))
% 168.50/168.39 [7282]~P1(f315(f315(f224(a1),x72822),f2(a1)))+E(f315(f239(a1,a1),f315(a44,f43(f315(f72(a1),x72821),f315(f72(a1),x72822)))),f315(f315(f29(a1),x72821),x72822))+~P1(f315(f315(f224(a1),f2(a1)),x72821))
% 168.50/168.39 [7300]~P1(f315(f315(f224(a1),x73002),f2(a1)))+E(f315(f244(a1,a1),f315(a44,f43(f315(f72(a1),x73001),f315(f72(a1),x73002)))),f38(a1,x73001,x73002))+~P1(f315(f315(f224(a1),f2(a1)),x73001))
% 168.50/168.39 [7353]E(f315(f315(f29(a1),f315(f315(f232(a1),x73531),x73532)),x73531),f315(f315(f232(a1),x73531),f315(f315(f3(a901),x73532),f315(a101,f2(a901)))))+~P1(f315(f315(f224(a901),f2(a901)),x73532))+~P1(f315(f315(f224(a1),f2(a1)),x73531))
% 168.50/168.39 [7457]~P1(f315(f315(f224(a901),f2(a901)),x74571))+~P1(f315(f315(f224(a901),f2(a901)),x74572))+P1(f315(f315(f224(a901),f315(f315(f3(a901),x74571),x74572)),x74571))
% 168.50/168.39 [7458]~P1(f315(f315(f224(a901),f2(a901)),x74581))+~P1(f315(f315(f224(a901),f71(a901)),x74582))+P1(f315(f315(f224(a901),f315(f315(f29(a901),x74581),x74582)),x74581))
% 168.50/168.39 [7459]~P1(f315(f315(f224(a1),f2(a1)),x74591))+~P1(f315(f315(f224(a1),f71(a1)),x74592))+P1(f315(f315(f224(a1),f315(f315(f29(a1),x74591),x74592)),x74591))
% 168.50/168.39 [7597]E(x75971,f2(a901))+~E(x75972,f2(a1))+~P1(f315(f315(f224(a1),f2(a1)),f315(f315(f232(a1),f315(f69(a1),x75972)),x75971)))
% 168.50/168.39 [8018]~E(x80182,f102(f902(x80181)))+E(f315(f178(f902(f902(x80181))),f168(x80181,x80182)),f2(a901))+~P13(a901,f315(f157(a901),f315(f315(f143(f902(x80181),a901),f178(f902(x80181))),x80182)))
% 168.50/168.39 [8098]P28(a898,x80981,x80982)+~P28(a898,x80981,f839(x80981))+~P1(f315(f315(f317(f900(a898)),x80982),f315(f315(f297(f900(a898)),a912),f177(f909(f900(a898),a899)))))
% 168.50/168.39 [8170]P28(a898,x81701,x81702)+P1(f315(f315(f317(f900(a898)),f839(x81701)),a910))+~P1(f315(f315(f317(f900(a898)),x81702),f315(f315(f297(f900(a898)),a912),f177(f909(f900(a898),a899)))))
% 168.50/168.39 [8274]P1(f315(x82741,x82742))+~P1(f315(x82741,f315(a95,f501(x82741,x82742))))+~P1(f315(f315(f317(f909(f908(a901,a901),a899)),x82742),a87))
% 168.50/168.39 [8290]E(x82901,f102(f902(x82902)))+E(f315(f178(f902(x82902)),f315(f315(f153(f902(x82902)),x82901),f2(a901))),f315(f178(f902(f902(x82902))),f168(x82902,x82901)))+~P13(a901,f315(f157(a901),f315(f315(f143(f902(x82902),a901),f178(f902(x82902))),x82901)))
% 168.50/168.39 [8430]~P40(x84301,x84302)+~P41(x84301,x84302)+P40(x84301,f315(f315(f3(f909(f908(x84301,x84301),a899)),x84302),f295(x84301,f177(f909(f908(x84301,x84301),a899)))))
% 168.50/168.39 [9003]~P1(f315(f54(x90031),f315(f250(x90031),x90032)))+~P1(f315(f54(x90031),f230(f909(x90031,a899))))+P1(f315(f54(x90031),f315(f250(x90031),f315(f315(f10(a899,a899,x90031),a310),x90032))))
% 168.50/168.39 [9068]E(f315(f315(f240(a901,a901),f315(a101,f315(f315(f29(a901),f315(f315(f3(a901),x90681),x90682)),x90682))),f38(a901,f315(f315(f3(a901),x90681),x90682),x90682)),f78(f908(a901,a901),f41(x90681,x90682)))+~P1(f315(f315(f224(a901),f2(a901)),x90682))+~P1(f315(f315(f223(a901),x90682),x90681))
% 168.50/168.39 [9351]~P1(f315(f54(x93511),f315(f250(x93511),x93512)))+P1(f315(f54(x93511),f230(f909(x93511,a899))))+~P1(f315(f54(x93511),f315(f250(x93511),f315(f315(f10(a899,a899,x93511),a310),x93512))))
% 168.50/168.39 [10076]P27(x100761,x100762)+~P39(x100761,f315(f239(f909(f908(x100761,x100761),a899),f909(f908(x100761,x100761),a899)),x100762))+~P1(f315(f315(f223(f909(f908(x100761,x100761),a899)),f315(f315(f277(x100761,x100761,x100761),f315(f239(f909(f908(x100761,x100761),a899),f909(f908(x100761,x100761),a899)),x100762)),f315(f244(f909(f908(x100761,x100761),a899),f909(f908(x100761,x100761),a899)),x100762))),f315(f239(f909(f908(x100761,x100761),a899),f909(f908(x100761,x100761),a899)),x100762)))
% 168.50/168.39 [10172]~E(f288(a901,f275(a901),f315(f315(f20(a901,f909(a901,a899),f909(a901,a899)),f315(f315(f10(f909(a901,f909(a899,a899)),f909(f909(a901,a899),f909(a901,a899)),a901),f20(a901,a899,a899)),f315(f315(f10(f909(a901,a899),f909(a901,f909(a899,a899)),a901),f315(f10(a899,f909(a899,a899),a901),a313)),f275(a901)))),f315(f315(f10(f909(a901,a899),f909(a901,a899),a901),f315(f10(a899,a899,a901),a310)),f315(f9(a901,a901,a899),f275(a901)))),x101722,x101721),f177(f909(a901,a899)))+~P1(f315(f315(f275(a901),x101722),x101721))+P1(f315(f315(f275(a901),x101721),x101722))
% 168.50/168.39 [10173]~E(f285(a901,f275(a901),f315(f315(f20(a901,f909(a901,a899),f909(a901,a899)),f315(f315(f10(f909(a901,f909(a899,a899)),f909(f909(a901,a899),f909(a901,a899)),a901),f20(a901,a899,a899)),f315(f315(f10(f909(a901,a899),f909(a901,f909(a899,a899)),a901),f315(f10(a899,f909(a899,a899),a901),a313)),f275(a901)))),f315(f315(f10(f909(a901,a899),f909(a901,a899),a901),f315(f10(a899,a899,a901),a310)),f315(f9(a901,a901,a899),f275(a901)))),x101732,x101731),f177(f909(a901,a899)))+~P1(f315(f315(f275(a901),x101732),x101731))+P1(f315(f315(f275(a901),x101731),x101732))
% 168.50/168.39 [7383]~P1(f315(f315(f224(a901),f2(a901)),x73832))+P1(f315(f315(f224(a901),x73831),x73832))+E(f315(a101,f315(f315(f29(a901),f315(f315(f3(a901),x73831),x73832)),x73832)),f315(f315(f29(a901),x73831),x73832))
% 168.50/168.39 [7524]~P1(f315(f315(f224(a901),f2(a901)),x75242))+~P1(f315(f315(f223(a901),x75242),x75241))+E(f315(a101,f315(f315(f29(a901),f315(f315(f3(a901),x75241),x75242)),x75242)),f315(f315(f29(a901),x75241),x75242))
% 168.50/168.39 [8494]~P97(x84941)+~P95(x84941)+~P30(x84941,f315(f92(x84941),f315(f315(f3(a1),f315(f315(f73(a1),x84942),x84942)),a86)))
% 168.50/168.39 [9257]E(x92571,f2(a901))+E(f315(f315(f245(a901,a901,f908(a901,a901)),f315(f315(f10(a901,f909(a901,f908(a901,a901)),a901),f240(a901,a901)),a101)),f78(f908(a901,a901),f41(f315(f315(f3(a901),x92572),x92571),x92571))),f78(f908(a901,a901),f41(x92572,x92571)))+P1(f315(f315(f224(a901),x92572),x92571))
% 168.50/168.39 [9440]~P40(x94401,x94402)+~P53(x94401,x94402)+P1(f315(f315(f223(f909(f908(x94401,x94401),a899)),f315(f315(f277(x94401,x94401,x94401),f315(f274(x94401,x94401),x94402)),x94402)),x94402))
% 168.50/168.39 [9702]P1(f315(x97022,f625(x97022,x97021)))+P1(f315(x97021,f625(x97022,x97021)))+E(f315(f250(a1),f315(f315(f20(a1,a899,a899),f315(f315(f10(a899,f909(a899,a899),a1),a313),f315(f223(a1),f2(a1)))),x97021)),f315(f250(a1),f315(f315(f20(a1,a899,a899),f315(f315(f10(a899,f909(a899,a899),a1),a313),f315(f223(a1),f2(a1)))),x97022)))
% 168.50/168.39 [9706]~P1(f315(x97062,f625(x97062,x97061)))+~P1(f315(x97061,f625(x97062,x97061)))+E(f315(f250(a1),f315(f315(f20(a1,a899,a899),f315(f315(f10(a899,f909(a899,a899),a1),a313),f315(f223(a1),f2(a1)))),x97061)),f315(f250(a1),f315(f315(f20(a1,a899,a899),f315(f315(f10(a899,f909(a899,a899),a1),a313),f315(f223(a1),f2(a1)))),x97062)))
% 168.50/168.39 [10255]~P1(f315(f315(f275(a901),x102552),x102551))+P1(f315(f315(f275(a901),x102551),x102552))+P1(f315(f315(f317(a901),x102551),f283(a901,f315(f315(f20(a901,f909(a901,a899),f909(a901,a899)),f315(f315(f10(f909(a901,f909(a899,a899)),f909(f909(a901,a899),f909(a901,a899)),a901),f20(a901,a899,a899)),f315(f315(f10(f909(a901,a899),f909(a901,f909(a899,a899)),a901),f315(f10(a899,f909(a899,a899),a901),a313)),f275(a901)))),f315(f315(f10(f909(a901,a899),f909(a901,a899),a901),f315(f10(a899,a899,a901),a310)),f315(f9(a901,a901,a899),f275(a901)))),x102552)))
% 168.50/168.39 [10256]~P1(f315(f315(f275(a901),x102562),x102561))+P1(f315(f315(f275(a901),x102561),x102562))+P1(f315(f315(f317(a901),x102562),f286(a901,f315(f315(f20(a901,f909(a901,a899),f909(a901,a899)),f315(f315(f10(f909(a901,f909(a899,a899)),f909(f909(a901,a899),f909(a901,a899)),a901),f20(a901,a899,a899)),f315(f315(f10(f909(a901,a899),f909(a901,f909(a899,a899)),a901),f315(f10(a899,f909(a899,a899),a901),a313)),f275(a901)))),f315(f315(f10(f909(a901,a899),f909(a901,a899),a901),f315(f10(a899,a899,a901),a310)),f315(f9(a901,a901,a899),f275(a901)))),x102561)))
% 168.50/168.39 [7735]~P66(x77351)+~P97(x77351)+E(f315(f315(f279(x77351),x77352),f315(f92(x77351),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))),x77352)
% 168.50/168.39 [9385]~P97(x93851)+~E(f315(f92(x93851),x93852),f71(x93851))+P30(x93851,f315(f92(x93851),f315(f315(f73(a1),x93852),f315(f72(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))))
% 168.50/168.39 [9572]~P144(x95721)+~E(x95722,f71(x95721))+E(f315(f315(f232(x95721),x95722),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),f71(x95721))
% 168.50/168.39 [9573]~P144(x95731)+~E(x95732,f2(x95731))+E(f315(f315(f232(x95731),x95732),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),f2(x95731))
% 168.50/168.39 [9588]~P144(x95881)+~E(x95882,f315(f72(x95881),f71(x95881)))+E(f315(f315(f232(x95881),x95882),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),f71(x95881))
% 168.50/168.39 [9639]~P97(x96391)+E(f315(f92(x96391),x96392),f71(x96391))+~P30(x96391,f315(f92(x96391),f315(f315(f73(a1),x96392),f315(f72(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))))
% 168.50/168.39 [10020]~P114(x100202)+E(x100201,f2(x100202))+P1(f315(f315(f224(x100202),f2(x100202)),f315(f315(f232(x100202),x100201),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))))))
% 168.50/168.39 [10075]~P114(x100752)+~E(x100751,f2(x100752))+~P1(f315(f315(f224(x100752),f2(x100752)),f315(f315(f232(x100752),x100751),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))))))
% 168.50/168.39 [10111]P1(f315(f315(f223(a1),x101111),f2(a1)))+P1(f315(f315(f224(a1),x101112),x101111))+E(f315(f36(x101111),f40(x101112,f315(f315(f74(a1),f315(f92(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),x101111))),f40(x101112,x101111))
% 168.50/168.39 [10112]~P1(f315(f315(f224(a1),f2(a1)),x101121))+P1(f315(f315(f224(a1),x101122),x101121))+E(f315(f36(x101121),f40(x101122,f315(f315(f74(a1),f315(f92(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),x101121))),f40(x101122,x101121))
% 168.50/168.39 [10113]P1(f315(f315(f223(a1),x101131),f2(a1)))+P1(f315(f315(f223(a1),f2(a1)),f315(f315(f73(a1),x101132),x101131)))+E(f315(f36(x101131),f43(x101132,f315(f315(f74(a1),f315(f92(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),x101131))),f43(x101132,x101131))
% 168.50/168.39 [10114]~P1(f315(f315(f224(a1),f2(a1)),x101141))+P1(f315(f315(f223(a1),f2(a1)),f315(f315(f73(a1),x101142),x101141)))+E(f315(f36(x101141),f43(x101142,f315(f315(f74(a1),f315(f92(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),x101141))),f43(x101142,x101141))
% 168.50/168.39 [10115]~P147(x101151)+~P1(f315(f315(f223(a1),f2(a1)),x101152))+E(f315(f89(x101151),f315(a93,f315(f315(f74(a1),f315(f92(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),x101152))),f315(f315(f73(x101151),f315(f89(x101151),f315(a93,x101152))),f315(f89(x101151),f315(a93,x101152))))
% 168.50/168.39 [5125]~P149(x51251,x51252,x51253)+~E(x51253,f2(a1))+P1(f315(x51251,x51252))
% 168.50/168.39 [5249]~P110(x52491)+~P13(x52491,x52493)+P13(x52491,f159(x52491,x52492,x52493))
% 168.50/168.39 [5250]~P110(x52501)+~P13(x52501,x52503)+P13(x52501,f166(x52501,x52502,x52503))
% 168.50/168.39 [4813]~P76(x48132)+~E(x48133,f315(f72(x48132),x48131))+E(x48131,f315(f72(x48132),x48133))
% 168.50/168.39 [4815]~P76(x48151)+~E(f315(f72(x48151),x48153),x48152)+E(f315(f72(x48151),x48152),x48153)
% 168.50/168.39 [4894]~P105(x48943)+E(x48941,x48942)+~E(f315(f89(x48943),x48941),f315(f89(x48943),x48942))
% 168.50/168.39 [4895]~P76(x48953)+E(x48951,x48952)+~E(f315(f72(x48953),x48951),f315(f72(x48953),x48952))
% 168.50/168.39 [4896]~P98(x48963)+E(x48961,x48962)+~E(f315(f72(x48963),x48961),f315(f72(x48963),x48962))
% 168.50/168.39 [4897]~P95(x48973)+E(x48971,x48972)+~E(f315(f91(x48973),x48971),f315(f91(x48973),x48972))
% 168.50/168.39 [4898]~P110(x48983)+E(x48981,x48982)+~E(f315(f270(x48983),x48981),f315(f270(x48983),x48982))
% 168.50/168.39 [4899]~P110(x48993)+E(x48991,x48992)+~E(f315(f289(x48993),x48991),f315(f289(x48993),x48992))
% 168.50/168.39 [4900]~P110(x49003)+E(x49001,x49002)+~E(f315(f271(x49003),x49001),f315(f271(x49003),x49002))
% 168.50/168.39 [4901]~P110(x49013)+E(x49011,x49012)+~E(f315(f292(x49013),x49011),f315(f292(x49013),x49012))
% 168.50/168.39 [5003]~P64(x50031)+~P1(f315(x50032,x50033))+P1(f315(f49(x50031),x50032))
% 168.50/168.39 [5043]~P64(x50433)+P1(f315(x50431,x50432))+~P1(f315(f50(x50433),x50431))
% 168.50/168.39 [5145]~P150(x51451,x51453,x51452)+~E(x51452,f2(a1))+P1(f315(x51451,f2(a1)))
% 168.50/168.39 [5185]~E(x51851,f2(a901))+E(f842(x51851,x51852,x51853),f177(f909(x51853,a899)))+~E(f315(f28(x51853),x51852),f315(a101,x51851))
% 168.50/168.39 [5334]~E(x53342,f2(a901))+E(f315(f239(a901,a901),x53341),f2(a901))+~P1(f315(f41(x53343,x53342),x53341))
% 168.50/168.39 [5374]P1(f315(x53741,x53742))+~E(x53743,f315(f89(a1),x53742))+~P1(f315(x53741,f315(a93,x53743)))
% 168.50/168.39 [5859]~E(x58593,f2(a901))+~P1(f315(x58591,x58592))+P1(f315(x58591,f38(a901,x58592,x58593)))
% 168.50/168.39 [6104]~P106(x61042)+~P106(x61041)+E(f120(x61041,x61042,f121(x61041,x61043),f121(x61042,x61043)),f121(f908(x61041,x61042),x61043))
% 168.50/168.39 [6293]~E(x62933,f2(a901))+P1(f315(x62931,x62932))+~P1(f315(x62931,f38(a901,x62932,x62933)))
% 168.50/168.39 [6993]E(x69931,f2(a901))+~P1(f315(x69932,f354(x69931,x69933,x69932)))+P1(f315(x69932,f38(a901,x69933,x69931)))
% 168.50/168.39 [7107]~P5(x71071)+~P1(f315(f315(f223(x71071),x71072),f363(x71073,x71072,x71071)))+P1(f315(f315(f223(x71071),x71072),f31(x71071,x71073)))
% 168.50/168.39 [7109]~P1(f315(x71091,x71092))+~P1(f315(x71091,f354(x71093,x71092,x71091)))+P1(f315(x71091,f38(a901,x71092,x71093)))
% 168.50/168.39 [7212]E(x72121,f102(x72122))+E(f315(f315(f140(x72122),f671(x72123,x72121,x72122)),f674(x72123,x72121,x72122)),x72121)+~P1(f315(f315(f317(f902(x72122)),x72121),f150(x72122,x72123)))
% 168.50/168.39 [7243]~P143(x72431)+~P1(f315(f315(f317(x72431),x72432),f98(x72431)))+P1(f315(f315(f317(x72431),f315(f315(f232(x72431),x72432),x72433)),f98(x72431)))
% 168.50/168.39 [7569]P39(x75691,x75692)+~P1(f315(f315(f317(x75691),x75693),f581(x75692,x75691)))+P1(f315(f315(f317(x75691),f594(x75692,x75691,x75693)),f581(x75692,x75691)))
% 168.50/168.39 [7840]E(x78401,f102(x78402))+~P1(f315(f315(f317(f902(x78402)),x78401),f150(x78402,x78403)))+P1(f315(f315(f317(f902(x78402)),f674(x78403,x78401,x78402)),f150(x78402,x78403)))
% 168.50/168.39 [7892]E(x78921,f2(a901))+E(f315(f315(f73(a901),f315(f315(f74(a901),x78921),f355(x78921,x78922,x78923))),f354(x78921,x78922,x78923)),x78922)+P1(f315(x78923,f38(a901,x78922,x78921)))
% 168.50/168.39 [7934]~P1(f315(x79343,x79342))+E(f315(f315(f73(a901),f315(f315(f74(a901),x79341),f355(x79341,x79342,x79343))),f354(x79341,x79342,x79343)),x79342)+P1(f315(x79343,f38(a901,x79342,x79341)))
% 168.50/168.39 [8074]P1(f315(f315(f224(a1),x80741),f338(x80742,x80743,x80741)))+P1(f315(f315(x80743,f315(f315(f29(a1),x80742),x80741)),f38(a1,x80742,x80741)))+~P1(f315(f315(f224(a1),x80741),f2(a1)))
% 168.50/168.39 [8345]P1(f315(f315(x83452,f315(f315(f29(a1),x83451),x83453)),f38(a1,x83451,x83453)))+~P1(f315(f315(f224(a1),x83453),f2(a1)))+P1(f315(f315(f223(a1),f338(x83451,x83452,x83453)),f2(a1)))
% 168.50/168.39 [8528]E(f315(f315(f73(a1),f315(f315(f74(a1),x85281),f341(x85282,x85283,x85281))),f338(x85282,x85283,x85281)),x85282)+P1(f315(f315(x85283,f315(f315(f29(a1),x85282),x85281)),f38(a1,x85282,x85281)))+~P1(f315(f315(f224(a1),x85281),f2(a1)))
% 168.50/168.39 [8766]~P1(f315(f315(x87661,f341(x87662,x87661,x87663)),f338(x87662,x87661,x87663)))+P1(f315(f315(x87661,f315(f315(f29(a1),x87662),x87663)),f38(a1,x87662,x87663)))+~P1(f315(f315(f224(a1),x87663),f2(a1)))
% 168.50/168.39 [9016]~P110(x90161)+~P13(x90161,x90163)+P13(x90161,f138(x90161,x90161,f7(x90161),x90162,x90163))
% 168.50/168.39 [9517]~P130(x95172)+E(x95171,f2(x95172))+~P1(f315(f315(f223(x95172),f315(f315(f73(x95172),f315(f315(f74(x95172),x95173),x95173)),f315(f315(f74(x95172),x95171),x95171))),f2(x95172)))
% 168.50/168.39 [9518]~P130(x95182)+E(x95181,f2(x95182))+~P1(f315(f315(f223(x95182),f315(f315(f73(x95182),f315(f315(f74(x95182),x95181),x95181)),f315(f315(f74(x95182),x95183),x95183))),f2(x95182)))
% 168.50/168.39 [10329]~P114(x103291)+~P1(f315(f315(f224(x103291),x103292),f2(x103291)))+P1(f315(f315(f224(x103291),f315(f315(f232(x103291),x103292),f315(a101,f315(f315(f74(a901),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),x103293)))),f2(x103291)))
% 168.50/168.39 [10338]~P114(x103382)+E(x103381,f2(x103382))+~P1(f315(f315(f223(x103382),f315(f315(f73(x103382),f315(f315(f232(x103382),x103383),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))))),f315(f315(f232(x103382),x103381),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))))),f2(x103382)))
% 168.50/168.39 [10339]~P114(x103392)+E(x103391,f2(x103392))+~P1(f315(f315(f223(x103392),f315(f315(f73(x103392),f315(f315(f232(x103392),x103391),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))))),f315(f315(f232(x103392),x103393),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))))),f2(x103392)))
% 168.50/168.39 [4849]~E(x48492,x48493)+~P69(x48491)+E(f315(f315(f3(x48491),x48492),x48493),f2(x48491))
% 168.50/168.39 [4850]~E(x48502,x48503)+~P76(x48501)+E(f315(f315(f3(x48501),x48502),x48503),f2(x48501))
% 168.50/168.39 [4863]~P145(x48631)+~E(x48633,f2(x48631))+E(f315(f315(f73(x48631),x48632),x48633),x48632)
% 168.50/168.39 [4880]~P142(x48801)+~E(x48803,f2(x48801))+E(f315(f315(f74(x48801),x48802),x48803),f2(x48801))
% 168.50/168.39 [4881]~P142(x48811)+~E(x48812,f2(x48811))+E(f315(f315(f74(x48811),x48812),x48813),f2(x48811))
% 168.50/168.39 [4903]~E(x49033,f102(x49031))+~E(x49032,f102(x49031))+E(f315(f315(f123(x49031),x49032),x49033),f102(x49031))
% 168.50/168.39 [4993]~P145(x49932)+E(x49931,f2(x49932))+~E(f315(f315(f73(x49932),x49933),x49931),x49933)
% 168.50/168.39 [4994]~P76(x49941)+~E(x49942,f315(f72(x49941),x49943))+E(f315(f315(f73(x49941),x49942),x49943),f2(x49941))
% 168.50/168.39 [5001]E(x50011,f102(x50012))+E(x50013,f2(a901))+~E(f315(f315(f164(x50012),x50013),x50011),f102(x50012))
% 168.50/168.39 [5011]~P69(x50113)+E(x50111,x50112)+~E(f315(f315(f3(x50113),x50111),x50112),f2(x50113))
% 168.50/168.39 [5012]~P76(x50123)+E(x50121,x50122)+~E(f315(f315(f3(x50123),x50121),x50122),f2(x50123))
% 168.50/168.39 [5025]~P144(x50252)+E(x50251,f2(x50252))+~E(f315(f315(f232(x50252),x50251),x50253),f2(x50252))
% 168.50/168.39 [5026]~P81(x50262)+E(x50261,f177(x50262))+~E(f315(f315(f99(x50262),x50263),x50261),f177(x50262))
% 168.50/168.39 [5027]~P81(x50272)+E(x50271,f177(x50272))+~E(f315(f315(f99(x50272),x50271),x50273),f177(x50272))
% 168.50/168.39 [5028]~P102(x50282)+E(x50281,f230(x50282))+~E(f315(f315(f90(x50282),x50283),x50281),f230(x50282))
% 168.50/168.39 [5029]~P102(x50292)+E(x50291,f230(x50292))+~E(f315(f315(f90(x50292),x50291),x50293),f230(x50292))
% 168.50/168.39 [5099]~P76(x50992)+E(x50991,f315(f72(x50992),x50993))+~E(f315(f315(f73(x50992),x50991),x50993),f2(x50992))
% 168.50/168.39 [5100]~P76(x51001)+E(f315(f72(x51001),x51002),x51003)+~E(f315(f315(f73(x51001),x51002),x51003),f2(x51001))
% 168.50/168.39 [5102]~E(x51022,x51023)+~P108(x51021)+P1(f315(f315(f223(x51021),x51022),x51023))
% 168.50/168.39 [5104]~E(x51042,x51043)+~P111(x51041)+P1(f315(f315(f223(x51041),x51042),x51043))
% 168.50/168.39 [5202]~P123(x52021)+~E(x52022,f315(f72(x52021),x52023))+E(f315(f315(f74(x52021),x52022),x52022),f315(f315(f74(x52021),x52023),x52023))
% 168.50/168.39 [5210]~P110(x52101)+~P13(x52101,x52103)+P13(x52101,f315(f315(f164(x52101),x52102),x52103))
% 168.50/168.39 [5211]~P110(x52111)+~P13(x52111,x52113)+P13(x52111,f315(f315(f127(x52111),x52112),x52113))
% 168.50/168.39 [5247]E(x52471,x52472)+E(x52473,f2(a901))+~E(f315(f315(f74(a901),x52473),x52471),f315(f315(f74(a901),x52473),x52472))
% 168.50/168.39 [5248]E(x52481,x52482)+E(x52483,f2(a901))+~E(f315(f315(f74(a901),x52481),x52483),f315(f315(f74(a901),x52482),x52483))
% 168.50/168.39 [5327]~E(x53272,x53273)+~P111(x53271)+E(f291(x53271,x53272,x53273),f315(f315(f297(x53271),x53272),f177(f909(x53271,a899))))
% 168.50/168.39 [5363]~P114(x53631)+~E(f315(f69(x53631),x53632),f315(f69(x53631),x53633))+P1(f315(f315(f275(x53631),x53632),x53633))
% 168.50/168.39 [5371]~E(x53711,x53712)+~P110(x53713)+~P1(f315(f315(f224(x53713),x53711),x53712))
% 168.50/168.39 [5372]~E(x53721,x53722)+~P111(x53723)+~P1(f315(f315(f224(x53723),x53721),x53722))
% 168.50/168.39 [5385]~P111(x53851)+E(f315(f290(x53851,x53852),x53853),f177(f909(x53851,a899)))+P1(f315(f315(f224(x53851),x53852),x53853))
% 168.50/168.39 [5433]~P111(x54331)+E(f291(x54331,x54332,x54333),f177(f909(x54331,a899)))+P1(f315(f315(f223(x54331),x54332),x54333))
% 168.50/168.39 [5434]~P111(x54341)+E(f293(x54341,x54342,x54343),f177(f909(x54341,a899)))+P1(f315(f315(f224(x54341),x54342),x54343))
% 168.50/168.39 [5435]~P111(x54351)+E(f177(f909(x54351,a899)),f291(x54351,x54352,x54353))+P1(f315(f315(f223(x54351),x54352),x54353))
% 168.50/168.39 [5436]~P111(x54361)+E(f177(f909(x54361,a899)),f293(x54361,x54362,x54363))+P1(f315(f315(f224(x54361),x54362),x54363))
% 168.50/168.39 [5444]~P103(x54441)+~E(f315(f315(f99(x54441),x54442),x54443),x54443)+P1(f315(f315(f223(x54441),x54442),x54443))
% 168.50/168.39 [5445]~P104(x54451)+~E(f315(f315(f90(x54451),x54452),x54453),x54452)+P1(f315(f315(f223(x54451),x54452),x54453))
% 168.50/168.39 [5446]~P110(x54461)+~E(f315(f315(f221(x54461),x54462),x54463),x54462)+P1(f315(f315(f223(x54461),x54462),x54463))
% 168.50/168.39 [5447]~P110(x54471)+~E(f315(f315(f222(x54471),x54472),x54473),x54473)+P1(f315(f315(f223(x54471),x54472),x54473))
% 168.50/168.39 [5466]~P110(x54661)+P13(x54661,x54662)+~P13(x54661,f315(f315(f140(x54661),x54663),x54662))
% 168.50/168.39 [5467]~P110(x54671)+P13(x54671,x54672)+~P13(x54671,f315(f315(f123(x54671),x54673),x54672))
% 168.50/168.39 [5468]~P110(x54681)+P13(x54681,x54682)+~P13(x54681,f315(f315(f123(x54681),x54682),x54683))
% 168.50/168.39 [5473]~P62(x54731)+~E(f38(x54731,x54733,x54732),f2(x54731))+P1(f315(f315(f275(x54731),x54732),x54733))
% 168.50/168.39 [5535]~P110(x55351)+P1(f315(f315(f223(x55351),x55353),x55352))+P1(f315(f315(f223(x55351),x55352),x55353))
% 168.50/168.39 [5540]~P110(x55401)+P1(f315(f315(f224(x55401),x55403),x55402))+P1(f315(f315(f223(x55401),x55402),x55403))
% 168.50/168.39 [5578]~P103(x55781)+E(f315(f315(f99(x55781),x55782),x55783),x55782)+~P1(f315(f315(f223(x55781),x55783),x55782))
% 168.50/168.39 [5580]~P103(x55801)+E(f315(f315(f99(x55801),x55802),x55803),x55803)+~P1(f315(f315(f223(x55801),x55802),x55803))
% 168.50/168.39 [5581]~P104(x55811)+E(f315(f315(f90(x55811),x55812),x55813),x55813)+~P1(f315(f315(f223(x55811),x55813),x55812))
% 168.50/168.39 [5583]~P104(x55831)+E(f315(f315(f90(x55831),x55832),x55833),x55832)+~P1(f315(f315(f223(x55831),x55832),x55833))
% 168.50/168.39 [5584]~P110(x55841)+E(f315(f315(f221(x55841),x55842),x55843),x55843)+~P1(f315(f315(f223(x55841),x55843),x55842))
% 168.50/168.39 [5586]~P110(x55861)+E(f315(f315(f221(x55861),x55862),x55863),x55862)+~P1(f315(f315(f223(x55861),x55862),x55863))
% 168.50/168.39 [5587]~P110(x55871)+E(f315(f315(f222(x55871),x55872),x55873),x55872)+~P1(f315(f315(f223(x55871),x55873),x55872))
% 168.50/168.39 [5589]~P110(x55891)+E(f315(f315(f222(x55891),x55892),x55893),x55893)+~P1(f315(f315(f223(x55891),x55892),x55893))
% 168.50/168.39 [5596]~P125(x55962)+E(x55961,f2(x55962))+E(f315(f315(f279(x55962),f315(f72(x55962),x55963)),f315(f72(x55962),x55961)),f315(f315(f279(x55962),x55963),x55961))
% 168.50/168.39 [5603]~P62(x56031)+E(f38(x56031,x56032,x56033),f2(x56031))+~P1(f315(f315(f275(x56031),x56033),x56032))
% 168.50/168.39 [5650]~P111(x56501)+E(f315(f290(x56501,x56502),x56503),f177(f909(x56501,a899)))+~P1(f315(f315(f223(x56501),x56503),x56502))
% 168.50/168.39 [5684]~P111(x56841)+E(f291(x56841,x56842,x56843),f177(f909(x56841,a899)))+~P1(f315(f315(f224(x56841),x56843),x56842))
% 168.50/168.39 [5685]~P111(x56851)+E(f294(x56851,x56852,x56853),f177(f909(x56851,a899)))+~P1(f315(f315(f223(x56851),x56853),x56852))
% 168.50/168.39 [5686]~P111(x56861)+E(f293(x56861,x56862,x56863),f177(f909(x56861,a899)))+~P1(f315(f315(f223(x56861),x56863),x56862))
% 168.50/168.39 [5738]~E(f315(f315(f3(a901),x57381),x57383),x57382)+E(x57381,f315(f315(f73(a901),x57382),x57383))+~P1(f315(f315(f223(a901),x57383),x57381))
% 168.50/168.39 [5739]~E(x57391,f315(f315(f73(a901),x57393),x57392))+E(f315(f315(f3(a901),x57391),x57392),x57393)+~P1(f315(f315(f223(a901),x57392),x57391))
% 168.50/168.39 [5784]~P1(f315(x57841,x57843))+P1(f315(x57841,f399(x57841,x57842)))+~P1(f315(f315(f223(a901),x57843),x57842))
% 168.50/168.39 [5785]~P1(f315(x57851,x57853))+P1(f315(x57851,f467(x57851,x57852)))+~P1(f315(f315(f224(a901),x57853),x57852))
% 168.50/168.39 [5793]~P111(x57931)+~E(f315(f290(x57931,x57932),x57933),f177(f909(x57931,a899)))+~P1(f315(f315(f224(x57931),x57932),x57933))
% 168.50/168.39 [5798]~P108(x57981)+~P1(f315(f315(f224(x57981),x57982),x57983))+P1(f315(f315(f223(x57981),x57982),x57983))
% 168.50/168.39 [5800]~P111(x58001)+~P1(f315(f315(f224(x58001),x58002),x58003))+P1(f315(f315(f223(x58001),x58002),x58003))
% 168.50/168.39 [5918]~P111(x59181)+~E(f291(x59181,x59182,x59183),f177(f909(x59181,a899)))+~P1(f315(f315(f223(x59181),x59182),x59183))
% 168.50/168.39 [5919]~P111(x59191)+~E(f293(x59191,x59192,x59193),f177(f909(x59191,a899)))+~P1(f315(f315(f224(x59191),x59192),x59193))
% 168.50/168.39 [5920]~P111(x59201)+~E(f177(f909(x59201,a899)),f291(x59201,x59202,x59203))+~P1(f315(f315(f223(x59201),x59202),x59203))
% 168.50/168.39 [5921]~P111(x59211)+~E(f177(f909(x59211,a899)),f293(x59211,x59212,x59213))+~P1(f315(f315(f224(x59211),x59212),x59213))
% 168.50/168.39 [5931]P1(f315(x59311,x59312))+~P1(f315(x59311,f422(x59311,x59313)))+~P1(f315(f315(f223(a901),x59312),x59313))
% 168.50/168.39 [5932]P1(f315(x59321,x59322))+~P1(f315(x59321,f468(x59321,x59323)))+~P1(f315(f315(f224(a901),x59322),x59323))
% 168.50/168.39 [5940]~E(x59401,f315(a101,x59403))+P1(f315(f315(f224(a901),x59401),f315(a101,x59402)))+~P1(f315(f315(f224(a901),x59403),x59402))
% 168.50/168.39 [5959]E(x59591,x59592)+~E(f315(f315(f74(a901),x59593),x59591),f315(f315(f74(a901),x59593),x59592))+~P1(f315(f315(f224(a901),f2(a901)),x59593))
% 168.50/168.39 [6019]E(f315(x60191,f763(x60191,x60192,x60193)),f71(a901))+~E(f315(f315(f8(x60193,a901),x60191),x60192),f71(a901))+~P1(f315(f54(x60193),x60192))
% 168.50/168.39 [6036]~P5(x60361)+P1(f315(f315(f223(x60361),x60362),f30(x60361,x60363)))+~P1(f315(f315(f317(x60361),x60362),x60363))
% 168.50/168.39 [6059]~P108(x60591)+~P1(f315(f315(f224(x60591),x60593),x60592))+~P1(f315(f315(f223(x60591),x60592),x60593))
% 168.50/168.39 [6063]~P108(x60631)+~P1(f315(f315(f224(x60631),x60633),x60632))+~P1(f315(f315(f224(x60631),x60632),x60633))
% 168.50/168.39 [6066]~P110(x60661)+~P1(f315(f315(f224(x60661),x60663),x60662))+~P1(f315(f315(f223(x60661),x60662),x60663))
% 168.50/168.39 [6067]~P110(x60671)+~P1(f315(f315(f224(x60671),x60673),x60672))+~P1(f315(f315(f224(x60671),x60672),x60673))
% 168.50/168.39 [6068]~P111(x60681)+~P1(f315(f315(f224(x60681),x60683),x60682))+~P1(f315(f315(f224(x60681),x60682),x60683))
% 168.50/168.39 [6088]~E(x60882,x60883)+~E(x60881,x60882)+E(f278(a901,f275(a901),x60881,x60882),f315(f315(f297(a901),x60883),f177(f909(a901,a899))))
% 168.50/168.39 [6096]~E(f315(x60962,f710(x60962,x60963,x60961)),f2(a901))+E(f315(f315(f8(x60961,a901),x60962),x60963),f2(a901))+~P1(f315(f54(x60961),x60963))
% 168.50/168.39 [6097]~E(f315(x60972,f656(x60972,x60973,x60971)),f71(a901))+E(f315(f315(f11(x60971,a901),x60972),x60973),f71(a901))+~P1(f315(f54(x60971),x60973))
% 168.50/168.39 [6113]~P109(x61131)+~P1(f315(f315(f223(x61131),x61133),x61132))+P1(f315(f315(f317(x61131),x61132),f315(f271(x61131),x61133)))
% 168.50/168.39 [6114]~P109(x61141)+~P1(f315(f315(f224(x61141),x61143),x61142))+P1(f315(f315(f317(x61141),x61142),f315(f292(x61141),x61143)))
% 168.50/168.39 [6115]~P109(x61151)+~P1(f315(f315(f224(x61151),x61152),x61153))+P1(f315(f315(f317(x61151),x61152),f315(f270(x61151),x61153)))
% 168.50/168.39 [6116]~P109(x61161)+~P1(f315(f315(f223(x61161),x61162),x61163))+P1(f315(f315(f317(x61161),x61162),f315(f289(x61161),x61163)))
% 168.50/168.39 [6117]~P114(x61171)+~P1(f315(f315(f275(x61171),x61172),x61173))+P1(f315(f315(f275(x61171),x61172),f315(f69(x61171),x61173)))
% 168.50/168.39 [6118]~P116(x61181)+~P1(f315(f315(f275(x61181),x61182),x61183))+P1(f315(f315(f275(x61181),x61182),f315(f72(x61181),x61183)))
% 168.50/168.39 [6130]E(f315(x61301,f740(x61301,x61302,x61303)),f315(a101,f2(a901)))+~E(f315(f315(f8(x61303,a901),x61301),x61302),f315(a101,f2(a901)))+~P1(f315(f54(x61303),x61302))
% 168.50/168.39 [6214]~P5(x62141)+~P1(f315(f315(f317(x62141),x62143),x62142))+P1(f315(f315(f223(x62141),f31(x62141,x62142)),x62143))
% 168.50/168.39 [6235]~P1(f315(f315(f223(a901),x62351),x62353))+P1(f315(f315(f223(a901),x62351),x62352))+~P1(f315(f315(f223(a901),x62353),x62352))
% 168.50/168.39 [6236]~P1(f315(f315(f223(a1),x62361),x62363))+P1(f315(f315(f223(a1),x62361),x62362))+~P1(f315(f315(f223(a1),x62363),x62362))
% 168.50/168.39 [6237]~P1(f315(f315(f275(a901),x62371),x62373))+P1(f315(f315(f275(a901),x62371),x62372))+~P1(f315(f315(f275(a901),x62373),x62372))
% 168.50/168.39 [6257]~P109(x62571)+~P1(f315(f315(f317(x62571),x62573),f315(f271(x62571),x62572)))+P1(f315(f315(f223(x62571),x62572),x62573))
% 168.50/168.39 [6258]~P109(x62581)+~P1(f315(f315(f317(x62581),x62582),f315(f289(x62581),x62583)))+P1(f315(f315(f223(x62581),x62582),x62583))
% 168.50/168.39 [6259]~P109(x62591)+~P1(f315(f315(f317(x62591),x62593),f315(f292(x62591),x62592)))+P1(f315(f315(f224(x62591),x62592),x62593))
% 168.50/168.39 [6260]~P109(x62601)+~P1(f315(f315(f317(x62601),x62602),f315(f270(x62601),x62603)))+P1(f315(f315(f224(x62601),x62602),x62603))
% 168.50/168.39 [6261]~P114(x62611)+~P1(f315(f315(f275(x62611),x62612),f315(f69(x62611),x62613)))+P1(f315(f315(f275(x62611),x62612),x62613))
% 168.50/168.39 [6262]~P116(x62621)+~P1(f315(f315(f275(x62621),x62622),f315(f72(x62621),x62623)))+P1(f315(f315(f275(x62621),x62622),x62623))
% 168.50/168.39 [6336]~P1(f315(x63361,x63362))+P1(f315(x63361,f765(x63361)))+~P1(f315(f315(f317(x63363),x63362),f230(f909(x63363,a899))))
% 168.50/168.39 [6483]~P67(x64831)+P1(f315(f315(f224(x64831),f2(x64831)),f861(x64833,x64832,x64831)))+P1(f315(f315(f223(x64831),x64832),x64833))
% 168.50/168.39 [6484]~P68(x64841)+P1(f315(f315(f224(x64841),f2(x64841)),f367(x64843,x64842,x64841)))+P1(f315(f315(f223(x64841),x64842),x64843))
% 168.50/168.39 [6555]~P82(x65551)+~P1(f315(f315(f223(x65551),x65553),f315(f72(x65551),x65552)))+P1(f315(f315(f223(x65551),x65552),f315(f72(x65551),x65553)))
% 168.50/168.39 [6557]~P82(x65571)+~P1(f315(f315(f224(x65571),x65573),f315(f72(x65571),x65572)))+P1(f315(f315(f224(x65571),x65572),f315(f72(x65571),x65573)))
% 168.50/168.39 [6569]~P1(f315(f315(f224(a901),x65691),x65693))+~P1(f315(f315(f224(a901),x65693),x65692))+P1(f315(f315(f224(a901),f315(a101,x65691)),x65692))
% 168.50/168.39 [6599]~P128(x65991)+P1(f315(f315(f223(x65991),f315(f89(x65991),x65992)),f315(f89(x65991),x65993)))+~P1(f315(f315(f223(a901),x65992),x65993))
% 168.50/168.39 [6600]~P114(x66001)+P1(f315(f315(f223(x66001),f315(f91(x66001),x66002)),f315(f91(x66001),x66003)))+~P1(f315(f315(f223(a1),x66002),x66003))
% 168.50/168.39 [6602]~P114(x66021)+P1(f315(f315(f224(x66021),f315(f91(x66021),x66022)),f315(f91(x66021),x66023)))+~P1(f315(f315(f224(a1),x66022),x66023))
% 168.50/168.39 [6603]~P128(x66031)+P1(f315(f315(f224(x66031),f315(f89(x66031),x66032)),f315(f89(x66031),x66033)))+~P1(f315(f315(f224(a901),x66032),x66033))
% 168.50/168.39 [6609]~P110(x66091)+E(f315(f315(f99(f909(x66091,a899)),f315(f270(x66091),x66092)),f315(f290(x66091,x66092),x66093)),f315(f270(x66091),x66093))+~P1(f315(f315(f223(x66091),x66092),x66093))
% 168.50/168.39 [6639]~P82(x66391)+~P1(f315(f315(f223(x66391),x66393),x66392))+P1(f315(f315(f223(x66391),f315(f72(x66391),x66392)),f315(f72(x66391),x66393)))
% 168.50/168.39 [6641]~P98(x66411)+~P1(f315(f315(f223(x66411),x66413),x66412))+P1(f315(f315(f223(x66411),f315(f72(x66411),x66412)),f315(f72(x66411),x66413)))
% 168.50/168.39 [6642]~P82(x66421)+~P1(f315(f315(f224(x66421),x66423),x66422))+P1(f315(f315(f224(x66421),f315(f72(x66421),x66422)),f315(f72(x66421),x66423)))
% 168.50/168.39 [6678]~P110(x66781)+E(f315(f315(f99(f909(x66781,a899)),f315(f270(x66781),x66782)),f291(x66781,x66782,x66783)),f315(f289(x66781),x66783))+~P1(f315(f315(f223(x66781),x66782),x66783))
% 168.50/168.39 [6679]~P110(x66791)+E(f315(f315(f99(f909(x66791,a899)),f315(f289(x66791),x66792)),f294(x66791,x66792,x66793)),f315(f270(x66791),x66793))+~P1(f315(f315(f224(x66791),x66792),x66793))
% 168.50/168.39 [6680]~P110(x66801)+E(f315(f315(f99(f909(x66801,a899)),f315(f289(x66801),x66802)),f293(x66801,x66802,x66803)),f315(f289(x66801),x66803))+~P1(f315(f315(f223(x66801),x66802),x66803))
% 168.50/168.39 [6714]~P110(x67141)+E(f315(f315(f99(f909(x67141,a899)),f315(f290(x67141,x67142),x67143)),f315(f271(x67141),x67143)),f315(f271(x67141),x67142))+~P1(f315(f315(f223(x67141),x67142),x67143))
% 168.50/168.39 [6876]~P110(x68761)+E(f315(f315(f99(f909(x68761,a899)),f291(x68761,x68762,x68763)),f315(f292(x68761),x68763)),f315(f271(x68761),x68762))+~P1(f315(f315(f223(x68761),x68762),x68763))
% 168.50/168.39 [6877]~P110(x68771)+E(f315(f315(f99(f909(x68771,a899)),f294(x68771,x68772,x68773)),f315(f271(x68771),x68773)),f315(f292(x68771),x68772))+~P1(f315(f315(f224(x68771),x68772),x68773))
% 168.50/168.39 [6878]~P110(x68781)+E(f315(f315(f99(f909(x68781,a899)),f293(x68781,x68782,x68783)),f315(f292(x68781),x68783)),f315(f292(x68781),x68782))+~P1(f315(f315(f223(x68781),x68782),x68783))
% 168.50/168.39 [6897]P1(f315(x68971,x68972))+~P1(f315(f315(f223(a901),x68972),x68973))+P1(f315(f315(f317(a901),f422(x68971,x68973)),f291(a901,f2(a901),x68973)))
% 168.50/168.39 [6931]E(x69311,x69312)+~E(f315(f315(f153(x69313),x69311),f609(x69313,x69312,x69311)),f315(f315(f153(x69313),x69312),f609(x69313,x69312,x69311)))+~E(f315(f178(f902(x69313)),x69311),f315(f178(f902(x69313)),x69312))
% 168.50/168.39 [6936]~E(x69363,f315(f315(f29(a901),x69361),x69362))+~P1(f315(f315(f224(a901),f2(a901)),x69362))+P1(f315(f315(f224(a901),x69361),f315(f315(f74(a901),x69362),f315(a101,x69363))))
% 168.50/168.39 [6952]~P1(f315(x69521,x69523))+~P1(f315(f315(f223(a901),x69523),x69522))+P1(f315(f315(f317(a901),f399(x69521,x69522)),f291(a901,f2(a901),x69522)))
% 168.50/168.39 [6991]~P1(f315(x69911,x69913))+P1(f315(x69911,f423(x69911,x69912)))+~P1(f315(f315(f317(a901),x69913),f291(a901,f2(a901),x69912)))
% 168.50/168.39 [7010]~P128(x70103)+~P1(f315(f315(f223(x70103),f315(f89(x70103),x70101)),f315(f89(x70103),x70102)))+P1(f315(f315(f223(a901),x70101),x70102))
% 168.50/168.39 [7011]~P114(x70113)+~P1(f315(f315(f223(x70113),f315(f91(x70113),x70111)),f315(f91(x70113),x70112)))+P1(f315(f315(f223(a1),x70111),x70112))
% 168.50/168.39 [7013]~P128(x70133)+~P1(f315(f315(f224(x70133),f315(f89(x70133),x70131)),f315(f89(x70133),x70132)))+P1(f315(f315(f224(a901),x70131),x70132))
% 168.50/168.39 [7014]~P114(x70143)+~P1(f315(f315(f224(x70143),f315(f91(x70143),x70141)),f315(f91(x70143),x70142)))+P1(f315(f315(f224(a1),x70141),x70142))
% 168.50/168.39 [7032]~P128(x70321)+~P1(f315(f315(f224(x70321),f71(x70321)),x70322))+P1(f315(f315(f224(x70321),f71(x70321)),f315(f315(f232(x70321),x70322),f315(a101,x70323))))
% 168.50/168.39 [7035]~P82(x70351)+~P1(f315(f315(f223(x70351),f315(f72(x70351),x70353)),f315(f72(x70351),x70352)))+P1(f315(f315(f223(x70351),x70352),x70353))
% 168.50/168.39 [7036]~P98(x70361)+~P1(f315(f315(f223(x70361),f315(f72(x70361),x70363)),f315(f72(x70361),x70362)))+P1(f315(f315(f223(x70361),x70362),x70363))
% 168.50/168.39 [7037]~P82(x70371)+~P1(f315(f315(f224(x70371),f315(f72(x70371),x70373)),f315(f72(x70371),x70372)))+P1(f315(f315(f224(x70371),x70372),x70373))
% 168.50/168.39 [7061]P1(f315(x70611,x70612))+~P1(f315(x70611,f424(x70611,x70613)))+~P1(f315(f315(f317(a901),x70612),f291(a901,f2(a901),x70613)))
% 168.50/168.39 [7083]~P67(x70831)+P1(f315(f315(f224(x70831),f861(x70833,x70832,x70831)),f71(x70831)))+P1(f315(f315(f223(x70831),x70832),x70833))
% 168.50/168.39 [7104]~E(f38(a901,x71043,x71042),f38(a901,x71041,x71042))+E(f315(f315(f73(a901),x71041),f315(f315(f74(a901),x71042),f358(x71041,x71042,x71043))),x71043)+~P1(f315(f315(f223(a901),x71041),x71043))
% 168.50/168.39 [7160]E(f315(f315(f8(x71601,a901),x71602),x71603),f2(a901))+~P1(f315(f54(x71601),x71603))+P1(f315(f315(f317(x71601),f710(x71602,x71603,x71601)),x71603))
% 168.50/168.39 [7161]E(f315(f315(f11(x71611,a901),x71612),x71613),f71(a901))+~P1(f315(f54(x71611),x71613))+P1(f315(f315(f317(x71611),f656(x71612,x71613,x71611)),x71613))
% 168.50/168.39 [7183]~P110(x71831)+~P1(f315(f315(f223(x71831),x71832),x71833))+P1(f315(f315(f223(f909(x71831,a899)),f315(f270(x71831),x71832)),f315(f270(x71831),x71833)))
% 168.50/168.39 [7184]~P111(x71841)+~P1(f315(f315(f223(x71841),x71842),x71843))+P1(f315(f315(f223(f909(x71841,a899)),f315(f289(x71841),x71842)),f315(f289(x71841),x71843)))
% 168.50/168.39 [7185]~P111(x71851)+~P1(f315(f315(f223(x71851),x71853),x71852))+P1(f315(f315(f223(f909(x71851,a899)),f315(f271(x71851),x71852)),f315(f271(x71851),x71853)))
% 168.50/168.39 [7186]~P110(x71861)+~P1(f315(f315(f223(x71861),x71863),x71862))+P1(f315(f315(f223(f909(x71861,a899)),f315(f292(x71861),x71862)),f315(f292(x71861),x71863)))
% 168.50/168.39 [7187]~P110(x71871)+~P1(f315(f315(f224(x71871),x71872),x71873))+P1(f315(f315(f224(f909(x71871,a899)),f315(f270(x71871),x71872)),f315(f270(x71871),x71873)))
% 168.50/168.39 [7198]~P5(x71981)+P1(f315(f315(f223(x71981),x71982),f31(x71981,x71983)))+P1(f315(f315(f317(x71981),f363(x71983,x71982,x71981)),x71983))
% 168.50/168.39 [7204]~P82(x72041)+P1(f315(f315(f223(x72041),f315(f315(f3(x72041),x72042),x72043)),f2(x72041)))+~P1(f315(f315(f223(x72041),x72042),x72043))
% 168.50/168.39 [7205]~P82(x72051)+P1(f315(f315(f224(x72051),f315(f315(f3(x72051),x72052),x72053)),f2(x72051)))+~P1(f315(f315(f224(x72051),x72052),x72053))
% 168.50/168.39 [7247]P1(f315(x72471,x72472))+P1(f315(f315(f223(a901),f424(x72471,x72473)),x72473))+~P1(f315(f315(f317(a901),x72472),f291(a901,f2(a901),x72473)))
% 168.50/168.39 [7289]~E(f315(f315(f8(x72891,a901),x72892),x72893),f71(a901))+~P1(f315(f54(x72891),x72893))+P1(f315(f315(f317(x72891),f763(x72892,x72893,x72891)),x72893))
% 168.50/168.39 [7290]~P1(f315(x72901,x72903))+P1(f315(f315(f223(a901),f423(x72901,x72902)),x72902))+~P1(f315(f315(f317(a901),x72903),f291(a901,f2(a901),x72902)))
% 168.50/168.39 [7330]~P5(x73301)+P1(f315(f315(f317(x73301),f864(x73303,x73302,x73301)),x73302))+P1(f315(f315(f223(x73301),f30(x73301,x73302)),x73303))
% 168.50/168.39 [7364]~E(f315(f315(f8(x73641,a901),x73642),x73643),f315(a101,f2(a901)))+~P1(f315(f54(x73641),x73643))+P1(f315(f315(f317(x73641),f740(x73642,x73643,x73641)),x73643))
% 168.50/168.39 [7375]E(x73751,f2(a901))+P1(f315(x73752,f38(a901,x73753,x73751)))+P1(f315(f315(f224(a901),f354(x73751,x73753,x73752)),x73751))
% 168.50/168.39 [7487]~P1(f315(x74871,x74872))+P1(f315(x74871,f38(a901,x74872,x74873)))+P1(f315(f315(f224(a901),f354(x74873,x74872,x74871)),x74873))
% 168.50/168.39 [7601]E(x76011,f102(x76012))+~P1(f315(f315(f317(f902(x76012)),x76011),f150(x76012,x76013)))+P1(f315(f315(f317(x76012),f671(x76013,x76011,x76012)),x76013))
% 168.50/168.39 [7624]~P110(x76241)+E(f315(f315(f99(f909(x76241,a899)),f315(f315(f297(x76241),x76242),f177(f909(x76241,a899)))),f294(x76241,x76242,x76243)),f315(f290(x76241,x76242),x76243))+~P1(f315(f315(f224(x76241),x76242),x76243))
% 168.50/168.39 [7646]~P110(x76461)+E(f315(f315(f99(f909(x76461,a899)),f315(f315(f297(x76461),x76462),f177(f909(x76461,a899)))),f293(x76461,x76462,x76463)),f291(x76461,x76462,x76463))+~P1(f315(f315(f223(x76461),x76462),x76463))
% 168.50/168.39 [7757]~P110(x77571)+P1(f315(f315(f223(x77571),x77572),x77573))+~P1(f315(f315(f223(f909(x77571,a899)),f315(f292(x77571),x77573)),f315(f292(x77571),x77572)))
% 168.50/168.39 [7758]~P111(x77581)+P1(f315(f315(f223(x77581),x77582),x77583))+~P1(f315(f315(f223(f909(x77581,a899)),f315(f271(x77581),x77583)),f315(f271(x77581),x77582)))
% 168.50/168.39 [7759]~P110(x77591)+P1(f315(f315(f223(x77591),x77592),x77593))+~P1(f315(f315(f223(f909(x77591,a899)),f315(f270(x77591),x77592)),f315(f270(x77591),x77593)))
% 168.50/168.39 [7760]~P111(x77601)+P1(f315(f315(f223(x77601),x77602),x77603))+~P1(f315(f315(f223(f909(x77601,a899)),f315(f289(x77601),x77602)),f315(f289(x77601),x77603)))
% 168.50/168.39 [7761]~P110(x77611)+P1(f315(f315(f224(x77611),x77612),x77613))+~P1(f315(f315(f224(f909(x77611,a899)),f315(f270(x77611),x77612)),f315(f270(x77611),x77613)))
% 168.50/168.39 [7784]~P82(x77841)+~P1(f315(f315(f223(x77841),f315(f315(f3(x77841),x77842),x77843)),f2(x77841)))+P1(f315(f315(f223(x77841),x77842),x77843))
% 168.50/168.39 [7785]~P82(x77851)+~P1(f315(f315(f224(x77851),f315(f315(f3(x77851),x77852),x77853)),f2(x77851)))+P1(f315(f315(f224(x77851),x77852),x77853))
% 168.50/168.39 [7941]E(x79411,f2(a901))+~E(f315(f131(a901,a901,f73(a901),x79412),x79413),f2(a901))+~P1(f315(f315(f317(a901),x79411),f315(f161(a901),x79413)))
% 168.50/168.39 [7945]~P5(x79451)+~P1(f315(f315(f223(x79451),f864(x79453,x79452,x79451)),x79453))+P1(f315(f315(f223(x79451),f30(x79451,x79452)),x79453))
% 168.50/168.39 [8100]P1(f315(f315(f223(a1),f2(a1)),f339(x81001,x81002,x81003)))+P1(f315(f315(x81002,f315(f315(f29(a1),x81001),x81003)),f38(a1,x81001,x81003)))+~P1(f315(f315(f224(a1),f2(a1)),x81003))
% 168.50/168.39 [8189]E(x81891,x81892)+~E(f315(f178(f902(x81893)),x81891),f315(f178(f902(x81893)),x81892))+~P1(f315(f315(f245(x81893,x81893,a899),a312),f645(x81893,x81891,x81892)))
% 168.50/168.39 [8261]~P39(x82612,x82613)+E(x82611,f177(f909(x82612,a899)))+~P1(f315(f315(f223(f909(x82612,a899)),x82611),f315(f273(x82612,x82612,x82613),x82611)))
% 168.50/168.39 [8292]~P68(x82921)+~P1(f315(f315(f223(x82921),x82922),f315(f315(f73(x82921),x82923),f367(x82923,x82922,x82921))))+P1(f315(f315(f223(x82921),x82922),x82923))
% 168.50/168.39 [8327]P54(x83271,x83272,x83273)+P1(f315(f315(f317(x83271),f472(x83273,x83272,x83271)),x83272))+P1(f315(f315(f317(f908(x83271,x83271)),f473(x83273,x83272,x83271)),x83273))
% 168.50/168.39 [8348]P1(f315(f315(x83482,f315(f315(f29(a1),x83481),x83483)),f38(a1,x83481,x83483)))+~P1(f315(f315(f224(a1),f2(a1)),x83483))+P1(f315(f315(f224(a1),f339(x83481,x83482,x83483)),x83483))
% 168.50/168.39 [8372]E(f315(f298(a901,a901,f315(f315(f9(a901,a901,a901),f3(a901)),x83721)),f315(f290(a901,x83722),x83723)),f177(f909(a901,a899)))+P1(f315(f315(f224(a901),x83721),x83723))+P1(f315(f315(f224(a901),x83722),x83723))
% 168.50/168.39 [8483]E(f315(f298(a901,a901,f315(f315(f9(a901,a901,a901),f3(a901)),x84831)),f315(f290(a901,x84832),x84833)),f315(f315(f297(a901),f2(a901)),f177(f909(a901,a899))))+P1(f315(f315(f224(a901),x84831),x84833))+~P1(f315(f315(f224(a901),x84832),x84833))
% 168.50/168.39 [8497]~P110(x84971)+E(f138(x84971,x84971,f7(x84971),x84972,x84973),x84973)+~P1(f315(f315(f317(x84971),x84972),f315(f161(x84971),x84973)))
% 168.50/168.39 [8510]P25(x85101,x85101,x85102,x85103)+~P1(f315(f54(x85101),x85103))+~P1(f315(f315(f223(f909(x85101,a899)),x85103),f315(f298(x85101,x85101,x85102),x85103)))
% 168.50/168.39 [8536]E(f315(f315(f73(a1),f315(f315(f74(a1),x85361),f340(x85362,x85363,x85361))),f339(x85362,x85363,x85361)),x85362)+P1(f315(f315(x85363,f315(f315(f29(a1),x85362),x85361)),f38(a1,x85362,x85361)))+~P1(f315(f315(f224(a1),f2(a1)),x85361))
% 168.50/168.39 [8773]~P1(f315(f315(x87731,f340(x87732,x87731,x87733)),f339(x87732,x87731,x87733)))+P1(f315(f315(x87731,f315(f315(f29(a1),x87732),x87733)),f38(a1,x87732,x87733)))+~P1(f315(f315(f224(a1),f2(a1)),x87733))
% 168.50/168.39 [9670]~P1(f315(f54(x96701),x96702))+~P1(f315(f315(f317(x96701),x96703),x96702))+P1(f315(f315(f224(a901),f315(f28(x96701),f315(f315(f3(f909(x96701,a899)),x96702),f315(f315(f297(x96701),x96703),f177(f909(x96701,a899)))))),f315(f28(x96701),x96702)))
% 168.50/168.39 [10269]P54(x102691,x102692,x102693)+~P1(f315(f315(f245(x102691,x102691,a899),f315(f315(f9(x102691,f909(x102691,a899),f909(x102691,a899)),f315(f315(f10(f909(a899,a899),f909(f909(x102691,a899),f909(x102691,a899)),x102691),f10(a899,a899,x102691)),f315(f315(f10(a899,f909(a899,a899),x102691),a313),f315(f315(f9(x102691,f909(x102691,a899),a899),f317(x102691)),x102692)))),f315(f315(f9(x102691,f909(x102691,a899),a899),f317(x102691)),x102692))),f473(x102693,x102692,x102691)))+P1(f315(f315(f317(x102691),f472(x102693,x102692,x102691)),x102692))
% 168.50/168.39 [5557]~P125(x55572)+E(x55571,f2(x55572))+E(f315(f315(f279(x55572),x55573),f315(f72(x55572),x55571)),f315(f72(x55572),f315(f315(f279(x55572),x55573),x55571)))
% 168.50/168.39 [5700]~E(x57003,f177(f909(x57001,a899)))+~E(x57002,f177(f909(x57001,a899)))+E(f315(f315(f99(f909(x57001,a899)),x57002),x57003),f177(f909(x57001,a899)))
% 168.50/168.39 [5758]~E(x57583,f2(a901))+~P1(f315(x57581,f2(a901)))+P1(f315(x57581,f315(f315(f29(a901),x57582),x57583)))
% 168.50/168.39 [5910]~P68(x59102)+E(x59101,f2(x59102))+E(f315(f315(f279(x59102),f315(f69(x59102),x59103)),f315(f69(x59102),x59101)),f315(f69(x59102),f315(f315(f279(x59102),x59103),x59101)))
% 168.50/168.39 [6029]~P62(x60291)+E(f315(f315(f74(x60291),x60292),f315(f315(f29(x60291),x60293),x60292)),x60293)+~P1(f315(f315(f275(x60291),x60292),x60293))
% 168.50/168.39 [6084]~P1(f315(f54(x60841),x60843))+E(f315(f28(x60841),f315(f315(f297(x60841),x60842),x60843)),f315(a101,f315(f28(x60841),x60843)))+P1(f315(f315(f317(x60841),x60842),x60843))
% 168.50/168.39 [6162]~E(x61622,f2(a901))+P1(f315(x61621,f2(a901)))+~P1(f315(x61621,f315(f315(f29(a901),x61623),x61622)))
% 168.50/168.39 [6179]~P1(f315(f54(x61791),x61793))+E(f315(f28(x61791),f315(f315(f297(x61791),x61792),x61793)),f315(f28(x61791),x61793))+~P1(f315(f315(f317(x61791),x61792),x61793))
% 168.50/168.39 [6216]~P1(f315(f54(x62161),x62163))+E(f315(f28(x62161),f315(f315(f297(x62161),x62162),x62163)),f315(f315(f73(a901),f71(a901)),f315(f28(x62161),x62163)))+P1(f315(f315(f317(x62161),x62162),x62163))
% 168.50/168.39 [6223]~P63(x62231)+E(f315(f315(f29(x62231),x62232),f315(f72(x62231),x62233)),f315(f72(x62231),f315(f315(f29(x62231),x62232),x62233)))+~P1(f315(f315(f275(x62231),x62233),x62232))
% 168.50/168.39 [6337]E(f315(f315(f73(a901),x63371),f722(x63371,x63372,x63373)),x63372)+~P1(f315(x63373,f2(a901)))+P1(f315(x63373,f315(f315(f3(a901),x63372),x63371)))
% 168.50/168.39 [6338]E(f315(f315(f73(a901),x63381),f733(x63381,x63382,x63383)),x63382)+~P1(f315(x63383,f2(a901)))+P1(f315(x63383,f315(f315(f3(a901),x63382),x63381)))
% 168.50/168.39 [6362]~P63(x63621)+E(f315(f315(f29(x63621),f315(f72(x63621),x63622)),x63623),f315(f72(x63621),f315(f315(f29(x63621),x63622),x63623)))+~P1(f315(f315(f275(x63621),x63623),x63622))
% 168.50/168.39 [6386]~P5(x63861)+~P1(f315(f54(x63861),x63863))+E(f315(f315(f57(x63861,x63861,f99(x63861)),x63862),x63863),f315(f315(f99(x63861),x63862),f30(x63861,x63863)))
% 168.50/168.39 [6387]~P5(x63871)+~P1(f315(f54(x63871),x63873))+E(f315(f315(f57(x63871,x63871,f90(x63871)),x63872),x63873),f315(f315(f90(x63871),x63872),f31(x63871,x63873)))
% 168.50/168.39 [6393]~P97(x63931)+~E(f315(f92(x63931),x63932),f315(f92(x63931),x63933))+P30(x63931,f315(f92(x63931),f315(f315(f73(a1),x63932),f315(f72(a1),x63933))))
% 168.50/168.39 [6402]~P143(x64021)+E(f315(f315(f3(x64021),f315(f89(x64021),x64022)),f315(f89(x64021),x64023)),f315(f89(x64021),f315(f315(f3(a901),x64022),x64023)))+~P1(f315(f315(f223(a901),x64023),x64022))
% 168.50/168.39 [6409]~P114(x64091)+~P1(f315(f315(f275(x64091),x64092),x64093))+P1(f315(f315(f275(x64091),f315(f69(x64091),x64092)),x64093))
% 168.50/168.39 [6410]~P116(x64101)+~P1(f315(f315(f275(x64101),x64102),x64103))+P1(f315(f315(f275(x64101),f315(f72(x64101),x64102)),x64103))
% 168.50/168.39 [6494]E(f315(f315(f73(a901),x64941),f722(x64941,x64942,x64943)),x64942)+P1(f315(f315(f224(a901),x64942),x64941))+P1(f315(x64943,f315(f315(f3(a901),x64942),x64941)))
% 168.50/168.39 [6495]E(f315(f315(f73(a901),x64951),f733(x64951,x64952,x64953)),x64952)+P1(f315(f315(f224(a901),x64952),x64951))+P1(f315(x64953,f315(f315(f3(a901),x64952),x64951)))
% 168.50/168.39 [6512]~P114(x65121)+E(f315(f315(f74(x65121),f315(f69(x65121),x65122)),x65123),f315(f69(x65121),f315(f315(f74(x65121),x65122),x65123)))+~P1(f315(f315(f223(x65121),f2(x65121)),x65123))
% 168.50/168.39 [6513]~P67(x65131)+E(f315(f315(f279(x65131),f315(f69(x65131),x65132)),x65133),f315(f69(x65131),f315(f315(f279(x65131),x65132),x65133)))+~P1(f315(f315(f224(x65131),f2(x65131)),x65133))
% 168.50/168.39 [6522]~P80(x65221)+~P1(f315(f54(x65221),x65223))+E(f315(f315(f57(x65221,x65221,f99(x65221)),x65222),x65223),f12(x65221,f315(f315(f297(x65221),x65222),x65223)))
% 168.50/168.39 [6523]~P80(x65231)+~P1(f315(f54(x65231),x65233))+E(f315(f315(f57(x65231,x65231,f90(x65231)),x65232),x65233),f13(x65231,f315(f315(f297(x65231),x65232),x65233)))
% 168.50/168.39 [6524]~P110(x65241)+~P1(f315(f54(x65241),x65243))+E(f315(f315(f57(x65241,x65241,f221(x65241)),x65242),x65243),f16(x65241,f315(f315(f297(x65241),x65242),x65243)))
% 168.50/168.39 [6525]~P110(x65251)+~P1(f315(f54(x65251),x65253))+E(f315(f315(f57(x65251,x65251,f222(x65251)),x65252),x65253),f17(x65251,f315(f315(f297(x65251),x65252),x65253)))
% 168.50/168.39 [6571]E(x65711,f102(x65712))+~E(f168(x65712,x65713),f102(f902(x65712)))+~P1(f315(f315(f317(f902(x65712)),x65711),f315(f161(f902(x65712)),x65713)))
% 168.50/168.39 [6617]~P1(f315(f126(x66171),x66173))+P1(f315(f315(f317(x66171),x66172),f315(f161(x66171),x66173)))+P1(f315(f126(x66171),f315(f315(f140(x66171),x66172),x66173)))
% 168.50/168.39 [6628]~P99(x66281)+~P1(f315(f54(x66281),x66283))+E(f315(f56(x66281,f74(x66281)),f315(f315(f297(x66281),x66282),x66283)),f315(f315(f57(x66281,x66281,f74(x66281)),x66282),x66283))
% 168.50/168.39 [6650]~P110(x66501)+~P1(f315(f54(x66501),x66503))+E(f14(x66501,f221(x66501),f315(f315(f297(x66501),x66502),x66503)),f315(f315(f57(x66501,x66501,f221(x66501)),x66502),x66503))
% 168.50/168.39 [6651]~P110(x66511)+~P1(f315(f54(x66511),x66513))+E(f15(x66511,f222(x66511),f315(f315(f297(x66511),x66512),x66513)),f315(f315(f57(x66511,x66511,f222(x66511)),x66512),x66513))
% 168.50/168.39 [6653]P1(f315(x66531,f2(a901)))+~P1(f315(f315(f224(a901),x66532),x66533))+~P1(f315(x66531,f315(f315(f3(a901),x66532),x66533)))
% 168.50/168.39 [6674]~P89(x66741)+P1(f315(f315(f223(x66741),x66742),x66743))+~P1(f315(f315(f223(x66741),f315(f69(x66741),x66742)),x66743))
% 168.50/168.39 [6675]~P114(x66751)+P1(f315(f315(f224(x66751),x66752),x66753))+~P1(f315(f315(f224(x66751),f315(f69(x66751),x66752)),x66753))
% 168.50/168.39 [6676]~P114(x66761)+P1(f315(f315(f275(x66761),x66762),x66763))+~P1(f315(f315(f275(x66761),f315(f69(x66761),x66762)),x66763))
% 168.50/168.39 [6677]~P116(x66771)+P1(f315(f315(f275(x66771),x66772),x66773))+~P1(f315(f315(f275(x66771),f315(f72(x66771),x66772)),x66773))
% 168.50/168.39 [6694]E(x66941,f102(x66942))+E(f315(f130(x66942),f315(f315(f127(x66942),x66943),x66941)),f315(f315(f153(x66942),x66941),x66943))+~P1(f315(f315(f224(a901),x66943),f315(f178(f902(x66942)),x66941)))
% 168.50/168.39 [6749]~P1(f315(x67491,x67493))+P1(f315(x67491,f483(x67491,x67492)))+~P1(f315(f315(f317(a901),x67493),f315(f290(a901,f2(a901)),x67492)))
% 168.50/168.39 [6769]P1(f315(x67691,x67692))+~P1(f315(f315(f224(a901),x67692),x67693))+P1(f315(f315(f317(a901),f468(x67691,x67693)),f315(f290(a901,f2(a901)),x67693)))
% 168.50/168.39 [6784]~P128(x67841)+~P1(f315(f315(f223(x67841),f71(x67841)),x67842))+P1(f315(f315(f223(x67841),f71(x67841)),f315(f315(f232(x67841),x67842),x67843)))
% 168.50/168.39 [6786]~P128(x67861)+~P1(f315(f315(f223(x67861),f2(x67861)),x67862))+P1(f315(f315(f223(x67861),f2(x67861)),f315(f315(f232(x67861),x67862),x67863)))
% 168.50/168.39 [6788]~P128(x67881)+~P1(f315(f315(f224(x67881),f2(x67881)),x67882))+P1(f315(f315(f224(x67881),f2(x67881)),f315(f315(f232(x67881),x67882),x67883)))
% 168.50/168.39 [6813]~P1(f315(x68131,x68133))+~P1(f315(f315(f224(a901),x68133),x68132))+P1(f315(f315(f317(a901),f467(x68131,x68132)),f315(f290(a901,f2(a901)),x68132)))
% 168.50/168.39 [6821]P1(f315(f54(x68211),x68212))+~P1(f315(f54(x68211),x68213))+~P1(f315(f315(f223(f909(x68211,a899)),x68212),x68213))
% 168.50/168.39 [6828]~P1(f315(f315(f275(a901),x68281),x68282))+~P1(f315(f315(f275(a901),x68281),x68283))+P1(f315(f315(f275(a901),x68281),f315(f315(f3(a901),x68282),x68283)))
% 168.50/168.39 [6829]P1(f315(x68291,x68292))+~P1(f315(x68291,f469(x68291,x68293)))+~P1(f315(f315(f317(a901),x68292),f315(f290(a901,f2(a901)),x68293)))
% 168.50/168.39 [6842]E(x68421,f2(a901))+P1(f315(x68422,f353(x68421,x68423,x68422)))+~P1(f315(x68422,f315(f315(f29(a901),x68423),x68421)))
% 168.50/168.39 [6850]~P130(x68502)+E(x68501,f2(x68502))+~E(f315(f315(f73(x68502),f315(f315(f74(x68502),x68503),x68503)),f315(f315(f74(x68502),x68501),x68501)),f2(x68502))
% 168.50/168.39 [6851]~P130(x68512)+E(x68511,f2(x68512))+~E(f315(f315(f73(x68512),f315(f315(f74(x68512),x68511),x68511)),f315(f315(f74(x68512),x68513),x68513)),f2(x68512))
% 168.50/168.39 [6898]E(x68981,f2(a901))+~P1(f315(x68982,f349(x68981,x68983,x68982)))+P1(f315(x68982,f315(f315(f29(a901),x68983),x68981)))
% 168.50/168.39 [6903]~P110(x69031)+~P13(x69031,x69033)+P13(x69031,f315(f315(f137(x69031,x69031,f7(x69031)),x69032),x69033))
% 168.50/168.39 [6945]P1(f315(x69451,f353(x69452,x69453,x69451)))+P1(f315(x69451,f2(a901)))+~P1(f315(x69451,f315(f315(f29(a901),x69453),x69452)))
% 168.50/168.39 [6951]~P97(x69511)+E(f315(f92(x69511),x69512),f315(f92(x69511),x69513))+~P30(x69511,f315(f92(x69511),f315(f315(f73(a1),x69512),f315(f72(a1),x69513))))
% 168.50/168.39 [7017]E(x70171,f2(a1))+E(x70172,f2(a1))+~P1(f315(f42(x70172,x70172),f315(f315(f240(a1,a1),x70173),x70171)))
% 168.50/168.39 [7018]E(x70181,f71(a1))+E(x70182,f2(a1))+~P1(f315(f42(x70182,x70182),f315(f315(f240(a1,a1),x70181),x70183)))
% 168.50/168.39 [7034]P1(f315(x70341,x70342))+P1(f315(f315(f224(a901),f469(x70341,x70343)),x70343))+~P1(f315(f315(f317(a901),x70342),f315(f290(a901,f2(a901)),x70343)))
% 168.50/168.39 [7057]~P1(f315(x70571,f722(x70573,x70572,x70571)))+~P1(f315(x70571,f2(a901)))+P1(f315(x70571,f315(f315(f3(a901),x70572),x70573)))
% 168.50/168.39 [7058]~P1(f315(x70581,f733(x70583,x70582,x70581)))+~P1(f315(x70581,f2(a901)))+P1(f315(x70581,f315(f315(f3(a901),x70582),x70583)))
% 168.50/168.39 [7059]~P1(f315(x70591,f349(x70593,x70592,x70591)))+~P1(f315(x70591,f2(a901)))+P1(f315(x70591,f315(f315(f29(a901),x70592),x70593)))
% 168.50/168.39 [7079]~P1(f315(x70791,x70793))+P1(f315(f315(f224(a901),f483(x70791,x70792)),x70792))+~P1(f315(f315(f317(a901),x70793),f315(f290(a901,f2(a901)),x70792)))
% 168.50/168.39 [7080]E(f315(f315(f3(a901),f315(f315(f3(a901),x70801),x70802)),f315(f315(f3(a901),x70803),x70802)),f315(f315(f3(a901),x70801),x70803))+~P1(f315(f315(f223(a901),x70802),x70801))+~P1(f315(f315(f223(a901),x70802),x70803))
% 168.50/168.39 [7117]~P82(x71171)+~P1(f315(f315(f223(x71171),f315(f72(x71171),x71173)),x71172))+P1(f315(f315(f223(x71171),f315(f72(x71171),x71172)),x71173))
% 168.50/168.39 [7119]~P89(x71191)+~P1(f315(f315(f223(x71191),f315(f69(x71191),x71192)),x71193))+P1(f315(f315(f223(x71191),f315(f72(x71191),x71192)),x71193))
% 168.50/168.39 [7121]~P82(x71211)+~P1(f315(f315(f224(x71211),f315(f72(x71211),x71213)),x71212))+P1(f315(f315(f224(x71211),f315(f72(x71211),x71212)),x71213))
% 168.50/168.39 [7122]~P114(x71221)+~P1(f315(f315(f224(x71221),f315(f69(x71221),x71222)),x71223))+P1(f315(f315(f224(x71221),f315(f72(x71221),x71222)),x71223))
% 168.50/168.39 [7155]~P1(f315(x71553,f722(x71552,x71551,x71553)))+P1(f315(f315(f224(a901),x71551),x71552))+P1(f315(x71553,f315(f315(f3(a901),x71551),x71552)))
% 168.50/168.39 [7156]~P1(f315(x71563,f733(x71562,x71561,x71563)))+P1(f315(f315(f224(a901),x71561),x71562))+P1(f315(x71563,f315(f315(f3(a901),x71561),x71562)))
% 168.50/168.39 [7208]~E(f872(x72083,x72082,x72081),f873(x72083,x72082,x72081))+E(f315(f315(f90(f909(x72081,a899)),x72082),f30(f909(x72081,a899),x72083)),f177(f909(x72081,a899)))+P1(f315(f315(f317(f909(x72081,a899)),x72082),x72083))
% 168.50/168.39 [7216]~P1(f315(f54(x72161),x72163))+P1(f315(f54(x72161),f31(f909(x72161,a899),x72162)))+~P1(f315(f315(f317(f909(x72161,a899)),x72163),x72162))
% 168.50/168.39 [7276]~P110(x72761)+E(f315(f315(f99(f909(x72761,a899)),f315(f290(x72761,x72762),x72763)),f315(f315(f297(x72761),x72763),f177(f909(x72761,a899)))),f291(x72761,x72762,x72763))+~P1(f315(f315(f223(x72761),x72762),x72763))
% 168.50/168.39 [7279]E(x72791,f2(a901))+P1(f315(f315(f224(a901),f350(x72791,x72793,x72792)),x72791))+P1(f315(x72792,f315(f315(f29(a901),x72793),x72791)))
% 168.50/168.39 [7308]P1(f315(f315(f224(a901),f315(f178(f902(x73081)),x73082)),f768(x73083,x73081)))+~P1(f315(f54(f902(x73081)),x73083))+~P1(f315(f315(f317(f902(x73081)),x73082),x73083))
% 168.50/168.39 [7314]E(x73141,x73142)+~P1(f315(f315(f223(f909(x73143,a899)),x73141),x73142))+P1(f315(f315(f224(f909(x73143,a899)),x73141),x73142))
% 168.50/168.39 [7327]E(x73271,x73272)+~E(f315(f178(f902(x73273)),x73271),f315(f178(f902(x73273)),x73272))+P1(f315(f315(f224(a901),f609(x73273,x73271,x73272)),f315(f178(f902(x73273)),x73272)))
% 168.50/168.39 [7376]P8(x73761,x73762,x73763)+~E(f315(f252(x73761,x73761),x73763),x73762)+~E(f315(f315(f277(x73761,x73761,x73761),f315(f274(x73761,x73761),x73763)),x73763),x73763)
% 168.50/168.39 [7456]~P1(f315(x74561,f2(a901)))+P1(f315(f315(f224(a901),f350(x74563,x74562,x74561)),x74563))+P1(f315(x74561,f315(f315(f29(a901),x74562),x74563)))
% 168.50/168.39 [7466]~P110(x74661)+E(f315(f315(f99(f909(x74661,a899)),f294(x74661,x74662,x74663)),f315(f315(f297(x74661),x74663),f177(f909(x74661,a899)))),f293(x74661,x74662,x74663))+~P1(f315(f315(f224(x74661),x74662),x74663))
% 168.50/168.39 [7558]~P1(f315(f54(x75581),x75583))+P1(f315(f315(f223(a901),f315(f28(x75581),x75582)),f315(f28(x75581),x75583)))+~P1(f315(f315(f223(f909(x75581,a899)),x75582),x75583))
% 168.50/168.39 [7559]~P1(f315(f54(x75591),x75593))+P1(f315(f315(f224(a901),f315(f28(x75591),x75592)),f315(f28(x75591),x75593)))+~P1(f315(f315(f224(f909(x75591,a899)),x75592),x75593))
% 168.50/168.39 [7692]E(x76921,x76922)+~P1(f315(f315(f223(f909(x76923,a899)),x76922),x76921))+~P1(f315(f315(f223(f909(x76923,a899)),x76921),x76922))
% 168.50/168.39 [7695]~P110(x76951)+P13(x76951,x76952)+~P13(x76951,f315(f315(f137(x76951,x76951,f7(x76951)),x76953),x76952))
% 168.50/168.39 [7766]~P1(f315(f315(f224(a901),x77663),x77662))+~P1(f315(f315(f224(a901),x77663),x77661))+P1(f315(f315(f224(a901),f315(f315(f3(a901),x77661),x77662)),f315(f315(f3(a901),x77661),x77663)))
% 168.50/168.39 [7767]~P1(f315(f315(f223(a901),x77672),x77671))+~P1(f315(f315(f224(a901),x77671),x77673))+P1(f315(f315(f224(a901),f315(f315(f3(a901),x77671),x77672)),f315(f315(f3(a901),x77673),x77672)))
% 168.50/168.39 [7782]~P1(f315(f315(f224(a1),x77822),f2(a1)))+~P1(f315(f315(f223(a1),x77823),x77821))+P1(f315(f315(f223(a1),f315(f315(f29(a1),x77821),x77822)),f315(f315(f29(a1),x77823),x77822)))
% 168.50/168.39 [7799]~P1(f315(f315(f224(a901),f2(a901)),x77993))+~P1(f315(f315(f223(a901),x77993),x77992))+P1(f315(f315(f223(a901),f315(f315(f29(a901),x77991),x77992)),f315(f315(f29(a901),x77991),x77993)))
% 168.50/168.39 [7800]~P1(f315(f315(f224(a1),f2(a1)),x78002))+~P1(f315(f315(f223(a1),x78001),x78003))+P1(f315(f315(f223(a1),f315(f315(f29(a1),x78001),x78002)),f315(f315(f29(a1),x78003),x78002)))
% 168.50/168.39 [7804]~P1(f315(f315(f224(a901),f2(a901)),x78042))+~P1(f315(f315(f224(a901),x78041),x78043))+P1(f315(f315(f224(a901),f315(f315(f74(a901),x78041),x78042)),f315(f315(f74(a901),x78043),x78042)))
% 168.50/168.39 [7805]~P1(f315(f315(f224(a901),f2(a901)),x78051))+~P1(f315(f315(f224(a901),x78052),x78053))+P1(f315(f315(f224(a901),f315(f315(f74(a901),x78051),x78052)),f315(f315(f74(a901),x78051),x78053)))
% 168.50/168.39 [7806]~P1(f315(f315(f224(a1),f2(a1)),x78061))+~P1(f315(f315(f224(a1),x78062),x78063))+P1(f315(f315(f224(a1),f315(f315(f74(a1),x78061),x78062)),f315(f315(f74(a1),x78061),x78063)))
% 168.50/168.39 [7855]E(x78551,f2(a901))+E(f315(f315(f73(a901),f315(f315(f74(a901),x78551),f349(x78551,x78552,x78553))),f350(x78551,x78552,x78553)),x78552)+P1(f315(x78553,f315(f315(f29(a901),x78552),x78551)))
% 168.50/168.39 [7914]E(f315(f315(f73(a901),f315(f315(f74(a901),x79141),f349(x79141,x79142,x79143))),f350(x79141,x79142,x79143)),x79142)+~P1(f315(x79143,f2(a901)))+P1(f315(x79143,f315(f315(f29(a901),x79142),x79141)))
% 168.50/168.39 [7932]~P1(f315(f54(x79321),x79323))+P1(f315(f315(f317(x79321),f658(x79322,x79323,x79321)),x79323))+P1(f315(f315(f224(a901),f2(a901)),f315(f315(f11(x79321,a901),x79322),x79323)))
% 168.50/168.39 [7933]~P1(f315(f54(x79331),x79333))+P1(f315(f315(f317(x79331),f874(x79332,x79333,x79331)),x79333))+P1(f315(f315(f224(a901),f2(a901)),f315(f315(f11(x79331,a901),x79332),x79333)))
% 168.50/168.39 [8033]E(x80331,f2(a901))+P1(f315(f315(f275(a901),x80332),x80333))+~P1(f315(f315(f275(a901),f315(f315(f74(a901),x80331),x80332)),f315(f315(f74(a901),x80331),x80333)))
% 168.50/168.39 [8225]E(x82251,f177(f909(x82252,a899)))+E(x82251,f315(f315(f297(x82252),x82253),f177(f909(x82252,a899))))+~P1(f315(f315(f223(f909(x82252,a899)),x82251),f315(f315(f297(x82252),x82253),f177(f909(x82252,a899)))))
% 168.50/168.39 [8262]~P1(f315(f315(f224(a901),f71(a901)),x82623))+P1(f315(f315(f223(a901),x82621),x82622))+~P1(f315(f315(f275(a901),f315(f315(f232(a901),x82623),x82621)),f315(f315(f232(a901),x82623),x82622)))
% 168.50/168.39 [8264]~P1(f315(f315(f224(a901),f2(a901)),x82643))+P1(f315(f315(f223(a901),x82641),x82642))+~P1(f315(f315(f223(a901),f315(f315(f74(a901),x82643),x82641)),f315(f315(f74(a901),x82643),x82642)))
% 168.50/168.39 [8265]~P1(f315(f315(f224(a901),f2(a901)),x82653))+P1(f315(f315(f223(a901),x82651),x82652))+~P1(f315(f315(f223(a901),f315(f315(f74(a901),x82651),x82653)),f315(f315(f74(a901),x82652),x82653)))
% 168.50/168.39 [8267]~P1(f315(f315(f224(a901),f2(a901)),x82673))+P1(f315(f315(f224(a901),x82671),x82672))+~P1(f315(f315(f224(a901),f315(f315(f232(a901),x82673),x82671)),f315(f315(f232(a901),x82673),x82672)))
% 168.50/168.39 [8269]~P1(f315(f315(f224(a901),f2(a901)),x82693))+P1(f315(f315(f275(a901),x82691),x82692))+~P1(f315(f315(f275(a901),f315(f315(f74(a901),x82693),x82691)),f315(f315(f74(a901),x82693),x82692)))
% 168.50/168.39 [8308]~E(f315(f315(f90(f909(x83081,a899)),f873(x83083,x83082,x83081)),f872(x83083,x83082,x83081)),f177(f909(x83081,a899)))+E(f315(f315(f90(f909(x83081,a899)),x83082),f30(f909(x83081,a899),x83083)),f177(f909(x83081,a899)))+P1(f315(f315(f317(f909(x83081,a899)),x83082),x83083))
% 168.50/168.39 [8322]E(x83221,f102(x83222))+~E(f315(f131(f902(x83222),f902(x83222),f123(x83222),f102(x83222)),x83223),f102(x83222))+~P1(f315(f315(f317(f902(x83222)),x83221),f315(f161(f902(x83222)),x83223)))
% 168.50/168.39 [8377]E(x83771,f177(f909(f909(x83772,a899),a899)))+P1(f315(f315(f317(f909(x83772,a899)),f371(x83773,x83771,x83772)),x83771))+P1(f315(f315(f223(f909(x83772,a899)),f31(f909(x83772,a899),x83771)),x83773))
% 168.50/168.39 [8383]~P72(x83831)+~P77(x83831)+E(f315(f315(f8(a1,x83831),f315(f315(f10(a901,x83831,a1),x83832),a93)),f315(f298(a901,a1,f89(a1)),x83833)),f315(f315(f8(a901,x83831),x83832),x83833))
% 168.50/168.39 [8384]~P72(x83841)+~P77(x83841)+E(f315(f315(f11(a1,x83841),f315(f315(f10(a901,x83841,a1),x83842),a93)),f315(f298(a901,a1,f89(a1)),x83843)),f315(f315(f11(a901,x83841),x83842),x83843))
% 168.50/168.39 [8426]~P1(f315(f54(x84261),x84263))+~P1(f315(f315(f224(a901),f2(a901)),f315(x84262,f658(x84262,x84263,x84261))))+P1(f315(f315(f224(a901),f2(a901)),f315(f315(f11(x84261,a901),x84262),x84263)))
% 168.50/168.39 [8427]~P1(f315(f54(x84271),x84273))+~P1(f315(f315(f224(a901),f2(a901)),f315(x84272,f874(x84272,x84273,x84271))))+P1(f315(f315(f224(a901),f2(a901)),f315(f315(f11(x84271,a901),x84272),x84273)))
% 168.50/168.39 [8463]~P66(x84632)+E(x84631,f71(x84632))+E(f315(f315(f279(x84632),f315(f315(f3(x84632),f315(f315(f232(x84632),x84631),x84633)),f71(x84632))),f315(f315(f3(x84632),x84631),f71(x84632))),f315(f315(f8(a901,x84632),f315(f232(x84632),x84631)),f315(f290(a901,f2(a901)),x84633)))
% 168.50/168.39 [8521]E(x85211,f2(a901))+~P1(f315(x85213,f315(f315(f29(a901),x85212),x85211)))+P1(f315(f315(f224(a901),x85212),f315(f315(f74(a901),x85211),f315(a101,f353(x85211,x85212,x85213)))))
% 168.50/168.39 [8540]P1(f315(x85401,f2(a901)))+~P1(f315(x85401,f315(f315(f29(a901),x85402),x85403)))+P1(f315(f315(f224(a901),x85402),f315(f315(f74(a901),x85403),f315(a101,f353(x85403,x85402,x85401)))))
% 168.50/168.39 [8578]E(x85781,f2(a901))+~P1(f315(x85783,f315(f315(f29(a901),x85782),x85781)))+P1(f315(f315(f223(a901),f315(f315(f74(a901),x85781),f353(x85781,x85782,x85783))),x85782))
% 168.50/168.39 [8609]P1(f315(x86091,f2(a901)))+~P1(f315(x86091,f315(f315(f29(a901),x86093),x86092)))+P1(f315(f315(f223(a901),f315(f315(f74(a901),x86092),f353(x86092,x86093,x86091))),x86093))
% 168.50/168.39 [8617]~P110(x86171)+E(f315(f315(f137(x86171,x86171,f7(x86171)),x86172),x86173),f138(x86171,x86171,f7(x86171),x86172,x86173))+P1(f315(f315(f317(x86171),x86172),f315(f161(x86171),x86173)))
% 168.50/168.39 [8652]~E(f315(x86523,f568(x86522,x86523,x86521)),f315(x86523,f570(x86522,x86523,x86521)))+~P61(x86521,f315(x86523,f569(x86522,x86523,x86521)))+P61(x86521,f315(f315(f33(x86522,f909(x86521,f909(x86521,a899))),f230(f909(x86522,a899))),x86523))
% 168.50/168.39 [8661]E(x86611,f177(f909(f909(x86612,a899),a899)))+~P1(f315(f315(f223(f909(x86612,a899)),f371(x86613,x86611,x86612)),x86613))+P1(f315(f315(f223(f909(x86612,a899)),f31(f909(x86612,a899),x86611)),x86613))
% 168.50/168.39 [8721]~P68(x87211)+~P1(f315(f315(f224(x87211),x87212),x87213))+P1(f315(f315(f224(x87211),x87212),f315(f315(f279(x87211),f315(f315(f73(x87211),x87212),x87213)),f315(f315(f73(x87211),f71(x87211)),f71(x87211)))))
% 168.50/168.39 [8779]~P1(f315(f315(x87791,f372(x87791,x87793,x87792)),f374(x87791,x87793,x87792)))+P1(f315(f315(x87791,x87792),x87793))+~P1(f315(f303(f908(a1,a1),a45),f315(f315(f240(a1,a1),x87792),x87793)))
% 168.50/168.39 [8780]~P1(f315(f315(x87801,f375(x87801,x87803,x87802)),f376(x87801,x87803,x87802)))+P1(f315(f315(x87801,x87802),x87803))+~P1(f315(f303(f908(a1,a1),a51),f315(f315(f240(a1,a1),x87802),x87803)))
% 168.50/168.39 [8781]~P1(f315(f315(x87811,f380(x87811,x87813,x87812)),f381(x87811,x87813,x87812)))+P1(f315(f315(x87811,x87812),x87813))+~P1(f315(f303(f908(a901,a901),a208),f315(f315(f240(a901,a901),x87812),x87813)))
% 168.50/168.39 [8782]~P1(f315(f315(x87821,f388(x87821,x87823,x87822)),f390(x87821,x87823,x87822)))+P1(f315(f315(x87821,x87822),x87823))+~P1(f315(f303(f908(a1,a1),a210),f315(f315(f240(a1,a1),x87822),x87823)))
% 168.50/168.39 [8783]~P1(f315(f315(x87831,f659(x87831,x87833,x87832)),f661(x87831,x87833,x87832)))+P1(f315(f315(x87831,x87832),x87833))+~P1(f315(f303(f908(a1,a1),a171),f315(f315(f240(a1,a1),x87832),x87833)))
% 168.50/168.39 [8784]~P1(f315(f315(x87841,f754(x87841,x87843,x87842)),f755(x87841,x87843,x87842)))+P1(f315(f315(x87841,x87842),x87843))+~P1(f315(f303(f908(a1,a1),a122),f315(f315(f240(a1,a1),x87842),x87843)))
% 168.50/168.39 [9058]P1(f315(f315(x90581,x90582),x90583))+P1(f315(f303(f908(a901,a901),a208),f315(f315(f240(a901,a901),f380(x90581,x90583,x90582)),f381(x90581,x90583,x90582))))+~P1(f315(f303(f908(a901,a901),a208),f315(f315(f240(a901,a901),x90582),x90583)))
% 168.50/168.39 [9059]P1(f315(f315(x90591,x90592),x90593))+P1(f315(f303(f908(a1,a1),a45),f315(f315(f240(a1,a1),f372(x90591,x90593,x90592)),f374(x90591,x90593,x90592))))+~P1(f315(f303(f908(a1,a1),a45),f315(f315(f240(a1,a1),x90592),x90593)))
% 168.50/168.39 [9060]P1(f315(f315(x90601,x90602),x90603))+P1(f315(f303(f908(a1,a1),a51),f315(f315(f240(a1,a1),f375(x90601,x90603,x90602)),f376(x90601,x90603,x90602))))+~P1(f315(f303(f908(a1,a1),a51),f315(f315(f240(a1,a1),x90602),x90603)))
% 168.50/168.39 [9061]P1(f315(f315(x90611,x90612),x90613))+P1(f315(f303(f908(a1,a1),a210),f315(f315(f240(a1,a1),f388(x90611,x90613,x90612)),f390(x90611,x90613,x90612))))+~P1(f315(f303(f908(a1,a1),a210),f315(f315(f240(a1,a1),x90612),x90613)))
% 168.50/168.39 [9062]P1(f315(f315(x90621,x90622),x90623))+P1(f315(f303(f908(a1,a1),a171),f315(f315(f240(a1,a1),f659(x90621,x90623,x90622)),f661(x90621,x90623,x90622))))+~P1(f315(f303(f908(a1,a1),a171),f315(f315(f240(a1,a1),x90622),x90623)))
% 168.50/168.39 [9063]P1(f315(f315(x90631,x90632),x90633))+P1(f315(f303(f908(a1,a1),a122),f315(f315(f240(a1,a1),f754(x90631,x90633,x90632)),f755(x90631,x90633,x90632))))+~P1(f315(f303(f908(a1,a1),a122),f315(f315(f240(a1,a1),x90632),x90633)))
% 168.50/168.39 [9398]~P1(f315(f54(x93981),x93983))+P1(f315(f315(f317(f908(f909(x93981,a899),f909(x93981,a899))),f315(f315(f240(f909(x93981,a899),f909(x93981,a899)),x93982),x93983)),f302(x93981)))+~P1(f315(f315(f224(f909(x93981,a899)),x93982),x93983))
% 168.50/168.39 [9473]~P61(x94731,f315(x94733,f569(x94732,x94733,x94731)))+P61(x94731,f315(f315(f33(x94732,f909(x94731,f909(x94731,a899))),f230(f909(x94732,a899))),x94733))+~E(f315(f315(f90(f909(x94731,a899)),f237(x94731,x94731,f315(x94733,f568(x94732,x94733,x94731)))),f238(x94731,x94731,f315(x94733,f570(x94732,x94733,x94731)))),f177(f909(x94731,a899)))
% 168.50/168.39 [9683]P54(x96831,x96832,x96833)+P1(f315(f315(f317(f908(x96831,x96831)),f473(x96833,x96832,x96831)),x96833))+~P1(f315(f315(f317(f908(x96831,x96831)),f315(f315(f240(x96831,x96831),f472(x96833,x96832,x96831)),f472(x96833,x96832,x96831))),x96833))
% 168.50/168.39 [10272]P54(x102721,x102722,x102723)+~P1(f315(f315(f245(x102721,x102721,a899),f315(f315(f9(x102721,f909(x102721,a899),f909(x102721,a899)),f315(f315(f10(f909(a899,a899),f909(f909(x102721,a899),f909(x102721,a899)),x102721),f10(a899,a899,x102721)),f315(f315(f10(a899,f909(a899,a899),x102721),a313),f315(f315(f9(x102721,f909(x102721,a899),a899),f317(x102721)),x102722)))),f315(f315(f9(x102721,f909(x102721,a899),a899),f317(x102721)),x102722))),f473(x102723,x102722,x102721)))+~P1(f315(f315(f317(f908(x102721,x102721)),f315(f315(f240(x102721,x102721),f472(x102723,x102722,x102721)),f472(x102723,x102722,x102721))),x102723))
% 168.50/168.39 [5740]~P62(x57402)+E(x57401,f2(x57402))+E(f315(f315(f29(x57402),f315(f315(f74(x57402),x57403),x57401)),x57401),x57403)
% 168.50/168.39 [5741]~P62(x57412)+E(x57411,f2(x57412))+E(f315(f315(f29(x57412),f315(f315(f74(x57412),x57411),x57413)),x57411),x57413)
% 168.50/168.39 [6403]~P62(x64031)+E(f315(f315(f74(x64031),f315(f315(f29(x64031),x64032),x64033)),x64033),x64032)+~P1(f315(f315(f275(x64031),x64033),x64032))
% 168.50/168.39 [6570]~P72(x65701)+~E(f315(x65702,f2(a901)),f2(x65701))+E(f315(f315(f8(a901,x65701),x65702),f315(f290(a901,f315(a101,f2(a901))),x65703)),f315(f315(f8(a901,x65701),x65702),f315(f290(a901,f2(a901)),x65703)))
% 168.50/168.39 [6707]~P62(x67072)+E(x67071,f2(x67072))+E(f315(f315(f29(x67072),f315(f315(f73(x67072),x67073),x67071)),x67071),f315(f315(f73(x67072),f315(f315(f29(x67072),x67073),x67071)),f71(x67072)))
% 168.50/168.39 [6708]~P62(x67082)+E(x67081,f2(x67082))+E(f315(f315(f29(x67082),f315(f315(f73(x67082),x67081),x67083)),x67081),f315(f315(f73(x67082),f315(f315(f29(x67082),x67083),x67081)),f71(x67082)))
% 168.50/168.39 [6934]~P1(f315(x69343,f2(a1)))+P1(f315(f315(f223(a901),x69341),x69342))+P1(f315(x69343,f315(f89(a1),f315(f315(f3(a901),x69342),x69341))))
% 168.50/168.39 [7040]P1(f315(f315(f224(a901),x70402),x70401))+P1(f315(f315(f223(a901),x70401),x70402))+P1(f315(x70403,f315(f89(a1),f315(f315(f3(a901),x70402),x70401))))
% 168.50/168.39 [7115]E(f315(f315(f73(a901),f315(f92(a901),x71151)),f315(f315(f73(a901),f315(f92(a901),x71152)),x71153)),f315(f315(f73(a901),f315(f92(a901),x71151)),x71153))+P1(f315(a182,f315(f92(a1),x71151)))+~P1(f315(a182,f315(f92(a1),x71152)))
% 168.50/168.39 [7195]~E(x71952,f315(f315(f29(a901),x71953),x71951))+~P1(f315(f315(f224(a901),f2(a901)),x71951))+P1(f315(f315(f223(a901),f315(f315(f74(a901),x71951),x71952)),x71953))
% 168.50/168.39 [7311]~P1(f315(f54(x73111),x73113))+~P1(f315(f54(x73111),x73112))+P1(f315(f54(x73111),f315(f315(f99(f909(x73111,a899)),x73112),x73113)))
% 168.50/168.39 [7361]~P40(x73611,x73613)+~P40(x73611,x73612)+P40(x73611,f315(f315(f90(f909(f908(x73611,x73611),a899)),x73612),x73613))
% 168.50/168.39 [7362]~P53(x73621,x73623)+~P53(x73621,x73622)+P53(x73621,f315(f315(f99(f909(f908(x73621,x73621),a899)),x73622),x73623))
% 168.50/168.39 [7363]~P53(x73631,x73633)+~P53(x73631,x73632)+P53(x73631,f315(f315(f90(f909(f908(x73631,x73631),a899)),x73632),x73633))
% 168.50/168.39 [7607]~P110(x76071)+~P1(f315(f54(x76071),x76072))+E(f128(x76071,f315(f315(f3(f909(x76071,a899)),x76072),f315(f315(f297(x76071),x76073),f177(f909(x76071,a899))))),f159(x76071,x76073,f128(x76071,x76072)))
% 168.50/168.39 [7671]P1(f315(x76711,f2(a1)))+~P1(f315(f315(f224(a901),x76712),x76713))+~P1(f315(x76711,f315(f89(a1),f315(f315(f3(a901),x76712),x76713))))
% 168.50/168.39 [7689]~P1(f315(f54(x76891),x76892))+E(f315(f28(x76891),f315(f315(f3(f909(x76891,a899)),x76892),f315(f315(f297(x76891),x76893),f177(f909(x76891,a899))))),f315(f28(x76891),x76892))+P1(f315(f315(f317(x76891),x76893),x76892))
% 168.50/168.39 [7822]~P128(x78221)+~P1(f315(f315(f224(x78221),f71(x78221)),x78222))+P1(f315(f315(f224(x78221),f71(x78221)),f315(f315(f74(x78221),x78222),f315(f315(f232(x78221),x78222),x78223))))
% 168.50/168.39 [7865]~P1(f315(f54(x78651),x78653))+E(f315(f315(f3(a901),f315(f28(x78651),x78652)),f315(f28(x78651),x78653)),f315(f28(x78651),f315(f315(f3(f909(x78651,a899)),x78652),x78653)))+~P1(f315(f315(f223(f909(x78651,a899)),x78653),x78652))
% 168.50/168.39 [7922]~P1(f315(f315(f223(a901),x79222),x79223))+~P1(f315(f315(f223(a901),x79221),f315(f315(f3(a901),x79223),x79222)))+P1(f315(f315(f223(a901),f315(f315(f73(a901),x79221),x79222)),x79223))
% 168.50/168.39 [7976]P1(f315(f54(x79761),x79762))+~P1(f315(f54(x79761),x79763))+~P1(f315(f54(x79761),f315(f315(f3(f909(x79761,a899)),x79762),x79763)))
% 168.50/168.39 [7982]~P1(f315(f54(x79821),x79822))+E(f315(f28(x79821),f315(f315(f3(f909(x79821,a899)),x79822),f315(f315(f297(x79821),x79823),f177(f909(x79821,a899))))),f315(f315(f3(a901),f315(f28(x79821),x79822)),f71(a901)))+~P1(f315(f315(f317(x79821),x79823),x79822))
% 168.50/168.39 [8058]P61(x80581,x80582)+~P61(x80581,x80583)+~P1(f315(f315(f223(f909(x80581,f909(x80581,a899))),x80582),x80583))
% 168.50/168.39 [8099]~P1(f315(f315(f223(a901),x80993),x80992))+P1(f315(f315(f223(a901),x80991),f315(f315(f3(a901),x80992),x80993)))+~P1(f315(f315(f223(a901),f315(f315(f73(a901),x80991),x80993)),x80992))
% 168.50/168.39 [8117]P39(x81171,x81172)+~P39(x81171,x81173)+~P1(f315(f315(f223(f909(f908(x81171,x81171),a899)),x81172),x81173))
% 168.50/168.39 [8118]P59(x81181,x81182)+~P59(x81181,x81183)+~P1(f315(f315(f223(f909(f908(x81181,x81181),a899)),x81182),x81183))
% 168.50/168.39 [8119]P41(x81191,x81192)+~P41(x81191,x81193)+~P1(f315(f315(f223(f909(f908(x81191,x81191),a899)),x81192),x81193))
% 168.50/168.39 [8355]~P128(x83551)+~P1(f315(f315(f224(x83551),f71(x83551)),x83552))+P1(f315(f315(f224(x83551),f315(f315(f232(x83551),x83552),x83553)),f315(f315(f74(x83551),x83552),f315(f315(f232(x83551),x83552),x83553))))
% 168.50/168.39 [8445]~P1(f315(x84451,f2(a1)))+~P1(f315(x84451,f315(f315(f3(a1),f315(f89(a1),x84452)),f315(f89(a1),x84453))))+P1(f315(x84451,f315(f89(a1),f315(f315(f3(a901),x84452),x84453))))
% 168.50/168.39 [8460]~P1(f315(f315(f223(a901),x84603),x84602))+P1(f315(x84601,f315(f315(f3(a1),f315(f89(a1),x84602)),f315(f89(a1),x84603))))+~P1(f315(x84601,f315(f89(a1),f315(f315(f3(a901),x84602),x84603))))
% 168.50/168.39 [8480]P1(f315(f315(f224(a901),x84801),x84802))+~P1(f315(x84803,f315(f315(f3(a1),f315(f89(a1),x84801)),f315(f89(a1),x84802))))+P1(f315(x84803,f315(f89(a1),f315(f315(f3(a901),x84801),x84802))))
% 168.50/168.39 [8533]~P130(x85332)+E(x85331,f2(x85332))+P1(f315(f315(f224(x85332),f2(x85332)),f315(f315(f73(x85332),f315(f315(f74(x85332),x85333),x85333)),f315(f315(f74(x85332),x85331),x85331))))
% 168.50/168.39 [8534]~P130(x85342)+E(x85341,f2(x85342))+P1(f315(f315(f224(x85342),f2(x85342)),f315(f315(f73(x85342),f315(f315(f74(x85342),x85341),x85341)),f315(f315(f74(x85342),x85343),x85343))))
% 168.50/168.39 [8634]~P1(f315(f315(f224(a901),f2(a901)),x86341))+~P1(f315(f315(f224(a1),x86342),x86343))+P1(f315(f315(f224(a1),f315(f315(f74(a1),f315(f89(a1),x86341)),x86342)),f315(f315(f74(a1),f315(f89(a1),x86341)),x86343)))
% 168.50/168.39 [8690]E(f315(f315(f90(f909(x86901,a899)),x86902),f30(f909(x86901,a899),x86903)),f177(f909(x86901,a899)))+P1(f315(f315(f317(f909(x86901,a899)),x86902),x86903))+P1(f315(f315(f317(f909(x86901,a899)),f873(x86903,x86902,x86901)),f315(f315(f297(f909(x86901,a899)),x86902),x86903)))
% 168.50/168.39 [8691]E(f315(f315(f90(f909(x86911,a899)),x86912),f30(f909(x86911,a899),x86913)),f177(f909(x86911,a899)))+P1(f315(f315(f317(f909(x86911,a899)),x86912),x86913))+P1(f315(f315(f317(f909(x86911,a899)),f872(x86913,x86912,x86911)),f315(f315(f297(f909(x86911,a899)),x86912),x86913)))
% 168.50/168.39 [8720]E(x87201,x87202)+~E(f315(f178(f902(x87203)),x87201),f315(f178(f902(x87203)),x87202))+P1(f315(f315(f317(f908(x87203,x87203)),f645(x87203,x87201,x87202)),f315(f161(f908(x87203,x87203)),f315(f315(f170(x87203,x87203),x87202),x87201))))
% 168.50/168.39 [8970]E(f295(x89701,x89702),f295(x89701,x89703))+~P1(f315(f315(f223(f909(f908(x89701,x89701),a899)),x89703),f295(x89701,x89702)))+~P1(f315(f315(f223(f909(f908(x89701,x89701),a899)),x89702),x89703))
% 168.50/168.39 [9038]~P54(x90381,f230(f909(x90381,a899)),x90383)+P1(f315(f315(f223(f909(f908(f902(x90381),f902(x90381)),a899)),f146(x90381,x90382)),f147(x90381,x90383)))+~P1(f315(f315(f223(f909(f908(x90381,x90381),a899)),x90382),x90383))
% 168.50/168.39 [9233]P39(x92331,x92332)+~P1(f315(f315(f317(x92331),x92333),f581(x92332,x92331)))+P1(f315(f315(f317(f908(x92331,x92331)),f315(f315(f240(x92331,x92331),f594(x92332,x92331,x92333)),x92333)),x92332))
% 168.50/168.39 [9268]~P1(f315(f54(x92681),x92682))+P1(f315(f54(f909(x92681,a899)),f315(f315(f53(x92681),x92682),x92683)))+~P1(f315(f315(f223(f909(f908(x92681,x92681),a899)),x92683),f315(f315(f242(x92681,x92681),x92682),f315(f18(f909(x92681,a899),x92681),x92682))))
% 168.50/168.39 [9304]P54(x93041,x93042,x93043)+P1(f315(f315(f317(x93041),f523(x93043,x93042,x93041)),x93042))+~P1(f315(f315(f223(f909(f908(x93041,x93041),a899)),x93043),f315(f315(f242(x93041,x93041),x93042),f315(f18(f909(x93041,a899),x93041),x93042))))
% 168.50/168.39 [9305]P54(x93051,x93052,x93053)+P1(f315(f315(f317(x93051),f527(x93052,x93053,x93051)),x93052))+~P1(f315(f315(f223(f909(f908(x93051,x93051),a899)),x93053),f315(f315(f242(x93051,x93051),x93052),f315(f18(f909(x93051,a899),x93051),x93052))))
% 168.50/168.39 [9340]~P68(x93401)+~P1(f315(f315(f224(x93401),x93402),x93403))+P1(f315(f315(f224(x93401),f315(f315(f279(x93401),f315(f315(f73(x93401),x93402),x93403)),f315(f315(f73(x93401),f71(x93401)),f71(x93401)))),x93403))
% 168.50/168.39 [9371]~P67(x93711)+P1(f315(f315(f223(x93711),x93712),x93713))+~P1(f315(f315(f223(x93711),f315(f315(f74(x93711),f861(x93713,x93712,x93711)),x93712)),x93713))
% 168.50/168.39 [9508]E(f315(f178(f902(f902(x95081))),f315(f125(f902(x95081),f315(f315(f10(a901,a899,f902(x95081)),f315(f224(a901),x95082)),f178(f902(x95081)))),f168(x95081,x95083))),f315(f178(f902(x95081)),f315(f315(f153(f902(x95081)),x95083),x95082)))+~P13(a901,f315(f157(a901),f315(f315(f143(f902(x95081),a901),f178(f902(x95081))),x95083)))+~P1(f315(f315(f224(a901),x95082),f315(f178(f902(f902(x95081))),x95083)))
% 168.50/168.39 [9631]~P39(x96311,x96312)+P27(x96311,f315(f315(f240(f909(f908(x96311,x96311),a899),f909(f908(x96311,x96311),a899)),x96312),x96313))+~P1(f315(f315(f223(f909(f908(x96311,x96311),a899)),f315(f315(f277(x96311,x96311,x96311),x96312),x96313)),x96312))
% 168.50/168.39 [9636]E(f315(f315(f143(f902(x96361),x96361),f315(f315(f9(f902(x96361),a901,x96361),f153(x96361)),x96362)),f315(f125(f902(x96361),f315(f315(f10(a901,a899,f902(x96361)),f315(f224(a901),x96362)),f178(f902(x96361)))),f168(x96361,x96363))),f315(f315(f153(f902(x96361)),x96363),x96362))+~P13(a901,f315(f157(a901),f315(f315(f143(f902(x96361),a901),f178(f902(x96361))),x96363)))+~P1(f315(f315(f224(a901),x96362),f315(f178(f902(f902(x96361))),x96363)))
% 168.50/168.39 [9771]P54(x97711,x97712,x97713)+~P1(f315(f315(f317(f908(x97711,x97711)),f315(f315(f240(x97711,x97711),f523(x97713,x97712,x97711)),f523(x97713,x97712,x97711))),x97713))+~P1(f315(f315(f223(f909(f908(x97711,x97711),a899)),x97713),f315(f315(f242(x97711,x97711),x97712),f315(f18(f909(x97711,a899),x97711),x97712))))
% 168.50/168.39 [9772]P54(x97721,x97722,x97723)+~P1(f315(f315(f317(f908(x97721,x97721)),f315(f315(f240(x97721,x97721),f527(x97722,x97723,x97721)),f527(x97722,x97723,x97721))),x97723))+~P1(f315(f315(f223(f909(f908(x97721,x97721),a899)),x97723),f315(f315(f242(x97721,x97721),x97722),f315(f18(f909(x97721,a899),x97721),x97722))))
% 168.50/168.39 [9940]~P143(x99401)+~P127(x99401)+E(f315(f315(f279(x99401),f315(f91(x99401),f315(f315(f66(f908(a1,a1),a1,x99402,f239(a1,a1)),f201(x99402)),x99403))),f315(f91(x99401),f315(f315(f66(f908(a1,a1),a1,x99402,f244(a1,a1)),f201(x99402)),x99403))),f211(x99402,x99401,x99403))
% 168.50/168.39 [10143]~E(x101433,f2(a901))+~E(f315(f178(f902(x101431)),f315(f315(f153(f902(x101431)),x101432),f695(x101433,x101431,x101432))),x101433)+E(f315(f315(f143(a901,f902(x101431)),f315(f315(f9(a901,f902(a901),f902(x101431)),f315(f315(f10(f909(a901,x101431),f909(f902(a901),f902(x101431)),a901),f143(a901,x101431)),f315(f9(a901,a901,x101431),f315(f315(f10(f902(x101431),f909(a901,x101431),a901),f153(x101431)),f315(f153(f902(x101431)),x101432))))),f128(a901,f315(f290(a901,f2(a901)),f315(f178(f902(f902(x101431))),x101432))))),f128(a901,f315(f290(a901,f2(a901)),x101433))),f168(x101431,x101432))
% 168.50/168.39 [10144]E(x101441,f102(f902(x101442)))+~E(f315(f178(f902(x101442)),f315(f315(f153(f902(x101442)),x101441),f695(x101443,x101442,x101441))),x101443)+E(f315(f315(f143(a901,f902(x101442)),f315(f315(f9(a901,f902(a901),f902(x101442)),f315(f315(f10(f909(a901,x101442),f909(f902(a901),f902(x101442)),a901),f143(a901,x101442)),f315(f9(a901,a901,x101442),f315(f315(f10(f902(x101442),f909(a901,x101442),a901),f153(x101442)),f315(f153(f902(x101442)),x101441))))),f128(a901,f315(f290(a901,f2(a901)),f315(f178(f902(f902(x101442))),x101441))))),f128(a901,f315(f290(a901,f2(a901)),x101443))),f168(x101442,x101441))
% 168.50/168.39 [10145]~E(x101453,f2(a901))+E(f315(f315(f143(a901,f902(x101451)),f315(f315(f9(a901,f902(a901),f902(x101451)),f315(f315(f10(f909(a901,x101451),f909(f902(a901),f902(x101451)),a901),f143(a901,x101451)),f315(f9(a901,a901,x101451),f315(f315(f10(f902(x101451),f909(a901,x101451),a901),f153(x101451)),f315(f153(f902(x101451)),x101452))))),f128(a901,f315(f290(a901,f2(a901)),f315(f178(f902(f902(x101451))),x101452))))),f128(a901,f315(f290(a901,f2(a901)),x101453))),f168(x101451,x101452))+P1(f315(f315(f224(a901),f695(x101453,x101451,x101452)),f315(f178(f902(f902(x101451))),x101452)))
% 168.50/168.39 [10146]E(x101461,f102(f902(x101462)))+E(f315(f315(f143(a901,f902(x101462)),f315(f315(f9(a901,f902(a901),f902(x101462)),f315(f315(f10(f909(a901,x101462),f909(f902(a901),f902(x101462)),a901),f143(a901,x101462)),f315(f9(a901,a901,x101462),f315(f315(f10(f902(x101462),f909(a901,x101462),a901),f153(x101462)),f315(f153(f902(x101462)),x101461))))),f128(a901,f315(f290(a901,f2(a901)),f315(f178(f902(f902(x101462))),x101461))))),f128(a901,f315(f290(a901,f2(a901)),x101463))),f168(x101462,x101461))+P1(f315(f315(f224(a901),f695(x101463,x101462,x101461)),f315(f178(f902(f902(x101462))),x101461)))
% 168.50/168.39 [7862]E(f315(f315(f73(a901),f315(f92(a901),x78621)),f315(f315(f73(a901),f315(f92(a901),x78622)),x78623)),f315(f315(f73(a901),f315(f92(a901),f315(f315(f73(a1),x78621),x78622))),x78623))+P1(f315(a182,f315(f92(a1),x78621)))+P1(f315(a182,f315(f92(a1),x78622)))
% 168.50/168.39 [8626]~P1(f315(f54(x86261),x86262))+~P1(f315(f315(f317(x86261),x86263),x86262))+E(f315(a101,f315(f28(x86261),f315(f315(f3(f909(x86261,a899)),x86262),f315(f315(f297(x86261),x86263),f177(f909(x86261,a899)))))),f315(f28(x86261),x86262))
% 168.50/168.39 [8642]~P1(f315(f54(x86421),x86422))+~P1(f315(f315(f317(x86421),x86423),x86422))+E(f315(f315(f73(a901),f71(a901)),f315(f28(x86421),f315(f315(f3(f909(x86421,a899)),x86422),f315(f315(f297(x86421),x86423),f177(f909(x86421,a899)))))),f315(f28(x86421),x86422))
% 168.50/168.39 [8729]~P110(x87291)+~P1(f315(f54(x87291),x87293))+E(f315(f315(f137(x87291,x87291,f7(x87291)),x87292),f128(x87291,f315(f315(f3(f909(x87291,a899)),x87293),f315(f315(f297(x87291),x87292),f177(f909(x87291,a899)))))),f128(x87291,f315(f315(f297(x87291),x87292),x87293)))
% 168.50/168.39 [8895]~P1(f315(f54(x88951),x88953))+~P1(f315(f54(x88951),x88952))+E(f315(f315(f73(a901),f315(f28(x88951),f315(f315(f99(f909(x88951,a899)),x88952),x88953))),f315(f28(x88951),f315(f315(f90(f909(x88951,a899)),x88952),x88953))),f315(f315(f73(a901),f315(f28(x88951),x88952)),f315(f28(x88951),x88953)))
% 168.50/168.39 [10092]~P25(x100921,f909(f909(x100921,a899),a899),f315(f315(f9(x100921,f909(f908(x100921,x100921),a899),f909(f909(x100921,a899),a899)),f315(f315(f10(f909(x100921,a899),f909(f909(f908(x100921,x100921),a899),f909(f909(x100921,a899),a899)),x100921),f53(x100921)),f315(f315(f9(x100921,f909(x100921,a899),f909(x100921,a899)),f297(x100921)),f177(f909(x100921,a899))))),x100923),x100922)+~P1(f315(f54(x100921),x100922))+E(f315(f28(f909(x100921,a899)),f315(f315(f53(x100921),x100922),x100923)),f315(f28(x100921),x100922))
% 168.50/168.39 [8131]~P97(x81311)+P1(f315(f315(f223(a1),f2(a1)),f315(f92(a1),x81313)))+E(f315(f315(f232(x81311),x81312),f315(f92(a901),f315(f315(f3(a1),f315(f315(f73(a1),x81313),x81313)),a86))),f71(x81311))
% 168.50/168.39 [9613]~P97(x96131)+~P1(f315(f315(f223(a1),f2(a1)),f315(f92(a1),x96133)))+E(f315(f315(f232(x96131),x96132),f315(f92(a901),f315(f315(f3(a1),f315(f315(f73(a1),x96133),x96133)),a86))),f315(f315(f79(x96131,x96131),f315(f315(f232(x96131),x96132),f315(f92(a901),x96133))),f315(f315(f20(x96131,x96131,x96131),f315(f315(f10(x96131,f909(x96131,x96131),x96131),f74(x96131)),f315(f74(x96131),x96132))),f7(x96131))))
% 168.50/168.39 [10002]~P1(f315(f126(x100021),x100023))+~P1(f315(f315(f317(x100021),x100022),f315(f161(x100021),x100023)))+E(f315(f315(f127(x100021),f315(f178(f902(x100021)),f166(x100021,f315(f315(f10(a899,a899,x100021),a310),f315(f315(f9(x100021,x100021,a899),a312),x100022)),f315(f157(x100021),x100023)))),f315(f157(x100021),x100023)),f315(f315(f140(x100021),x100022),f315(f157(x100021),f166(x100021,f315(f315(f10(a899,a899,x100021),a310),f315(f315(f9(x100021,x100021,a899),a312),x100022)),x100023))))
% 168.50/168.39 [10062]P1(f315(f315(f223(f909(f908(x100621,x100621),a899)),f295(x100621,x100622)),x100623))+~P1(f315(f315(f223(f909(f908(x100621,x100621),a899)),f295(x100621,f177(f909(f908(x100621,x100621),a899)))),x100623))+~P1(f315(f315(f223(f909(f908(x100621,x100621),a899)),f315(f315(f277(x100621,x100621,x100621),f315(f315(f90(f909(f908(x100621,x100621),a899)),f295(x100621,x100622)),x100623)),x100622)),x100623))
% 168.50/168.39 [9920]~P1(f315(f54(x99201),f315(f250(x99201),x99203)))+~P1(f315(f54(x99201),f315(f250(x99201),x99202)))+P1(f315(f54(x99201),f315(f250(x99201),f315(f315(f20(x99201,a899,a899),f315(f315(f10(a899,f909(a899,a899),x99201),a314),x99202)),x99203))))
% 168.50/168.39 [10207]P1(f315(f315(f223(f909(f908(x102071,x102071),a899)),f315(f315(f277(x102071,x102071,x102071),x102072),f295(x102071,x102072))),x102073))+~P1(f315(f315(f223(f909(f908(x102071,x102071),a899)),x102072),x102073))+~P1(f315(f315(f223(f909(f908(x102071,x102071),a899)),f315(f315(f277(x102071,x102071,x102071),f315(f315(f90(f909(f908(x102071,x102071),a899)),f315(f315(f277(x102071,x102071,x102071),x102072),f295(x102071,x102072))),x102073)),x102072)),x102073))
% 168.50/168.39 [10159]~P114(x101592)+E(x101591,f2(x101592))+~E(f315(f315(f73(x101592),f315(f315(f232(x101592),x101593),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))))),f315(f315(f232(x101592),x101591),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))))),f2(x101592))
% 168.50/168.39 [10160]~P114(x101602)+E(x101601,f2(x101602))+~E(f315(f315(f73(x101602),f315(f315(f232(x101602),x101601),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))))),f315(f315(f232(x101602),x101603),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))))),f2(x101602))
% 168.50/168.39 [10165]~P1(f315(f126(x101651),x101653))+~P1(f315(f315(f317(x101651),x101652),f315(f161(x101651),x101653)))+E(f315(f157(x101651),f315(f160(x101651),f315(f315(f127(x101651),f315(f178(f902(x101651)),f166(x101651,f315(f315(f10(a899,a899,x101651),a310),f315(f315(f9(x101651,x101651,a899),a312),x101652)),x101653))),x101653))),f166(x101651,f315(f315(f10(a899,a899,x101651),a310),f315(f315(f9(x101651,x101651,a899),a312),x101652)),f315(f157(x101651),x101653)))
% 168.50/168.39 [10252]~P114(x102522)+E(x102521,f2(x102522))+P1(f315(f315(f224(x102522),f2(x102522)),f315(f315(f73(x102522),f315(f315(f232(x102522),x102523),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))))),f315(f315(f232(x102522),x102521),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))))))
% 168.50/168.39 [10253]~P114(x102532)+E(x102531,f2(x102532))+P1(f315(f315(f224(x102532),f2(x102532)),f315(f315(f73(x102532),f315(f315(f232(x102532),x102531),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))))),f315(f315(f232(x102532),x102533),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))))))
% 168.50/168.39 [10314]~P114(x103141)+P1(f315(f315(f223(x103141),f2(x103141)),x103142))+~P1(f315(f315(f223(x103141),f2(x103141)),f315(f315(f232(x103141),x103142),f315(a101,f315(f315(f74(a901),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),x103143)))))
% 168.50/168.39 [5570]~P14(x55701,x55704,x55703)+P14(x55701,x55702,x55703)+~P14(x55701,x55702,x55704)
% 168.50/168.39 [5035]~E(x50352,f83(x50353,x50351))+P1(f315(x50351,x50352))+~P1(f315(x50351,x50354))
% 168.50/168.39 [5281]E(f61(x52813,x52812,x52814),x52812)+E(x52811,f720(x52812,x52813,x52814))+~P1(f315(x52814,x52811))
% 168.50/168.39 [6629]E(f61(x66291,x66292,x66293),f78(x66291,x66293))+~E(f757(x66292,x66291,x66293,x66294),x66294)+~P1(f315(x66293,x66294))
% 168.50/168.39 [6843]~P39(x68432,x68434)+~P39(x68431,x68433)+P39(f908(x68431,x68432),f307(x68431,x68432,x68433,x68434))
% 168.50/168.39 [6844]~P40(x68442,x68444)+~P40(x68441,x68443)+P40(f908(x68441,x68442),f307(x68441,x68442,x68443,x68444))
% 168.50/168.39 [5221]~P7(x52214,x52211)+~E(f315(x52211,x52212),f315(x52211,x52213))+P1(f315(f315(x52211,x52212),x52213))
% 168.50/168.39 [5382]~P7(x53824,x53821)+E(f315(x53821,x53822),f315(x53821,x53823))+~P1(f315(f315(x53821,x53822),x53823))
% 168.50/168.39 [5383]~P16(x53834,x53831)+E(f315(x53831,x53832),f315(x53831,x53833))+~P1(f315(f315(x53831,x53832),x53833))
% 168.50/168.39 [5476]~P19(x54763,x54764,x54761)+E(f315(x54761,x54762),f315(f56(x54763,x54764),x54762))+~P1(f315(f54(x54763),x54762))
% 168.50/168.39 [5477]~P9(x54773,x54774,x54771)+E(f315(x54771,x54772),f315(f56(x54773,x54774),x54772))+~P1(f315(f54(x54773),x54772))
% 168.50/168.39 [5605]~P7(x56054,x56051)+~P1(f315(f315(x56051,x56053),x56052))+P1(f315(f315(x56051,x56052),x56053))
% 168.50/168.39 [5606]~P52(x56064,x56061)+~P1(f315(f315(x56061,x56063),x56062))+P1(f315(f315(x56061,x56062),x56063))
% 168.50/168.39 [5607]~P16(x56074,x56071)+~P1(f315(f315(x56071,x56073),x56072))+P1(f315(f315(x56071,x56072),x56073))
% 168.50/168.39 [5608]~P16(x56083,x56081)+P1(f315(f315(x56081,x56082),x56082))+~P1(f315(f315(x56081,x56084),x56082))
% 168.50/168.39 [5609]~P16(x56093,x56091)+P1(f315(f315(x56091,x56092),x56092))+~P1(f315(f315(x56091,x56092),x56094))
% 168.50/168.39 [5681]E(x56811,x56812)+~E(f315(f239(x56813,x56814),x56811),f315(f239(x56813,x56814),x56812))+~E(f315(f244(x56813,x56814),x56811),f315(f244(x56813,x56814),x56812))
% 168.50/168.39 [5709]E(x57091,x57092)+~P1(f315(f41(x57093,x57094),x57092))+~P1(f315(f41(x57093,x57094),x57091))
% 168.50/168.39 [5909]~P72(x59092)+E(f220(x59091,x59092,x59093,x59094),f2(x59092))+P1(f315(f54(x59091),x59094))
% 168.50/168.39 [5957]~P7(x59573,x59572)+~P1(f315(x59571,x59574))+P1(f315(x59571,f802(x59571,x59572,x59573)))
% 168.50/168.39 [6054]~P1(f315(f303(x60541,x60542),x60544))+P1(f315(f303(x60541,x60542),x60543))+~P1(f315(f315(x60542,x60543),x60544))
% 168.50/168.39 [6881]~P31(x68811,x68813,x68814)+P1(f315(x68811,x68812))+~P1(f315(f315(f317(a1),x68812),f291(a1,x68813,x68814)))
% 168.50/168.39 [7076]~P7(x70761,x70763)+~P1(f315(x70762,x70764))+P1(f315(f315(f317(x70761),f802(x70762,x70763,x70761)),f258(x70761,x70763)))
% 168.50/168.39 [7971]E(x79711,f2(a901))+~P1(f315(x79712,x79713))+P1(f315(x79712,f752(x79712,x79713,x79711,x79714)))
% 168.50/168.39 [8053]~P110(x80532)+~P1(f315(f126(x80531),x80534))+P1(f315(f126(x80531),f139(x80531,x80532,x80533,x80534)))
% 168.50/168.39 [8097]E(f61(x80971,x80972,x80973),f78(x80971,x80973))+~P1(f315(x80973,x80974))+P1(f315(x80973,f757(x80972,x80971,x80973,x80974)))
% 168.50/168.39 [8282]~P1(f315(f54(x82822),x82824))+~P1(f315(f54(x82821),x82823))+P1(f315(f54(f907(x82821,x82822)),f301(x82821,x82822,x82823,x82824)))
% 168.50/168.39 [8283]~P1(f315(f126(x82832),x82834))+~P1(f315(f126(x82831),x82833))+P1(f315(f126(f908(x82831,x82832)),f52(x82831,x82832,x82833,x82834)))
% 168.50/168.39 [8286]P1(f315(f315(f317(f902(x82861)),f315(f315(f123(x82861),x82862),x82863)),f150(x82861,x82864)))+~P1(f315(f315(f317(f902(x82861)),x82863),f150(x82861,x82864)))+~P1(f315(f315(f317(f902(x82861)),x82862),f150(x82861,x82864)))
% 168.50/168.39 [8564]E(x85641,f2(a901))+P1(f315(x85642,x85643))+~P1(f315(x85642,f753(x85642,x85643,x85641,x85644)))
% 168.50/168.39 [8601]~P110(x86013)+~P1(f315(f126(x86011),f139(x86011,x86013,x86014,x86012)))+P1(f315(f126(x86011),x86012))
% 168.50/168.39 [8884]~P1(f315(f315(f317(f908(x88841,x88841)),f315(f315(f240(x88841,x88841),x88842),x88844)),f295(x88841,x88843)))+P1(f315(f315(f317(x88841),x88842),f304(x88841,x88843)))+~P1(f315(f315(f317(x88841),x88844),f304(x88841,x88843)))
% 168.50/168.39 [5205]~P72(x52052)+E(f315(f315(f8(x52051,x52052),x52053),x52054),f2(x52052))+P1(f315(f54(x52051),x52054))
% 168.50/168.39 [5208]~P77(x52082)+E(f315(f315(f11(x52081,x52082),x52083),x52084),f71(x52082))+P1(f315(f54(x52081),x52084))
% 168.50/168.39 [5344]~P73(x53443)+E(x53441,x53442)+~E(f315(f315(f73(x53443),x53444),x53441),f315(f315(f73(x53443),x53444),x53442))
% 168.50/168.39 [5345]~P74(x53453)+E(x53451,x53452)+~E(f315(f315(f73(x53453),x53454),x53451),f315(f315(f73(x53453),x53454),x53452))
% 168.50/168.39 [5347]~P73(x53473)+E(x53471,x53472)+~E(f315(f315(f73(x53473),x53471),x53474),f315(f315(f73(x53473),x53472),x53474))
% 168.50/168.39 [5443]~P124(x54431)+~E(x54433,f315(f315(f74(x54431),x54432),x54434))+P1(f315(f315(f275(x54431),x54432),x54433))
% 168.50/168.39 [5471]~P5(x54713)+E(x54711,f177(f909(x54712,a899)))+E(f315(f315(f32(x54712,x54713),x54711),f315(f18(x54713,x54712),x54714)),x54714)
% 168.50/168.39 [5472]~P5(x54723)+E(x54721,f177(f909(x54722,a899)))+E(f315(f315(f33(x54722,x54723),x54721),f315(f18(x54723,x54722),x54724)),x54724)
% 168.50/168.39 [5626]~E(x56264,f177(f909(x56261,a899)))+~E(x56264,f315(f315(f297(x56261),x56262),x56263))+P1(f315(f315(f317(x56261),x56262),x56263))
% 168.50/168.39 [5695]~P111(x56953)+E(x56951,x56952)+~E(f291(x56953,x56954,x56951),f315(f315(f297(x56953),x56952),f177(f909(x56953,a899))))
% 168.50/168.39 [5696]~P111(x56963)+E(x56961,x56962)+~E(f291(x56963,x56961,x56962),f315(f315(f297(x56963),x56964),f177(f909(x56963,a899))))
% 168.50/168.39 [5756]~P37(x57563,x57561,x57564)+P37(x57563,x57561,f315(f315(f140(x57563),x57562),x57564))+P1(f315(x57561,x57562))
% 168.50/168.39 [5858]~P33(x58581,x58582,x58584)+~P1(f315(x58582,x58583))+P33(x58581,x58582,f315(f315(f140(x58581),x58583),x58584))
% 168.50/168.39 [6009]P1(f315(x60091,x60092))+~P1(f315(f236(x60093,x60091),x60094))+~P1(f315(f315(f317(x60093),x60092),x60094))
% 168.50/168.39 [6018]~P33(x60181,x60182,x60184)+~P33(x60181,x60182,x60183)+P33(x60181,x60182,f315(f315(f123(x60181),x60183),x60184))
% 168.50/168.39 [6033]P35(x60331,x60332,x60333)+~P35(x60331,x60332,f315(f315(f140(x60331),x60334),x60333))+P1(f315(x60332,x60334))
% 168.50/168.39 [6034]P37(x60341,x60342,x60343)+~P37(x60341,x60342,f315(f315(f140(x60341),x60344),x60343))+P1(f315(x60342,x60344))
% 168.50/168.39 [6110]P35(x61101,x61102,x61103)+P35(x61101,x61102,x61104)+~P35(x61101,x61102,f315(f315(f123(x61101),x61104),x61103))
% 168.50/168.39 [6131]~P72(x61311)+E(f315(f315(f8(a901,x61311),x61312),f315(f290(a901,x61313),f315(a101,x61314))),f2(x61311))+~P1(f315(f315(f224(a901),x61314),x61313))
% 168.50/168.39 [6136]~P63(x61361)+~E(f38(x61361,x61362,x61363),f38(x61361,x61364,x61363))+E(f38(x61361,f315(f72(x61361),x61362),x61363),f38(x61361,f315(f72(x61361),x61364),x61363))
% 168.50/168.39 [6205]P1(f315(x62051,x62052))+~E(f315(f125(x62053,x62051),x62054),x62054)+~P1(f315(f315(f317(x62053),x62052),f315(f161(x62053),x62054)))
% 168.50/168.39 [6225]~E(f315(f315(f73(a901),x62253),x62252),f315(f315(f73(a901),x62251),x62254))+~P1(f315(f315(f224(a901),x62253),x62254))+P1(f315(f315(f224(a901),x62251),x62252))
% 168.50/168.39 [6231]P35(x62311,x62312,x62313)+~P1(f315(x62312,x62314))+~P1(f315(f315(f317(x62311),x62314),f315(f161(x62311),x62313)))
% 168.50/168.39 [6234]~P62(x62341)+E(f38(x62341,f38(x62341,x62342,x62343),x62344),f38(x62341,x62342,x62344))+~P1(f315(f315(f275(x62341),x62344),x62343))
% 168.50/168.39 [6274]~P33(x62743,x62741,x62744)+P1(f315(x62741,x62742))+~P1(f315(f315(f317(x62743),x62742),f315(f161(x62743),x62744)))
% 168.50/168.39 [6276]~E(f315(f125(x62761,x62762),x62763),f102(x62761))+~P1(f315(x62762,x62764))+~P1(f315(f315(f317(x62761),x62764),f315(f161(x62761),x62763)))
% 168.50/168.39 [6277]~E(f166(x62773,x62771,x62774),x62774)+P1(f315(x62771,x62772))+~P1(f315(f315(f317(x62773),x62772),f315(f161(x62773),x62774)))
% 168.50/168.39 [6304]~E(x63044,f177(f909(x63042,a899)))+~E(x63043,f177(f909(x63041,a899)))+E(f301(x63041,x63042,x63043,x63044),f177(f909(f907(x63041,x63042),a899)))
% 168.50/168.39 [6455]P1(f315(x64551,x64552))+~P1(f315(f149(x64553,x64551),x64554))+~P1(f315(f315(f317(x64553),x64552),f315(f161(x64553),x64554)))
% 168.50/168.39 [6598]~P32(x65981,x65983,x65984)+P1(f315(x65981,x65982))+~P1(f315(f315(f317(a901),x65982),f315(f290(a901,x65983),x65984)))
% 168.50/168.39 [6737]~P72(x67371)+E(f315(f315(f8(a901,x67371),x67372),f291(a901,x67373,f315(a101,x67374))),f2(x67371))+~P1(f315(f315(f224(a901),f315(a101,x67374)),x67373))
% 168.50/168.39 [6884]~P110(x68841)+E(f315(f315(f3(f909(x68841,a899)),f315(f290(x68841,x68842),x68843)),f315(f290(x68841,x68842),x68844)),f315(f290(x68841,x68844),x68843))+~P1(f315(f315(f223(x68841),x68842),x68844))
% 168.50/168.39 [6955]~E(x69553,x69554)+E(x69551,f2(a901))+P1(f315(f315(f317(x69552),x69553),f315(f161(x69552),f158(x69552,x69551,x69554))))
% 168.50/168.39 [7241]~P1(f315(f315(f317(f902(x72411)),x72414),f150(x72411,x72413)))+P1(f315(f315(f317(x72411),x72412),x72413))+~P1(f315(f315(f317(x72411),x72412),f315(f161(x72411),x72414)))
% 168.50/168.39 [7248]~P39(x72481,x72482)+P1(f315(f315(f317(x72481),f582(x72482,x72481,x72483)),x72483))+~P1(f315(f315(f317(x72481),x72484),x72483))
% 168.50/168.39 [7305]~P72(x73051)+E(f315(f315(f315(f58(x73051,x73052,f73(x73051)),x73053),f2(x73051)),x73054),f315(f315(f8(x73052,x73051),x73053),x73054))+~P1(f315(f54(x73052),x73054))
% 168.50/168.39 [7307]~P77(x73071)+E(f315(f315(f315(f58(x73071,x73072,f74(x73071)),x73073),f71(x73071)),x73074),f315(f315(f11(x73072,x73071),x73073),x73074))+~P1(f315(f54(x73072),x73074))
% 168.50/168.39 [7336]P25(x73361,x73362,x73363,x73364)+~E(f315(f28(x73362),f315(f298(x73361,x73362,x73363),x73364)),f315(f28(x73361),x73364))+~P1(f315(f54(x73361),x73364))
% 168.50/168.39 [7530]~P72(x75301)+E(f315(f315(f73(x75301),f315(x75302,x75303)),f315(f315(f8(a901,x75301),x75302),f293(a901,x75303,x75304))),f315(f315(f8(a901,x75301),x75302),f291(a901,x75303,x75304)))+~P1(f315(f315(f223(a901),x75303),x75304))
% 168.50/168.39 [7539]~P72(x75391)+~P25(x75392,x75391,x75393,x75394)+E(f315(f315(f8(x75391,x75391),f25(x75391)),f315(f298(x75392,x75391,x75393),x75394)),f315(f315(f8(x75392,x75391),x75393),x75394))
% 168.50/168.39 [7540]~P77(x75401)+~P25(x75402,x75401,x75403,x75404)+E(f315(f315(f11(x75401,x75401),f25(x75401)),f315(f298(x75402,x75401,x75403),x75404)),f315(f315(f11(x75402,x75401),x75403),x75404))
% 168.50/168.39 [7589]E(f315(f28(f907(x75891,x75892)),f301(x75891,x75892,x75893,x75894)),f315(f315(f73(a901),f315(f28(x75891),x75893)),f315(f28(x75892),x75894)))+~P1(f315(f54(x75892),x75894))+~P1(f315(f54(x75891),x75893))
% 168.50/168.39 [7672]E(x76721,x76722)+P1(f315(f315(f317(x76723),x76721),f315(f161(x76723),f159(x76723,x76722,x76724))))+~P1(f315(f315(f317(x76723),x76721),f315(f161(x76723),x76724)))
% 168.50/168.39 [7901]~P72(x79011)+E(f315(f315(f73(x79011),f315(f315(f8(a901,x79011),x79012),f315(f290(a901,x79013),x79014))),f315(x79012,x79014)),f315(f315(f8(a901,x79011),x79012),f315(f290(a901,x79013),f315(a101,x79014))))+P1(f315(f315(f224(a901),x79014),x79013))
% 168.50/168.39 [7951]~P25(x79511,x79512,x79513,f230(f909(x79511,a899)))+~P1(f315(f54(x79512),x79514))+P1(f315(f54(x79511),f315(f299(x79511,x79512,x79513),x79514)))
% 168.50/168.39 [8068]P1(f315(f315(f317(f902(x80681)),f315(f315(f140(x80681),x80682),x80683)),f150(x80681,x80684)))+~P1(f315(f315(f317(f902(x80681)),x80683),f150(x80681,x80684)))+~P1(f315(f315(f317(x80681),x80682),x80684))
% 168.50/168.39 [8155]~E(f315(f298(x81553,x81551,x81554),f230(f909(x81553,a899))),f230(f909(x81551,a899)))+P1(f315(f54(x81551),x81552))+~P1(f315(f54(x81553),f315(f299(x81553,x81551,x81554),x81552)))
% 168.50/168.39 [8252]~P25(x82521,x82523,x82524,x82522)+P1(f315(f54(x82521),x82522))+~P1(f315(f54(x82523),f315(f298(x82521,x82523,x82524),x82522)))
% 168.50/168.39 [8276]~E(x82762,x82763)+P1(f315(f315(f317(f908(x82761,x82761)),f315(f315(f240(x82761,x82761),x82762),x82763)),f251(x82761,x82764)))+~P1(f315(f315(f317(x82761),x82762),x82764))
% 168.50/168.39 [8309]~P72(x83091)+E(f315(f315(f73(x83091),f315(f315(f8(a901,x83091),x83092),f291(a901,x83093,x83094))),f315(x83092,f315(a101,x83094))),f315(f315(f8(a901,x83091),x83092),f291(a901,x83093,f315(a101,x83094))))+P1(f315(f315(f224(a901),f315(a101,x83094)),x83093))
% 168.50/168.39 [8369]P1(f315(x83691,x83692))+~P1(f315(x83691,f315(f315(f153(x83693),x83694),f644(x83691,x83694,x83693))))+~P1(f315(f315(f317(x83693),x83692),f315(f161(x83693),x83694)))
% 168.50/168.39 [8509]~P1(f315(f315(f317(x85091),x85092),f304(x85091,x85094)))+P1(f315(f315(f317(f902(x85091)),f315(f315(f140(x85091),x85092),x85093)),f304(f902(x85091),f146(x85091,x85094))))+~P1(f315(f315(f317(f902(x85091)),x85093),f304(f902(x85091),f146(x85091,x85094))))
% 168.50/168.39 [8524]~P25(x85242,x85243,x85244,f502(x85244,x85243,x85242,x85241))+P25(x85242,x85243,x85244,f31(f909(x85242,a899),x85241))+E(x85241,f177(f909(f909(x85242,a899),a899)))
% 168.50/168.39 [8793]E(x87931,x87932)+~P1(f315(f315(f317(f908(x87933,x87933)),f315(f315(f240(x87933,x87933),x87931),x87932)),f295(x87933,x87934)))+P1(f315(f315(f317(x87933),x87931),f315(f252(x87933,x87933),x87934)))
% 168.50/168.39 [9072]E(x90721,f2(a901))+P1(f315(x90722,x90723))+P1(f315(f315(f317(x90724),f753(x90722,x90723,x90721,x90724)),f315(f161(x90724),f158(x90724,x90721,x90723))))
% 168.50/168.39 [9084]E(x90841,f2(a901))+~P1(f315(x90843,x90844))+P1(f315(f315(f317(x90842),f752(x90843,x90844,x90841,x90842)),f315(f161(x90842),f158(x90842,x90841,x90844))))
% 168.50/168.39 [9086]~P26(x90861,x90862,x90863,f230(f909(x90861,a899)),f230(f909(x90862,a899)))+~P1(f315(f54(x90862),x90864))+P1(f315(f54(x90861),f315(f299(x90861,x90862,x90863),x90864)))
% 168.50/168.39 [9089]P25(x90892,x90893,x90894,f31(f909(x90892,a899),x90891))+E(x90891,f177(f909(f909(x90892,a899),a899)))+P1(f315(f315(f317(f909(x90892,a899)),f502(x90894,x90893,x90892,x90891)),x90891))
% 168.50/168.39 [9204]~P26(x92043,x92041,x92044,f230(f909(x92043,a899)),f230(f909(x92041,a899)))+P1(f315(f54(x92041),x92042))+~P1(f315(f54(x92043),f315(f299(x92043,x92041,x92044),x92042)))
% 168.50/168.39 [9221]P1(f315(f54(x92211),x92212))+~P1(f315(f54(x92214),f315(f298(x92211,x92214,x92213),x92212)))+P1(f315(f315(f317(x92211),f560(x92213,x92214,x92212,x92211)),x92212))
% 168.50/168.39 [9316]~P5(x93162)+E(f315(f315(f57(x93161,x93162,f315(f315(f10(x93162,f909(x93162,x93162),x93161),f90(x93162)),x93163)),f230(x93162)),x93164),f315(f315(f32(x93161,x93162),x93164),x93163))+~P1(f315(f54(x93161),x93164))
% 168.50/168.39 [9317]~P5(x93172)+E(f315(f315(f57(x93171,x93172,f315(f315(f10(x93172,f909(x93172,x93172),x93171),f99(x93172)),x93173)),f177(x93172)),x93174),f315(f315(f33(x93171,x93172),x93174),x93173))+~P1(f315(f54(x93171),x93174))
% 168.50/168.39 [9347]~P1(f315(f315(f275(a901),x93473),x93474))+P1(f315(f315(f275(a901),x93471),x93472))+P1(f315(f315(f224(f909(a901,a899)),f278(a901,f275(a901),x93471,x93472)),f278(a901,f275(a901),x93473,x93474)))
% 168.50/168.39 [9360]~P1(f315(f315(f275(a901),x93602),x93604))+~P1(f315(f315(f275(a901),x93603),x93601))+P1(f315(f315(f223(f909(a901,a899)),f278(a901,f275(a901),x93601,x93602)),f278(a901,f275(a901),x93603,x93604)))
% 168.50/168.39 [9403]P1(f315(x94031,x94032))+~P1(f315(x94031,f315(f315(f153(x94033),x94034),f680(x94032,x94031,x94034,x94033))))+~P1(f315(f315(f317(x94033),x94032),f315(f161(x94033),x94034)))
% 168.50/168.39 [9424]E(x94241,x94242)+~P1(f315(f315(f317(f908(x94243,x94243)),f315(f315(f240(x94243,x94243),x94241),x94242)),f295(x94243,x94244)))+P1(f315(f315(f317(f908(x94243,x94243)),f315(f315(f240(x94243,x94243),x94241),x94242)),f315(f315(f277(x94243,x94243,x94243),x94244),f295(x94243,x94244))))
% 168.50/168.39 [9474]~E(f315(f178(f902(x94741)),x94742),f315(f178(f902(x94741)),x94743))+~P1(f315(f315(f317(f908(f902(x94741),f902(x94741))),f315(f315(f240(f902(x94741),f902(x94741)),x94742),x94743)),f136(x94741,x94744)))+P1(f315(f315(f317(f908(f902(x94741),f902(x94741))),f315(f315(f240(f902(x94741),f902(x94741)),x94742),x94743)),f134(x94741,x94744)))
% 168.50/168.39 [9597]P1(f315(f315(f275(a901),x95971),x95972))+~P1(f315(f315(f275(a901),x95973),x95971))+~P1(f315(f315(f223(f909(a901,a899)),f278(a901,f275(a901),x95973,x95971)),f278(a901,f275(a901),x95974,x95972)))
% 168.50/168.39 [9598]P1(f315(f315(f275(a901),x95981),x95982))+~P1(f315(f315(f275(a901),x95983),x95981))+~P1(f315(f315(f224(f909(a901,a899)),f278(a901,f275(a901),x95983,x95981)),f278(a901,f275(a901),x95984,x95982)))
% 168.50/168.39 [9599]P1(f315(f315(f275(a901),x95991),x95992))+~P1(f315(f315(f275(a901),x95992),x95993))+~P1(f315(f315(f223(f909(a901,a899)),f278(a901,f275(a901),x95992,x95993)),f278(a901,f275(a901),x95991,x95994)))
% 168.50/168.39 [9600]P1(f315(f315(f275(a901),x96001),x96002))+~P1(f315(f315(f275(a901),x96002),x96003))+~P1(f315(f315(f224(f909(a901,a899)),f278(a901,f275(a901),x96002,x96003)),f278(a901,f275(a901),x96001,x96004)))
% 168.50/168.39 [9719]P33(x97191,f315(f315(f20(x97191,a899,a899),f315(f315(f10(a899,f909(a899,a899),x97191),a314),f315(f315(f10(a899,a899,x97191),a310),x97192))),f315(a312,x97193)),x97194)+~P1(f315(x97192,x97193))+~P37(x97191,x97192,f315(f315(f140(x97191),x97193),x97194))
% 168.50/168.39 [9884]~P33(x98841,f315(f315(f20(x98841,a899,a899),f315(f315(f10(a899,f909(a899,a899),x98841),a314),f315(f315(f10(a899,a899,x98841),a310),x98842))),f315(a312,x98843)),x98844)+~P1(f315(x98842,x98843))+P37(x98841,x98842,f315(f315(f140(x98841),x98843),x98844))
% 168.50/168.39 [9888]~P37(x98881,x98882,x98884)+~P33(x98881,f315(f315(f20(x98881,a899,a899),f315(f315(f10(a899,f909(a899,a899),x98881),a314),f315(f315(f10(a899,a899,x98881),a310),x98882))),f315(a312,x98883)),x98884)+P37(x98881,x98882,f315(f315(f140(x98881),x98883),x98884))
% 168.50/168.39 [9921]~P69(x99211)+E(f315(f315(f8(a901,x99211),f315(f315(f20(a901,x99211,x99211),f315(f315(f10(x99211,f909(x99211,x99211),a901),f3(x99211)),x99212)),f315(f315(f10(a901,x99211,a901),x99212),f315(f315(f9(a901,a901,a901),f73(a901)),f71(a901))))),f291(a901,x99213,x99214)),f2(x99211))+P1(f315(f315(f223(a901),x99213),x99214))
% 168.50/168.39 [10158]~P39(x101582,x101584)+~P25(x101582,x101581,x101583,f230(f909(x101582,a899)))+P39(x101581,f315(f298(f908(x101582,x101582),f908(x101581,x101581),f246(x101582,x101581,x101582,x101581,x101583,x101583)),x101584))
% 168.50/168.39 [10349]~E(f315(f178(f902(x103491)),x103493),f315(f178(f902(x103491)),x103492))+P1(f315(f315(f317(f908(f902(x103491),f902(x103491))),f315(f315(f240(f902(x103491),f902(x103491)),x103492),x103493)),f147(x103491,x103494)))+~P1(f315(f315(f245(x103491,x103491,a899),f315(f315(f9(x103491,f909(f908(x103491,x103491),a899),f909(x103491,a899)),f315(f315(f10(f909(x103491,f909(f909(f908(x103491,x103491),a899),a899)),f909(f909(f908(x103491,x103491),a899),f909(x103491,a899)),x103491),f9(x103491,f909(f908(x103491,x103491),a899),a899)),f315(f315(f10(f909(x103491,f908(x103491,x103491)),f909(x103491,f909(f909(f908(x103491,x103491),a899),a899)),x103491),f315(f10(f908(x103491,x103491),f909(f909(f908(x103491,x103491),a899),a899),x103491),f317(f908(x103491,x103491)))),f240(x103491,x103491)))),x103494)),f646(x103494,x103493,x103492,x103491)))
% 168.50/168.39 [6186]~P62(x61861)+~E(x61862,f2(x61861))+E(f315(f315(f29(x61861),f315(f315(f74(x61861),x61862),x61863)),f315(f315(f74(x61861),x61862),x61864)),f2(x61861))
% 168.50/168.39 [6228]E(x62281,f102(x62282))+E(x62283,f315(f315(f3(a901),f315(f178(f902(x62282)),x62281)),f71(a901)))+E(f133(x62282,f315(f315(f148(x62282,x62281),x62283),x62284)),f133(x62282,x62281))
% 168.50/168.39 [6265]E(x62651,x62652)+P1(f315(x62653,x62652))+~P1(f315(f315(f315(f297(x62654),x62651),x62653),x62652))
% 168.50/168.39 [6281]~P72(x62811)+~P1(f315(f126(x62812),x62814))+E(f315(f154(x62811),f315(f315(f143(x62812,x62811),x62813),x62814)),f315(f315(f8(x62812,x62811),x62813),f315(f161(x62812),x62814)))
% 168.50/168.39 [6297]~P77(x62972)+~P1(f315(f54(x62971),x62974))+E(f315(f315(f11(x62971,x62972),f315(f18(x62972,x62971),x62973)),x62974),f315(f315(f232(x62972),x62973),f315(f28(x62971),x62974)))
% 168.50/168.39 [6351]~P65(x63512)+E(x63511,f2(x63512))+E(f315(f315(f279(x63512),f315(f315(f74(x63512),x63513),x63511)),f315(f315(f74(x63512),x63514),x63511)),f315(f315(f279(x63512),x63513),x63514))
% 168.50/168.39 [6352]~P65(x63522)+E(x63521,f2(x63522))+E(f315(f315(f279(x63522),f315(f315(f74(x63522),x63521),x63523)),f315(f315(f74(x63522),x63521),x63524)),f315(f315(f279(x63522),x63523),x63524))
% 168.50/168.39 [6353]~P62(x63532)+E(x63531,f2(x63532))+E(f315(f315(f29(x63532),f315(f315(f74(x63532),x63533),x63531)),f315(f315(f74(x63532),x63534),x63531)),f315(f315(f29(x63532),x63533),x63534))
% 168.50/168.39 [6355]~P62(x63552)+E(x63551,f2(x63552))+E(f315(f315(f29(x63552),f315(f315(f74(x63552),x63551),x63553)),f315(f315(f74(x63552),x63551),x63554)),f315(f315(f29(x63552),x63553),x63554))
% 168.50/168.39 [6423]P1(f315(x64231,x64232))+~E(x64233,f315(f315(f73(a901),x64234),x64232))+~P1(f315(x64231,f315(f315(f3(a901),x64233),x64234)))
% 168.50/168.39 [6507]P29(x65071,x65072,x65073)+P28(x65071,f649(x65073,x65072,x65071),x65074)+~P1(f315(f315(f317(f900(x65071)),x65074),x65072))
% 168.50/168.39 [6511]~P1(f315(x65112,x65113))+~P1(f315(f149(x65111,x65112),x65114))+P1(f315(f149(x65111,x65112),f315(f315(f140(x65111),x65113),x65114)))
% 168.50/168.39 [6553]E(x65531,f102(x65532))+~E(x65533,f315(f315(f3(a901),f315(f178(f902(x65532)),x65531)),f71(a901)))+E(f133(x65532,f315(f315(f148(x65532,x65531),x65533),x65534)),x65534)
% 168.50/168.39 [6576]~P103(x65761)+~P1(f315(f315(f223(x65761),x65762),x65764))+P1(f315(f315(f223(x65761),x65762),f315(f315(f99(x65761),x65763),x65764)))
% 168.50/168.39 [6577]~P103(x65771)+~P1(f315(f315(f223(x65771),x65772),x65773))+P1(f315(f315(f223(x65771),x65772),f315(f315(f99(x65771),x65773),x65774)))
% 168.50/168.39 [6579]~P110(x65791)+~P1(f315(f315(f223(x65791),x65792),x65794))+P1(f315(f315(f223(x65791),x65792),f315(f315(f222(x65791),x65793),x65794)))
% 168.50/168.39 [6581]~P110(x65811)+~P1(f315(f315(f223(x65811),x65812),x65813))+P1(f315(f315(f223(x65811),x65812),f315(f315(f222(x65811),x65813),x65814)))
% 168.50/168.39 [6582]~P103(x65821)+~P1(f315(f315(f224(x65821),x65822),x65824))+P1(f315(f315(f224(x65821),x65822),f315(f315(f99(x65821),x65823),x65824)))
% 168.50/168.39 [6583]~P103(x65831)+~P1(f315(f315(f224(x65831),x65832),x65833))+P1(f315(f315(f224(x65831),x65832),f315(f315(f99(x65831),x65833),x65834)))
% 168.50/168.39 [6585]~P110(x65851)+~P1(f315(f315(f224(x65851),x65852),x65854))+P1(f315(f315(f224(x65851),x65852),f315(f315(f222(x65851),x65853),x65854)))
% 168.50/168.39 [6587]~P110(x65871)+~P1(f315(f315(f224(x65871),x65872),x65873))+P1(f315(f315(f224(x65871),x65872),f315(f315(f222(x65871),x65873),x65874)))
% 168.50/168.39 [6588]~P121(x65881)+~P1(f315(f315(f275(x65881),x65882),x65884))+P1(f315(f315(f275(x65881),x65882),f315(f315(f74(x65881),x65883),x65884)))
% 168.50/168.39 [6589]~P121(x65891)+~P1(f315(f315(f275(x65891),x65892),x65893))+P1(f315(f315(f275(x65891),x65892),f315(f315(f74(x65891),x65893),x65894)))
% 168.50/168.39 [6681]~E(f315(f315(f153(x66811),x66812),x66813),x66814)+E(f315(f315(f148(x66811,x66812),x66813),x66814),x66812)+~P1(f315(f315(f224(a901),x66813),f315(f178(f902(x66811)),x66812)))
% 168.50/168.39 [6721]P1(f315(x67211,x67212))+~P1(f315(x67213,x67212))+~P1(f315(f315(f223(f909(x67214,a899)),x67213),x67211))
% 168.50/168.39 [6756]~E(f315(f315(f148(x67561,x67562),x67563),x67564),x67562)+E(f315(f315(f153(x67561),x67562),x67563),x67564)+~P1(f315(f315(f224(a901),x67563),f315(f178(f902(x67561)),x67562)))
% 168.50/168.39 [6770]~P1(f315(f149(x67701,x67702),x67704))+~P1(f315(f149(x67701,x67702),x67703))+P1(f315(f149(x67701,x67702),f315(f315(f123(x67701),x67703),x67704)))
% 168.50/168.39 [6873]P28(x68731,x68732,x68733)+~P28(x68731,f315(a101,x68732),f853(x68732,x68734,x68731))+~P1(f315(f315(f317(f900(x68731)),x68733),x68734))
% 168.50/168.39 [6880]E(x68801,f177(f909(x68802,a899)))+E(x68803,f177(f909(x68804,a899)))+~E(f315(f315(f242(x68804,x68802),x68803),f315(f18(f909(x68802,a899),x68804),x68801)),f177(f909(f908(x68804,x68802),a899)))
% 168.50/168.39 [6900]E(x69001,x69002)+P1(f315(f315(f317(x69003),x69001),x69004))+~P1(f315(f315(f317(x69003),x69001),f315(f315(f297(x69003),x69002),x69004)))
% 168.50/168.39 [6917]~P110(x69171)+P1(f315(f315(f223(x69171),x69172),x69173))+~P1(f315(f315(f223(x69171),x69172),f315(f315(f221(x69171),x69174),x69173)))
% 168.50/168.39 [6919]~P110(x69191)+P1(f315(f315(f223(x69191),x69192),x69193))+~P1(f315(f315(f223(x69191),x69192),f315(f315(f221(x69191),x69193),x69194)))
% 168.50/168.39 [6921]~P104(x69211)+P1(f315(f315(f223(x69211),x69212),x69213))+~P1(f315(f315(f223(x69211),x69212),f315(f315(f90(x69211),x69214),x69213)))
% 168.50/168.39 [6923]~P104(x69231)+P1(f315(f315(f223(x69231),x69232),x69233))+~P1(f315(f315(f223(x69231),x69232),f315(f315(f90(x69231),x69233),x69234)))
% 168.50/168.39 [6924]~P110(x69241)+P1(f315(f315(f224(x69241),x69242),x69243))+~P1(f315(f315(f224(x69241),x69242),f315(f315(f221(x69241),x69244),x69243)))
% 168.50/168.39 [6925]~P110(x69251)+P1(f315(f315(f224(x69251),x69252),x69253))+~P1(f315(f315(f224(x69251),x69252),f315(f315(f221(x69251),x69253),x69254)))
% 168.50/168.39 [6946]~E(f315(f315(f153(x69461),x69463),x69464),x69462)+P1(f315(f315(f317(x69461),x69462),f315(f161(x69461),x69463)))+~P1(f315(f315(f224(a901),x69464),f315(f178(f902(x69461)),x69463)))
% 168.50/168.39 [6956]~P110(x69561)+~P13(x69561,f315(f315(f140(x69561),x69562),f315(f315(f140(x69561),x69563),x69564)))+P1(f315(f315(f223(x69561),x69562),x69563))
% 168.50/168.39 [7105]~P33(x71052,x71051,x71053)+P1(f315(x71051,f315(f315(f153(x71052),x71053),x71054)))+~P1(f315(f315(f224(a901),x71054),f315(f178(f902(x71052)),x71053)))
% 168.50/168.39 [7123]E(x71231,f2(a1))+E(f315(f315(f29(a1),x71232),x71231),x71233)+~P1(f315(f42(x71232,x71231),f315(f315(f240(a1,a1),x71233),x71234)))
% 168.50/168.39 [7145]E(f38(a1,x71452,x71451),x71453)+E(x71451,f2(a1))+~P1(f315(f42(x71452,x71451),f315(f315(f240(a1,a1),x71454),x71453)))
% 168.50/168.39 [7265]P1(f315(f315(f317(x72651),x72652),x72653))+~P1(f315(f315(f317(x72651),x72652),x72654))+~P1(f315(f315(f224(f909(x72651,a899)),x72654),x72653))
% 168.50/168.39 [7266]P1(f315(f315(f317(x72661),x72662),x72663))+~P1(f315(f315(f317(x72661),x72662),x72664))+~P1(f315(f315(f223(f909(x72661,a899)),x72664),x72663))
% 168.50/168.39 [7277]~P123(x72771)+~E(x72773,f2(x72771))+P1(f315(f315(f275(x72771),f315(f315(f74(x72771),x72772),x72773)),f315(f315(f74(x72771),x72774),x72773)))
% 168.50/168.39 [7278]~P123(x72781)+~E(x72782,f2(x72781))+P1(f315(f315(f275(x72781),f315(f315(f74(x72781),x72782),x72783)),f315(f315(f74(x72781),x72782),x72784)))
% 168.50/168.39 [7380]P35(x73801,x73802,x73803)+~P1(f315(x73802,f315(f315(f153(x73801),x73803),x73804)))+~P1(f315(f315(f224(a901),x73804),f315(f178(f902(x73801)),x73803)))
% 168.50/168.39 [7495]~P109(x74952)+~P1(f315(f315(f224(f909(x74951,x74952)),x74953),x74954))+P1(f315(f315(f223(f909(x74951,x74952)),x74953),x74954))
% 168.50/168.39 [7578]~P14(x75781,x75782,x75784)+P14(x75781,x75782,f315(f315(f297(f900(x75781)),x75783),x75784))+~P14(x75781,x75782,f315(f315(f297(f900(x75781)),x75783),f177(f909(f900(x75781),a899))))
% 168.50/168.39 [7620]~P1(f315(f315(f317(x76201),x76202),x76204))+P1(f315(f315(f317(x76201),x76202),f30(f909(x76201,a899),x76203)))+~P1(f315(f315(f317(f909(x76201,a899)),x76204),x76203))
% 168.50/168.39 [7622]~P121(x76221)+~P1(f315(f315(f223(a901),x76223),x76224))+P1(f315(f315(f275(x76221),f315(f315(f232(x76221),x76222),x76223)),f315(f315(f232(x76221),x76222),x76224)))
% 168.50/168.39 [7631]P28(x76311,x76312,x76313)+P1(f315(f315(f317(f900(x76311)),f853(x76312,x76314,x76311)),x76314))+~P1(f315(f315(f317(f900(x76311)),x76313),x76314))
% 168.50/168.39 [7649]~P87(x76491)+~P1(f315(f315(f223(x76491),x76493),x76494))+P1(f315(f315(f223(x76491),f315(f315(f73(x76491),x76492),x76493)),f315(f315(f73(x76491),x76492),x76494)))
% 168.50/168.39 [7650]~P88(x76501)+~P1(f315(f315(f223(x76501),x76503),x76504))+P1(f315(f315(f223(x76501),f315(f315(f73(x76501),x76502),x76503)),f315(f315(f73(x76501),x76502),x76504)))
% 168.50/168.39 [7651]~P87(x76511)+~P1(f315(f315(f223(x76511),x76512),x76514))+P1(f315(f315(f223(x76511),f315(f315(f73(x76511),x76512),x76513)),f315(f315(f73(x76511),x76514),x76513)))
% 168.50/168.39 [7652]~P88(x76521)+~P1(f315(f315(f223(x76521),x76522),x76524))+P1(f315(f315(f223(x76521),f315(f315(f73(x76521),x76522),x76523)),f315(f315(f73(x76521),x76524),x76523)))
% 168.50/168.39 [7653]~P86(x76531)+~P1(f315(f315(f224(x76531),x76533),x76534))+P1(f315(f315(f224(x76531),f315(f315(f73(x76531),x76532),x76533)),f315(f315(f73(x76531),x76532),x76534)))
% 168.50/168.39 [7654]~P87(x76541)+~P1(f315(f315(f224(x76541),x76543),x76544))+P1(f315(f315(f224(x76541),f315(f315(f73(x76541),x76542),x76543)),f315(f315(f73(x76541),x76542),x76544)))
% 168.50/168.39 [7655]~P86(x76551)+~P1(f315(f315(f224(x76551),x76552),x76554))+P1(f315(f315(f224(x76551),f315(f315(f73(x76551),x76552),x76553)),f315(f315(f73(x76551),x76554),x76553)))
% 168.50/168.39 [7656]~P87(x76561)+~P1(f315(f315(f224(x76561),x76562),x76564))+P1(f315(f315(f224(x76561),f315(f315(f73(x76561),x76562),x76563)),f315(f315(f73(x76561),x76564),x76563)))
% 168.50/168.39 [7657]~P123(x76571)+~P1(f315(f315(f275(x76571),x76573),x76574))+P1(f315(f315(f275(x76571),f315(f315(f74(x76571),x76572),x76573)),f315(f315(f74(x76571),x76572),x76574)))
% 168.50/168.39 [7658]~P123(x76581)+~P1(f315(f315(f275(x76581),x76582),x76584))+P1(f315(f315(f275(x76581),f315(f315(f74(x76581),x76582),x76583)),f315(f315(f74(x76581),x76584),x76583)))
% 168.50/168.39 [7659]~P121(x76591)+~P1(f315(f315(f275(x76591),x76592),x76594))+P1(f315(f315(f275(x76591),f315(f315(f232(x76591),x76592),x76593)),f315(f315(f232(x76591),x76594),x76593)))
% 168.50/168.39 [7666]~P112(x76661)+~P96(x76661)+E(f315(f315(f3(x76661),f315(f315(f74(x76661),x76662),f315(f92(x76661),x76663))),f315(f315(f74(x76661),x76664),f315(f92(x76661),x76663))),f315(f315(f74(x76661),f315(f315(f3(x76661),x76662),x76664)),f315(f92(x76661),x76663)))
% 168.50/168.39 [7667]~P141(x76671)+~P96(x76671)+E(f315(f315(f73(x76671),f315(f315(f74(x76671),x76672),f315(f92(x76671),x76673))),f315(f315(f74(x76671),x76674),f315(f92(x76671),x76673))),f315(f315(f74(x76671),f315(f315(f73(x76671),x76672),x76674)),f315(f92(x76671),x76673)))
% 168.50/168.39 [7703]~P72(x77031)+E(f315(f315(f73(x77031),f315(x77032,x77033)),f315(f315(f8(a901,x77031),x77032),f291(a901,f315(a101,x77033),x77034))),f315(f315(f8(a901,x77031),x77032),f291(a901,x77033,x77034)))+~P1(f315(f315(f223(a901),x77033),x77034))
% 168.50/168.39 [7715]~P25(x77152,x77151,x77153,f315(f161(x77152),x77154))+~P1(f315(f126(x77152),x77154))+P1(f315(f126(x77151),f315(f315(f143(x77152,x77151),x77153),x77154)))
% 168.50/168.39 [7764]~P1(f315(f315(f223(a901),x77642),x77644))+~P1(f315(f315(f223(a901),x77641),x77643))+P1(f315(f315(f223(a901),f315(f315(f74(a901),x77641),x77642)),f315(f315(f74(a901),x77643),x77644)))
% 168.50/168.39 [7765]~P1(f315(f315(f223(a901),x77652),x77654))+~P1(f315(f315(f223(a901),x77651),x77653))+P1(f315(f315(f223(a901),f315(f315(f73(a901),x77651),x77652)),f315(f315(f73(a901),x77653),x77654)))
% 168.50/168.39 [7768]~P1(f315(f315(f224(a901),x77682),x77684))+~P1(f315(f315(f224(a901),x77681),x77683))+P1(f315(f315(f224(a901),f315(f315(f73(a901),x77681),x77682)),f315(f315(f73(a901),x77683),x77684)))
% 168.50/168.39 [7769]~P1(f315(f315(f223(a1),x77692),x77694))+~P1(f315(f315(f224(a1),x77691),x77693))+P1(f315(f315(f224(a1),f315(f315(f73(a1),x77691),x77692)),f315(f315(f73(a1),x77693),x77694)))
% 168.50/168.39 [7817]P1(f315(f315(f317(x78171),x78172),x78173))+~P1(f315(f315(f317(x78171),x78172),f31(f909(x78171,a899),x78174)))+~P1(f315(f315(f317(f909(x78171,a899)),x78173),x78174))
% 168.50/168.39 [7834]~P1(f315(x78341,f641(x78341,x78343,x78342)))+P1(f315(x78341,f315(f315(f153(x78342),x78343),x78344)))+~P1(f315(f315(f224(a901),x78344),f315(f178(f902(x78342)),x78343)))
% 168.50/168.39 [7839]P1(f315(x78391,x78392))+~P1(f315(f315(f317(x78394),x78392),f315(f161(x78394),x78393)))+P1(f315(f315(f224(a901),f644(x78391,x78393,x78394)),f315(f178(f902(x78394)),x78393)))
% 168.50/168.39 [7886]~P109(x78861)+~P1(f315(f315(f224(f909(x78862,x78861)),x78864),x78863))+~P1(f315(f315(f223(f909(x78862,x78861)),x78863),x78864))
% 168.50/168.39 [7930]~P1(f315(x79304,x79302))+~P1(f315(f315(f317(x79301),x79302),x79303))+P1(f315(f315(f317(x79301),x79302),f315(f315(f90(f909(x79301,a899)),x79303),f315(f250(x79301),x79304))))
% 168.50/168.39 [8075]~P1(f315(f315(f317(x80751),x80753),x80754))+~P1(f315(f315(f224(f909(x80751,a899)),x80752),x80754))+P1(f315(f315(f224(f909(x80751,a899)),x80752),f315(f315(f297(x80751),x80753),x80754)))
% 168.50/168.39 [8077]E(f315(f315(f90(f909(x80771,a899)),x80772),x80773),f177(f909(x80771,a899)))+~E(f315(f315(f90(f909(x80771,a899)),f30(f909(x80771,a899),x80774)),x80773),f177(f909(x80771,a899)))+~P1(f315(f315(f317(f909(x80771,a899)),x80772),x80774))
% 168.50/168.39 [8151]P1(f315(f315(f317(x81511),x81512),x81513))+~P1(f315(f315(f223(f909(x81511,a899)),x81513),f315(f315(f297(x81511),x81512),x81514)))+P1(f315(f315(f223(f909(x81511,a899)),x81513),x81514))
% 168.50/168.39 [8168]P1(f315(f315(f317(x81682),f641(x81681,x81683,x81682)),f315(f161(x81682),x81683)))+P1(f315(x81681,f315(f315(f153(x81682),x81683),x81684)))+~P1(f315(f315(f224(a901),x81684),f315(f178(f902(x81682)),x81683)))
% 168.50/168.39 [8177]~P1(f315(f315(f223(f909(x81771,a899)),x81772),x81774))+P1(f315(f315(f223(f909(x81771,a899)),x81772),x81773))+~P1(f315(f315(f223(f909(x81771,a899)),x81774),x81773))
% 168.50/168.39 [8178]~P1(f315(f315(f224(f909(x81781,a899)),x81782),x81784))+~P1(f315(f315(f223(f909(x81781,a899)),x81784),x81783))+P1(f315(f315(f224(f909(x81781,a899)),x81782),x81783))
% 168.50/168.39 [8179]~P1(f315(f315(f223(f909(x81791,a899)),x81792),x81794))+~P1(f315(f315(f224(f909(x81791,a899)),x81794),x81793))+P1(f315(f315(f224(f909(x81791,a899)),x81792),x81793))
% 168.50/168.39 [8180]~P1(f315(f315(f224(f909(x81801,a899)),x81802),x81804))+P1(f315(f315(f224(f909(x81801,a899)),x81802),x81803))+~P1(f315(f315(f224(f909(x81801,a899)),x81804),x81803))
% 168.50/168.39 [8224]~P1(f315(f315(f317(x82241),x82244),x82243))+~P1(f315(f315(f224(f909(x82241,a899)),x82242),f315(f315(f297(x82241),x82244),x82243)))+P1(f315(f315(f224(f909(x82241,a899)),x82242),x82243))
% 168.50/168.39 [8235]~P87(x82351)+P1(f315(f315(f223(x82351),x82352),x82353))+~P1(f315(f315(f223(x82351),f315(f315(f73(x82351),x82354),x82352)),f315(f315(f73(x82351),x82354),x82353)))
% 168.50/168.39 [8237]~P87(x82371)+P1(f315(f315(f223(x82371),x82372),x82373))+~P1(f315(f315(f223(x82371),f315(f315(f73(x82371),x82372),x82374)),f315(f315(f73(x82371),x82373),x82374)))
% 168.50/168.39 [8239]~P87(x82391)+P1(f315(f315(f224(x82391),x82392),x82393))+~P1(f315(f315(f224(x82391),f315(f315(f73(x82391),x82394),x82392)),f315(f315(f73(x82391),x82394),x82393)))
% 168.50/168.39 [8241]~P87(x82411)+P1(f315(f315(f224(x82411),x82412),x82413))+~P1(f315(f315(f224(x82411),f315(f315(f73(x82411),x82412),x82414)),f315(f315(f73(x82411),x82413),x82414)))
% 168.50/168.39 [8293]P1(f315(x82931,x82932))+~E(f315(f315(f127(x82933),f315(f178(f902(x82933)),f166(x82933,x82931,x82934))),x82934),f102(x82933))+~P1(f315(f315(f317(x82933),x82932),f315(f161(x82933),x82934)))
% 168.50/168.39 [8411]P1(f315(x84111,x84112))+~P1(f315(f315(f317(x84113),x84112),f315(f161(x84113),x84114)))+P1(f315(f315(f224(a901),f315(f178(f902(x84113)),f315(f125(x84113,x84111),x84114))),f315(f178(f902(x84113)),x84114)))
% 168.50/168.39 [8900]~P1(f315(x89001,f735(x89001,x89003,x89002,x89004)))+P1(f315(x89001,f315(f315(f153(x89002),x89003),x89004)))+~P1(f315(f315(f224(a901),x89004),f315(f178(f902(x89002)),x89003)))
% 168.50/168.39 [8924]~P25(x89244,x89243,x89241,f230(f909(x89244,a899)))+E(f315(x89241,f490(x89242,x89241,x89243,x89244)),x89242)+~P1(f315(f315(f317(x89243),x89242),f315(f298(x89244,x89243,x89241),f230(f909(x89244,a899)))))
% 168.50/168.39 [8992]E(f166(x89921,x89922,x89923),f315(f315(f164(x89921),x89924),x89923))+P1(f315(f315(f224(a901),f705(x89922,x89923,x89921,x89924)),x89924))+P1(f315(f315(f224(a901),x89924),f315(f178(f902(x89921)),x89923)))
% 168.50/168.39 [8995]E(f166(x89951,x89952,x89953),f315(f315(f164(x89951),x89954),x89953))+P1(f315(f315(f224(a901),f705(x89952,x89953,x89951,x89954)),x89954))+P1(f315(x89952,f315(f315(f153(x89951),x89953),x89954)))
% 168.50/168.39 [9030]P1(f315(x90301,x90302))+~P1(f315(f315(f317(x90304),x90302),f315(f161(x90304),x90303)))+P1(f315(f315(f224(a901),f680(x90302,x90301,x90303,x90304)),f315(f178(f902(x90304)),x90303)))
% 168.50/168.39 [9033]E(f166(x90331,x90332,x90333),f315(f315(f164(x90331),x90334),x90333))+P1(f315(f315(f224(a901),x90334),f315(f178(f902(x90331)),x90333)))+P1(f315(f315(f224(a901),f705(x90332,x90333,x90331,x90334)),f315(f178(f902(x90331)),x90333)))
% 168.50/168.39 [9040]E(f166(x90401,x90402,x90403),f315(f315(f164(x90401),x90404),x90403))+P1(f315(x90402,f315(f315(f153(x90401),x90403),x90404)))+P1(f315(f315(f224(a901),f705(x90402,x90403,x90401,x90404)),f315(f178(f902(x90401)),x90403)))
% 168.50/168.39 [9065]~P128(x90654)+P1(f315(f315(f317(x90651),f888(x90652,x90653,x90651,x90654)),x90653))+P1(f315(f315(f224(x90654),f2(x90654)),f315(f315(f11(x90651,x90654),x90652),x90653)))
% 168.50/168.39 [9066]~P128(x90664)+P1(f315(f315(f317(x90661),f890(x90662,x90663,x90661,x90664)),x90663))+P1(f315(f315(f223(x90664),f2(x90664)),f315(f315(f11(x90661,x90664),x90662),x90663)))
% 168.50/168.39 [9091]~P1(f315(f54(x90911),x90914))+P1(f315(f315(f317(x90911),f526(x90912,x90913,x90914,x90911)),x90914))+P1(f315(f54(f908(x90911,x90913)),f315(f315(f242(x90911,x90913),x90914),x90912)))
% 168.50/168.39 [9123]P1(f315(f315(f317(x91232),f735(x91231,x91233,x91232,x91234)),f315(f161(x91232),x91233)))+P1(f315(x91231,f315(f315(f153(x91232),x91233),x91234)))+~P1(f315(f315(f224(a901),x91234),f315(f178(f902(x91232)),x91233)))
% 168.50/168.39 [9252]P1(f315(f315(f223(a901),x92524),f315(f178(f902(x92522)),f166(x92522,x92523,x92521))))+P1(f315(f315(f224(a901),f706(x92521,x92522,x92523,x92524)),x92524))+~P1(f315(f315(f223(a901),x92524),f315(f178(f902(x92522)),x92521)))
% 168.50/168.39 [9407]E(f166(x94071,x94072,x94073),f315(f315(f164(x94071),x94074),x94073))+~P1(f315(x94072,f315(f315(f153(x94071),x94073),f705(x94072,x94073,x94071,x94074))))+P1(f315(f315(f224(a901),x94074),f315(f178(f902(x94071)),x94073)))
% 168.50/168.39 [9414]E(f166(x94141,x94142,x94143),f315(f315(f164(x94141),x94144),x94143))+~P1(f315(x94142,f315(f315(f153(x94141),x94143),f705(x94142,x94143,x94141,x94144))))+P1(f315(x94142,f315(f315(f153(x94141),x94143),x94144)))
% 168.50/168.39 [9418]~P1(f315(f54(x94181),x94183))+~P1(f315(f54(x94182),f315(x94184,f526(x94184,x94182,x94183,x94181))))+P1(f315(f54(f908(x94181,x94182)),f315(f315(f242(x94181,x94182),x94183),x94184)))
% 168.50/168.39 [9426]~P128(x94261)+~P1(f315(f315(f223(x94261),f2(x94261)),f315(x94263,f890(x94263,x94264,x94262,x94261))))+P1(f315(f315(f223(x94261),f2(x94261)),f315(f315(f11(x94262,x94261),x94263),x94264)))
% 168.50/168.39 [9427]~P128(x94271)+~P1(f315(f315(f224(x94271),f2(x94271)),f315(x94273,f888(x94273,x94274,x94272,x94271))))+P1(f315(f315(f224(x94271),f2(x94271)),f315(f315(f11(x94272,x94271),x94273),x94274)))
% 168.50/168.39 [9435]~E(f315(f178(f902(x94354)),x94352),f315(f178(f902(x94354)),x94353))+P1(f315(f315(f317(f908(f902(x94354),f902(x94354))),f315(f315(f240(f902(x94354),f902(x94354)),x94353),x94352)),f147(x94354,x94351)))+P1(f315(f315(f224(a901),f630(x94351,x94352,x94353,x94354)),f315(f178(f902(x94354)),x94353)))
% 168.50/168.39 [9487]~P1(f315(x94873,f315(f315(f153(x94872),x94874),f706(x94874,x94872,x94873,x94871))))+P1(f315(f315(f223(a901),x94871),f315(f178(f902(x94872)),f166(x94872,x94873,x94874))))+~P1(f315(f315(f223(a901),x94871),f315(f178(f902(x94872)),x94874)))
% 168.50/168.39 [9568]E(f315(f315(f164(x95681),f642(x95682,x95683,x95684,x95681)),x95683),f315(f315(f164(x95681),f642(x95682,x95683,x95684,x95681)),x95684))+~P1(f315(f315(f317(f908(f902(x95681),f902(x95681))),f315(f315(f240(f902(x95681),f902(x95681)),x95684),x95683)),f136(x95681,x95682)))+P1(f315(f315(f224(a901),f315(f178(f902(x95681)),x95684)),f315(f178(f902(x95681)),x95683)))
% 168.50/168.39 [9633]~P1(f315(f315(f224(a901),f2(a901)),x96333))+~P1(f315(f315(f224(a901),x96334),x96331))+P1(f315(f315(f224(a901),f315(f315(f73(a901),f315(f315(f74(a901),x96331),f38(a901,x96332,x96333))),x96334)),f315(f315(f74(a901),x96331),x96333)))
% 168.50/168.39 [9824]~P109(x98242)+~P1(f315(f315(f223(x98242),f315(x98243,f870(x98244,x98243,x98241,x98242))),f315(x98244,f870(x98244,x98243,x98241,x98242))))+P1(f315(f315(f223(f909(x98241,x98242)),x98243),x98244))
% 168.50/168.39 [9926]~P69(x99261)+E(f315(f315(f8(a901,x99261),f315(f315(f20(a901,x99261,x99261),f315(f315(f10(x99261,f909(x99261,x99261),a901),f3(x99261)),x99262)),f315(f315(f10(a901,x99261,a901),x99262),f315(f315(f9(a901,a901,a901),f73(a901)),f71(a901))))),f291(a901,x99263,x99264)),f315(f315(f3(x99261),f315(x99262,x99263)),f315(x99262,f315(f315(f73(a901),x99264),f71(a901)))))+~P1(f315(f315(f223(a901),x99263),x99264))
% 168.50/168.39 [10001]~P39(x100013,f315(f315(f277(x100013,x100013,x100013),x100012),f295(x100013,x100012)))+~P1(f315(f315(f317(f908(x100013,x100013)),f315(f315(f240(x100013,x100013),f315(x100011,f315(a101,f820(x100012,x100011,x100013)))),f315(x100011,f820(x100012,x100011,x100013)))),f295(x100013,x100012)))+E(f315(x100011,f315(f315(f73(a901),f819(x100012,x100011,x100013)),x100014)),f315(x100011,f819(x100012,x100011,x100013)))
% 168.50/168.39 [6862]~P62(x68621)+E(f315(f315(f29(x68621),f315(f315(f74(x68621),x68622),x68623)),x68624),f315(f315(f74(x68621),x68622),f315(f315(f29(x68621),x68623),x68624)))+~P1(f315(f315(f275(x68621),x68624),x68623))
% 168.50/168.39 [6950]E(f315(f315(f123(x69501),x69502),x69503),x69504)+~E(x69503,f315(f315(f127(x69501),f315(f178(f902(x69501)),x69502)),x69504))+~E(f315(f315(f164(x69501),f315(f178(f902(x69501)),x69502)),x69504),x69502)
% 168.50/168.39 [7006]~P66(x70062)+E(x70061,f2(x70062))+E(f315(f315(f279(x70062),f315(f315(f232(x70062),x70063),x70064)),f315(f315(f232(x70062),x70061),x70064)),f315(f315(f232(x70062),f315(f315(f279(x70062),x70063),x70061)),x70064))
% 168.50/168.39 [7154]~P62(x71541)+E(f315(f315(f29(x71541),f315(f315(f74(x71541),x71542),x71543)),x71544),f315(f315(f74(x71541),f315(f315(f29(x71541),x71542),x71544)),x71543))+~P1(f315(f315(f275(x71541),x71544),x71542))
% 168.50/168.39 [7162]~P104(x71621)+~P1(f315(f315(f223(x71621),x71623),x71624))+P1(f315(f315(f223(x71621),f315(f315(f90(x71621),x71622),x71623)),x71624))
% 168.50/168.39 [7163]~P104(x71631)+~P1(f315(f315(f223(x71631),x71632),x71634))+P1(f315(f315(f223(x71631),f315(f315(f90(x71631),x71632),x71633)),x71634))
% 168.50/168.39 [7165]~P110(x71651)+~P1(f315(f315(f223(x71651),x71653),x71654))+P1(f315(f315(f223(x71651),f315(f315(f221(x71651),x71652),x71653)),x71654))
% 168.50/168.39 [7167]~P110(x71671)+~P1(f315(f315(f223(x71671),x71672),x71674))+P1(f315(f315(f223(x71671),f315(f315(f221(x71671),x71672),x71673)),x71674))
% 168.50/168.39 [7168]~P104(x71681)+~P1(f315(f315(f224(x71681),x71683),x71684))+P1(f315(f315(f224(x71681),f315(f315(f90(x71681),x71682),x71683)),x71684))
% 168.50/168.39 [7169]~P104(x71691)+~P1(f315(f315(f224(x71691),x71692),x71694))+P1(f315(f315(f224(x71691),f315(f315(f90(x71691),x71692),x71693)),x71694))
% 168.50/168.39 [7171]~P110(x71711)+~P1(f315(f315(f224(x71711),x71713),x71714))+P1(f315(f315(f224(x71711),f315(f315(f221(x71711),x71712),x71713)),x71714))
% 168.50/168.39 [7173]~P110(x71731)+~P1(f315(f315(f224(x71731),x71732),x71734))+P1(f315(f315(f224(x71731),f315(f315(f221(x71731),x71732),x71733)),x71734))
% 168.50/168.39 [7196]~P1(f315(x71963,x71964))+~P1(f315(x71962,x71964))+P1(f315(f315(f315(f90(f909(x71961,a899)),x71962),x71963),x71964))
% 168.60/168.39 [7322]P14(x73221,x73222,x73223)+~P14(x73221,x73224,x73223)+~P1(f315(f315(f223(f909(f900(x73221),a899)),x73224),x73222))
% 168.60/168.39 [7323]P14(x73231,x73232,x73233)+~P14(x73231,x73232,x73234)+~P1(f315(f315(f223(f909(f900(x73231),a899)),x73233),x73234))
% 168.60/168.39 [7460]~P62(x74601)+E(f315(f315(f29(x74601),f315(f315(f232(x74601),x74602),x74603)),f315(f315(f232(x74601),x74604),x74603)),f315(f315(f232(x74601),f315(f315(f29(x74601),x74602),x74604)),x74603))+~P1(f315(f315(f275(x74601),x74604),x74602))
% 168.60/168.39 [7693]~P72(x76931)+E(f315(f315(f73(x76931),f315(x76932,x76933)),f315(f315(f8(a901,x76931),x76932),f315(f290(a901,f315(a101,x76933)),x76934))),f315(f315(f8(a901,x76931),x76932),f315(f290(a901,x76933),x76934)))+~P1(f315(f315(f224(a901),x76933),x76934))
% 168.60/168.39 [7711]E(x77111,x77112)+P1(f315(f315(f161(x77113),x77114),x77112))+~P1(f315(f315(f161(x77113),f315(f315(f140(x77113),x77111),x77114)),x77112))
% 168.60/168.39 [7723]~P110(x77231)+P1(f315(f315(f223(x77231),x77232),x77233))+~P1(f315(f315(f223(x77231),f315(f315(f222(x77231),x77234),x77232)),x77233))
% 168.60/168.39 [7725]~P110(x77251)+P1(f315(f315(f223(x77251),x77252),x77253))+~P1(f315(f315(f223(x77251),f315(f315(f222(x77251),x77252),x77254)),x77253))
% 168.60/168.39 [7727]~P103(x77271)+P1(f315(f315(f223(x77271),x77272),x77273))+~P1(f315(f315(f223(x77271),f315(f315(f99(x77271),x77274),x77272)),x77273))
% 168.60/168.39 [7729]~P103(x77291)+P1(f315(f315(f223(x77291),x77292),x77293))+~P1(f315(f315(f223(x77291),f315(f315(f99(x77291),x77292),x77294)),x77293))
% 168.60/168.39 [7730]~P110(x77301)+P1(f315(f315(f224(x77301),x77302),x77303))+~P1(f315(f315(f224(x77301),f315(f315(f222(x77301),x77304),x77302)),x77303))
% 168.60/168.39 [7731]~P110(x77311)+P1(f315(f315(f224(x77311),x77312),x77313))+~P1(f315(f315(f224(x77311),f315(f315(f222(x77311),x77312),x77314)),x77313))
% 168.60/168.39 [7732]~P121(x77321)+P1(f315(f315(f275(x77321),x77322),x77323))+~P1(f315(f315(f275(x77321),f315(f315(f74(x77321),x77324),x77322)),x77323))
% 168.60/168.39 [7733]~P121(x77331)+P1(f315(f315(f275(x77331),x77332),x77333))+~P1(f315(f315(f275(x77331),f315(f315(f74(x77331),x77332),x77334)),x77333))
% 168.60/168.39 [7809]~P1(f315(f315(f317(x78091),x78092),x78094))+P1(f315(f315(f317(x78091),x78092),x78093))+P1(f315(f315(f317(x78091),x78092),f315(f315(f3(f909(x78091,a899)),x78094),x78093)))
% 168.60/168.39 [7893]P1(f315(x78931,x78932))+P1(f315(x78933,x78932))+~P1(f315(f315(f315(f99(f909(x78934,a899)),x78933),x78931),x78932))
% 168.60/168.39 [7904]~P1(f315(f315(f317(x79041),x79042),x79044))+~P1(f315(f315(f317(x79041),x79042),x79043))+P1(f315(f315(f317(x79041),x79042),f315(f315(f90(f909(x79041,a899)),x79043),x79044)))
% 168.60/168.39 [7952]~P103(x79521)+~P1(f315(f54(x79521),x79524))+E(f315(f315(f57(x79521,x79521,f99(x79521)),x79522),f315(f315(f297(x79521),x79523),x79524)),f315(f315(f99(x79521),x79523),f315(f315(f57(x79521,x79521,f99(x79521)),x79522),x79524)))
% 168.60/168.39 [7953]~P104(x79531)+~P1(f315(f54(x79531),x79534))+E(f315(f315(f57(x79531,x79531,f90(x79531)),x79532),f315(f315(f297(x79531),x79533),x79534)),f315(f315(f90(x79531),x79533),f315(f315(f57(x79531,x79531,f90(x79531)),x79532),x79534)))
% 168.60/168.39 [7954]~P110(x79541)+~P1(f315(f54(x79541),x79544))+E(f315(f315(f57(x79541,x79541,f221(x79541)),x79542),f315(f315(f297(x79541),x79543),x79544)),f315(f315(f221(x79541),x79543),f315(f315(f57(x79541,x79541,f221(x79541)),x79542),x79544)))
% 168.60/168.39 [7955]~P110(x79551)+~P1(f315(f54(x79551),x79554))+E(f315(f315(f57(x79551,x79551,f222(x79551)),x79552),f315(f315(f297(x79551),x79553),x79554)),f315(f315(f222(x79551),x79553),f315(f315(f57(x79551,x79551,f222(x79551)),x79552),x79554)))
% 168.60/168.39 [7957]~P112(x79571)+~P96(x79571)+E(f315(f315(f3(x79571),f315(f315(f74(x79571),f315(f92(x79571),x79572)),x79573)),f315(f315(f74(x79571),f315(f92(x79571),x79572)),x79574)),f315(f315(f74(x79571),f315(f92(x79571),x79572)),f315(f315(f3(x79571),x79573),x79574)))
% 168.60/168.39 [7958]~P141(x79581)+~P96(x79581)+E(f315(f315(f73(x79581),f315(f315(f74(x79581),f315(f92(x79581),x79582)),x79583)),f315(f315(f74(x79581),f315(f92(x79581),x79582)),x79584)),f315(f315(f74(x79581),f315(f92(x79581),x79582)),f315(f315(f73(x79581),x79583),x79584)))
% 168.60/168.39 [8073]E(x80731,x80732)+P1(f315(f315(f317(x80733),x80731),f315(f161(x80733),x80734)))+~P1(f315(f315(f317(x80733),x80731),f315(f161(x80733),f315(f315(f140(x80733),x80732),x80734))))
% 168.60/168.39 [8247]P56(x82471,x82472,x82473)+~P56(x82471,x82472,x82474)+~P1(f315(f315(f223(f909(f908(x82471,x82472),a899)),x82473),x82474))
% 168.60/168.39 [8295]P1(f315(f315(f317(x82951),x82952),x82953))+P1(f315(f315(f317(x82951),x82952),x82954))+~P1(f315(f315(f317(x82951),x82952),f315(f315(f99(f909(x82951,a899)),x82954),x82953)))
% 168.60/168.39 [8305]~P54(x83051,x83054,x83053)+~P1(f315(f315(f317(x83051),x83052),x83054))+P1(f315(f315(f317(f908(x83051,x83051)),f315(f315(f240(x83051,x83051),x83052),x83052)),x83053))
% 168.60/168.39 [8317]~P1(f315(f54(x83172),x83174))+~P1(f315(f54(x83171),x83173))+P1(f315(f54(f908(x83171,x83172)),f315(f315(f242(x83171,x83172),x83173),f315(f18(f909(x83172,a899),x83171),x83174))))
% 168.60/168.39 [8318]~P1(f315(f315(f317(x83181),x83182),x83184))+~P1(f315(f315(f223(f909(x83181,a899)),x83183),x83184))+P1(f315(f315(f223(f909(x83181,a899)),f315(f315(f297(x83181),x83182),x83183)),x83184))
% 168.60/168.39 [8325]~P77(x83252)+~P147(x83252)+E(f315(f315(f11(x83251,x83252),f315(f315(f10(a901,x83252,x83251),f89(x83252)),x83253)),x83254),f315(f89(x83252),f315(f315(f11(x83251,a901),x83253),x83254)))
% 168.60/168.39 [8326]~P77(x83262)+~P143(x83262)+E(f315(f315(f11(x83261,x83262),f315(f315(f10(a1,x83262,x83261),f91(x83262)),x83263)),x83264),f315(f91(x83262),f315(f315(f11(x83261,a1),x83263),x83264)))
% 168.60/168.39 [8350]E(f315(f315(f3(f909(x83501,a899)),x83502),f315(f315(f3(f909(x83501,a899)),x83503),x83504)),x83504)+~P1(f315(f315(f223(f909(x83501,a899)),x83502),x83503))+~P1(f315(f315(f223(f909(x83501,a899)),x83504),x83502))
% 168.60/168.39 [8446]~P1(f315(f54(x84461),x84464))+E(f315(f315(f3(a901),f315(f315(f8(x84461,a901),x84462),x84463)),f315(f315(f8(x84461,a901),x84462),x84464)),f315(f315(f8(x84461,a901),x84462),f315(f315(f3(f909(x84461,a899)),x84463),x84464)))+~P1(f315(f315(f223(f909(x84461,a899)),x84464),x84463))
% 168.60/168.39 [8598]~P8(x85981,x85984,x85983)+~P1(f315(f315(f317(x85981),x85982),x85984))+P1(f315(f315(f317(x85981),x85982),f315(f273(x85981,x85981,x85983),f315(f315(f297(x85981),x85982),f177(f909(x85981,a899))))))
% 168.60/168.39 [8659]~P1(f315(f315(f223(f909(x86591,a899)),x86592),x86593))+~P1(f315(f315(f223(f909(x86591,a899)),x86592),x86594))+P1(f315(f315(f223(f909(x86591,a899)),x86592),f315(f315(f90(f909(x86591,a899)),x86593),x86594)))
% 168.60/168.39 [8761]E(x87611,f177(f909(x87612,a899)))+P1(f315(f54(x87613),x87614))+~P1(f315(f54(f908(x87613,x87612)),f315(f315(f242(x87613,x87612),x87614),f315(f18(f909(x87612,a899),x87613),x87611))))
% 168.60/168.39 [8762]E(x87621,f177(f909(x87622,a899)))+P1(f315(f54(x87623),x87624))+~P1(f315(f54(f908(x87622,x87623)),f315(f315(f242(x87622,x87623),x87621),f315(f18(f909(x87623,a899),x87622),x87624))))
% 168.60/168.39 [8835]P1(f315(f315(f317(x88351),x88352),f304(x88351,x88353)))+~P1(f315(f315(f317(x88351),x88354),f304(x88351,x88353)))+~P1(f315(f315(f317(f908(x88351,x88351)),f315(f315(f240(x88351,x88351),x88352),x88354)),x88353))
% 168.60/168.39 [8892]~P39(x88921,x88924)+P1(f315(f315(f317(f908(x88921,x88921)),f315(f315(f240(x88921,x88921),x88923),x88922)),f295(x88921,x88924)))+P39(x88921,f315(f315(f297(f908(x88921,x88921)),f315(f315(f240(x88921,x88921),x88922),x88923)),x88924))
% 168.60/168.39 [8893]~P59(x88931,x88934)+P1(f315(f315(f317(f908(x88931,x88931)),f315(f315(f240(x88931,x88931),x88933),x88932)),f295(x88931,x88934)))+P59(x88931,f315(f315(f297(f908(x88931,x88931)),f315(f315(f240(x88931,x88931),x88932),x88933)),x88934))
% 168.60/168.39 [8975]~E(x89752,x89753)+~P1(f315(f315(f317(x89751),x89752),f315(f161(x89751),x89754)))+P1(f315(f315(f317(f908(x89751,x89751)),f315(f315(f240(x89751,x89751),x89752),x89753)),f315(f161(f908(x89751,x89751)),f315(f315(f170(x89751,x89751),x89754),x89754))))
% 168.60/168.39 [9064]~E(x90643,x90644)+P1(f315(f315(f245(x90641,x90641,a899),a312),x90642))+~P1(f315(f315(f317(f908(x90641,x90641)),x90642),f315(f161(f908(x90641,x90641)),f315(f315(f170(x90641,x90641),x90643),x90644))))
% 168.60/168.39 [9108]P1(f315(f315(f317(f908(f902(x91081),f902(x91081))),f315(f315(f240(f902(x91081),f902(x91081)),x91082),x91083)),f136(x91081,x91084)))+~E(f315(f315(f164(x91081),f315(f178(f902(x91081)),x91082)),x91083),x91082)+~P1(f315(f315(f224(a901),f315(f178(f902(x91081)),x91082)),f315(f178(f902(x91081)),x91083)))
% 168.60/168.39 [9111]~P53(x91111,x91114)+~P1(f315(f315(f317(f908(x91111,x91111)),f315(f315(f240(x91111,x91111),x91113),x91112)),x91114))+P1(f315(f315(f317(f908(x91111,x91111)),f315(f315(f240(x91111,x91111),x91112),x91113)),x91114))
% 168.60/168.39 [9202]~P1(f315(f54(x92021),x92024))+P1(f315(f315(f317(x92021),f402(x92022,x92023,x92024,x92021)),x92024))+P1(f315(f54(x92023),f315(f315(f33(x92021,f909(x92023,a899)),x92024),x92022)))
% 168.60/168.39 [9203]~P1(f315(f54(x92031),x92034))+P1(f315(f315(f317(x92031),f567(x92032,x92033,x92034,x92031)),x92034))+P1(f315(f54(x92033),f315(f315(f33(x92031,f909(x92033,a899)),x92034),x92032)))
% 168.60/168.39 [9288]P1(f315(f315(f317(f908(x92881,x92881)),x92882),f315(f315(f277(x92881,x92881,x92881),x92883),f295(x92881,x92883))))+~P1(f315(f315(f224(a901),f2(a901)),x92884))+~P1(f315(f315(f317(f908(x92881,x92881)),x92882),f315(f315(f172(f908(x92881,x92881),a899),x92884),x92883)))
% 168.60/168.39 [9296]~P39(x92961,x92962)+~P1(f315(f315(f317(f908(x92961,x92961)),f315(f315(f240(x92961,x92961),x92964),x92963)),x92962))+~P1(f315(f315(f317(f908(x92961,x92961)),f315(f315(f240(x92961,x92961),x92963),x92964)),x92962))
% 168.60/168.39 [9425]~P1(f315(f54(x94251),x94254))+E(f315(f315(f8(x94251,a901),f315(f315(f10(f909(x94252,a899),a901,x94251),f28(x94252)),x94253)),x94254),f315(f28(f908(x94251,x94252)),f315(f315(f242(x94251,x94252),x94254),x94253)))+P1(f315(f315(f317(x94251),f528(x94253,x94252,x94254,x94251)),x94254))
% 168.60/168.39 [9429]~P1(f315(f126(x94291),x94292))+P1(f315(f126(x94291),f315(f315(f148(x94291,x94292),x94293),x94294)))+P1(f315(f315(f317(x94291),x94294),f315(f315(f3(f909(x94291,a899)),f315(f161(x94291),x94292)),f315(f315(f297(x94291),f315(f315(f153(x94291),x94292),x94293)),f177(f909(x94291,a899))))))
% 168.60/168.39 [9446]~P1(f315(f54(x94462),x94463))+~P1(f315(f54(x94461),f315(x94464,f402(x94464,x94461,x94463,x94462))))+P1(f315(f54(x94461),f315(f315(f33(x94462,f909(x94461,a899)),x94463),x94464)))
% 168.60/168.39 [9447]~P1(f315(f54(x94472),x94473))+~P1(f315(f54(x94471),f315(x94474,f567(x94474,x94471,x94473,x94472))))+P1(f315(f54(x94471),f315(f315(f33(x94472,f909(x94471,a899)),x94473),x94474)))
% 168.60/168.39 [9525]~P1(f315(f315(f317(f908(x95251,x95251)),x95252),f315(f315(f277(x95251,x95251,x95251),x95254),f295(x95251,x95254))))+P1(f315(f315(f317(f908(x95251,x95251)),x95252),f315(f315(f277(x95251,x95251,x95251),x95253),f295(x95251,x95253))))+~P1(f315(f315(f223(f909(f908(x95251,x95251),a899)),x95254),x95253))
% 168.60/168.39 [9535]E(f315(f315(f164(x95351),f642(x95354,x95353,x95352,x95351)),x95353),f315(f315(f164(x95351),f642(x95354,x95353,x95352,x95351)),x95352))+~P1(f315(f315(f317(f908(f902(x95351),f902(x95351))),f315(f315(f240(f902(x95351),f902(x95351)),x95352),x95353)),f136(x95351,x95354)))+E(f315(f315(f164(x95351),f315(f178(f902(x95351)),x95352)),x95353),x95352)
% 168.60/168.39 [9551]~P1(f315(f54(x95511),x95514))+E(f315(f315(f8(x95511,a901),f315(f315(f10(f909(x95512,a899),a901,x95511),f28(x95512)),x95513)),x95514),f315(f28(f908(x95511,x95512)),f315(f315(f242(x95511,x95512),x95514),x95513)))+~P1(f315(f54(x95512),f315(x95513,f528(x95513,x95512,x95514,x95511))))
% 168.60/168.39 [9555]~E(f315(f178(f902(x95551)),x95553),f315(f178(f902(x95551)),x95552))+P1(f315(f315(f317(f908(f902(x95551),f902(x95551))),f315(f315(f240(f902(x95551),f902(x95551)),x95552),x95553)),f147(x95551,x95554)))+P1(f315(f315(f317(f908(x95551,x95551)),f646(x95554,x95553,x95552,x95551)),f315(f161(f908(x95551,x95551)),f315(f315(f170(x95551,x95551),x95552),x95553))))
% 168.60/168.39 [9644]~P1(f315(f315(f317(f908(f902(x96441),f902(x96441))),f315(f315(f240(f902(x96441),f902(x96441)),x96442),x96443)),f136(x96441,x96444)))+E(f315(f315(f164(x96441),f315(f178(f902(x96441)),x96442)),x96443),x96442)+P1(f315(f315(f224(a901),f642(x96444,x96443,x96442,x96441)),f315(f315(f221(a901),f315(f178(f902(x96441)),x96442)),f315(f178(f902(x96441)),x96443))))
% 168.60/168.39 [9668]~P1(f315(f315(f317(f908(f902(x96681),f902(x96681))),f315(f315(f240(f902(x96681),f902(x96681)),x96682),x96683)),f136(x96681,x96684)))+P1(f315(f315(f224(a901),f315(f178(f902(x96681)),x96682)),f315(f178(f902(x96681)),x96683)))+P1(f315(f315(f224(a901),f642(x96684,x96683,x96682,x96681)),f315(f315(f221(a901),f315(f178(f902(x96681)),x96682)),f315(f178(f902(x96681)),x96683))))
% 168.60/168.39 [10068]~P1(f315(f315(f317(f908(f902(x100681),f902(x100681))),f315(f315(f240(f902(x100681),f902(x100681)),x100682),x100683)),f136(x100681,x100684)))+E(f315(f315(f164(x100681),f315(f178(f902(x100681)),x100682)),x100683),x100682)+P1(f315(f315(f317(f908(x100681,x100681)),f315(f315(f240(x100681,x100681),f315(f315(f153(x100681),x100682),f642(x100684,x100683,x100682,x100681))),f315(f315(f153(x100681),x100683),f642(x100684,x100683,x100682,x100681)))),x100684))
% 168.60/168.39 [10069]~P1(f315(f315(f317(f908(f902(x100691),f902(x100691))),f315(f315(f240(f902(x100691),f902(x100691)),x100692),x100693)),f136(x100691,x100694)))+P1(f315(f315(f224(a901),f315(f178(f902(x100691)),x100692)),f315(f178(f902(x100691)),x100693)))+P1(f315(f315(f317(f908(x100691,x100691)),f315(f315(f240(x100691,x100691),f315(f315(f153(x100691),x100692),f642(x100694,x100693,x100692,x100691))),f315(f315(f153(x100691),x100693),f642(x100694,x100693,x100692,x100691)))),x100694))
% 168.60/168.39 [10136]~E(f315(f178(f902(x101361)),x101362),f315(f178(f902(x101361)),x101363))+P1(f315(f315(f317(f908(f902(x101361),f902(x101361))),f315(f315(f240(f902(x101361),f902(x101361)),x101362),x101363)),f147(x101361,x101364)))+~P1(f315(f315(f317(f908(x101361,x101361)),f315(f315(f240(x101361,x101361),f315(f315(f153(x101361),x101362),f630(x101364,x101363,x101362,x101361))),f315(f315(f153(x101361),x101363),f630(x101364,x101363,x101362,x101361)))),x101364))
% 168.60/168.39 [10283]~P72(x102831)+~P1(f315(f54(x102832),x102834))+E(f315(f154(x102831),f315(f315(f143(x102832,x102831),x102833),f83(f902(x102832),f315(f315(f20(f902(x102832),a899,a899),f315(f315(f10(a899,f909(a899,a899),f902(x102832)),a313),f315(f315(f9(f902(x102832),f909(x102832,a899),a899),f315(f315(f10(f909(x102832,a899),f909(f909(x102832,a899),a899),f902(x102832)),a312),f161(x102832))),x102834))),f126(x102832))))),f220(x102832,x102831,x102833,x102834))
% 168.60/168.39 [7541]~P65(x75412)+E(x75411,f2(x75412))+E(f315(f315(f279(x75412),f315(f315(f73(x75412),x75413),f315(f315(f74(x75412),x75414),x75411))),x75411),f315(f315(f73(x75412),x75414),f315(f315(f279(x75412),x75413),x75411)))
% 168.60/168.39 [7542]~P62(x75422)+E(x75421,f2(x75422))+E(f315(f315(f29(x75422),f315(f315(f73(x75422),x75423),f315(f315(f74(x75422),x75424),x75421))),x75421),f315(f315(f73(x75422),x75424),f315(f315(f29(x75422),x75423),x75421)))
% 168.60/168.39 [7543]~P62(x75432)+E(x75431,f2(x75432))+E(f315(f315(f29(x75432),f315(f315(f73(x75432),x75433),f315(f315(f74(x75432),x75431),x75434))),x75431),f315(f315(f73(x75432),x75434),f315(f315(f29(x75432),x75433),x75431)))
% 168.60/168.39 [7772]~P66(x77722)+E(x77721,f2(x77722))+E(f315(f315(f279(x77722),f315(f315(f3(x77722),x77723),f315(f315(f74(x77722),x77721),x77724))),x77721),f315(f315(f3(x77722),f315(f315(f279(x77722),x77723),x77721)),x77724))
% 168.60/168.39 [7773]~P65(x77732)+E(x77731,f2(x77732))+E(f315(f315(f279(x77732),f315(f315(f73(x77732),x77733),f315(f315(f74(x77732),x77734),x77731))),x77731),f315(f315(f73(x77732),f315(f315(f279(x77732),x77733),x77731)),x77734))
% 168.60/168.39 [7774]~P66(x77742)+E(x77741,f2(x77742))+E(f315(f315(f279(x77742),f315(f315(f73(x77742),x77743),f315(f315(f74(x77742),x77741),x77744))),x77741),f315(f315(f73(x77742),f315(f315(f279(x77742),x77743),x77741)),x77744))
% 168.60/168.39 [8478]~P1(f315(f149(x84781,x84783),x84784))+~P1(f315(f149(x84781,x84782),x84784))+P1(f315(f149(x84781,f315(f315(f90(f909(x84781,a899)),x84782),x84783)),x84784))
% 168.60/168.39 [8850]~E(f315(f315(f277(x88501,x88501,x88501),x88502),x88504),f177(f909(f908(x88501,x88501),a899)))+~E(f315(f315(f277(x88501,x88501,x88501),x88502),x88503),f177(f909(f908(x88501,x88501),a899)))+E(f315(f315(f277(x88501,x88501,x88501),x88502),f315(f315(f99(f909(f908(x88501,x88501),a899)),x88503),x88504)),f177(f909(f908(x88501,x88501),a899)))
% 168.60/168.39 [8976]~P1(f315(f315(f223(f909(x89761,a899)),x89763),x89764))+~P1(f315(f315(f223(f909(x89761,a899)),x89762),x89764))+P1(f315(f315(f223(f909(x89761,a899)),f315(f315(f99(f909(x89761,a899)),x89762),x89763)),x89764))
% 168.60/168.39 [9352]~P1(f315(f54(x93521),x93524))+~P1(f315(f54(x93521),x93523))+E(f315(f315(f3(a901),f315(f315(f73(a901),f315(f315(f8(x93521,a901),x93522),x93523)),f315(f315(f8(x93521,a901),x93522),x93524))),f315(f315(f8(x93521,a901),x93522),f315(f315(f90(f909(x93521,a899)),x93523),x93524))),f315(f315(f8(x93521,a901),x93522),f315(f315(f99(f909(x93521,a899)),x93523),x93524)))
% 168.60/168.39 [9443]~P1(f315(f315(f317(x94431),x94433),x94432))+~P1(f315(f315(f223(f909(x94431,a899)),x94432),f315(f315(f297(x94431),x94433),x94434)))+P1(f315(f315(f223(f909(x94431,a899)),f315(f315(f3(f909(x94431,a899)),x94432),f315(f315(f297(x94431),x94433),f177(f909(x94431,a899))))),x94434))
% 168.60/168.39 [9619]~P1(f315(f315(f317(x96191),x96193),x96192))+P1(f315(f315(f223(f909(x96191,a899)),x96192),f315(f315(f297(x96191),x96193),x96194)))+~P1(f315(f315(f223(f909(x96191,a899)),f315(f315(f3(f909(x96191,a899)),x96192),f315(f315(f297(x96191),x96193),f177(f909(x96191,a899))))),x96194))
% 168.60/168.39 [9708]~P1(f315(f315(f223(a901),x97081),x97083))+~P1(f315(f315(f224(a901),x97082),x97084))+P1(f315(f315(f317(f908(f908(a901,a901),f908(a901,a901))),f315(f315(f240(f908(a901,a901),f908(a901,a901)),f315(f315(f240(a901,a901),x97081),x97082)),f315(f315(f240(a901,a901),x97083),x97084))),a26))
% 168.60/168.39 [9709]~P1(f315(f315(f223(a901),x97092),x97094))+~P1(f315(f315(f223(a901),x97091),x97093))+P1(f315(f315(f317(f908(f908(a901,a901),f908(a901,a901))),f315(f315(f240(f908(a901,a901),f908(a901,a901)),f315(f315(f240(a901,a901),x97091),x97092)),f315(f315(f240(a901,a901),x97093),x97094))),a64))
% 168.60/168.39 [9999]~P1(f315(f315(f317(f902(x99991)),x99994),f150(x99991,x99993)))+~P1(f315(f315(f317(f902(x99991)),x99994),f150(x99991,x99992)))+P1(f315(f149(x99991,f315(f315(f90(f909(x99991,a899)),f315(f315(f9(x99991,f909(x99991,a899),a899),f317(x99991)),x99992)),f315(f315(f9(x99991,f909(x99991,a899),a899),f317(x99991)),x99993))),x99994))
% 168.60/168.39 [10102]~P25(x101021,f909(f909(x101021,a899),a899),f315(f315(f9(x101021,f909(f908(x101021,x101021),a899),f909(f909(x101021,a899),a899)),f315(f315(f10(f909(x101021,a899),f909(f909(f908(x101021,x101021),a899),f909(f909(x101021,a899),a899)),x101021),f53(x101021)),f315(f315(f9(x101021,f909(x101021,a899),f909(x101021,a899)),f297(x101021)),f177(f909(x101021,a899))))),x101023),x101022)+~P1(f315(f315(f317(x101021),x101024),x101022))+E(f315(f315(f3(f909(f909(x101021,a899),a899)),f315(f315(f53(x101021),x101022),x101023)),f315(f315(f53(x101021),f315(f315(f297(x101021),x101024),f177(f909(x101021,a899)))),x101023)),f315(f315(f53(x101021),f315(f315(f3(f909(x101021,a899)),x101022),f315(f315(f297(x101021),x101024),f177(f909(x101021,a899))))),x101023))
% 168.60/168.39 [10237]~P54(x102371,x102372,x102374)+~P1(f315(f315(f317(f908(x102371,x102371)),x102373),x102374))+P1(f315(f315(f245(x102371,x102371,a899),f315(f315(f9(x102371,f909(x102371,a899),f909(x102371,a899)),f315(f315(f10(f909(a899,a899),f909(f909(x102371,a899),f909(x102371,a899)),x102371),f10(a899,a899,x102371)),f315(f315(f10(a899,f909(a899,a899),x102371),a313),f315(f315(f9(x102371,f909(x102371,a899),a899),f317(x102371)),x102372)))),f315(f315(f9(x102371,f909(x102371,a899),a899),f317(x102371)),x102372))),x102373))
% 168.60/168.39 [10249]P1(f315(f54(x102491),x102492))+~P1(f315(f54(x102493),f315(f298(x102491,x102493,x102494),x102492)))+~P1(f315(f54(x102491),f315(f250(x102491),f315(f315(f20(x102491,a899,a899),f315(f315(f10(a899,f909(a899,a899),x102491),a313),f315(f315(f9(x102491,f909(x102491,a899),a899),f317(x102491)),x102492))),f315(f315(f9(x102491,x102493,a899),f315(f315(f10(x102493,f909(x102493,a899),x102491),a312),x102494)),f315(x102494,f560(x102494,x102493,x102492,x102491)))))))
% 168.60/168.39 [8230]~P66(x82302)+E(x82301,f2(x82302))+E(f315(f315(f279(x82302),f315(f315(f3(x82302),f315(f315(f74(x82302),x82301),x82303)),x82304)),x82301),f315(f315(f3(x82302),x82303),f315(f315(f279(x82302),x82304),x82301)))
% 168.60/168.39 [8231]~P66(x82312)+E(x82311,f2(x82312))+E(f315(f315(f279(x82312),f315(f315(f73(x82312),f315(f315(f74(x82312),x82311),x82313)),x82314)),x82311),f315(f315(f73(x82312),x82313),f315(f315(f279(x82312),x82314),x82311)))
% 168.60/168.39 [9137]~E(f315(f315(f277(x91371,x91371,x91371),x91373),x91374),f177(f909(f908(x91371,x91371),a899)))+~E(f315(f315(f277(x91371,x91371,x91371),x91372),x91374),f177(f909(f908(x91371,x91371),a899)))+E(f315(f315(f277(x91371,x91371,x91371),f315(f315(f99(f909(f908(x91371,x91371),a899)),x91372),x91373)),x91374),f177(f909(f908(x91371,x91371),a899)))
% 168.60/168.39 [9916]~P1(f315(f149(x99161,x99163),x99164))+~P1(f315(f149(x99161,x99162),x99164))+P1(f315(f149(x99161,f315(f315(f20(x99161,a899,a899),f315(f315(f10(a899,f909(a899,a899),x99161),a313),x99162)),x99163)),x99164))
% 168.60/168.39 [10175]P1(f315(x101751,f546(x101752,x101753,x101751,x101754)))+~P1(f315(f54(x101754),f315(f250(x101754),x101751)))+P1(f315(f54(x101753),f315(f250(x101753),f315(f315(f10(f909(x101754,a899),a899,x101753),f80(x101754)),f315(f315(f10(f909(x101754,a899),f909(x101754,a899),x101753),f315(f20(x101754,a899,a899),f315(f315(f10(a899,f909(a899,a899),x101754),a313),x101751))),x101752)))))
% 168.60/168.39 [10193]~P1(f315(f54(x101932),f315(f250(x101932),x101933)))+~P1(f315(f54(x101931),f315(f250(x101931),f315(f315(f9(x101931,x101932,a899),x101934),f546(x101934,x101931,x101933,x101932)))))+P1(f315(f54(x101931),f315(f250(x101931),f315(f315(f10(f909(x101932,a899),a899,x101931),f80(x101932)),f315(f315(f10(f909(x101932,a899),f909(x101932,a899),x101931),f315(f20(x101932,a899,a899),f315(f315(f10(a899,f909(a899,a899),x101932),a313),x101933))),x101934)))))
% 168.60/168.39 [10262]~P1(f315(f54(x102621),x102624))+P1(f315(f315(f317(x102621),f775(x102622,x102623,x102624,x102621)),x102624))+P1(f315(f54(x102623),f315(f250(x102623),f315(f315(f10(f909(x102621,a899),a899,x102623),f80(x102621)),f315(f315(f10(f909(x102621,a899),f909(x102621,a899),x102623),f315(f20(x102621,a899,a899),f315(f315(f10(a899,f909(a899,a899),x102621),a313),f315(f315(f9(x102621,f909(x102621,a899),a899),f317(x102621)),x102624)))),x102622)))))
% 168.60/168.39 [10268]~P1(f315(f54(x102682),x102683))+~P1(f315(f54(x102681),f315(f250(x102681),f315(f315(f9(x102681,x102682,a899),x102684),f775(x102684,x102681,x102683,x102682)))))+P1(f315(f54(x102681),f315(f250(x102681),f315(f315(f10(f909(x102682,a899),a899,x102681),f80(x102682)),f315(f315(f10(f909(x102682,a899),f909(x102682,a899),x102681),f315(f20(x102682,a899,a899),f315(f315(f10(a899,f909(a899,a899),x102682),a313),f315(f315(f9(x102682,f909(x102682,a899),a899),f317(x102682)),x102683)))),x102684)))))
% 168.60/168.39 [5113]~E(x51132,x51134)+E(f158(x51131,x51132,x51133),f158(x51131,x51134,x51135))+~E(x51132,f2(a901))
% 168.60/168.39 [5362]E(x53621,x53622)+~E(f158(x53624,x53623,x53621),f158(x53624,x53625,x53622))+E(x53623,f2(a901))
% 168.60/168.39 [6659]E(x66591,x66592)+~E(f315(x66593,x66591),f315(x66593,x66592))+~P25(x66594,x66595,x66593,f230(f909(x66594,a899)))
% 168.60/168.39 [7573]E(x75731,x75732)+~P25(x75733,x75734,x75735,f230(f909(x75733,a899)))+~E(f315(f298(x75733,x75734,x75735),x75731),f315(f298(x75733,x75734,x75735),x75732))
% 168.60/168.39 [7827]P25(x78272,x78273,f484(x78274,x78273,x78272,x78271),x78271)+~E(f315(f298(x78273,x78272,x78275),x78274),x78271)+E(x78271,f177(f909(x78272,a899)))
% 168.60/168.39 [8361]~P1(f315(f315(x83613,x83612),x83615))+~P1(f315(f315(x83613,x83614),x83612))+P1(f315(f315(f317(x83611),x83612),f287(x83611,x83613,x83614,x83615)))
% 168.60/168.39 [8362]~P1(f315(f315(x83623,x83622),x83625))+~P1(f315(f315(x83623,x83624),x83622))+P1(f315(f315(f317(x83621),x83622),f278(x83621,x83623,x83624,x83625)))
% 168.60/168.39 [8667]~P25(x86671,x86672,x86673,x86674)+P26(x86671,x86672,x86673,x86674,x86675)+~E(f315(f298(x86671,x86672,x86673),x86674),x86675)
% 168.60/168.39 [8800]~P26(x88001,x88003,x88004,x88002,x88005)+~P1(f315(f54(x88003),x88005))+P1(f315(f54(x88001),x88002))
% 168.60/168.39 [8801]~P26(x88013,x88011,x88014,x88015,x88012)+~P1(f315(f54(x88013),x88015))+P1(f315(f54(x88011),x88012))
% 168.60/168.39 [8933]~P25(x89331,x89333,x89335,f230(f909(x89331,a899)))+~P25(x89333,x89332,x89334,f230(f909(x89333,a899)))+P25(x89331,x89332,f315(f66(x89333,x89332,x89331,x89334),x89335),f230(f909(x89331,a899)))
% 168.60/168.39 [9502]P1(f315(f315(f317(f908(x95021,x95021)),f315(f315(f240(x95021,x95021),x95022),x95023)),f295(x95021,x95024)))+~P1(f315(f315(f317(f908(x95021,x95021)),f315(f315(f240(x95021,x95021),x95022),x95025)),f295(x95021,x95024)))+~P1(f315(f315(f317(f908(x95021,x95021)),f315(f315(f240(x95021,x95021),x95025),x95023)),f295(x95021,x95024)))
% 168.60/168.39 [9542]~P110(x95422)+~P1(f315(f126(x95421),x95425))+P1(f315(f126(x95421),f138(x95421,x95422,x95423,x95424,x95425)))
% 168.60/168.39 [5438]~E(x54382,f102(x54381))+E(f315(f315(f123(x54381),x54382),x54383),f315(f315(f140(x54381),x54384),x54385))+~E(x54383,f315(f315(f140(x54381),x54384),x54385))
% 168.60/168.39 [5439]~E(x54392,f102(x54391))+E(f315(f315(f123(x54391),x54392),x54393),f315(f315(f140(x54391),x54394),x54395))+~E(f315(f315(f140(x54391),x54394),x54395),x54393)
% 168.60/168.39 [6615]~E(f315(f178(f902(x66151)),x66155),f315(f178(f902(x66152)),x66154))+E(f315(f315(f143(f908(x66151,x66152),x66152),f244(x66151,x66152)),x66153),x66154)+~E(f315(f315(f170(x66151,x66152),x66155),x66154),x66153)
% 168.60/168.39 [6616]~E(f315(f178(f902(x66161)),x66164),f315(f178(f902(x66162)),x66165))+E(f315(f315(f143(f908(x66161,x66162),x66161),f239(x66161,x66162)),x66163),x66164)+~E(f315(f315(f170(x66161,x66162),x66164),x66165),x66163)
% 168.60/168.39 [7106]~P110(x71061)+~P13(x71061,f315(f315(f143(x71062,x71061),x71063),x71065))+P13(x71061,f315(f315(f143(x71062,x71061),x71063),f315(f125(x71062,x71064),x71065)))
% 168.60/168.39 [7249]~P110(x72491)+P13(x72491,f315(f315(f143(x72492,x72491),x72493),f159(x72492,x72494,x72495)))+~P13(x72491,f315(f315(f143(x72492,x72491),x72493),x72495))
% 168.60/168.39 [7272]~P56(x72723,x72722,x72725)+~P56(x72721,x72723,x72724)+P56(x72721,x72722,f315(f315(f277(x72721,x72723,x72722),x72724),x72725))
% 168.60/168.39 [7369]E(x73691,x73692)+~P25(x73693,x73694,x73695,f230(f909(x73693,a899)))+~E(f315(f315(f143(x73693,x73694),x73695),x73691),f315(f315(f143(x73693,x73694),x73695),x73692))
% 168.60/168.39 [7528]~P1(f315(f315(f223(a901),x75281),f315(x75283,x75285)))+P1(f315(f315(f223(a901),x75281),f144(x75282,x75283,x75284)))+~P1(f315(f315(f317(x75282),x75285),f315(f161(x75282),x75284)))
% 168.60/168.39 [7529]~P1(f315(f315(f224(a901),x75291),f315(x75293,x75295)))+P1(f315(f315(f224(a901),x75291),f144(x75292,x75293,x75294)))+~P1(f315(f315(f317(x75292),x75295),f315(f161(x75292),x75294)))
% 168.60/168.39 [7923]P1(f315(x79231,x79232))+~P1(f315(x79231,x79233))+~P1(f315(f315(f317(x79234),x79232),f315(f161(x79234),f158(x79234,x79235,x79233))))
% 168.60/168.39 [7924]P1(f315(x79241,x79242))+~P1(f315(x79241,x79243))+~P1(f315(f315(f317(x79244),x79243),f315(f161(x79244),f158(x79244,x79245,x79242))))
% 168.60/168.39 [7929]~P111(x79291)+P1(f315(f315(f223(f909(x79291,a899)),f291(x79291,x79292,x79293)),f291(x79291,x79294,x79295)))+P1(f315(f315(f223(x79291),x79292),x79293))
% 168.60/168.39 [7950]~P5(x79501)+P1(f315(f315(f223(x79501),f315(f315(f32(x79502,x79501),x79503),x79504)),f315(x79504,x79505)))+~P1(f315(f315(f317(x79502),x79505),x79503))
% 168.60/168.39 [8019]~P25(x80191,x80192,x80194,x80193)+E(f315(f70(x80191,x80192,x80193,x80194),f315(x80194,x80195)),x80195)+~P1(f315(f315(f317(x80191),x80195),x80193))
% 168.60/168.39 [8020]~P25(x80201,x80202,x80204,x80203)+E(f315(f84(x80201,x80202,x80203,x80204),f315(x80204,x80205)),x80205)+~P1(f315(f315(f317(x80201),x80205),x80203))
% 168.60/168.39 [8219]~P1(f315(x82191,x82195))+P1(f315(x82191,f894(x82191,x82192,x82193,x82194)))+~P1(f315(f315(f317(x82194),x82195),x82193))
% 168.60/168.39 [8220]~P1(f315(x82201,x82205))+P1(f315(x82201,f894(x82201,x82202,x82203,x82204)))+~P1(f315(f315(f317(x82204),x82205),x82202))
% 168.60/168.39 [8315]P1(f315(f54(x83151),x83152))+~P1(f315(f54(x83153),x83154))+~P1(f315(f315(f223(f909(x83151,a899)),x83152),f315(f298(x83153,x83151,x83155),x83154)))
% 168.60/168.39 [8482]E(x84821,x84822)+~P25(x84823,x84824,x84825,f315(f315(f99(f909(x84823,a899)),f315(f161(x84823),x84821)),f315(f161(x84823),x84822)))+~E(f315(f315(f143(x84823,x84824),x84825),x84821),f315(f315(f143(x84823,x84824),x84825),x84822))
% 168.60/168.39 [8535]~P111(x85351)+~P1(f315(f315(f224(f909(x85351,a899)),f291(x85351,x85354,x85355)),f291(x85351,x85352,x85353)))+P1(f315(f315(f223(x85351),x85352),x85353))
% 168.60/168.39 [8597]~P25(x85971,x85974,x85975,f230(f909(x85971,a899)))+~P1(f315(f315(f317(x85974),f315(x85975,x85972)),f315(f298(x85971,x85974,x85975),x85973)))+P1(f315(f315(f317(x85971),x85972),x85973))
% 168.60/168.39 [8673]P1(f315(x86731,x86732))+~P1(f315(x86731,f333(x86731,x86733,x86734,x86735)))+~P1(f315(f315(f317(x86735),x86732),x86734))
% 168.60/168.39 [8674]P1(f315(x86741,x86742))+~P1(f315(x86741,f333(x86741,x86743,x86744,x86745)))+~P1(f315(f315(f317(x86745),x86742),x86743))
% 168.60/168.39 [8973]~P25(x89732,x89733,x89731,x89734)+E(f315(x89731,f315(f70(x89732,x89733,x89734,x89731),x89735)),x89735)+~P1(f315(f315(f317(x89733),x89735),f315(f298(x89732,x89733,x89731),x89734)))
% 168.60/168.39 [9077]E(x90771,f102(x90772))+E(f315(f315(f140(x90772),x90773),f662(x90774,x90773,x90775,x90771,x90772)),x90771)+~E(f315(f315(f123(x90772),x90771),x90775),f315(f315(f140(x90772),x90773),x90774))
% 168.60/168.39 [9078]E(x90781,f102(x90782))+E(f315(f315(f140(x90782),x90783),f663(x90784,x90781,x90785,x90783,x90782)),x90781)+~E(f315(f315(f123(x90782),x90781),x90784),f315(f315(f140(x90782),x90783),x90785))
% 168.60/168.39 [9096]E(f315(f315(f140(x90962),x90963),f662(x90964,x90963,x90961,x90965,x90962)),x90965)+~E(f315(f315(f123(x90962),x90965),x90961),f315(f315(f140(x90962),x90963),x90964))+E(x90961,f315(f315(f140(x90962),x90963),x90964))
% 168.60/168.39 [9097]E(f315(f315(f140(x90971),x90972),f663(x90974,x90975,x90973,x90972,x90971)),x90975)+~E(f315(f315(f123(x90971),x90975),x90974),f315(f315(f140(x90971),x90972),x90973))+E(f315(f315(f140(x90971),x90972),x90973),x90974)
% 168.60/168.39 [9173]~E(f315(f298(x91733,x91732,x91734),f230(f909(x91733,a899))),f230(f909(x91732,a899)))+~E(f315(f298(x91731,x91733,x91735),f230(f909(x91731,a899))),f230(f909(x91733,a899)))+E(f315(f298(x91731,x91732,f315(f66(x91733,x91732,x91731,x91734),x91735)),f230(f909(x91731,a899))),f230(f909(x91732,a899)))
% 168.60/168.39 [9548]E(x95481,f102(x95482))+~E(f315(f315(f123(x95482),x95481),x95483),f315(f315(f140(x95482),x95485),x95484))+E(f315(f315(f123(x95482),f663(x95483,x95481,x95484,x95485,x95482)),x95483),x95484)
% 168.60/168.39 [9549]E(x95491,f102(x95492))+~E(f315(f315(f123(x95492),x95491),x95495),f315(f315(f140(x95492),x95494),x95493))+E(f315(f315(f123(x95492),f662(x95493,x95494,x95495,x95491,x95492)),x95495),x95493)
% 168.60/168.39 [9556]E(f315(f315(f123(x95562),f662(x95564,x95563,x95561,x95565,x95562)),x95561),x95564)+~E(f315(f315(f123(x95562),x95565),x95561),f315(f315(f140(x95562),x95563),x95564))+E(x95561,f315(f315(f140(x95562),x95563),x95564))
% 168.60/168.39 [9557]~E(f315(f315(f123(x95571),x95575),x95574),f315(f315(f140(x95571),x95572),x95573))+E(f315(f315(f123(x95571),f663(x95574,x95575,x95573,x95572,x95571)),x95574),x95573)+E(f315(f315(f140(x95571),x95572),x95573),x95574)
% 168.60/168.39 [9558]E(f315(f315(f123(x95581),x95585),f665(x95583,x95582,x95584,x95585,x95581)),x95582)+E(f315(f315(f123(x95581),x95582),f664(x95583,x95582,x95584,x95585,x95581)),x95585)+~E(f315(f315(f123(x95581),x95585),x95584),f315(f315(f123(x95581),x95582),x95583))
% 168.60/168.39 [9595]~P110(x95951)+P13(x95951,f315(f315(f143(x95952,x95951),x95953),f138(x95952,x95951,x95953,x95954,x95955)))+~P13(x95951,f315(f315(f143(x95952,x95951),x95953),x95955))
% 168.60/168.39 [9614]~P60(x96145,x96141,x96144,x96143)+P1(f315(f315(x96141,x96142),f519(x96143,x96144,x96141,x96145,x96142)))+~P1(f315(f315(f317(x96145),x96142),x96144))
% 168.60/168.39 [9615]~P60(x96155,x96151,x96154,x96153)+P1(f315(f315(x96151,x96152),f781(x96153,x96154,x96151,x96155,x96152)))+~P1(f315(f315(f317(x96155),x96152),x96154))
% 168.60/168.39 [9720]~P1(f315(f315(f317(f908(x97201,x97201)),f315(f315(f240(x97201,x97201),x97205),x97203)),f295(x97201,x97204)))+P1(f315(f315(f317(f908(x97201,x97201)),f315(f315(f240(x97201,x97201),x97202),x97203)),f315(f315(f277(x97201,x97201,x97201),x97204),f295(x97201,x97204))))+~P1(f315(f315(f317(f908(x97201,x97201)),f315(f315(f240(x97201,x97201),x97202),x97205)),f315(f315(f277(x97201,x97201,x97201),x97204),f295(x97201,x97204))))
% 168.60/168.39 [9721]~P1(f315(f315(f317(f908(x97211,x97211)),f315(f315(f240(x97211,x97211),x97212),x97215)),f295(x97211,x97214)))+P1(f315(f315(f317(f908(x97211,x97211)),f315(f315(f240(x97211,x97211),x97212),x97213)),f315(f315(f277(x97211,x97211,x97211),x97214),f295(x97211,x97214))))+~P1(f315(f315(f317(f908(x97211,x97211)),f315(f315(f240(x97211,x97211),x97215),x97213)),f315(f315(f277(x97211,x97211,x97211),x97214),f295(x97211,x97214))))
% 168.60/168.39 [9723]P1(f315(f315(f317(f908(f902(x97231),f902(x97231))),f315(f315(f240(f902(x97231),f902(x97231)),x97232),x97233)),f147(x97231,f295(x97231,x97234))))+~P1(f315(f315(f317(f908(f902(x97231),f902(x97231))),f315(f315(f240(f902(x97231),f902(x97231)),x97232),x97235)),f147(x97231,f295(x97231,x97234))))+~P1(f315(f315(f317(f908(f902(x97231),f902(x97231))),f315(f315(f240(f902(x97231),f902(x97231)),x97235),x97233)),f147(x97231,f295(x97231,x97234))))
% 168.60/168.39 [9727]E(f315(f315(f123(x97271),x97272),f664(x97273,x97272,x97274,x97275,x97271)),x97275)+E(f315(f315(f123(x97271),f665(x97273,x97272,x97274,x97275,x97271)),x97273),x97274)+~E(f315(f315(f123(x97271),x97272),x97273),f315(f315(f123(x97271),x97275),x97274))
% 168.60/168.39 [9728]E(f315(f315(f123(x97281),x97282),f665(x97283,x97284,x97285,x97282,x97281)),x97284)+E(f315(f315(f123(x97281),f664(x97283,x97284,x97285,x97282,x97281)),x97285),x97283)+~E(f315(f315(f123(x97281),x97282),x97285),f315(f315(f123(x97281),x97284),x97283))
% 168.60/168.39 [9782]P1(f315(f315(f317(f908(x97821,x97821)),f315(f315(f240(x97821,x97821),x97822),x97823)),f315(f315(f277(x97821,x97821,x97821),x97824),f295(x97821,x97824))))+~P1(f315(f315(f317(f908(x97821,x97821)),f315(f315(f240(x97821,x97821),x97822),x97825)),f315(f315(f277(x97821,x97821,x97821),x97824),f295(x97821,x97824))))+~P1(f315(f315(f317(f908(x97821,x97821)),f315(f315(f240(x97821,x97821),x97825),x97823)),f315(f315(f277(x97821,x97821,x97821),x97824),f295(x97821,x97824))))
% 168.60/168.39 [9809]P36(x98091,x98092,x98093,x98094,x98095)+~E(f315(f178(f902(x98091)),x98094),f315(f178(f902(x98092)),x98095))+~P1(f315(f315(f245(x98091,x98092,a899),x98093),f681(x98095,x98094,x98093,x98092,x98091)))
% 168.60/168.39 [9810]P36(x98101,x98102,x98103,x98104,x98105)+~E(f315(f178(f902(x98101)),x98104),f315(f178(f902(x98102)),x98105))+~P1(f315(f315(f245(x98101,x98102,a899),x98103),f682(x98103,x98105,x98104,x98102,x98101)))
% 168.60/168.39 [9815]E(f315(f315(f123(x98151),f664(x98152,x98153,x98154,x98155,x98151)),x98154),x98152)+~E(f315(f315(f123(x98151),x98153),x98152),f315(f315(f123(x98151),x98155),x98154))+E(f315(f315(f123(x98151),f665(x98152,x98153,x98154,x98155,x98151)),x98152),x98154)
% 168.60/168.39 [9830]~P110(x98302)+E(f315(f315(f137(x98301,x98302,x98303),x98304),x98305),f315(f315(f140(x98301),x98304),x98305))+P1(f315(f315(f317(x98301),f727(x98304,x98303,x98305,x98301,x98302)),f315(f161(x98301),x98305)))
% 168.60/168.39 [9834]~P60(x98341,x98344,x98343,x98342)+~P1(f315(f315(f317(x98341),x98345),x98343))+P1(f315(f315(f317(x98341),f519(x98342,x98343,x98344,x98341,x98345)),x98342))
% 168.60/168.39 [9835]~P60(x98351,x98354,x98353,x98352)+~P1(f315(f315(f317(x98351),x98355),x98353))+P1(f315(f315(f317(x98351),f781(x98352,x98353,x98354,x98351,x98355)),x98352))
% 168.60/168.39 [9949]~P1(f315(f315(f317(f908(f909(x99491,a899),f909(x99491,a899))),f315(f315(f240(f909(x99491,a899),f909(x99491,a899)),x99494),x99493)),f306(x99491,x99492)))+~P1(f315(f315(f317(x99491),x99495),x99494))+P1(f315(f315(f317(x99491),f589(x99492,x99493,x99494,x99491,x99495)),x99493))
% 168.60/168.39 [9959]~P110(x99592)+E(f315(f315(f137(x99591,x99592,x99593),x99594),x99595),f315(f315(f140(x99591),x99594),x99595))+~P1(f315(f315(f223(x99592),f315(x99593,x99594)),f315(x99593,f727(x99594,x99593,x99595,x99591,x99592))))
% 168.60/168.39 [10008]~P25(x100083,x100084,x100085,f230(f909(x100083,a899)))+P1(f315(x100081,x100082))+~P1(f315(x100081,f315(f84(x100083,x100084,f230(f909(x100083,a899)),x100085),f794(x100082,x100081,x100085,x100084,x100083))))
% 168.60/168.39 [10153]P36(x101531,x101532,x101533,x101534,x101535)+~E(f315(f178(f902(x101531)),x101534),f315(f178(f902(x101532)),x101535))+~P1(f315(f315(x101533,f315(f315(f153(x101531),x101534),f683(x101535,x101534,x101533,x101532,x101531))),f315(f315(f153(x101532),x101535),f683(x101535,x101534,x101533,x101532,x101531))))
% 168.60/168.39 [10154]P36(x101541,x101542,x101543,x101544,x101545)+~E(f315(f178(f902(x101541)),x101544),f315(f178(f902(x101542)),x101545))+~P1(f315(f315(x101543,f315(f315(f153(x101541),x101544),f718(x101543,x101545,x101542,x101544,x101541))),f315(f315(f153(x101542),x101545),f718(x101543,x101545,x101542,x101544,x101541))))
% 168.60/168.39 [6690]~P18(x66902,x66905,x66901)+~P1(f315(f54(x66902),x66904))+E(f315(x66901,f315(f315(f297(x66902),x66903),x66904)),f315(f315(f57(x66902,x66902,x66905),x66903),x66904))
% 168.60/168.39 [6691]~E(x66913,x66914)+~E(x66912,x66915)+E(f315(f315(f297(x66911),x66912),f315(f315(f297(x66911),x66913),f177(f909(x66911,a899)))),f315(f315(f297(x66911),x66914),f315(f315(f297(x66911),x66915),f177(f909(x66911,a899)))))
% 168.60/168.39 [6702]P1(f315(x67022,x67025))+E(f166(x67021,x67022,f315(f315(f123(x67021),x67023),x67024)),f166(x67021,x67022,x67023))+~P1(f315(f315(f317(x67021),x67025),f315(f161(x67021),x67023)))
% 168.60/168.39 [6740]E(f315(x67401,x67402),f177(f909(x67403,a899)))+~E(f315(f315(f33(x67404,f909(x67403,a899)),x67405),x67401),f177(f909(x67403,a899)))+~P1(f315(f315(f317(x67404),x67402),x67405))
% 168.60/168.39 [6741]E(f315(x67411,x67412),f230(f909(x67413,a899)))+~E(f315(f315(f32(x67414,f909(x67413,a899)),x67415),x67411),f230(f909(x67413,a899)))+~P1(f315(f315(f317(x67414),x67412),x67415))
% 168.60/168.39 [7259]~E(x72592,x72594)+~P145(x72591)+E(f315(f315(f73(x72591),f315(f315(f74(x72591),x72592),x72593)),f315(f315(f74(x72591),x72594),x72595)),f315(f315(f73(x72591),f315(f315(f74(x72591),x72592),x72595)),f315(f315(f74(x72591),x72594),x72593)))
% 168.60/168.39 [7321]~P5(x73211)+~P1(f315(f315(f317(x73214),x73213),x73215))+P1(f315(f315(f223(x73211),f315(x73212,x73213)),f315(f315(f33(x73214,x73211),x73215),x73212)))
% 168.60/168.39 [7374]~P109(x73741)+P1(f315(f315(f223(x73741),f315(x73742,x73743)),f315(x73744,x73743)))+~P1(f315(f315(f223(f909(x73745,x73741)),x73742),x73744))
% 168.60/168.39 [7497]E(x74971,x74972)+E(x74973,x74971)+~E(f315(f315(f297(x74974),x74971),f315(f315(f297(x74974),x74975),f177(f909(x74974,a899)))),f315(f315(f297(x74974),x74972),f315(f315(f297(x74974),x74973),f177(f909(x74974,a899)))))
% 168.60/168.39 [7498]E(x74981,x74982)+E(x74983,x74981)+~E(f315(f315(f297(x74984),x74983),f315(f315(f297(x74984),x74982),f177(f909(x74984,a899)))),f315(f315(f297(x74984),x74985),f315(f315(f297(x74984),x74981),f177(f909(x74984,a899)))))
% 168.60/168.39 [7499]E(x74991,x74992)+E(x74991,x74993)+~E(f315(f315(f297(x74994),x74993),f315(f315(f297(x74994),x74992),f177(f909(x74994,a899)))),f315(f315(f297(x74994),x74995),f315(f315(f297(x74994),x74991),f177(f909(x74994,a899)))))
% 168.60/168.39 [7500]E(x75001,x75002)+E(x75001,x75003)+~E(f315(f315(f297(x75004),x75001),f315(f315(f297(x75004),x75005),f177(f909(x75004,a899)))),f315(f315(f297(x75004),x75002),f315(f315(f297(x75004),x75003),f177(f909(x75004,a899)))))
% 168.60/168.39 [8029]P25(x80291,x80292,x80293,x80294)+~P25(x80291,x80292,x80293,x80295)+~P1(f315(f315(f223(f909(x80291,a899)),x80294),x80295))
% 168.60/168.39 [8059]~E(f315(x80593,x80595),x80594)+~P25(x80591,x80592,x80593,f230(f909(x80591,a899)))+E(f315(f84(x80591,x80592,f230(f909(x80591,a899)),x80593),x80594),x80595)
% 168.60/168.39 [8207]E(x82071,x82072)+~E(f315(f298(x82073,x82074,x82075),x82071),f315(f298(x82073,x82074,x82075),x82072))+~P25(x82073,x82074,x82075,f315(f315(f99(f909(x82073,a899)),x82071),x82072))
% 168.60/168.39 [8285]P1(f315(x82852,x82854))+E(f315(f315(f127(x82851),f315(f178(f902(x82851)),f166(x82851,x82852,x82853))),x82853),f315(f315(f140(x82851),x82854),x82855))+~E(f315(f315(f123(x82851),f166(x82851,x82852,x82853)),f315(f315(f140(x82851),x82854),x82855)),x82853)
% 168.60/168.39 [8313]~P25(x83131,x83132,x83133,x83135)+~P25(x83131,x83132,x83133,x83134)+P25(x83131,x83132,x83133,f315(f315(f90(f909(x83131,a899)),x83134),x83135))
% 168.60/168.39 [8420]~P72(x84201)+E(f315(f315(f73(x84201),f315(x84202,x84203)),f315(f154(x84201),f315(f315(f143(x84204,x84201),x84202),f159(x84204,x84203,x84205)))),f315(f154(x84201),f315(f315(f143(x84204,x84201),x84202),x84205)))+~P1(f315(f315(f317(x84204),x84203),f315(f161(x84204),x84205)))
% 168.60/168.39 [8508]~P110(x85081)+~P13(x85081,f315(f315(f143(x85082,x85081),x85083),x85085))+P13(x85081,f315(f315(f143(x85082,x85081),x85083),f315(f315(f137(x85082,x85081,x85083),x85084),x85085)))
% 168.60/168.39 [8593]~P5(x85931)+P1(f315(f315(f223(x85931),f315(f315(f32(x85932,x85931),x85933),x85934)),f315(f315(f32(x85932,x85931),x85935),x85934)))+~P1(f315(f315(f223(f909(x85932,a899)),x85935),x85933))
% 168.60/168.39 [8594]~P5(x85941)+P1(f315(f315(f223(x85941),f315(f315(f33(x85942,x85941),x85943),x85944)),f315(f315(f33(x85942,x85941),x85945),x85944)))+~P1(f315(f315(f223(f909(x85942,a899)),x85943),x85945))
% 168.60/168.39 [8627]~P110(x86273)+P1(f315(f126(x86271),x86272))+~P1(f315(f126(x86271),f315(f315(f137(x86271,x86273,x86274),x86275),x86272)))
% 168.60/168.39 [8772]~P110(x87721)+~P1(f315(f315(f317(x87722),x87723),f315(f161(x87722),x87724)))+~P1(f315(f126(x87722),f315(f315(f137(x87722,x87721,x87725),x87723),x87724)))
% 168.60/168.39 [8862]~P110(x88621)+P13(x88621,f315(f315(f143(x88622,x88621),x88623),x88624))+~P13(x88621,f315(f315(f143(x88622,x88621),x88623),f315(f315(f137(x88622,x88621,x88623),x88625),x88624)))
% 168.60/168.39 [8908]~P25(x89082,x89081,x89084,x89083)+E(f315(f298(x89081,x89082,f84(x89082,x89081,x89083,x89084)),f315(f298(x89082,x89081,x89084),x89085)),x89085)+~P1(f315(f315(f223(f909(x89082,a899)),x89085),x89083))
% 168.60/168.39 [8961]~P110(x89612)+E(f315(f315(f137(x89611,x89612,x89613),x89614),x89615),f138(x89611,x89612,x89613,x89614,x89615))+P1(f315(f315(f317(x89612),f315(x89613,x89614)),f315(f298(x89611,x89612,x89613),f315(f161(x89611),x89615))))
% 168.60/168.39 [9043]~P110(x90432)+E(f138(x90431,x90432,x90433,x90434,x90435),x90435)+~P1(f315(f315(f317(x90432),f315(x90433,x90434)),f315(f298(x90431,x90432,x90433),f315(f161(x90431),x90435))))
% 168.60/168.39 [9057]~P25(x90572,x90571,x90573,x90575)+P1(f315(f315(f224(f909(x90571,a899)),f315(f298(x90572,x90571,x90573),x90574)),f315(f298(x90572,x90571,x90573),x90575)))+~P1(f315(f315(f224(f909(x90572,a899)),x90574),x90575))
% 168.60/168.39 [9214]~P25(x92141,x92142,x92143,f230(f909(x92141,a899)))+~P1(f315(f315(f223(f909(x92142,a899)),x92144),f315(f298(x92141,x92142,x92143),x92145)))+P1(f315(f315(f223(f909(x92141,a899)),f315(f299(x92141,x92142,x92143),x92144)),x92145))
% 168.60/168.39 [9237]~E(f315(f298(x92373,x92371,x92374),f230(f909(x92373,a899))),f230(f909(x92371,a899)))+P1(f315(f315(f223(f909(x92371,a899)),x92372),f315(f298(x92373,x92371,x92374),x92375)))+~P1(f315(f315(f223(f909(x92373,a899)),f315(f299(x92373,x92371,x92374),x92372)),x92375))
% 168.60/168.39 [9344]~P25(x93441,x93444,x93445,f230(f909(x93441,a899)))+~P1(f315(f315(f223(f909(x93444,a899)),f315(f298(x93441,x93444,x93445),x93442)),f315(f298(x93441,x93444,x93445),x93443)))+P1(f315(f315(f223(f909(x93441,a899)),x93442),x93443))
% 168.60/168.39 [9470]~P85(x94701)+~E(f315(x94703,f702(x94703,x94704,x94705,x94702,x94701)),f2(x94701))+E(f315(f154(x94701),f315(f315(f143(x94702,x94701),x94703),f315(f125(x94702,x94704),x94705))),f315(f154(x94701),f315(f315(f143(x94702,x94701),x94703),x94705)))
% 168.60/168.39 [9497]~P26(x94971,x94972,x94973,f230(f909(x94971,a899)),f230(f909(x94972,a899)))+~P1(f315(f315(f223(f909(x94972,a899)),x94974),f315(f298(x94971,x94972,x94973),x94975)))+P1(f315(f315(f223(f909(x94971,a899)),f315(f299(x94971,x94972,x94973),x94974)),x94975))
% 168.60/168.39 [9526]~P26(x95263,x95261,x95264,f230(f909(x95263,a899)),f230(f909(x95261,a899)))+P1(f315(f315(f223(f909(x95261,a899)),x95262),f315(f298(x95263,x95261,x95264),x95265)))+~P1(f315(f315(f223(f909(x95263,a899)),f315(f299(x95263,x95261,x95264),x95262)),x95265))
% 168.60/168.39 [9661]~P17(x96611,x96612,x96613)+~P1(f315(f54(x96611),x96615))+P1(f315(f59(x96611,x96612,x96613,x96614,x96615),f315(f315(f57(x96611,x96612,x96613),x96614),x96615)))
% 168.60/168.39 [9740]~P26(x97402,x97401,x97404,f230(f909(x97402,a899)),f230(f909(x97401,a899)))+~P26(x97401,x97403,x97405,f230(f909(x97401,a899)),f230(f909(x97403,a899)))+E(f315(f66(x97401,x97402,x97403,f84(x97402,x97401,f230(f909(x97402,a899)),x97404)),f84(x97401,x97403,f230(f909(x97401,a899)),x97405)),f84(x97402,x97403,f230(f909(x97402,a899)),f315(f66(x97401,x97403,x97402,x97405),x97404)))
% 168.60/168.39 [9741]P1(f315(x97411,f626(x97412,x97411,x97413,x97414,x97415)))+~P1(f315(f315(f223(f909(x97415,a899)),x97414),x97413))+P1(f315(f315(f223(f909(x97415,a899)),f315(f315(f90(f909(x97415,a899)),x97414),f315(f250(x97415),x97411))),f315(f315(f90(f909(x97415,a899)),x97413),f315(f250(x97415),x97412))))
% 168.60/168.39 [9755]~P85(x97551)+~P1(f315(x97554,f702(x97553,x97554,x97555,x97552,x97551)))+E(f315(f154(x97551),f315(f315(f143(x97552,x97551),x97553),f315(f125(x97552,x97554),x97555))),f315(f154(x97551),f315(f315(f143(x97552,x97551),x97553),x97555)))
% 168.60/168.39 [9832]~P5(x98325)+P1(f315(f315(f317(x98321),f417(x98322,x98323,x98321,x98324,x98325)),x98323))+P1(f315(f315(f223(x98325),x98324),f315(f315(f32(x98321,x98325),x98323),x98322)))
% 168.60/168.39 [9836]~P85(x98361)+E(f315(f154(x98361),f315(f315(f143(x98362,x98361),x98363),f315(f125(x98362,x98364),x98365))),f315(f154(x98361),f315(f315(f143(x98362,x98361),x98363),x98365)))+P1(f315(f315(f317(x98362),f702(x98363,x98364,x98365,x98362,x98361)),f315(f161(x98362),x98365)))
% 168.60/168.39 [9846]~P1(f315(x98465,f626(x98465,x98463,x98464,x98462,x98461)))+~P1(f315(f315(f223(f909(x98461,a899)),x98462),x98464))+P1(f315(f315(f223(f909(x98461,a899)),f315(f315(f90(f909(x98461,a899)),x98462),f315(f250(x98461),x98463))),f315(f315(f90(f909(x98461,a899)),x98464),f315(f250(x98461),x98465))))
% 168.60/168.39 [9862]~P25(x98625,x98623,x98624,f230(f909(x98625,a899)))+P1(f315(x98621,x98622))+P1(f315(f315(f317(x98623),f794(x98622,x98621,x98624,x98623,x98625)),f315(f298(x98625,x98623,x98624),f230(f909(x98625,a899)))))
% 168.60/168.39 [9885]P36(x98851,x98852,x98853,x98854,x98855)+~E(f315(f178(f902(x98852)),x98855),f315(f178(f902(x98851)),x98854))+P1(f315(f315(f224(a901),f683(x98855,x98854,x98853,x98852,x98851)),f315(f178(f902(x98851)),x98854)))
% 168.60/168.39 [9886]P36(x98861,x98862,x98863,x98864,x98865)+~E(f315(f178(f902(x98862)),x98865),f315(f178(f902(x98861)),x98864))+P1(f315(f315(f224(a901),f718(x98863,x98865,x98862,x98864,x98861)),f315(f178(f902(x98861)),x98864)))
% 168.60/168.39 [9917]P1(f315(f315(f317(x99171),f626(x99172,x99173,x99174,x99175,x99171)),x99175))+~P1(f315(f315(f223(f909(x99171,a899)),x99175),x99174))+P1(f315(f315(f223(f909(x99171,a899)),f315(f315(f90(f909(x99171,a899)),x99175),f315(f250(x99171),x99173))),f315(f315(f90(f909(x99171,a899)),x99174),f315(f250(x99171),x99172))))
% 168.60/168.39 [9960]~P5(x99601)+~P1(f315(f315(f223(x99601),x99602),f315(x99605,f417(x99605,x99604,x99603,x99602,x99601))))+P1(f315(f315(f223(x99601),x99602),f315(f315(f32(x99603,x99601),x99604),x99605)))
% 168.60/168.39 [9997]~P77(x99971)+~P1(f315(f54(x99972),x99975))+E(f315(f315(f315(f58(x99971,x99972,f74(x99971)),f315(f315(f20(x99972,x99971,x99971),f315(f315(f10(x99971,f909(x99971,x99971),x99972),f74(x99971)),x99973)),x99974)),f71(x99971)),x99975),f315(f315(f74(x99971),f315(f315(f315(f58(x99971,x99972,f74(x99971)),x99973),f71(x99971)),x99975)),f315(f315(f315(f58(x99971,x99972,f74(x99971)),x99974),f71(x99971)),x99975)))
% 168.60/168.39 [10052]~P1(f315(f315(f317(f908(f909(x100521,a899),f909(x100521,a899))),f315(f315(f240(f909(x100521,a899),f909(x100521,a899)),x100525),x100524)),f306(x100521,x100523)))+~P1(f315(f315(f317(x100521),x100522),x100525))+P1(f315(f315(f317(f908(x100521,x100521)),f315(f315(f240(x100521,x100521),x100522),f589(x100523,x100524,x100525,x100521,x100522))),x100523))
% 168.60/168.39 [10190]~P1(f315(f315(f317(f908(f902(x101901),f902(x101901))),f315(f315(f240(f902(x101901),f902(x101901)),f315(f315(f123(x101901),x101905),x101902)),f315(f315(f123(x101901),x101905),x101903))),f136(x101901,x101904)))+P1(f315(f315(f317(f908(f902(x101901),f902(x101901))),f315(f315(f240(f902(x101901),f902(x101901)),x101902),x101903)),f136(x101901,x101904)))+P1(f315(f315(f317(f908(x101901,x101901)),f315(f315(f240(x101901,x101901),f670(x101904,x101903,x101902,x101905,x101901)),f670(x101904,x101903,x101902,x101905,x101901))),x101904))
% 168.60/168.39 [7377]~E(x73773,x73775)+E(f315(f315(f153(x73771),f315(f315(f148(x73771,x73772),x73773),x73774)),x73775),x73774)+~P1(f315(f315(f224(a901),x73773),f315(f178(f902(x73771)),x73772)))
% 168.60/168.39 [7493]~E(f315(f315(f123(x74931),x74932),x74934),f315(f315(f123(x74931),x74933),x74935))+E(f315(f315(f164(x74931),f315(f178(f902(x74931)),x74932)),x74933),x74932)+P1(f315(f315(f223(a901),f315(f178(f902(x74931)),x74933)),f315(f178(f902(x74931)),x74932)))
% 168.60/168.39 [7990]~E(f315(f315(f123(x79901),x79902),x79904),f315(f315(f123(x79901),x79903),x79905))+E(f315(f315(f164(x79901),f315(f178(f902(x79901)),x79902)),x79903),x79902)+~P1(f315(f315(f223(a901),f315(f178(f902(x79901)),x79902)),f315(f178(f902(x79901)),x79903)))
% 168.60/168.39 [8014]~P1(f315(f54(x80141),f315(x80144,x80145)))+~P1(f315(f315(f317(x80142),x80145),x80143))+P1(f315(f54(x80141),f315(f315(f32(x80142,f909(x80141,a899)),x80143),x80144)))
% 168.60/168.39 [8191]~P54(x81911,x81913,x81915)+~P54(x81911,x81912,x81914)+P54(x81911,f315(f315(f99(f909(x81911,a899)),x81912),x81913),f315(f315(f99(f909(f908(x81911,x81911),a899)),x81914),x81915))
% 168.60/168.39 [8192]~P54(x81921,x81923,x81925)+~P54(x81921,x81922,x81924)+P54(x81921,f315(f315(f90(f909(x81921,a899)),x81922),x81923),f315(f315(f90(f909(f908(x81921,x81921),a899)),x81924),x81925))
% 168.60/168.39 [8548]E(f315(f315(f240(x85481,x85482),f315(f315(f153(x85481),x85483),x85484)),f315(f315(f153(x85482),x85485),x85484)),f315(f315(f153(f908(x85481,x85482)),f315(f315(f170(x85481,x85482),x85483),x85485)),x85484))+~P1(f315(f315(f224(a901),x85484),f315(f178(f902(x85481)),x85483)))+~P1(f315(f315(f224(a901),x85484),f315(f178(f902(x85482)),x85485)))
% 168.60/168.39 [8701]~P54(x87011,x87013,x87014)+P1(f315(f315(f317(x87011),x87012),x87013))+~P1(f315(f315(f317(f908(x87011,x87011)),f315(f315(f240(x87011,x87011),x87015),x87012)),x87014))
% 168.60/168.39 [8702]~P54(x87021,x87023,x87024)+P1(f315(f315(f317(x87021),x87022),x87023))+~P1(f315(f315(f317(f908(x87021,x87021)),f315(f315(f240(x87021,x87021),x87022),x87025)),x87024))
% 168.60/168.39 [8703]~P8(x87031,x87033,x87034)+P1(f315(f315(f317(x87031),x87032),x87033))+~P1(f315(f315(f317(f908(x87031,x87031)),f315(f315(f240(x87031,x87031),x87035),x87032)),x87034))
% 168.60/168.39 [8704]~P8(x87041,x87043,x87044)+P1(f315(f315(f317(x87041),x87042),x87043))+~P1(f315(f315(f317(f908(x87041,x87041)),f315(f315(f240(x87041,x87041),x87042),x87045)),x87044))
% 168.60/168.39 [8985]~P8(x89851,x89855,x89852)+E(f315(f273(x89851,x89851,x89852),f315(f315(f297(x89851),x89853),f177(f909(x89851,a899)))),f315(f273(x89851,x89851,x89852),f315(f315(f297(x89851),x89854),f177(f909(x89851,a899)))))+~P1(f315(f315(f317(f908(x89851,x89851)),f315(f315(f240(x89851,x89851),x89853),x89854)),x89852))
% 168.60/168.39 [9170]P1(f315(x91701,x91702))+~P1(f315(f315(f317(x91703),x91702),x91705))+P1(f315(f315(f317(x91703),f333(x91701,x91704,x91705,x91703)),f315(f315(f99(f909(x91703,a899)),x91705),x91704)))
% 168.60/168.39 [9171]P1(f315(x91711,x91712))+~P1(f315(f315(f317(x91713),x91712),x91714))+P1(f315(f315(f317(x91713),f333(x91711,x91714,x91715,x91713)),f315(f315(f99(f909(x91713,a899)),x91715),x91714)))
% 168.60/168.39 [9179]~P1(f315(x91792,x91795))+~P1(f315(f315(f317(x91791),x91795),x91794))+P1(f315(f315(f317(x91791),f894(x91792,x91793,x91794,x91791)),f315(f315(f99(f909(x91791,a899)),x91794),x91793)))
% 168.60/168.39 [9180]~P1(f315(x91802,x91805))+~P1(f315(f315(f317(x91801),x91805),x91803))+P1(f315(f315(f317(x91801),f894(x91802,x91803,x91804,x91801)),f315(f315(f99(f909(x91801,a899)),x91804),x91803)))
% 168.60/168.39 [9195]~P1(f315(f315(f223(f909(x91951,a899)),x91953),x91955))+~P1(f315(f315(f223(f909(x91951,a899)),x91952),x91954))+P1(f315(f315(f223(f909(x91951,a899)),f315(f315(f99(f909(x91951,a899)),x91952),x91953)),f315(f315(f99(f909(x91951,a899)),x91954),x91955)))
% 168.60/168.39 [9196]~P1(f315(f315(f223(f909(x91961,a899)),x91965),x91963))+~P1(f315(f315(f223(f909(x91961,a899)),x91962),x91964))+P1(f315(f315(f223(f909(x91961,a899)),f315(f315(f3(f909(x91961,a899)),x91962),x91963)),f315(f315(f3(f909(x91961,a899)),x91964),x91965)))
% 168.60/168.39 [9197]~P1(f315(f315(f223(f909(x91971,a899)),x91973),x91975))+~P1(f315(f315(f223(f909(x91971,a899)),x91972),x91974))+P1(f315(f315(f223(f909(x91971,a899)),f315(f315(f90(f909(x91971,a899)),x91972),x91973)),f315(f315(f90(f909(x91971,a899)),x91974),x91975)))
% 168.60/168.39 [9291]P1(f315(f315(f317(f908(x92911,x92911)),f315(f315(f240(x92911,x92911),x92912),x92913)),f309(x92911,x92914,x92915)))+~P1(f315(f315(f223(a901),f315(x92914,x92912)),f315(x92914,x92913)))+~P1(f315(f315(f317(f908(x92911,x92911)),f315(f315(f240(x92911,x92911),x92912),x92913)),x92915))
% 168.60/168.39 [9480]P1(f315(f315(f317(f908(x94801,x94801)),f315(f315(f240(x94801,x94801),x94802),x94803)),f295(x94801,x94804)))+~P1(f315(f315(f317(f908(x94801,x94801)),f315(f315(f240(x94801,x94801),x94802),x94805)),f295(x94801,x94804)))+~P1(f315(f315(f317(f908(x94801,x94801)),f315(f315(f240(x94801,x94801),x94805),x94803)),x94804))
% 168.60/168.39 [9481]P1(f315(f315(f317(f908(x94811,x94811)),f315(f315(f240(x94811,x94811),x94812),x94813)),f295(x94811,x94814)))+~P1(f315(f315(f317(f908(x94811,x94811)),f315(f315(f240(x94811,x94811),x94815),x94813)),f295(x94811,x94814)))+~P1(f315(f315(f317(f908(x94811,x94811)),f315(f315(f240(x94811,x94811),x94812),x94815)),x94814))
% 168.60/168.39 [9582]E(x95821,x95822)+E(f315(a101,f606(x95823,x95824,x95821,x95822,x95825)),x95824)+~P1(f315(f315(f317(f908(x95825,x95825)),f315(f315(f240(x95825,x95825),x95822),x95821)),f315(f315(f172(f908(x95825,x95825),a899),x95824),x95823)))
% 168.60/168.39 [9583]E(x95831,x95832)+E(f315(a101,f612(x95833,x95834,x95831,x95832,x95835)),x95834)+~P1(f315(f315(f317(f908(x95835,x95835)),f315(f315(f240(x95835,x95835),x95832),x95831)),f315(f315(f172(f908(x95835,x95835),a899),x95834),x95833)))
% 168.60/168.39 [9584]E(x95841,f2(a901))+E(f315(a101,f606(x95842,x95841,x95843,x95844,x95845)),x95841)+~P1(f315(f315(f317(f908(x95845,x95845)),f315(f315(f240(x95845,x95845),x95844),x95843)),f315(f315(f172(f908(x95845,x95845),a899),x95841),x95842)))
% 168.60/168.39 [9585]E(x95851,f2(a901))+E(f315(a101,f612(x95852,x95851,x95853,x95854,x95855)),x95851)+~P1(f315(f315(f317(f908(x95855,x95855)),f315(f315(f240(x95855,x95855),x95854),x95853)),f315(f315(f172(f908(x95855,x95855),a899),x95851),x95852)))
% 168.60/168.39 [9610]P1(f315(f315(f317(f908(x96101,x96101)),f315(f315(f240(x96101,x96101),x96102),x96103)),f315(f315(f277(x96101,x96101,x96101),x96104),f295(x96101,x96104))))+~P1(f315(f315(f317(f908(x96101,x96101)),f315(f315(f240(x96101,x96101),x96102),x96105)),x96104))+~P1(f315(f315(f317(f908(x96101,x96101)),f315(f315(f240(x96101,x96101),x96105),x96103)),x96104))
% 168.60/168.39 [9620]~P1(f315(f315(f317(f908(x96201,x96201)),f315(f315(f240(x96201,x96201),x96202),x96205)),f295(x96201,x96204)))+P1(f315(f315(f317(f908(x96201,x96201)),f315(f315(f240(x96201,x96201),x96202),x96203)),f315(f315(f277(x96201,x96201,x96201),x96204),f295(x96201,x96204))))+~P1(f315(f315(f317(f908(x96201,x96201)),f315(f315(f240(x96201,x96201),x96205),x96203)),x96204))
% 168.60/168.39 [9655]~P8(x96551,x96555,x96552)+~P1(f315(f315(f317(f908(x96551,x96551)),f315(f315(f240(x96551,x96551),x96553),x96554)),x96552))+P1(f315(f315(f223(f909(x96551,a899)),f315(f273(x96551,x96551,x96552),f315(f315(f297(x96551),x96553),f177(f909(x96551,a899))))),f315(f273(x96551,x96551,x96552),f315(f315(f297(x96551),x96554),f177(f909(x96551,a899))))))
% 168.60/168.39 [9713]P1(f315(f315(f317(f908(x97131,x97131)),f315(f315(f240(x97131,x97131),x97132),x97133)),f315(f315(f277(x97131,x97131,x97131),x97134),f295(x97131,x97134))))+~P1(f315(f315(f317(f908(x97131,x97131)),f315(f315(f240(x97131,x97131),x97132),x97135)),f315(f315(f277(x97131,x97131,x97131),x97134),f295(x97131,x97134))))+~P1(f315(f315(f317(f908(x97131,x97131)),f315(f315(f240(x97131,x97131),x97135),x97133)),x97134))
% 168.60/168.39 [9714]P1(f315(f315(f317(f908(x97141,x97141)),f315(f315(f240(x97141,x97141),x97142),x97143)),f315(f315(f277(x97141,x97141,x97141),x97144),f295(x97141,x97144))))+~P1(f315(f315(f317(f908(x97141,x97141)),f315(f315(f240(x97141,x97141),x97145),x97143)),f315(f315(f277(x97141,x97141,x97141),x97144),f295(x97141,x97144))))+~P1(f315(f315(f317(f908(x97141,x97141)),f315(f315(f240(x97141,x97141),x97142),x97145)),x97144))
% 168.60/168.39 [9764]~P1(f315(f59(x97641,x97641,x97644,x97642,x97643),x97645))+P1(f315(f315(f317(x97641),x97642),x97643))+P1(f315(f55(x97641,x97644,f315(f315(f297(x97641),x97642),x97643)),x97645))
% 168.60/168.39 [9802]~E(f315(f298(x98023,x98022,x98025),x98024),x98021)+E(x98021,f177(f909(x98022,a899)))+P1(f315(f315(f223(f909(x98023,a899)),f315(f298(x98022,x98023,f484(x98024,x98023,x98022,x98021)),x98021)),x98024))
% 168.60/168.39 [9849]~P5(x98495)+P1(f315(f315(f317(x98491),f419(x98492,x98493,x98494,x98491,x98495)),x98494))+P1(f315(f315(f223(x98495),f315(f315(f33(x98491,x98495),x98494),x98493)),x98492))
% 168.60/168.39 [9904]P36(x99041,x99042,x99043,x99044,x99045)+~E(f315(f178(f902(x99041)),x99044),f315(f178(f902(x99042)),x99045))+P1(f315(f315(f317(f908(x99041,x99042)),f681(x99045,x99044,x99043,x99042,x99041)),f315(f161(f908(x99041,x99042)),f315(f315(f170(x99041,x99042),x99044),x99045))))
% 168.60/168.39 [9905]P36(x99051,x99052,x99053,x99054,x99055)+~E(f315(f178(f902(x99051)),x99054),f315(f178(f902(x99052)),x99055))+P1(f315(f315(f317(f908(x99051,x99052)),f682(x99053,x99055,x99054,x99052,x99051)),f315(f161(f908(x99051,x99052)),f315(f315(f170(x99051,x99052),x99054),x99055))))
% 168.60/168.39 [10031]E(x100311,x100312)+P1(f315(f315(f317(f908(x100313,x100313)),f315(f315(f240(x100313,x100313),x100311),f613(x100314,x100315,x100312,x100311,x100313))),x100314))+~P1(f315(f315(f317(f908(x100313,x100313)),f315(f315(f240(x100313,x100313),x100311),x100312)),f315(f315(f172(f908(x100313,x100313),a899),x100315),x100314)))
% 168.60/168.39 [10032]E(x100321,f2(a901))+P1(f315(f315(f317(f908(x100322,x100322)),f315(f315(f240(x100322,x100322),x100323),f613(x100324,x100321,x100325,x100323,x100322))),x100324))+~P1(f315(f315(f317(f908(x100322,x100322)),f315(f315(f240(x100322,x100322),x100323),x100325)),f315(f315(f172(f908(x100322,x100322),a899),x100321),x100324)))
% 168.60/168.39 [10071]~P5(x100711)+~P1(f315(f315(f223(x100711),f315(x100714,f419(x100715,x100714,x100713,x100712,x100711))),x100715))+P1(f315(f315(f223(x100711),f315(f315(f33(x100712,x100711),x100713),x100714)),x100715))
% 168.60/168.39 [10123]E(x101231,x101232)+P1(f315(f315(f317(f908(x101233,x101233)),f315(f315(f240(x101233,x101233),f607(x101234,x101235,x101231,x101232,x101233)),x101231)),x101234))+~P1(f315(f315(f317(f908(x101233,x101233)),f315(f315(f240(x101233,x101233),x101232),x101231)),f315(f315(f172(f908(x101233,x101233),a899),x101235),x101234)))
% 168.60/168.39 [10124]E(x101241,f2(a901))+P1(f315(f315(f317(f908(x101242,x101242)),f315(f315(f240(x101242,x101242),f607(x101243,x101241,x101244,x101245,x101242)),x101244)),x101243))+~P1(f315(f315(f317(f908(x101242,x101242)),f315(f315(f240(x101242,x101242),x101245),x101244)),f315(f315(f172(f908(x101242,x101242),a899),x101241),x101243)))
% 168.60/168.39 [10128]E(x101281,x101282)+P1(f315(f315(f317(f908(x101283,x101283)),f315(f315(f240(x101283,x101283),x101281),f607(x101284,x101285,x101282,x101281,x101283))),f315(f315(f172(f908(x101283,x101283),a899),f606(x101284,x101285,x101282,x101281,x101283)),x101284)))+~P1(f315(f315(f317(f908(x101283,x101283)),f315(f315(f240(x101283,x101283),x101281),x101282)),f315(f315(f172(f908(x101283,x101283),a899),x101285),x101284)))
% 168.60/168.39 [10129]E(x101291,f2(a901))+P1(f315(f315(f317(f908(x101292,x101292)),f315(f315(f240(x101292,x101292),x101293),f607(x101294,x101291,x101295,x101293,x101292))),f315(f315(f172(f908(x101292,x101292),a899),f606(x101294,x101291,x101295,x101293,x101292)),x101294)))+~P1(f315(f315(f317(f908(x101292,x101292)),f315(f315(f240(x101292,x101292),x101293),x101295)),f315(f315(f172(f908(x101292,x101292),a899),x101291),x101294)))
% 168.60/168.39 [10181]E(x101811,x101812)+P1(f315(f315(f317(f908(x101813,x101813)),f315(f315(f240(x101813,x101813),f613(x101814,x101815,x101811,x101812,x101813)),x101811)),f315(f315(f172(f908(x101813,x101813),a899),f612(x101814,x101815,x101811,x101812,x101813)),x101814)))+~P1(f315(f315(f317(f908(x101813,x101813)),f315(f315(f240(x101813,x101813),x101812),x101811)),f315(f315(f172(f908(x101813,x101813),a899),x101815),x101814)))
% 168.60/168.39 [10182]E(x101821,f2(a901))+P1(f315(f315(f317(f908(x101822,x101822)),f315(f315(f240(x101822,x101822),f613(x101823,x101821,x101824,x101825,x101822)),x101824)),f315(f315(f172(f908(x101822,x101822),a899),f612(x101823,x101821,x101824,x101825,x101822)),x101823)))+~P1(f315(f315(f317(f908(x101822,x101822)),f315(f315(f240(x101822,x101822),x101825),x101824)),f315(f315(f172(f908(x101822,x101822),a899),x101821),x101823)))
% 168.60/168.39 [10215]~P72(x102152)+~P1(f315(f54(x102151),x102155))+E(f315(f315(f8(x102151,x102152),f315(f315(f9(x102151,x102152,x102152),f315(f315(f20(x102151,x102152,f909(x102152,x102152)),f315(f315(f10(a899,f909(x102152,f909(x102152,x102152)),x102151),f85(x102152)),f315(f315(f9(x102151,f909(x102151,a899),a899),f317(x102151)),x102153))),x102154)),f2(x102152))),x102155),f315(f315(f8(x102151,x102152),x102154),f315(f315(f90(f909(x102151,a899)),x102155),x102153)))
% 168.60/168.39 [8769]~P72(x87691)+~P1(f315(f54(x87694),x87695))+E(f315(f315(f73(x87691),f315(x87692,x87693)),f315(f315(f8(x87694,x87691),x87692),f315(f315(f3(f909(x87694,a899)),x87695),f315(f315(f297(x87694),x87693),f177(f909(x87694,a899)))))),f315(f315(f8(x87694,x87691),x87692),f315(f315(f297(x87694),x87693),x87695)))
% 168.60/168.39 [8770]~P77(x87701)+~P1(f315(f54(x87704),x87705))+E(f315(f315(f74(x87701),f315(x87702,x87703)),f315(f315(f11(x87704,x87701),x87702),f315(f315(f3(f909(x87704,a899)),x87705),f315(f315(f297(x87704),x87703),f177(f909(x87704,a899)))))),f315(f315(f11(x87704,x87701),x87702),f315(f315(f297(x87704),x87703),x87705)))
% 168.60/168.39 [9103]~P110(x91032)+~P13(x91032,f315(f157(x91032),f315(f315(f143(x91031,x91032),x91034),x91035)))+E(f315(f125(x91031,f315(f315(f10(x91032,a899,x91031),f315(f224(x91032),x91033)),x91034)),x91035),f166(x91031,f315(f315(f10(x91032,a899,x91031),f315(f224(x91032),x91033)),x91034),x91035))
% 168.60/168.39 [9127]~P72(x91271)+E(f315(f315(f73(x91271),f315(f315(f8(a901,x91271),x91272),f291(a901,x91273,x91274))),f315(f315(f8(a901,x91271),x91272),f291(a901,f315(f315(f73(a901),x91274),f71(a901)),f315(f315(f73(a901),x91274),x91275)))),f315(f315(f8(a901,x91271),x91272),f291(a901,x91273,f315(f315(f73(a901),x91274),x91275))))+~P1(f315(f315(f223(a901),x91273),f315(f315(f73(a901),x91274),f71(a901))))
% 168.60/168.39 [9128]~P1(f315(f315(f317(x91281),x91284),x91285))+~P1(f315(f315(f223(f909(x91281,a899)),f315(f161(x91281),x91282)),x91285))+P1(f315(f315(f223(f909(x91281,a899)),f315(f161(x91281),f315(f315(f148(x91281,x91282),x91283),x91284))),x91285))
% 168.60/168.39 [9353]~P5(x93532)+~P1(f315(f54(x93531),x93535))+E(f315(f315(f57(x93531,x93532,f315(f315(f10(x93532,f909(x93532,x93532),x93531),f99(x93532)),x93533)),x93534),x93535),f315(f315(f99(x93532),x93534),f315(f315(f33(x93531,x93532),x93535),x93533)))
% 168.60/168.39 [9354]~P5(x93542)+~P1(f315(f54(x93541),x93545))+E(f315(f315(f57(x93541,x93542,f315(f315(f10(x93542,f909(x93542,x93542),x93541),f90(x93542)),x93543)),x93544),x93545),f315(f315(f90(x93542),x93544),f315(f315(f32(x93541,x93542),x93545),x93543)))
% 168.60/168.39 [9405]E(f315(x94051,x94052),f315(x94051,x94053))+P1(f315(f315(f224(a901),f315(x94051,x94052)),f315(x94051,x94053)))+~P1(f315(f315(f317(f908(x94054,x94054)),f315(f315(f240(x94054,x94054),x94052),x94053)),f142(x94054,f315(f315(f140(f909(x94054,a901)),x94051),x94055))))
% 168.60/168.39 [9438]~E(f315(x94384,x94382),f315(x94384,x94383))+~P1(f315(f315(f317(f908(x94381,x94381)),f315(f315(f240(x94381,x94381),x94382),x94383)),f142(x94381,x94385)))+P1(f315(f315(f317(f908(x94381,x94381)),f315(f315(f240(x94381,x94381),x94382),x94383)),f142(x94381,f315(f315(f140(f909(x94381,a901)),x94384),x94385))))
% 168.60/168.39 [9458]~P25(x94581,x94582,x94583,x94585)+P25(x94581,x94582,x94583,f315(f315(f297(x94581),x94584),x94585))+P1(f315(f315(f317(x94582),f315(x94583,x94584)),f315(f298(x94581,x94582,x94583),f315(f315(f3(f909(x94581,a899)),x94585),f315(f315(f297(x94581),x94584),f177(f909(x94581,a899)))))))
% 168.60/168.39 [9461]P1(f315(x94612,x94615))+~P1(f315(f315(f317(x94611),x94615),f315(f161(x94611),x94613)))+E(f315(f315(f127(x94611),f315(f178(f902(x94611)),f166(x94611,x94612,f315(f315(f123(x94611),x94613),x94614)))),f315(f315(f123(x94611),x94613),x94614)),f315(f315(f123(x94611),f315(f315(f127(x94611),f315(f178(f902(x94611)),f166(x94611,x94612,x94613))),x94613)),x94614))
% 168.60/168.39 [9466]~P1(f315(f315(f317(f908(x94661,x94661)),f315(f315(f240(x94661,x94661),x94662),x94663)),f142(x94661,x94665)))+~P1(f315(f315(f223(a901),f315(x94664,x94662)),f315(x94664,x94663)))+P1(f315(f315(f317(f908(x94661,x94661)),f315(f315(f240(x94661,x94661),x94662),x94663)),f142(x94661,f315(f315(f140(f909(x94661,a901)),x94664),x94665))))
% 168.60/168.39 [9533]P1(f315(f315(f317(f908(x95334,x95334)),f315(f315(f240(x95334,x95334),x95332),x95333)),f142(x95334,x95335)))+P1(f315(f315(f224(a901),f315(x95331,x95332)),f315(x95331,x95333)))+~P1(f315(f315(f317(f908(x95334,x95334)),f315(f315(f240(x95334,x95334),x95332),x95333)),f142(x95334,f315(f315(f140(f909(x95334,a901)),x95331),x95335))))
% 168.60/168.39 [9685]~P1(f315(f315(f317(f908(f902(x96851),f902(x96851))),f315(f315(f240(f902(x96851),f902(x96851)),x96852),x96854)),f147(x96851,x96855)))+~P1(f315(f315(f224(a901),x96853),f315(f178(f902(x96851)),x96852)))+P1(f315(f315(f317(f908(x96851,x96851)),f315(f315(f240(x96851,x96851),f315(f315(f153(x96851),x96852),x96853)),f315(f315(f153(x96851),x96854),x96853))),x96855))
% 168.60/168.39 [9927]E(x99271,f2(a1))+~P1(f315(f42(x99273,x99271),f315(f315(f240(a1,a1),x99274),x99275)))+P1(f315(f42(f315(f315(f74(a1),x99272),x99273),x99271),f315(f315(f240(a1,a1),f315(f315(f73(a1),f315(f315(f74(a1),x99272),x99274)),f315(f315(f29(a1),f315(f315(f74(a1),x99272),x99275)),x99271))),f38(a1,f315(f315(f74(a1),x99272),x99275),x99271))))
% 168.60/168.39 [9928]~P1(f315(f315(f224(a901),f2(a901)),x99283))+~P1(f315(f41(x99282,x99283),f315(f315(f240(a901,a901),x99284),x99285)))+P1(f315(f41(f315(f315(f74(a901),x99281),x99282),x99283),f315(f315(f240(a901,a901),f315(f315(f73(a901),f315(f315(f74(a901),x99281),x99284)),f315(f315(f29(a901),f315(f315(f74(a901),x99281),x99285)),x99283))),f38(a901,f315(f315(f74(a901),x99281),x99285),x99283))))
% 168.60/168.39 [10238]~P72(x102382)+~P1(f315(f54(x102381),x102384))+E(f315(f315(f8(x102381,x102382),x102383),f315(f250(x102381),f315(f315(f20(x102381,a899,a899),f315(f315(f10(a899,f909(a899,a899),x102381),a313),f315(f315(f9(x102381,f909(x102381,a899),a899),f317(x102381)),x102384))),f315(f315(f9(x102381,f909(x102381,a899),a899),f317(x102381)),x102385)))),f315(f315(f8(x102381,x102382),f315(f315(f9(x102381,x102382,x102382),f315(f315(f20(x102381,x102382,f909(x102382,x102382)),f315(f315(f10(a899,f909(x102382,f909(x102382,x102382)),x102381),f85(x102382)),f315(f315(f9(x102381,f909(x102381,a899),a899),f317(x102381)),x102385))),x102383)),f2(x102382))),x102384))
% 168.60/168.39 [8399]~E(f315(f315(f123(x83991),x83992),x83995),f315(f315(f123(x83991),x83993),x83994))+E(f315(f315(f123(x83991),f315(f315(f127(x83991),f315(f178(f902(x83991)),x83992)),x83993)),x83994),x83995)+P1(f315(f315(f223(a901),f315(f178(f902(x83991)),x83993)),f315(f178(f902(x83991)),x83992)))
% 168.60/168.39 [8596]~E(f315(f315(f123(x85962),x85963),x85961),f315(f315(f123(x85962),x85964),x85965))+E(x85961,f315(f315(f123(x85962),f315(f315(f127(x85962),f315(f178(f902(x85962)),x85963)),x85964)),x85965))+~P1(f315(f315(f223(a901),f315(f178(f902(x85962)),x85963)),f315(f178(f902(x85962)),x85964)))
% 168.60/168.39 [8684]~E(f315(f315(f73(a901),f315(f315(f74(a901),x86843),x86844)),x86841),f315(f315(f73(a901),f315(f315(f74(a901),x86842),x86844)),x86845))+~P1(f315(f315(f223(a901),x86843),x86842))+E(x86841,f315(f315(f73(a901),f315(f315(f74(a901),f315(f315(f3(a901),x86842),x86843)),x86844)),x86845))
% 168.60/168.39 [8685]~E(f315(f315(f73(a901),f315(f315(f74(a901),x86851),x86853)),x86854),f315(f315(f73(a901),f315(f315(f74(a901),x86852),x86853)),x86855))+~P1(f315(f315(f223(a901),x86852),x86851))+E(f315(f315(f73(a901),f315(f315(f74(a901),f315(f315(f3(a901),x86851),x86852)),x86853)),x86854),x86855)
% 168.60/168.39 [8853]E(f315(f315(f73(a901),f315(f315(f74(a901),x88531),x88532)),x88533),f315(f315(f73(a901),f315(f315(f74(a901),x88534),x88532)),x88535))+~P1(f315(f315(f223(a901),x88534),x88531))+~E(x88535,f315(f315(f73(a901),f315(f315(f74(a901),f315(f315(f3(a901),x88531),x88534)),x88532)),x88533))
% 168.60/168.39 [8854]E(f315(f315(f73(a901),f315(f315(f74(a901),x88541),x88542)),x88543),f315(f315(f73(a901),f315(f315(f74(a901),x88544),x88542)),x88545))+~P1(f315(f315(f223(a901),x88544),x88541))+~E(f315(f315(f73(a901),f315(f315(f74(a901),f315(f315(f3(a901),x88541),x88544)),x88542)),x88543),x88545)
% 168.60/168.39 [9739]~P65(x97392)+~P1(f315(f54(x97391),x97395))+E(f315(f315(f11(x97391,x97392),f315(f315(f20(x97391,x97392,x97392),f315(f315(f10(x97392,f909(x97392,x97392),x97391),f279(x97392)),x97393)),x97394)),x97395),f315(f315(f279(x97392),f315(f315(f11(x97391,x97392),x97393),x97395)),f315(f315(f11(x97391,x97392),x97394),x97395)))
% 168.60/168.39 [9868]~E(f615(x98685,x98684,x98683,x98682,x98681),f616(x98685,x98684,x98683,x98682,x98681))+P1(f315(f315(f317(f908(x98681,x98681)),f315(f315(f240(x98681,x98681),x98682),x98683)),f295(x98681,x98684)))+~P1(f315(f315(f317(f908(x98681,x98681)),f315(f315(f240(x98681,x98681),x98682),x98683)),f295(x98681,f315(f315(f99(f909(f908(x98681,x98681),a899)),x98684),x98685))))
% 168.60/168.39 [9869]~E(f617(x98695,x98694,x98693,x98692,x98691),f618(x98695,x98694,x98693,x98692,x98691))+P1(f315(f315(f317(f908(x98691,x98691)),f315(f315(f240(x98691,x98691),x98692),x98693)),f295(x98691,x98694)))+~P1(f315(f315(f317(f908(x98691,x98691)),f315(f315(f240(x98691,x98691),x98692),x98693)),f295(x98691,f315(f315(f99(f909(f908(x98691,x98691),a899)),x98694),x98695))))
% 168.60/168.39 [10061]P1(f315(f315(f317(f908(x100611,x100611)),f315(f315(f240(x100611,x100611),x100612),f616(x100615,x100614,x100613,x100612,x100611))),f295(x100611,x100614)))+P1(f315(f315(f317(f908(x100611,x100611)),f315(f315(f240(x100611,x100611),x100612),x100613)),f295(x100611,x100614)))+~P1(f315(f315(f317(f908(x100611,x100611)),f315(f315(f240(x100611,x100611),x100612),x100613)),f295(x100611,f315(f315(f99(f909(f908(x100611,x100611),a899)),x100614),x100615))))
% 168.60/168.39 [10150]P1(f315(f315(f317(f908(x101501,x101501)),f315(f315(f240(x101501,x101501),f618(x101505,x101504,x101503,x101502,x101501)),x101503)),f295(x101501,x101504)))+P1(f315(f315(f317(f908(x101501,x101501)),f315(f315(f240(x101501,x101501),x101502),x101503)),f295(x101501,x101504)))+~P1(f315(f315(f317(f908(x101501,x101501)),f315(f315(f240(x101501,x101501),x101502),x101503)),f295(x101501,f315(f315(f99(f909(f908(x101501,x101501),a899)),x101504),x101505))))
% 168.60/168.39 [10188]P1(f315(f315(f317(f908(x101881,x101881)),f315(f315(f240(x101881,x101881),x101882),x101883)),f295(x101881,x101884)))+P1(f315(f315(f317(f908(x101881,x101881)),f315(f315(f240(x101881,x101881),f616(x101885,x101884,x101883,x101882,x101881)),f615(x101885,x101884,x101883,x101882,x101881))),x101885))+~P1(f315(f315(f317(f908(x101881,x101881)),f315(f315(f240(x101881,x101881),x101882),x101883)),f295(x101881,f315(f315(f99(f909(f908(x101881,x101881),a899)),x101884),x101885))))
% 168.60/168.39 [10189]P1(f315(f315(f317(f908(x101891,x101891)),f315(f315(f240(x101891,x101891),x101892),x101893)),f295(x101891,x101894)))+P1(f315(f315(f317(f908(x101891,x101891)),f315(f315(f240(x101891,x101891),f617(x101895,x101894,x101893,x101892,x101891)),f618(x101895,x101894,x101893,x101892,x101891))),x101895))+~P1(f315(f315(f317(f908(x101891,x101891)),f315(f315(f240(x101891,x101891),x101892),x101893)),f295(x101891,f315(f315(f99(f909(f908(x101891,x101891),a899)),x101894),x101895))))
% 168.60/168.39 [10336]~P1(f315(f315(f317(f908(f902(x103361),f902(x103361))),f315(f315(f240(f902(x103361),f902(x103361)),x103364),x103365)),f147(x103361,x103362)))+~P1(f315(f315(f317(f908(x103361,x103361)),x103363),f315(f161(f908(x103361,x103361)),f315(f315(f170(x103361,x103361),x103364),x103365))))+P1(f315(f315(f245(x103361,x103361,a899),f315(f315(f9(x103361,f909(f908(x103361,x103361),a899),f909(x103361,a899)),f315(f315(f10(f909(x103361,f909(f909(f908(x103361,x103361),a899),a899)),f909(f909(f908(x103361,x103361),a899),f909(x103361,a899)),x103361),f9(x103361,f909(f908(x103361,x103361),a899),a899)),f315(f315(f10(f909(x103361,f908(x103361,x103361)),f909(x103361,f909(f909(f908(x103361,x103361),a899),a899)),x103361),f315(f10(f908(x103361,x103361),f909(f909(f908(x103361,x103361),a899),a899),x103361),f317(f908(x103361,x103361)))),f240(x103361,x103361)))),x103362)),x103363))
% 168.60/168.39 [9768]~P1(f315(f315(f223(a901),x97683),x97682))+~P1(f315(f315(f223(a901),f315(f315(f73(a901),f315(f315(f74(a901),x97683),x97684)),x97681)),f315(f315(f73(a901),f315(f315(f74(a901),x97682),x97684)),x97685)))+P1(f315(f315(f223(a901),x97681),f315(f315(f73(a901),f315(f315(f74(a901),f315(f315(f3(a901),x97682),x97683)),x97684)),x97685)))
% 168.60/168.39 [9769]~P1(f315(f315(f223(a901),x97693),x97692))+~P1(f315(f315(f224(a901),f315(f315(f73(a901),f315(f315(f74(a901),x97693),x97694)),x97691)),f315(f315(f73(a901),f315(f315(f74(a901),x97692),x97694)),x97695)))+P1(f315(f315(f224(a901),x97691),f315(f315(f73(a901),f315(f315(f74(a901),f315(f315(f3(a901),x97692),x97693)),x97694)),x97695)))
% 168.60/168.39 [9786]~P1(f315(f315(f223(a901),x97861),x97864))+P1(f315(f315(f223(a901),f315(f315(f73(a901),f315(f315(f74(a901),x97861),x97862)),x97863)),f315(f315(f73(a901),f315(f315(f74(a901),x97864),x97862)),x97865)))+~P1(f315(f315(f223(a901),x97863),f315(f315(f73(a901),f315(f315(f74(a901),f315(f315(f3(a901),x97864),x97861)),x97862)),x97865)))
% 168.60/168.39 [9787]~P1(f315(f315(f223(a901),x97871),x97874))+P1(f315(f315(f224(a901),f315(f315(f73(a901),f315(f315(f74(a901),x97871),x97872)),x97873)),f315(f315(f73(a901),f315(f315(f74(a901),x97874),x97872)),x97875)))+~P1(f315(f315(f224(a901),x97873),f315(f315(f73(a901),f315(f315(f74(a901),f315(f315(f3(a901),x97874),x97871)),x97872)),x97875)))
% 168.60/168.39 [9902]~P1(f315(f315(f223(a901),x99022),x99021))+~P1(f315(f315(f223(a901),f315(f315(f73(a901),f315(f315(f74(a901),x99021),x99023)),x99024)),f315(f315(f73(a901),f315(f315(f74(a901),x99022),x99023)),x99025)))+P1(f315(f315(f223(a901),f315(f315(f73(a901),f315(f315(f74(a901),f315(f315(f3(a901),x99021),x99022)),x99023)),x99024)),x99025))
% 168.60/168.39 [9903]~P1(f315(f315(f223(a901),x99032),x99031))+~P1(f315(f315(f224(a901),f315(f315(f73(a901),f315(f315(f74(a901),x99031),x99033)),x99034)),f315(f315(f73(a901),f315(f315(f74(a901),x99032),x99033)),x99035)))+P1(f315(f315(f224(a901),f315(f315(f73(a901),f315(f315(f74(a901),f315(f315(f3(a901),x99031),x99032)),x99033)),x99034)),x99035))
% 168.60/168.39 [9946]~P1(f315(f315(f223(a901),x99464),x99461))+P1(f315(f315(f223(a901),f315(f315(f73(a901),f315(f315(f74(a901),x99461),x99462)),x99463)),f315(f315(f73(a901),f315(f315(f74(a901),x99464),x99462)),x99465)))+~P1(f315(f315(f223(a901),f315(f315(f73(a901),f315(f315(f74(a901),f315(f315(f3(a901),x99461),x99464)),x99462)),x99463)),x99465))
% 168.60/168.39 [9947]~P1(f315(f315(f223(a901),x99474),x99471))+P1(f315(f315(f224(a901),f315(f315(f73(a901),f315(f315(f74(a901),x99471),x99472)),x99473)),f315(f315(f73(a901),f315(f315(f74(a901),x99474),x99472)),x99475)))+~P1(f315(f315(f224(a901),f315(f315(f73(a901),f315(f315(f74(a901),f315(f315(f3(a901),x99471),x99474)),x99472)),x99473)),x99475))
% 168.60/168.39 [10176]~P11(x101761,x101762,x101765,x101763)+~P1(f315(f315(f317(f908(x101761,x101761)),x101764),x101765))+P1(f315(f315(f245(x101761,x101761,a899),f315(f315(f9(x101761,f909(x101761,x101762),f909(x101761,a899)),f315(f315(f10(f909(x101762,a899),f909(f909(x101761,x101762),f909(x101761,a899)),x101761),f10(x101762,a899,x101761)),f315(f315(f10(x101762,f909(x101762,a899),x101761),a312),x101763))),x101763)),x101764))
% 168.60/168.39 [8560]~P20(x85606,x85601,x85602,x85604)+E(f315(f66(x85601,x85601,x85601,f315(x85602,x85603)),f315(x85604,x85605)),f315(f66(x85601,x85601,x85601,f315(x85604,x85605)),f315(x85602,x85603)))+~P1(f315(f54(x85606),x85605))
% 168.60/168.39 [8997]~P25(x89971,x89973,x89975,x89976)+~P25(x89973,x89972,x89974,f315(f298(x89971,x89973,x89975),x89976))+P25(x89971,x89972,f315(f66(x89973,x89972,x89971,x89974),x89975),x89976)
% 168.60/168.39 [9565]~P1(f315(f315(x95653,x95652),x95656))+~P1(f315(f315(x95654,x95655),x95652))+P1(f315(f315(f317(x95651),x95652),f288(x95651,x95653,x95654,x95655,x95656)))
% 168.60/168.39 [9566]~P1(f315(f315(x95664,x95662),x95666))+~P1(f315(f315(x95663,x95665),x95662))+P1(f315(f315(f317(x95661),x95662),f285(x95661,x95663,x95664,x95665,x95666)))
% 168.60/168.39 [9686]E(x96861,x96862)+E(x96863,x96864)+~P1(f315(f315(f317(f908(f902(x96865),f902(x96865))),f315(f315(f240(f902(x96865),f902(x96865)),f315(f315(f140(x96865),x96863),x96861)),f315(f315(f140(x96865),x96864),x96862))),f146(x96865,x96866)))
% 168.60/168.39 [9695]~E(x96952,x96954)+P1(f315(f315(f317(f908(f902(x96951),f902(x96951))),f315(f315(f240(f902(x96951),f902(x96951)),f315(f315(f140(x96951),x96952),x96953)),f315(f315(f140(x96951),x96954),x96955))),f134(x96951,x96956)))+~P1(f315(f315(f317(f908(f902(x96951),f902(x96951))),f315(f315(f240(f902(x96951),f902(x96951)),x96953),x96955)),f134(x96951,x96956)))
% 168.60/168.39 [9696]~E(x96962,x96964)+P1(f315(f315(f317(f908(f902(x96961),f902(x96961))),f315(f315(f240(f902(x96961),f902(x96961)),f315(f315(f140(x96961),x96962),x96963)),f315(f315(f140(x96961),x96964),x96965))),f136(x96961,x96966)))+~P1(f315(f315(f317(f908(f902(x96961),f902(x96961))),f315(f315(f240(f902(x96961),f902(x96961)),x96963),x96965)),f136(x96961,x96966)))
% 168.60/168.39 [9697]~E(x96972,x96974)+P1(f315(f315(f317(f908(f902(x96971),f902(x96971))),f315(f315(f240(f902(x96971),f902(x96971)),f315(f315(f140(x96971),x96972),x96973)),f315(f315(f140(x96971),x96974),x96975))),f146(x96971,x96976)))+~P1(f315(f315(f317(f908(f902(x96971),f902(x96971))),f315(f315(f240(f902(x96971),f902(x96971)),x96973),x96975)),f146(x96971,x96976)))
% 168.60/168.39 [9698]~E(x96982,x96984)+P1(f315(f315(f317(f908(f902(x96981),f902(x96981))),f315(f315(f240(f902(x96981),f902(x96981)),f315(f315(f123(x96981),x96982),x96983)),f315(f315(f123(x96981),x96984),x96985))),f146(x96981,x96986)))+~P1(f315(f315(f317(f908(f902(x96981),f902(x96981))),f315(f315(f240(f902(x96981),f902(x96981)),x96983),x96985)),f146(x96981,x96986)))
% 168.60/168.39 [9699]~E(x96993,x96995)+P1(f315(f315(f317(f908(f902(x96991),f902(x96991))),f315(f315(f240(f902(x96991),f902(x96991)),f315(f315(f123(x96991),x96992),x96993)),f315(f315(f123(x96991),x96994),x96995))),f146(x96991,x96996)))+~P1(f315(f315(f317(f908(f902(x96991),f902(x96991))),f315(f315(f240(f902(x96991),f902(x96991)),x96992),x96994)),f146(x96991,x96996)))
% 168.60/168.39 [9756]E(x97561,x97562)+P1(f315(f315(f317(f908(f902(x97563),f902(x97563))),f315(f315(f240(f902(x97563),f902(x97563)),x97561),x97562)),f146(x97563,x97564)))+~P1(f315(f315(f317(f908(f902(x97563),f902(x97563))),f315(f315(f240(f902(x97563),f902(x97563)),f315(f315(f140(x97563),x97565),x97561)),f315(f315(f140(x97563),x97566),x97562))),f146(x97563,x97564)))
% 168.60/168.39 [9906]~E(x99063,x99065)+P1(f315(f315(f317(f908(f902(x99061),f902(x99061))),f315(f315(f240(f902(x99061),f902(x99061)),f315(f315(f123(x99061),x99062),f315(f315(f140(x99061),x99063),f102(x99061)))),f315(f315(f123(x99061),x99064),f315(f315(f140(x99061),x99065),f102(x99061))))),f146(x99061,x99066)))+~P1(f315(f315(f317(f908(f902(x99061),f902(x99061))),f315(f315(f240(f902(x99061),f902(x99061)),x99062),x99064)),f146(x99061,x99066)))
% 168.60/168.39 [9950]E(x99501,x99502)+E(x99503,x99504)+~P1(f315(f315(f317(f908(f902(x99505),f902(x99505))),f315(f315(f240(f902(x99505),f902(x99505)),f315(f315(f123(x99505),x99503),f315(f315(f140(x99505),x99501),f102(x99505)))),f315(f315(f123(x99505),x99504),f315(f315(f140(x99505),x99502),f102(x99505))))),f146(x99505,x99506)))
% 168.60/168.39 [9976]E(x99761,x99762)+~P1(f315(f315(f317(f908(f902(x99763),f902(x99763))),f315(f315(f240(f902(x99763),f902(x99763)),f315(f315(f123(x99763),x99761),f315(f315(f140(x99763),x99765),f102(x99763)))),f315(f315(f123(x99763),x99762),f315(f315(f140(x99763),x99766),f102(x99763))))),f146(x99763,x99764)))+P1(f315(f315(f317(f908(f902(x99763),f902(x99763))),f315(f315(f240(f902(x99763),f902(x99763)),x99761),x99762)),f146(x99763,x99764)))
% 168.60/168.39 [10014]~P1(f315(f315(f317(f908(f909(x100141,a899),f909(x100141,a899))),f315(f315(f240(f909(x100141,a899),f909(x100141,a899)),x100142),x100144)),f306(x100141,x100146)))+~P1(f315(f315(f317(f908(f909(x100141,a899),f909(x100141,a899))),f315(f315(f240(f909(x100141,a899),f909(x100141,a899)),x100143),x100145)),f306(x100141,x100146)))+P1(f315(f315(f317(f908(f909(x100141,a899),f909(x100141,a899))),f315(f315(f240(f909(x100141,a899),f909(x100141,a899)),f315(f315(f99(f909(x100141,a899)),x100142),x100143)),f315(f315(f99(f909(x100141,a899)),x100144),x100145))),f306(x100141,x100146)))
% 168.60/168.39 [5748]~E(f315(f315(f123(x57481),x57486),x57483),x57485)+E(f315(f315(f123(x57481),x57482),x57483),f315(f315(f140(x57481),x57484),x57485))+~E(x57482,f315(f315(f140(x57481),x57484),x57486))
% 168.60/168.39 [5749]~E(f315(f315(f123(x57491),x57496),x57493),x57495)+E(f315(f315(f123(x57491),x57492),x57493),f315(f315(f123(x57491),x57494),x57495))+~E(x57492,f315(f315(f123(x57491),x57494),x57496))
% 168.60/168.39 [5751]E(f315(f315(f123(x57511),x57512),x57513),f315(f315(f140(x57511),x57514),x57515))+~E(f315(f315(f140(x57511),x57514),x57516),x57512)+~E(x57515,f315(f315(f123(x57511),x57516),x57513))
% 168.60/168.39 [5753]~E(f315(f315(f123(x57531),x57532),x57536),x57534)+E(f315(f315(f123(x57531),x57532),x57533),f315(f315(f123(x57531),x57534),x57535))+~E(x57533,f315(f315(f123(x57531),x57536),x57535))
% 168.60/168.39 [6932]E(f315(x69321,x69322),f315(x69323,x69322))+~E(f315(f315(f143(x69324,x69325),x69321),x69326),f315(f315(f143(x69324,x69325),x69323),x69326))+~P1(f315(f315(f317(x69324),x69322),f315(f161(x69324),x69326)))
% 168.60/168.39 [7324]~P20(x73244,x73245,x73246,x73241)+E(f315(f315(x73241,x73242),x73243),f315(f315(f57(x73244,x73245,x73246),x73243),x73242))+~P1(f315(f54(x73244),x73242))
% 168.60/168.39 [7395]~E(x73952,f315(x73954,x73956))+~P1(f315(f315(f317(x73953),x73956),x73955))+P1(f315(f315(f317(x73951),x73952),f315(f298(x73953,x73951,x73954),x73955)))
% 168.60/168.39 [7396]~E(f315(x73964,x73962),x73966)+~P1(f315(f315(f317(x73963),x73966),x73965))+P1(f315(f315(f317(x73961),x73962),f315(f299(x73961,x73963,x73964),x73965)))
% 168.60/168.39 [7848]~P34(x78481,x78482,x78484,x78486)+P34(x78481,x78482,f315(f315(f140(x78481),x78483),x78484),f315(f315(f140(x78481),x78485),x78486))+~P1(f315(f315(x78482,x78483),x78485))
% 168.60/168.39 [8863]~P58(x88634,x88635,x88631,x88632,x88636)+E(f315(x88631,f315(x88632,x88633)),x88633)+~P1(f315(f315(f317(x88635),x88633),x88636))
% 168.60/168.39 [9363]~P26(x93632,x93631,x93635,x93634,x93633)+E(f315(f84(x93631,x93632,x93633,f84(x93632,x93631,x93634,x93635)),x93636),f315(x93635,x93636))+~P1(f315(f315(f317(x93632),x93636),x93634))
% 168.60/168.39 [9374]~P25(x93741,x93742,x93743,x93746)+P25(x93741,x93742,f68(x93741,x93742,x93743,x93744,x93745),x93746)+P1(f315(f315(f317(x93742),x93745),f315(f298(x93741,x93742,x93743),x93746)))
% 168.60/168.39 [9688]E(x96881,x96882)+E(f315(f178(f902(x96883)),x96884),f315(f178(f902(x96883)),x96885))+~P1(f315(f315(f317(f908(f902(x96883),f902(x96883))),f315(f315(f240(f902(x96883),f902(x96883)),f315(f315(f140(x96883),x96881),x96884)),f315(f315(f140(x96883),x96882),x96885))),f134(x96883,x96886)))
% 168.60/168.39 [9751]~P17(x97511,x97512,x97513)+E(f315(f315(f57(x97511,x97512,x97513),x97514),x97515),x97516)+~P1(f315(f59(x97511,x97512,x97513,x97514,x97515),x97516))
% 168.60/168.39 [9759]E(f315(f178(f902(x97591)),x97592),f315(f178(f902(x97591)),x97593))+P1(f315(f315(f317(f908(f902(x97591),f902(x97591))),f315(f315(f240(f902(x97591),f902(x97591)),x97592),x97593)),f134(x97591,x97594)))+~P1(f315(f315(f317(f908(f902(x97591),f902(x97591))),f315(f315(f240(f902(x97591),f902(x97591)),f315(f315(f140(x97591),x97595),x97592)),f315(f315(f140(x97591),x97596),x97593))),f134(x97591,x97594)))
% 168.60/168.39 [9780]~P1(f315(f315(f317(f908(x97801,x97801)),f315(f315(f240(x97801,x97801),x97802),x97804)),f295(x97801,x97806)))+P1(f315(f315(f317(f908(f902(x97801),f902(x97801))),f315(f315(f240(f902(x97801),f902(x97801)),f315(f315(f140(x97801),x97802),x97803)),f315(f315(f140(x97801),x97804),x97805))),f295(f902(x97801),f146(x97801,x97806))))+~P1(f315(f315(f317(f908(f902(x97801),f902(x97801))),f315(f315(f240(f902(x97801),f902(x97801)),x97803),x97805)),f295(f902(x97801),f146(x97801,x97806))))
% 168.60/168.39 [9956]~P1(f315(x99562,x99566))+~E(f315(f125(x99561,x99562),x99563),f315(f315(f140(x99561),x99564),x99565))+~P1(f315(f315(f317(x99561),x99566),f315(f161(x99561),f728(x99565,x99564,x99563,x99562,x99561))))
% 168.60/168.39 [9957]~P1(f315(x99574,x99576))+~E(f315(f315(f140(x99571),x99572),x99573),f315(f125(x99571,x99574),x99575))+~P1(f315(f315(f317(x99571),x99576),f315(f161(x99571),f726(x99575,x99574,x99573,x99572,x99571))))
% 168.60/168.39 [10273]~P72(x102732)+E(f315(f315(f8(x102731,x102732),f315(f315(f10(f909(x102733,a899),x102732,x102731),f315(f8(x102733,x102732),x102734)),f315(f315(f10(f909(x102733,a899),f909(x102733,a899),x102731),f250(x102733)),f315(f315(f10(f909(x102733,a899),f909(x102733,a899),x102731),f315(f20(x102733,a899,a899),f315(f315(f10(a899,f909(a899,a899),x102733),a313),f315(f315(f9(x102733,f909(x102733,a899),a899),f317(x102733)),x102735)))),f315(f9(x102733,x102731,a899),f315(f315(f10(x102731,f909(x102731,a899),x102733),a312),x102736)))))),f315(f298(x102733,x102731,x102736),x102735)),f315(f315(f8(x102733,x102732),x102734),x102735))+~P1(f315(f54(x102733),x102735))
% 168.60/168.39 [6990]~P110(x69903)+P1(f315(x69902,x69905))+E(f315(f125(x69901,x69902),f315(f315(f137(x69901,x69903,x69904),x69905),x69906)),f315(f125(x69901,x69902),x69906))
% 168.60/168.39 [6992]P1(f315(x69921,x69922))+~E(f155(x69923,x69921,x69924),f315(f315(f240(f902(x69923),f902(x69923)),x69925),x69926))+~P1(f315(f315(f317(x69923),x69922),f315(f161(x69923),x69925)))
% 168.60/168.39 [7038]~P1(f315(x70382,x70386))+~E(f155(x70381,x70382,x70383),f315(f315(f240(f902(x70381),f902(x70381)),x70384),x70385))+~P1(f315(f315(f317(x70381),x70386),f315(f161(x70381),x70385)))
% 168.60/168.39 [7710]~P15(x77101,x77102,x77103)+~P1(f315(f54(x77101),x77106))+E(f315(f315(f57(x77101,x77102,x77103),x77104),f315(f315(f297(x77101),x77105),x77106)),f315(f315(f57(x77101,x77102,x77103),f315(f315(x77103,x77105),x77104)),x77106))
% 168.60/168.39 [7763]~P110(x77632)+~P1(f315(f315(f223(x77632),f315(x77633,x77634)),f315(x77633,x77635)))+E(f315(f315(f137(x77631,x77632,x77633),x77634),f315(f315(f140(x77631),x77635),x77636)),f315(f315(f140(x77631),x77634),f315(f315(f140(x77631),x77635),x77636)))
% 168.60/168.39 [7876]E(x78761,x78762)+~E(f315(f315(f242(x78763,x78764),x78761),f315(f18(f909(x78764,a899),x78763),x78765)),f315(f315(f242(x78763,x78764),x78762),f315(f18(f909(x78764,a899),x78763),x78765)))+~P1(f315(f315(f317(x78764),x78766),x78765))
% 168.60/168.39 [7942]~P15(x79421,x79422,x79423)+~P1(f315(f54(x79421),x79426))+E(f315(f315(f57(x79421,x79422,x79423),x79424),f315(f315(f297(x79421),x79425),x79426)),f315(f315(x79423,x79425),f315(f315(f57(x79421,x79422,x79423),x79424),x79426)))
% 168.60/168.39 [8060]~P17(x80601,x80602,x80603)+~P1(f315(f54(x80601),x80606))+E(f315(f315(f57(x80601,x80602,x80603),f315(f315(x80603,x80604),x80605)),x80606),f315(f315(x80603,x80604),f315(f315(f57(x80601,x80602,x80603),x80605),x80606)))
% 168.60/168.39 [8129]~P21(x81292,x81295,x81296,x81291)+~P1(f315(f54(x81292),x81294))+E(f315(x81291,f315(f315(f297(x81292),x81293),x81294)),f315(f66(x81295,x81295,x81295,f315(x81291,x81294)),f315(x81296,x81293)))
% 168.60/168.39 [8161]~P110(x81612)+P1(f315(f315(f223(x81612),f315(x81613,x81614)),f315(x81613,x81615)))+E(f315(f315(f137(x81611,x81612,x81613),x81614),f315(f315(f140(x81611),x81615),x81616)),f315(f315(f140(x81611),x81615),f315(f315(f137(x81611,x81612,x81613),x81614),x81616)))
% 168.60/168.39 [8306]~E(f315(f178(f902(x83061)),x83065),f315(f178(f902(x83062)),x83066))+~E(f315(f178(f902(x83061)),x83063),f315(f178(f902(x83062)),x83064))+E(f315(f315(f123(f908(x83061,x83062)),f315(f315(f170(x83061,x83062),x83063),x83064)),f315(f315(f170(x83061,x83062),x83065),x83066)),f315(f315(f170(x83061,x83062),f315(f315(f123(x83061),x83063),x83065)),f315(f315(f123(x83062),x83064),x83066)))
% 168.60/168.39 [8417]~E(x84172,f315(f298(x84173,x84171,x84174),x84176))+P1(f315(f315(f223(f909(x84171,a899)),x84172),f315(f298(x84173,x84171,x84174),x84175)))+~P1(f315(f315(f223(f909(x84173,a899)),x84176),x84175))
% 168.60/168.39 [8519]~P110(x85195)+E(f315(x85191,x85192),f315(x85191,x85193))+E(f315(f315(f137(x85194,x85195,x85191),x85192),f315(f315(f137(x85194,x85195,x85191),x85193),x85196)),f315(f315(f137(x85194,x85195,x85191),x85193),f315(f315(f137(x85194,x85195,x85191),x85192),x85196)))
% 168.60/168.39 [8693]~P1(f315(f315(f317(x86932),x86934),f315(x86936,x86933)))+~P1(f315(f315(f317(x86931),x86933),x86935))+P1(f315(f315(f317(f908(x86931,x86932)),f315(f315(f240(x86931,x86932),x86933),x86934)),f315(f315(f242(x86931,x86932),x86935),x86936)))
% 168.60/168.39 [9168]~P72(x91682)+~P25(x91684,x91681,x91685,x91686)+E(f315(f315(f8(x91681,x91682),x91683),f315(f298(x91684,x91681,x91685),x91686)),f315(f315(f8(x91684,x91682),f315(f66(x91681,x91682,x91684,x91683),x91685)),x91686))
% 168.60/168.39 [9169]~P77(x91692)+~P25(x91694,x91691,x91695,x91696)+E(f315(f315(f11(x91691,x91692),x91693),f315(f298(x91694,x91691,x91695),x91696)),f315(f315(f11(x91694,x91692),f315(f66(x91691,x91692,x91694,x91693),x91695)),x91696))
% 168.60/168.39 [9216]~P36(x92162,x92165,x92161,x92163,x92166)+P1(f315(f315(x92161,f315(f315(f153(x92162),x92163),x92164)),f315(f315(f153(x92165),x92166),x92164)))+~P1(f315(f315(f224(a901),x92164),f315(f178(f902(x92165)),x92166)))
% 168.60/168.39 [9217]~P36(x92172,x92175,x92171,x92173,x92176)+P1(f315(f315(x92171,f315(f315(f153(x92172),x92173),x92174)),f315(f315(f153(x92175),x92176),x92174)))+~P1(f315(f315(f224(a901),x92174),f315(f178(f902(x92172)),x92173)))
% 168.60/168.39 [9228]~E(f315(f298(x92281,x92282,x92283),x92284),x92286)+E(f315(f298(x92281,x92282,x92283),f315(f298(x92282,x92281,f84(x92281,x92282,x92284,x92283)),x92285)),x92285)+~P1(f315(f315(f223(f909(x92282,a899)),x92285),x92286))
% 168.60/168.39 [9433]~P20(x94333,x94331,x94336,x94332)+~P1(f315(f54(x94333),x94334))+E(f315(f66(x94331,x94331,x94331,f315(x94332,f315(f315(f3(f909(x94333,a899)),x94334),f315(f315(f297(x94333),x94335),f177(f909(x94333,a899)))))),f315(x94336,x94335)),f315(x94332,f315(f315(f297(x94333),x94335),x94334)))
% 168.60/168.39 [10043]~E(f315(f298(x100432,x100434,x100436),f230(f909(x100432,a899))),f230(f909(x100434,a899)))+~E(f315(f298(x100431,x100433,x100435),f230(f909(x100431,a899))),f230(f909(x100433,a899)))+E(f315(f298(f908(x100431,x100432),f908(x100433,x100434),f246(x100431,x100433,x100432,x100434,x100435,x100436)),f230(f909(f908(x100431,x100432),a899))),f230(f909(f908(x100433,x100434),a899)))
% 168.60/168.39 [10100]~P25(x101003,x101004,x101005,f315(x101006,f524(x101006,x101005,x101004,x101003,x101002,x101001)))+P25(x101003,x101004,x101005,f315(f315(f32(x101002,f909(x101003,a899)),x101001),x101006))+E(x101001,f177(f909(x101002,a899)))
% 168.60/168.39 [10157]P25(x101576,x101575,x101574,f315(f315(f32(x101572,f909(x101576,a899)),x101571),x101573))+E(x101571,f177(f909(x101572,a899)))+P1(f315(f315(f317(x101572),f524(x101573,x101574,x101575,x101576,x101572,x101571)),x101571))
% 168.60/168.39 [10162]P1(f315(f315(f317(x101621),f585(x101622,x101623,x101624,x101625,x101626,x101621)),x101626))+P1(f315(f315(f223(f909(f908(x101621,x101624),a899)),f315(f315(f242(x101621,x101624),x101626),x101623)),f315(f315(f242(x101621,x101624),x101625),x101622)))+~P1(f315(f315(f223(f909(x101621,a899)),x101626),x101625))
% 168.60/168.39 [10291]~P1(f315(f315(f223(f909(x102912,a899)),f315(x102914,f585(x102916,x102914,x102912,x102915,x102913,x102911))),f315(x102916,f585(x102916,x102914,x102912,x102915,x102913,x102911))))+~P1(f315(f315(f223(f909(x102911,a899)),x102913),x102915))+P1(f315(f315(f223(f909(f908(x102911,x102912),a899)),f315(f315(f242(x102911,x102912),x102913),x102914)),f315(f315(f242(x102911,x102912),x102915),x102916)))
% 168.60/168.39 [7898]~P1(f315(x78981,x78985))+~P1(f315(x78986,x78984))+P1(f315(x78981,f315(f244(x78982,x78983),f315(f315(f240(x78982,x78983),x78984),x78985))))
% 168.60/168.39 [7899]~P1(f315(x78991,x78994))+~P1(f315(x78996,x78995))+P1(f315(x78991,f315(f239(x78992,x78993),f315(f315(f240(x78992,x78993),x78994),x78995))))
% 168.60/168.39 [7947]~P1(f315(f315(x79474,x79476),x79475))+~P1(f315(f315(f317(x79471),x79476),x79473))+P1(f315(f315(f315(f33(x79471,f909(x79472,a899)),x79473),x79474),x79475))
% 168.60/168.39 [8256]~P1(f315(f315(f317(x82561),x82562),f315(x82565,x82566)))+~P1(f315(f315(f317(x82563),x82566),x82564))+P1(f315(f315(f317(x82561),x82562),f315(f315(f33(x82563,f909(x82561,a899)),x82564),x82565)))
% 168.60/168.39 [8300]P1(f315(f315(x83001,x83002),x83003))+~P1(f315(f315(x83004,x83002),x83003))+~P1(f315(f315(f223(f909(x83005,f909(x83006,a899))),x83004),x83001))
% 168.60/168.39 [8440]P1(f315(f315(x84401,x84402),x84403))+~P1(f315(f315(f317(x84404),x84402),x84405))+~P1(f315(f315(f315(f32(x84404,f909(x84406,a899)),x84405),x84401),x84403))
% 168.60/168.39 [8575]P1(f315(f315(f317(x85751),x85752),f315(x85753,x85754)))+~P1(f315(f315(f317(x85755),x85754),x85756))+~P1(f315(f315(f317(x85751),x85752),f315(f315(f32(x85755,f909(x85751,a899)),x85756),x85753)))
% 168.60/168.39 [8842]~P11(x88424,x88425,x88426,x88421)+E(f315(x88421,x88422),f315(x88421,x88423))+~P1(f315(f315(f317(f908(x88424,x88424)),f315(f315(f240(x88424,x88424),x88422),x88423)),x88426))
% 168.60/168.39 [8877]P1(f315(f315(f223(f909(x88771,a899)),x88772),f315(x88773,x88774)))+~P1(f315(f315(f317(x88775),x88774),x88776))+~P1(f315(f315(f223(f909(x88771,a899)),x88772),f315(f315(f32(x88775,f909(x88771,a899)),x88776),x88773)))
% 168.60/168.39 [8910]~P56(x89103,x89104,f315(f274(x89104,x89103),x89105))+E(x89101,f177(f909(x89102,a899)))+E(f315(f315(f32(x89102,f909(x89103,a899)),x89101),f315(f315(f10(f909(x89104,a899),f909(x89103,a899),x89102),f273(x89104,x89103,x89105)),x89106)),f315(f273(x89104,x89103,x89105),f315(f315(f32(x89102,f909(x89104,a899)),x89101),x89106)))
% 168.60/168.39 [8988]P1(f315(f315(f317(x89881),x89882),f315(f273(x89883,x89881,x89884),x89885)))+~P1(f315(f315(f317(x89883),x89886),x89885))+~P1(f315(f315(f317(f908(x89883,x89881)),f315(f315(f240(x89883,x89881),x89886),x89882)),x89884))
% 168.60/168.39 [9293]P1(f315(f315(f223(f909(x92931,a899)),f315(f273(x92932,x92931,x92933),x92934)),f315(f273(x92932,x92931,x92935),x92936)))+~P1(f315(f315(f223(f909(x92932,a899)),x92934),x92936))+~P1(f315(f315(f223(f909(f908(x92932,x92931),a899)),x92933),x92935))
% 168.60/168.39 [9482]~P1(f315(f315(f317(x94822),x94826),x94824))+~P1(f315(f315(f223(f909(x94821,a899)),x94823),x94825))+P1(f315(f315(f223(f909(f908(x94821,x94822),a899)),f315(f315(f242(x94821,x94822),x94823),f315(f18(f909(x94822,a899),x94821),x94824))),f315(f315(f242(x94821,x94822),x94825),f315(f18(f909(x94822,a899),x94821),x94824))))
% 168.60/168.39 [9494]~P36(x94941,x94942,x94943,x94945,x94946)+P1(f315(f315(f245(x94941,x94942,a899),x94943),x94944))+~P1(f315(f315(f317(f908(x94941,x94942)),x94944),f315(f161(f908(x94941,x94942)),f315(f315(f170(x94941,x94942),x94945),x94946))))
% 168.60/168.39 [9642]~E(x96423,x96425)+P1(f315(f315(f317(f908(f902(x96421),f902(x96421))),f315(f315(f240(f902(x96421),f902(x96421)),f315(f315(f140(x96421),x96422),x96423)),f315(f315(f140(x96421),x96424),x96425))),f146(x96421,x96426)))+~P1(f315(f315(f317(f908(x96421,x96421)),f315(f315(f240(x96421,x96421),x96422),x96424)),x96426))
% 168.60/168.39 [9648]~E(f315(f178(f902(x96481)),x96483),f315(f178(f902(x96481)),x96485))+P1(f315(f315(f317(f908(f902(x96481),f902(x96481))),f315(f315(f240(f902(x96481),f902(x96481)),f315(f315(f140(x96481),x96482),x96483)),f315(f315(f140(x96481),x96484),x96485))),f134(x96481,x96486)))+~P1(f315(f315(f317(f908(x96481,x96481)),f315(f315(f240(x96481,x96481),x96482),x96484)),x96486))
% 168.60/168.39 [9680]P1(f315(f315(f317(f908(x96801,x96801)),f315(f315(f240(x96801,x96801),x96802),x96803)),f315(f315(f172(f908(x96801,x96801),a899),f315(a101,x96804)),x96805)))+~P1(f315(f315(f317(f908(x96801,x96801)),f315(f315(f240(x96801,x96801),x96806),x96803)),x96805))+~P1(f315(f315(f317(f908(x96801,x96801)),f315(f315(f240(x96801,x96801),x96802),x96806)),f315(f315(f172(f908(x96801,x96801),a899),x96804),x96805)))
% 168.60/168.39 [9681]P1(f315(f315(f317(f908(x96811,x96811)),f315(f315(f240(x96811,x96811),x96812),x96813)),f315(f315(f172(f908(x96811,x96811),a899),f315(a101,x96814)),x96815)))+~P1(f315(f315(f317(f908(x96811,x96811)),f315(f315(f240(x96811,x96811),x96812),x96816)),x96815))+~P1(f315(f315(f317(f908(x96811,x96811)),f315(f315(f240(x96811,x96811),x96816),x96813)),f315(f315(f172(f908(x96811,x96811),a899),x96814),x96815)))
% 168.60/168.39 [9684]~P1(f315(f315(f317(x96844),x96845),x96846))+P1(f315(f315(f223(f909(x96841,a899)),x96842),x96843))+~P1(f315(f315(f223(f909(f908(x96841,x96844),a899)),f315(f315(f242(x96841,x96844),x96842),f315(f18(f909(x96844,a899),x96841),x96846))),f315(f315(f242(x96841,x96844),x96843),f315(f18(f909(x96844,a899),x96841),x96846))))
% 168.60/168.39 [9729]E(x97291,x97292)+~P1(f315(f315(f317(f908(f902(x97293),f902(x97293))),f315(f315(f240(f902(x97293),f902(x97293)),f315(f315(f140(x97293),x97291),x97295)),f315(f315(f140(x97293),x97292),x97296))),f134(x97293,x97294)))+P1(f315(f315(f317(f908(x97293,x97293)),f315(f315(f240(x97293,x97293),x97291),x97292)),x97294))
% 168.60/168.39 [9730]E(x97301,x97302)+~P1(f315(f315(f317(f908(f902(x97303),f902(x97303))),f315(f315(f240(f902(x97303),f902(x97303)),f315(f315(f140(x97303),x97301),x97305)),f315(f315(f140(x97303),x97302),x97306))),f136(x97303,x97304)))+P1(f315(f315(f317(f908(x97303,x97303)),f315(f315(f240(x97303,x97303),x97301),x97302)),x97304))
% 168.60/168.39 [9731]E(x97311,x97312)+~P1(f315(f315(f317(f908(f902(x97313),f902(x97313))),f315(f315(f240(f902(x97313),f902(x97313)),f315(f315(f140(x97313),x97311),x97315)),f315(f315(f140(x97313),x97312),x97316))),f146(x97313,x97314)))+P1(f315(f315(f317(f908(x97313,x97313)),f315(f315(f240(x97313,x97313),x97311),x97312)),x97314))
% 168.60/168.39 [9767]P1(f315(f315(f317(f908(f902(x97671),f902(x97671))),f315(f315(f240(f902(x97671),f902(x97671)),f315(f315(f140(x97671),x97672),x97673)),f315(f315(f140(x97671),x97674),x97675))),f147(x97671,x97676)))+~P1(f315(f315(f317(f908(f902(x97671),f902(x97671))),f315(f315(f240(f902(x97671),f902(x97671)),x97673),x97675)),f147(x97671,x97676)))+~P1(f315(f315(f317(f908(x97671,x97671)),f315(f315(f240(x97671,x97671),x97672),x97674)),x97676))
% 168.60/168.39 [9784]P1(f315(x97841,x97842))+~P1(f315(x97841,f445(x97841,x97843,x97844,x97845,x97846)))+~P1(f315(f315(f317(x97846),x97842),f315(f315(f33(x97845,f909(x97846,a899)),x97844),x97843)))
% 168.60/168.39 [9789]~P1(f315(f315(f317(f908(f902(x97891),f902(x97891))),f315(f315(f240(f902(x97891),f902(x97891)),f315(f315(f140(x97891),x97892),x97895)),f315(f315(f140(x97891),x97893),x97896))),f134(x97891,x97894)))+P1(f315(f315(f317(f908(f902(x97891),f902(x97891))),f315(f315(f240(f902(x97891),f902(x97891)),x97895),x97896)),f134(x97891,x97894)))+P1(f315(f315(f317(f908(x97891,x97891)),f315(f315(f240(x97891,x97891),x97892),x97893)),x97894))
% 168.60/168.39 [9790]~P1(f315(f315(f317(f908(f902(x97901),f902(x97901))),f315(f315(f240(f902(x97901),f902(x97901)),f315(f315(f140(x97901),x97902),x97905)),f315(f315(f140(x97901),x97903),x97906))),f136(x97901,x97904)))+P1(f315(f315(f317(f908(f902(x97901),f902(x97901))),f315(f315(f240(f902(x97901),f902(x97901)),x97905),x97906)),f136(x97901,x97904)))+P1(f315(f315(f317(f908(x97901,x97901)),f315(f315(f240(x97901,x97901),x97902),x97903)),x97904))
% 168.60/168.39 [9791]~P1(f315(f315(f317(f908(f902(x97911),f902(x97911))),f315(f315(f240(f902(x97911),f902(x97911)),f315(f315(f140(x97911),x97912),x97915)),f315(f315(f140(x97911),x97913),x97916))),f146(x97911,x97914)))+P1(f315(f315(f317(f908(f902(x97911),f902(x97911))),f315(f315(f240(f902(x97911),f902(x97911)),x97915),x97916)),f146(x97911,x97914)))+P1(f315(f315(f317(f908(x97911,x97911)),f315(f315(f240(x97911,x97911),x97912),x97913)),x97914))
% 168.60/168.39 [9879]P1(f315(x98791,x98792))+P1(f315(f315(f317(x98793),f430(x98791,x98794,x98795,x98793,x98796)),x98795))+~P1(f315(f315(f317(x98796),x98792),f315(f315(f33(x98793,f909(x98796,a899)),x98795),x98794)))
% 168.60/168.39 [9890]~E(x98902,x98904)+P1(f315(f315(f317(f908(f902(x98901),f902(x98901))),f315(f315(f240(f902(x98901),f902(x98901)),f315(f315(f123(x98901),x98902),f315(f315(f140(x98901),x98903),f102(x98901)))),f315(f315(f123(x98901),x98904),f315(f315(f140(x98901),x98905),f102(x98901))))),f146(x98901,x98906)))+~P1(f315(f315(f317(f908(x98901,x98901)),f315(f315(f240(x98901,x98901),x98903),x98905)),x98906))
% 168.60/168.39 [9964]E(x99641,x99642)+~P1(f315(f315(f317(f908(f902(x99643),f902(x99643))),f315(f315(f240(f902(x99643),f902(x99643)),f315(f315(f123(x99643),x99645),f315(f315(f140(x99643),x99641),f102(x99643)))),f315(f315(f123(x99643),x99646),f315(f315(f140(x99643),x99642),f102(x99643))))),f146(x99643,x99644)))+P1(f315(f315(f317(f908(x99643,x99643)),f315(f315(f240(x99643,x99643),x99641),x99642)),x99644))
% 168.60/168.39 [9995]~P1(f315(f315(f317(f908(f902(x99951),f902(x99951))),f315(f315(f240(f902(x99951),f902(x99951)),f315(f315(f123(x99951),x99955),f315(f315(f140(x99951),x99952),f102(x99951)))),f315(f315(f123(x99951),x99956),f315(f315(f140(x99951),x99953),f102(x99951))))),f146(x99951,x99954)))+P1(f315(f315(f317(f908(f902(x99951),f902(x99951))),f315(f315(f240(f902(x99951),f902(x99951)),x99955),x99956)),f146(x99951,x99954)))+P1(f315(f315(f317(f908(x99951,x99951)),f315(f315(f240(x99951,x99951),x99952),x99953)),x99954))
% 168.60/168.39 [10015]P1(f315(x100151,x100152))+P1(f315(f315(f317(x100153),f445(x100151,x100154,x100155,x100156,x100153)),f315(x100154,f430(x100151,x100154,x100155,x100156,x100153))))+~P1(f315(f315(f317(x100153),x100152),f315(f315(f33(x100156,f909(x100153,a899)),x100155),x100154)))
% 168.60/168.39 [10166]P1(f315(f315(f317(x101661),f821(x101662,x101663,x101664,x101665,x101666,x101661)),x101665))+~P1(f315(f315(f223(f909(x101661,a899)),x101666),x101665))+P1(f315(f315(f223(f909(x101664,a899)),f315(f315(f32(x101661,f909(x101664,a899)),x101665),x101663)),f315(f315(f32(x101661,f909(x101664,a899)),x101665),x101662)))
% 168.60/168.39 [10292]~P1(f315(f315(f223(f909(x102921,a899)),f315(x102924,f821(x102925,x102924,x102921,x102923,x102926,x102922))),f315(x102925,f821(x102925,x102924,x102921,x102923,x102926,x102922))))+~P1(f315(f315(f223(f909(x102922,a899)),x102926),x102923))+P1(f315(f315(f223(f909(x102921,a899)),f315(f315(f32(x102922,f909(x102921,a899)),x102923),x102924)),f315(f315(f32(x102922,f909(x102921,a899)),x102923),x102925)))
% 168.60/168.39 [9008]~P17(x90083,x90084,x90081)+~P1(f315(f54(x90083),x90086))+E(f315(f315(x90081,x90082),f315(f315(f57(x90083,x90084,x90081),x90085),f315(f315(f3(f909(x90083,a899)),x90086),f315(f315(f297(x90083),x90082),f177(f909(x90083,a899)))))),f315(f315(f57(x90083,x90084,x90081),x90085),f315(f315(f297(x90083),x90082),x90086)))
% 168.60/168.39 [9302]~P1(f315(f315(f317(x93025),x93023),x93026))+P1(f315(f315(f223(f909(x93021,a899)),f315(x93022,x93023)),x93024))+~P1(f315(f315(f223(f909(x93021,a899)),f315(f315(f33(x93025,f909(x93021,a899)),x93026),x93022)),x93024))
% 168.60/168.39 [9939]~P8(x99391,x99395,x99394)+P1(f315(f315(f317(f908(x99391,x99391)),f315(f315(f240(x99391,x99391),x99392),x99393)),x99394))+~P1(f315(f315(f317(x99391),x99396),f315(f315(f90(f909(x99391,a899)),f315(f273(x99391,x99391,x99394),f315(f315(f297(x99391),x99392),f177(f909(x99391,a899))))),f315(f273(x99391,x99391,x99394),f315(f315(f297(x99391),x99393),f177(f909(x99391,a899)))))))
% 168.60/168.39 [8730]~P112(x87302)+~E(f315(f315(f73(x87302),f315(f315(f74(x87302),x87304),x87305)),x87301),f315(f315(f73(x87302),f315(f315(f74(x87302),x87303),x87305)),x87306))+E(x87301,f315(f315(f73(x87302),f315(f315(f74(x87302),f315(f315(f3(x87302),x87303),x87304)),x87305)),x87306))
% 168.60/168.39 [8731]~P112(x87311)+~E(f315(f315(f73(x87311),f315(f315(f74(x87311),x87312),x87314)),x87315),f315(f315(f73(x87311),f315(f315(f74(x87311),x87313),x87314)),x87316))+E(f315(f315(f73(x87311),f315(f315(f74(x87311),f315(f315(f3(x87311),x87312),x87313)),x87314)),x87315),x87316)
% 168.60/168.39 [8913]~P112(x89131)+E(f315(f315(f73(x89131),f315(f315(f74(x89131),x89132),x89133)),x89134),f315(f315(f73(x89131),f315(f315(f74(x89131),x89135),x89133)),x89136))+~E(x89136,f315(f315(f73(x89131),f315(f315(f74(x89131),f315(f315(f3(x89131),x89132),x89135)),x89133)),x89134))
% 168.60/168.39 [8914]~P112(x89141)+E(f315(f315(f73(x89141),f315(f315(f74(x89141),x89142),x89143)),x89144),f315(f315(f73(x89141),f315(f315(f74(x89141),x89145),x89143)),x89146))+~E(f315(f315(f73(x89141),f315(f315(f74(x89141),f315(f315(f3(x89141),x89142),x89145)),x89143)),x89144),x89146)
% 168.60/168.39 [9239]~P1(f315(f315(x92394,x92395),x92396))+~P1(f315(f315(x92393,x92395),x92396))+P1(f315(f315(f315(f315(f90(f909(x92391,f909(x92392,a899))),x92393),x92394),x92395),x92396))
% 168.60/168.39 [9503]P1(f315(f315(x95031,x95032),x95033))+P1(f315(f315(x95034,x95032),x95033))+~P1(f315(f315(f315(f315(f99(f909(x95035,f909(x95036,a899))),x95034),x95031),x95032),x95033))
% 168.60/168.39 [9804]~P113(x98041)+~P1(f315(f315(f223(x98041),f315(f315(f73(x98041),f315(f315(f74(x98041),x98044),x98045)),x98042)),f315(f315(f73(x98041),f315(f315(f74(x98041),x98043),x98045)),x98046)))+P1(f315(f315(f223(x98041),x98042),f315(f315(f73(x98041),f315(f315(f74(x98041),f315(f315(f3(x98041),x98043),x98044)),x98045)),x98046)))
% 168.60/168.39 [9805]~P113(x98051)+~P1(f315(f315(f224(x98051),f315(f315(f73(x98051),f315(f315(f74(x98051),x98054),x98055)),x98052)),f315(f315(f73(x98051),f315(f315(f74(x98051),x98053),x98055)),x98056)))+P1(f315(f315(f224(x98051),x98052),f315(f315(f73(x98051),f315(f315(f74(x98051),f315(f315(f3(x98051),x98053),x98054)),x98055)),x98056)))
% 168.60/168.39 [9828]~P113(x98281)+P1(f315(f315(f223(x98281),f315(f315(f73(x98281),f315(f315(f74(x98281),x98282),x98283)),x98284)),f315(f315(f73(x98281),f315(f315(f74(x98281),x98285),x98283)),x98286)))+~P1(f315(f315(f223(x98281),x98284),f315(f315(f73(x98281),f315(f315(f74(x98281),f315(f315(f3(x98281),x98285),x98282)),x98283)),x98286)))
% 168.60/168.39 [9829]~P113(x98291)+P1(f315(f315(f224(x98291),f315(f315(f73(x98291),f315(f315(f74(x98291),x98292),x98293)),x98294)),f315(f315(f73(x98291),f315(f315(f74(x98291),x98295),x98293)),x98296)))+~P1(f315(f315(f224(x98291),x98294),f315(f315(f73(x98291),f315(f315(f74(x98291),f315(f315(f3(x98291),x98295),x98292)),x98293)),x98296)))
% 168.60/168.39 [9931]~P113(x99311)+~P1(f315(f315(f223(x99311),f315(f315(f73(x99311),f315(f315(f74(x99311),x99312),x99314)),x99315)),f315(f315(f73(x99311),f315(f315(f74(x99311),x99313),x99314)),x99316)))+P1(f315(f315(f223(x99311),f315(f315(f73(x99311),f315(f315(f74(x99311),f315(f315(f3(x99311),x99312),x99313)),x99314)),x99315)),x99316))
% 168.60/168.39 [9932]~P113(x99321)+~P1(f315(f315(f224(x99321),f315(f315(f73(x99321),f315(f315(f74(x99321),x99322),x99324)),x99325)),f315(f315(f73(x99321),f315(f315(f74(x99321),x99323),x99324)),x99326)))+P1(f315(f315(f224(x99321),f315(f315(f73(x99321),f315(f315(f74(x99321),f315(f315(f3(x99321),x99322),x99323)),x99324)),x99325)),x99326))
% 168.60/168.39 [9978]~P113(x99781)+P1(f315(f315(f223(x99781),f315(f315(f73(x99781),f315(f315(f74(x99781),x99782),x99783)),x99784)),f315(f315(f73(x99781),f315(f315(f74(x99781),x99785),x99783)),x99786)))+~P1(f315(f315(f223(x99781),f315(f315(f73(x99781),f315(f315(f74(x99781),f315(f315(f3(x99781),x99782),x99785)),x99783)),x99784)),x99786))
% 168.60/168.39 [9979]~P113(x99791)+P1(f315(f315(f224(x99791),f315(f315(f73(x99791),f315(f315(f74(x99791),x99792),x99793)),x99794)),f315(f315(f73(x99791),f315(f315(f74(x99791),x99795),x99793)),x99796)))+~P1(f315(f315(f224(x99791),f315(f315(f73(x99791),f315(f315(f74(x99791),f315(f315(f3(x99791),x99792),x99795)),x99793)),x99794)),x99796))
% 168.60/168.39 [10151]~P72(x101512)+~P1(f315(f54(x101511),x101516))+E(f315(f315(f8(x101511,x101512),f315(f315(f20(x101511,x101512,x101512),f315(f315(f20(x101511,x101512,f909(x101512,x101512)),f315(f315(f10(a899,f909(x101512,f909(x101512,x101512)),x101511),f85(x101512)),x101513)),x101514)),x101515)),x101516),f315(f315(f73(x101512),f315(f315(f8(x101511,x101512),x101514),f315(f315(f90(f909(x101511,a899)),x101516),f315(f250(x101511),x101513)))),f315(f315(f8(x101511,x101512),x101515),f315(f315(f90(f909(x101511,a899)),x101516),f315(f72(f909(x101511,a899)),f315(f250(x101511),x101513))))))
% 168.60/168.39 [10211]P1(f315(f315(f317(x102112),x102114),x102116))+P1(f315(f315(f317(x102112),x102115),x102116))+E(f315(f299(x102111,x102112,f315(f315(f9(x102111,x102112,x102112),f315(f315(f9(x102111,x102112,f909(x102112,x102112)),f315(f315(f10(a899,f909(x102112,f909(x102112,x102112)),x102111),f85(x102112)),f315(f315(f9(x102111,f909(x102111,a899),a899),f317(x102111)),x102113))),x102114)),x102115)),x102116),f177(f909(x102111,a899)))
% 168.60/168.39 [10212]P1(f315(f315(f317(x102122),x102125),x102126))+~P1(f315(f315(f317(x102122),x102124),x102126))+E(f315(f299(x102121,x102122,f315(f315(f9(x102121,x102122,x102122),f315(f315(f9(x102121,x102122,f909(x102122,x102122)),f315(f315(f10(a899,f909(x102122,f909(x102122,x102122)),x102121),f85(x102122)),f315(f315(f9(x102121,f909(x102121,a899),a899),f317(x102121)),x102123))),x102124)),x102125)),x102126),x102123)
% 168.60/168.39 [10213]P1(f315(f315(f317(x102132),x102134),x102136))+~P1(f315(f315(f317(x102132),x102135),x102136))+E(f315(f299(x102131,x102132,f315(f315(f9(x102131,x102132,x102132),f315(f315(f9(x102131,x102132,f909(x102132,x102132)),f315(f315(f10(a899,f909(x102132,f909(x102132,x102132)),x102131),f85(x102132)),f315(f315(f9(x102131,f909(x102131,a899),a899),f317(x102131)),x102133))),x102134)),x102135)),x102136),f315(f72(f909(x102131,a899)),x102133))
% 168.60/168.39 [10214]~P1(f315(f315(f317(x102142),x102144),x102146))+~P1(f315(f315(f317(x102142),x102145),x102146))+E(f315(f299(x102141,x102142,f315(f315(f9(x102141,x102142,x102142),f315(f315(f9(x102141,x102142,f909(x102142,x102142)),f315(f315(f10(a899,f909(x102142,f909(x102142,x102142)),x102141),f85(x102142)),f315(f315(f9(x102141,f909(x102141,a899),a899),f317(x102141)),x102143))),x102144)),x102145)),x102146),f230(f909(x102141,a899)))
% 168.60/168.39 [8763]E(x87631,x87632)+~P58(x87634,x87635,x87633,x87636,x87637)+~E(f315(x87633,x87631),f315(x87633,x87632))
% 168.60/168.39 [8792]~P10(x87926,x87925,x87927,x87924,x87921)+E(f315(f315(x87921,x87922),x87923),x87924)+P1(f315(f54(x87925),x87923))
% 168.60/168.39 [9671]P44(x96711,x96712,x96713,x96714,x96715,f315(f315(x96713,x96716),x96717))+~E(f315(f315(x96713,x96716),x96717),x96714)+~E(x96715,f177(f909(x96711,a899)))
% 168.60/168.39 [9850]~P1(f315(x98506,x98503))+~P1(f315(f315(f317(f908(x98502,x98502)),f315(f315(f240(x98502,x98502),x98504),x98505)),f315(x98507,x98503)))+P1(f315(f315(f317(f908(f908(x98501,x98502),f908(x98501,x98502))),f315(f315(f240(f908(x98501,x98502),f908(x98501,x98502)),f315(f315(f240(x98501,x98502),x98503),x98504)),f315(f315(f240(x98501,x98502),x98503),x98505))),f268(x98501,x98502,x98506,x98507)))
% 168.60/168.39 [10276]~P44(x102762,x102767,x102763,x102766,x102761,f315(f315(x102763,x102765),x102764))+E(f315(f315(x102763,f413(x102764,x102765,x102761,x102766,x102763,x102767,x102762)),f421(x102764,x102765,x102761,x102766,x102763,x102767,x102762)),f315(f315(x102763,x102765),x102764))+E(x102761,f177(f909(x102762,a899)))
% 168.60/168.39 [10277]~P44(x102777,x102776,x102771,x102774,x102775,f315(f315(x102771,x102772),x102773))+E(f315(f315(x102771,f413(x102773,x102772,x102775,x102774,x102771,x102776,x102777)),f421(x102773,x102772,x102775,x102774,x102771,x102776,x102777)),f315(f315(x102771,x102772),x102773))+E(f315(f315(x102771,x102772),x102773),x102774)
% 168.60/168.39 [9336]~P36(x93361,x93362,x93363,x93365,x93367)+P36(x93361,x93362,x93363,f315(f315(f140(x93361),x93364),x93365),f315(f315(f140(x93362),x93366),x93367))+~P1(f315(f315(x93363,x93364),x93366))
% 168.60/168.39 [9355]P36(x93551,x93552,x93553,x93554,x93555)+~P36(x93551,x93552,x93553,f315(f315(f123(x93551),x93556),x93554),f315(f315(f123(x93552),x93557),x93555))+~E(f315(f178(f902(x93551)),x93556),f315(f178(f902(x93552)),x93557))
% 168.60/168.39 [9356]P36(x93561,x93562,x93563,x93564,x93565)+~P36(x93561,x93562,x93563,f315(f315(f123(x93561),x93564),x93566),f315(f315(f123(x93562),x93565),x93567))+~E(f315(f178(f902(x93561)),x93564),f315(f178(f902(x93562)),x93565))
% 168.60/168.39 [9570]~P36(x95701,x95702,x95703,x95705,x95707)+~P36(x95701,x95702,x95703,x95704,x95706)+P36(x95701,x95702,x95703,f315(f315(f123(x95701),x95704),x95705),f315(f315(f123(x95702),x95706),x95707))
% 168.60/168.39 [9924]~P1(f315(f59(x99241,x99244,x99245,x99246,x99243),x99247))+P1(f315(f59(x99241,x99244,x99245,x99246,f315(f315(f297(x99241),x99242),x99243)),f315(f315(x99245,x99242),x99247)))+P1(f315(f315(f317(x99241),x99242),x99243))
% 168.60/168.39 [10308]~P44(x103082,x103087,x103086,x103085,x103081,f315(f315(x103086,x103084),x103083))+E(x103081,f177(f909(x103082,a899)))+P1(f315(f315(f317(x103082),f413(x103083,x103084,x103081,x103085,x103086,x103087,x103082)),x103081))
% 168.60/168.39 [10309]~P44(x103095,x103097,x103091,x103094,x103096,f315(f315(x103091,x103092),x103093))+E(f315(f315(x103091,x103092),x103093),x103094)+P1(f315(f315(f317(x103095),f413(x103093,x103092,x103096,x103094,x103091,x103097,x103095)),x103096))
% 168.60/168.39 [10396]E(f315(f315(f240(x103961,x103962),x103963),x103964),f315(f315(f240(x103961,x103962),x103965),x103966))+P1(f315(f315(f317(f908(f908(x103961,x103962),f908(x103961,x103962))),f315(f315(f240(f908(x103961,x103962),f908(x103961,x103962)),f315(f315(f240(x103961,x103962),f828(x103967,x103964,x103963,x103966,x103965,x103962,x103961)),f829(x103967,x103964,x103963,x103966,x103965,x103962,x103961))),f315(f315(f240(x103961,x103962),x103963),x103964))),f295(f908(x103961,x103962),x103967)))+~P1(f315(f315(f317(f908(f908(x103961,x103962),f908(x103961,x103962))),f315(f315(f240(f908(x103961,x103962),f908(x103961,x103962)),f315(f315(f240(x103961,x103962),x103965),x103966)),f315(f315(f240(x103961,x103962),x103963),x103964))),f295(f908(x103961,x103962),x103967)))
% 168.60/168.39 [9034]~P22(x90344,x90345,x90346,x90347,x90341)+~P1(f315(f54(x90345),x90343))+E(f315(f315(x90341,x90342),x90343),f315(f315(f315(f58(x90344,x90345,x90346),x90342),x90347),x90343))
% 168.60/168.39 [9035]~P10(x90354,x90355,x90356,x90357,x90351)+~P1(f315(f54(x90355),x90353))+E(f315(f315(x90351,x90352),x90353),f315(f315(f315(f58(x90354,x90355,x90356),x90352),x90357),x90353))
% 168.60/168.39 [9823]~P24(x98233,x98234,x98235,x98237,x98236,x98231)+~P1(f315(f54(x98234),x98232))+E(f315(x98231,x98232),f315(f315(f315(f58(x98233,x98234,x98235),x98236),x98237),x98232))
% 168.60/168.39 [9973]P44(x99731,x99732,x99733,x99734,x99735,f315(f315(x99733,x99736),x99737))+~P44(x99731,x99732,x99733,x99734,f315(f315(f3(f909(x99731,a899)),x99735),f315(f315(f297(x99731),x99736),f177(f909(x99731,a899)))),x99737)+~P1(f315(f315(f317(x99731),x99736),x99735))
% 168.60/168.39 [10332]P1(f315(f315(x103327,f771(x103324,x103325,x103321,x103326,x103323,x103322,x103327)),f772(x103324,x103325,x103321,x103326,x103323,x103322,x103327)))+~P1(f315(f315(x103327,f315(f244(x103322,x103323),x103326)),f315(f239(x103322,x103323),x103326)))+P1(f315(x103321,f315(f315(f245(x103322,x103323,x103324),x103325),x103326)))
% 168.60/168.39 [10342]~P44(x103422,x103423,x103424,x103425,x103421,f315(f315(x103424,x103427),x103426))+P44(x103422,x103423,x103424,x103425,f315(f315(f3(f909(x103422,a899)),x103421),f315(f315(f297(x103422),f413(x103426,x103427,x103421,x103425,x103424,x103423,x103422)),f177(f909(x103422,a899)))),f421(x103426,x103427,x103421,x103425,x103424,x103423,x103422))+E(x103421,f177(f909(x103422,a899)))
% 168.60/168.39 [10343]~P44(x103435,x103436,x103431,x103434,x103437,f315(f315(x103431,x103432),x103433))+P44(x103435,x103436,x103431,x103434,f315(f315(f3(f909(x103435,a899)),x103437),f315(f315(f297(x103435),f413(x103433,x103432,x103437,x103434,x103431,x103436,x103435)),f177(f909(x103435,a899)))),f421(x103433,x103432,x103437,x103434,x103431,x103436,x103435))+E(f315(f315(x103431,x103432),x103433),x103434)
% 168.60/168.39 [10363]~P1(f315(x103631,f315(f315(x103635,f772(x103634,x103635,x103631,x103636,x103633,x103632,x103637)),f771(x103634,x103635,x103631,x103636,x103633,x103632,x103637))))+~P1(f315(f315(x103637,f315(f244(x103632,x103633),x103636)),f315(f239(x103632,x103633),x103636)))+P1(f315(x103631,f315(f315(f245(x103632,x103633,x103634),x103635),x103636)))
% 168.60/168.39 [9656]P1(f315(f315(f223(f909(f908(x96561,x96562),a899)),f315(f315(f277(x96561,x96563,x96562),x96564),x96565)),f315(f315(f277(x96561,x96563,x96562),x96566),x96567)))+~P1(f315(f315(f223(f909(f908(x96563,x96562),a899)),x96565),x96567))+~P1(f315(f315(f223(f909(f908(x96561,x96563),a899)),x96564),x96566))
% 168.60/168.39 [10390]E(f315(f315(f240(x103901,x103902),x103903),x103904),f315(f315(f240(x103901,x103902),x103905),x103906))+~P1(f315(f315(f317(f908(f908(x103901,x103902),f908(x103901,x103902))),f315(f315(f240(f908(x103901,x103902),f908(x103901,x103902)),f315(f315(f240(x103901,x103902),x103903),x103904)),f315(f315(f240(x103901,x103902),x103905),x103906))),f295(f908(x103901,x103902),x103907)))+P1(f315(f315(f317(f908(f908(x103901,x103902),f908(x103901,x103902))),f315(f315(f240(f908(x103901,x103902),f908(x103901,x103902)),f315(f315(f240(x103901,x103902),x103903),x103904)),f315(f315(f240(x103901,x103902),f828(x103907,x103906,x103905,x103904,x103903,x103902,x103901)),f829(x103907,x103906,x103905,x103904,x103903,x103902,x103901)))),x103907))
% 168.60/168.39 [9984]~P1(f315(f315(f317(x99841),x99846),x99845))+P1(f315(f59(x99841,x99842,x99843,x99844,x99845),f315(f315(x99843,x99846),x99847)))+~P1(f315(f59(x99841,x99842,x99843,x99844,f315(f315(f3(f909(x99841,a899)),x99845),f315(f315(f297(x99841),x99846),f177(f909(x99841,a899))))),x99847))
% 168.60/168.39 [10403]~P148(x104031)+~P25(f908(x104032,x104033),x104031,f315(f245(x104032,x104033,x104031),f315(f315(f9(x104032,f909(x104033,x104031),f909(x104033,x104031)),f315(f315(f10(f909(x104031,x104031),f909(f909(x104033,x104031),f909(x104033,x104031)),x104032),f10(x104031,x104031,x104033)),f315(f315(f10(x104031,f909(x104031,x104031),x104032),f74(x104031)),x104034))),x104035)),f315(f315(f242(x104032,x104033),x104036),f315(f18(f909(x104033,a899),x104032),x104037)))+E(f315(f315(f8(x104031,x104031),f25(x104031)),f315(f250(x104031),f315(f315(f10(f909(x104032,a899),a899,x104031),f80(x104032)),f315(f315(f10(f909(x104032,f909(x104033,a899)),f909(x104032,a899),x104031),f315(f10(f909(x104033,a899),a899,x104032),f80(x104033))),f315(f315(f9(x104031,f909(x104032,f909(x104033,a899)),f909(x104032,f909(x104033,a899))),f315(f315(f10(f909(x104032,f909(f909(x104033,a899),f909(x104033,a899))),f909(f909(x104032,f909(x104033,a899)),f909(x104032,f909(x104033,a899))),x104031),f20(x104032,f909(x104033,a899),f909(x104033,a899))),f315(f315(f10(f909(x104032,f909(x104033,f909(a899,a899))),f909(x104032,f909(f909(x104033,a899),f909(x104033,a899))),x104031),f315(f10(f909(x104033,f909(a899,a899)),f909(f909(x104033,a899),f909(x104033,a899)),x104032),f20(x104033,a899,a899))),f315(f315(f10(f909(x104032,f909(x104033,a899)),f909(x104032,f909(x104033,f909(a899,a899))),x104031),f315(f10(f909(x104033,a899),f909(x104033,f909(a899,a899)),x104032),f315(f10(a899,f909(a899,a899),x104033),a313))),f315(f315(f9(x104031,f909(x104032,f909(x104033,x104031)),f909(x104032,f909(x104033,a899))),f315(f315(f10(f909(f909(x104033,x104031),f909(x104033,a899)),f909(f909(x104032,f909(x104033,x104031)),f909(x104032,f909(x104033,a899))),x104031),f10(f909(x104033,x104031),f909(x104033,a899),x104032)),f315(f315(f10(f909(x104031,a899),f909(f909(x104033,x104031),f909(x104033,a899)),x104031),f10(x104031,a899,x104033)),a312))),f315(f315(f9(x104032,f909(x104033,x104031),f909(x104033,x104031)),f315(f315(f10(f909(x104031,x104031),f909(f909(x104033,x104031),f909(x104033,x104031)),x104032),f10(x104031,x104031,x104033)),f315(f315(f10(x104031,f909(x104031,x104031),x104032),f74(x104031)),x104034))),x104035)))))),f315(f315(f9(x104032,f909(x104033,a899),f909(x104033,a899)),f315(f315(f10(f909(a899,a899),f909(f909(x104033,a899),f909(x104033,a899)),x104032),f10(a899,a899,x104033)),f315(f315(f10(a899,f909(a899,a899),x104032),a313),f315(f315(f9(x104032,f909(x104032,a899),a899),f317(x104032)),x104036)))),f315(f315(f9(x104033,f909(x104033,a899),a899),f317(x104033)),x104037))))))),f315(f315(f74(x104031),f315(f315(f8(x104032,x104031),x104034),x104036)),f315(f315(f8(x104033,x104031),x104035),x104037)))
% 168.60/168.39 [9660]~P26(x96601,x96603,x96605,x96606,x96608)+~P26(x96603,x96602,x96604,x96608,x96607)+P26(x96601,x96602,f315(f66(x96603,x96602,x96601,x96604),x96605),x96606,x96607)
% 168.60/168.39 [9689]P26(x96891,x96892,x96893,x96894,x96895)+~P26(x96896,x96891,x96897,x96898,x96894)+~P26(x96896,x96892,f315(f66(x96891,x96892,x96896,x96893),x96897),x96898,x96895)
% 168.60/168.39 [9821]~P1(f315(f315(x98214,x98216),x98218))+~P1(f315(f315(x98215,x98218),x98217))+P1(f315(f315(f241(x98211,x98212,x98213,x98214,x98215),x98216),x98217))
% 168.60/168.39 [9410]~P20(x94108,x94101,x94103,x94105)+~P1(f315(f54(x94108),x94106))+E(f315(f66(x94101,x94101,x94102,f315(x94103,x94104)),f315(f66(x94101,x94101,x94102,f315(x94105,x94106)),x94107)),f315(f66(x94101,x94101,x94102,f315(x94105,x94106)),f315(f66(x94101,x94101,x94102,f315(x94103,x94104)),x94107)))
% 168.60/168.39 [9811]~P23(x98117,x98112,x98115,x98118,x98116,x98111)+~P1(f315(f54(x98112),x98114))+E(f315(x98111,f315(f315(f297(x98112),x98113),x98114)),f315(f315(x98115,f315(x98116,x98113)),f315(x98111,x98114)))
% 168.60/168.39 [9929]~P25(x99292,x99294,x99296,x99298)+~P25(x99291,x99293,x99295,x99297)+P25(f908(x99291,x99292),f908(x99293,x99294),f246(x99291,x99293,x99292,x99294,x99295,x99296),f315(f315(f242(x99291,x99292),x99297),f315(f18(f909(x99292,a899),x99291),x99298)))
% 168.60/168.39 [9596]P1(f315(f315(f317(f908(x95961,x95962)),f315(f315(f240(x95961,x95962),x95963),x95964)),f315(f315(f277(x95961,x95965,x95962),x95966),x95967)))+~P1(f315(f315(f317(f908(x95961,x95965)),f315(f315(f240(x95961,x95965),x95963),x95968)),x95966))+~P1(f315(f315(f317(f908(x95965,x95962)),f315(f315(f240(x95965,x95962),x95968),x95964)),x95967))
% 168.60/168.39 [9792]~P1(f315(f315(f223(f909(f908(x97923,x97922),a899)),x97925),f315(f315(f242(x97923,x97922),x97928),f315(f18(f909(x97922,a899),x97923),x97927))))+~P1(f315(f315(f223(f909(f908(x97921,x97923),a899)),x97924),f315(f315(f242(x97921,x97923),x97926),f315(f18(f909(x97923,a899),x97921),x97928))))+P1(f315(f315(f223(f909(f908(x97921,x97922),a899)),f315(f315(f277(x97921,x97923,x97922),x97924),x97925)),f315(f315(f242(x97921,x97922),x97926),f315(f18(f909(x97922,a899),x97921),x97927))))
% 168.60/168.39 [9845]~E(x98453,x98455)+P1(f315(f315(f317(f908(f908(x98451,x98452),f908(x98451,x98452))),f315(f315(f240(f908(x98451,x98452),f908(x98451,x98452)),f315(f315(f240(x98451,x98452),x98453),x98454)),f315(f315(f240(x98451,x98452),x98455),x98456))),f307(x98451,x98452,x98457,x98458)))+~P1(f315(f315(f317(f908(x98452,x98452)),f315(f315(f240(x98452,x98452),x98454),x98456)),x98458))
% 168.60/168.39 [9948]E(x99481,x99482)+~P1(f315(f315(f317(f908(f908(x99483,x99485),f908(x99483,x99485))),f315(f315(f240(f908(x99483,x99485),f908(x99483,x99485)),f315(f315(f240(x99483,x99485),x99481),x99486)),f315(f315(f240(x99483,x99485),x99482),x99487))),f307(x99483,x99485,x99484,x99488)))+P1(f315(f315(f317(f908(x99483,x99483)),f315(f315(f240(x99483,x99483),x99481),x99482)),x99484))
% 168.60/168.39 [9963]~P1(f315(f315(f317(f908(f908(x99631,x99635),f908(x99631,x99635))),f315(f315(f240(f908(x99631,x99635),f908(x99631,x99635)),f315(f315(f240(x99631,x99635),x99632),x99636)),f315(f315(f240(x99631,x99635),x99633),x99637))),f307(x99631,x99635,x99634,x99638)))+P1(f315(f315(f317(f908(x99631,x99631)),f315(f315(f240(x99631,x99631),x99632),x99633)),x99634))+P1(f315(f315(f317(f908(x99635,x99635)),f315(f315(f240(x99635,x99635),x99636),x99637)),x99638))
% 168.60/168.39 [9880]~P24(x98807,x98805,x98801,x98808,x98802,x98804)+~P1(f315(f54(x98805),x98806))+E(f315(f315(x98801,f315(x98802,x98803)),f315(x98804,f315(f315(f3(f909(x98805,a899)),x98806),f315(f315(f297(x98805),x98803),f177(f909(x98805,a899)))))),f315(x98804,f315(f315(f297(x98805),x98803),x98806)))
% 168.60/168.39 [9362]~P1(f315(f315(f315(x93625,x93628),x93626),x93627))+~P1(f315(f315(f317(x93621),x93628),x93624))+P1(f315(f315(f315(f315(f33(x93621,f909(x93622,f909(x93623,a899))),x93624),x93625),x93626),x93627))
% 168.60/168.39 [9581]P1(f315(f315(f315(x95811,x95812),x95813),x95814))+~P1(f315(f315(f317(x95815),x95812),x95816))+~P1(f315(f315(f315(f315(f32(x95815,f909(x95817,f909(x95818,a899))),x95816),x95811),x95813),x95814))
% 168.60/168.39 [9785]~P22(x97853,x97852,x97854,x97858,x97851)+~P1(f315(f54(x97852),x97857))+E(f315(f315(x97851,f315(f315(f20(x97852,x97853,x97853),f315(f315(f10(x97853,f909(x97853,x97853),x97852),x97854),x97855)),x97856)),x97857),f315(f315(x97854,f315(f315(x97851,x97855),x97857)),f315(f315(x97851,x97856),x97857)))
% 168.60/168.39 [10049]~E(f315(f298(x100492,x100494,x100496),x100498),x1004910)+~E(f315(f298(x100491,x100493,x100495),x100497),x100499)+E(f315(f298(f908(x100491,x100492),f908(x100493,x100494),f246(x100491,x100493,x100492,x100494,x100495,x100496)),f315(f315(f242(x100491,x100492),x100497),f315(f18(f909(x100492,a899),x100491),x100498))),f315(f315(f242(x100493,x100494),x100499),f315(f18(f909(x100494,a899),x100493),x1004910)))
% 168.60/168.39 [4953]~P45(x49531,x49532)+~P51(x49531,x49532)+~P52(x49531,x49532)+P7(x49531,x49532)
% 168.60/168.39 [4909]~P110(x49092)+~P13(x49092,x49091)+P13(x49092,f103(x49092,x49091))+E(x49091,f102(x49092))
% 168.60/168.39 [4910]~P110(x49102)+~P13(x49102,x49101)+P13(x49102,f690(x49101,x49102))+E(x49101,f102(x49102))
% 168.60/168.39 [5157]~P5(x51572)+E(f12(x51572,x51571),f30(x51572,x51571))+E(x51571,f177(f909(x51572,a899)))+~P1(f315(f54(x51572),x51571))
% 168.60/168.39 [5158]~P5(x51582)+E(f13(x51582,x51581),f31(x51582,x51581))+E(x51581,f177(f909(x51582,a899)))+~P1(f315(f54(x51582),x51581))
% 168.60/168.39 [5316]~P110(x53162)+~P13(x53162,x53161)+E(x53161,f102(x53162))+E(f315(f315(f140(x53162),f709(x53161,x53162)),f690(x53161,x53162)),x53161)
% 168.60/168.39 [6142]~P80(x61422)+E(x61421,f177(f909(x61422,a899)))+P1(f315(f315(f223(x61422),f13(x61422,x61421)),f12(x61422,x61421)))+~P1(f315(f54(x61422),x61421))
% 168.60/168.39 [6153]~P42(x61532)+~P42(x61531)+E(x61531,x61532)+~E(f315(f298(a1,a901,a93),x61531),f315(f298(a1,a901,a93),x61532))
% 168.60/168.39 [9218]~P114(x92181)+~P1(f315(f315(f317(x92181),x92182),f98(x92181)))+P1(f315(f315(f224(x92181),f315(f315(f73(x92181),f315(f315(f73(x92181),f71(x92181)),x92182)),x92182)),f2(x92181)))+~P1(f315(f315(f224(x92181),x92182),f2(x92181)))
% 168.60/168.39 [9463]~P114(x94631)+~P1(f315(f315(f317(x94631),x94632),f98(x94631)))+~P1(f315(f315(f224(x94631),f315(f315(f73(x94631),f315(f315(f73(x94631),f71(x94631)),x94632)),x94632)),f2(x94631)))+P1(f315(f315(f224(x94631),x94632),f2(x94631)))
% 168.60/168.39 [4968]~P117(x49682)+~P148(x49682)+E(x49681,f2(a901))+E(f315(f315(f232(x49682),f2(x49682)),x49681),f2(x49682))
% 168.60/168.39 [4971]~P117(x49711)+~P148(x49711)+~E(x49712,f2(a901))+E(f315(f315(f232(x49711),f2(x49711)),x49712),f71(x49711))
% 168.60/168.39 [5143]~P144(x51432)+E(x51431,f71(x51432))+E(x51431,f315(f72(x51432),f71(x51432)))+~E(f315(f315(f74(x51432),x51431),x51431),f71(x51432))
% 168.60/168.39 [5393]~P93(x53932)+E(x53931,f2(x53932))+E(f75(x53932,x53931),f315(f72(x53932),f71(x53932)))+P1(f315(f315(f224(x53932),f2(x53932)),x53931))
% 168.60/168.39 [5637]~P93(x56372)+E(f75(x56372,x56371),f71(x56372))+E(x56371,f2(x56372))+~P1(f315(f315(f224(x56372),f2(x56372)),x56371))
% 168.60/168.39 [5646]E(x56461,x56462)+~E(f315(f92(a901),x56461),f315(f92(a901),x56462))+P1(f315(a182,f315(f92(a1),x56462)))+P1(f315(a182,f315(f92(a1),x56461)))
% 168.60/168.39 [5698]~P95(x56981)+~E(x56982,f2(x56981))+E(f315(f315(f73(x56981),x56982),x56982),f2(x56981))+~P1(f315(f315(f317(x56981),x56982),f98(x56981)))
% 168.60/168.39 [5737]E(x57371,f2(a1))+~E(f315(f315(f29(a1),x57372),x57371),f2(a1))+P1(f315(f315(f224(a1),x57371),x57372))+P1(f315(f315(f224(a1),x57372),x57371))
% 168.60/168.39 [5767]E(x57671,f2(a1))+~E(f315(f315(f29(a1),x57672),x57671),f2(a1))+P1(f315(f315(f223(a1),x57672),f2(a1)))+P1(f315(f315(f224(a1),x57672),x57671))
% 168.60/168.39 [5801]E(x58011,f2(a1))+~E(f315(f315(f29(a1),x58012),x58011),f2(a1))+P1(f315(f315(f223(a1),f2(a1)),x58012))+P1(f315(f315(f224(a1),x58011),x58012))
% 168.60/168.39 [5836]~P95(x58362)+E(x58361,f2(x58362))+~E(f315(f315(f73(x58362),x58361),x58361),f2(x58362))+~P1(f315(f315(f317(x58362),x58361),f98(x58362)))
% 168.60/168.39 [5907]E(f315(f92(a901),x59071),f315(f92(a901),x59072))+~E(f315(f92(a1),x59072),f2(a1))+P1(f315(a182,f315(f92(a1),x59072)))+~P1(f315(a182,f315(f92(a1),x59071)))
% 168.60/168.39 [5936]~E(f315(f92(a901),x59362),f315(f92(a901),x59361))+E(f315(f92(a1),x59361),f2(a1))+P1(f315(a182,f315(f92(a1),x59361)))+~P1(f315(a182,f315(f92(a1),x59362)))
% 168.60/168.39 [5946]~P110(x59462)+E(x59461,f177(f909(x59462,a899)))+~P1(f315(f54(x59462),x59461))+P1(f315(f315(f317(x59462),f16(x59462,x59461)),x59461))
% 168.60/168.39 [5947]~P110(x59472)+E(x59471,f177(f909(x59472,a899)))+~P1(f315(f54(x59472),x59471))+P1(f315(f315(f317(x59472),f17(x59472,x59471)),x59471))
% 168.60/168.39 [6119]~P114(x61191)+~P97(x61191)+P1(f315(f315(f223(x61191),f2(x61191)),f315(f92(x61191),x61192)))+~P1(f315(f315(f223(a1),a76),x61192))
% 168.60/168.39 [6120]~P114(x61201)+~P97(x61201)+P1(f315(f315(f224(x61201),f2(x61201)),f315(f92(x61201),x61202)))+~P1(f315(f315(f224(a1),a76),x61202))
% 168.60/168.39 [6141]~P114(x61411)+~P97(x61411)+E(f315(f69(x61411),f315(f92(x61411),x61412)),f315(f92(x61411),x61412))+P1(f315(f315(f224(x61411),f315(f92(x61411),x61412)),f2(x61411)))
% 168.60/168.39 [6177]E(x61771,x61772)+~E(f315(a93,x61771),f315(a93,x61772))+~P1(f315(f315(f223(a1),f2(a1)),x61772))+~P1(f315(f315(f223(a1),f2(a1)),x61771))
% 168.60/168.39 [6378]~P97(x63782)+~P114(x63782)+~P1(f315(f315(f223(x63782),f2(x63782)),f315(f92(x63782),x63781)))+P1(f315(f315(f223(a1),a76),x63781))
% 168.60/168.39 [6379]~P97(x63792)+~P114(x63792)+~P1(f315(f315(f224(x63792),f2(x63792)),f315(f92(x63792),x63791)))+P1(f315(f315(f224(a1),a76),x63791))
% 168.60/168.39 [6384]~P114(x63841)+~P97(x63841)+P1(f315(f315(f223(x63841),f315(f92(x63841),x63842)),f2(x63841)))+~P1(f315(f315(f223(a1),x63842),a76))
% 168.60/168.39 [6385]~P114(x63851)+~P97(x63851)+P1(f315(f315(f224(x63851),f315(f92(x63851),x63852)),f2(x63851)))+~P1(f315(f315(f224(a1),x63852),a76))
% 168.60/168.39 [6712]~P97(x67122)+~P114(x67122)+~P1(f315(f315(f223(x67122),f315(f92(x67122),x67121)),f2(x67122)))+P1(f315(f315(f223(a1),x67121),a76))
% 168.60/168.39 [6713]~P97(x67132)+~P114(x67132)+~P1(f315(f315(f224(x67132),f315(f92(x67132),x67131)),f2(x67132)))+P1(f315(f315(f224(a1),x67131),a76))
% 168.60/168.39 [6806]~P114(x68061)+~P97(x68061)+E(f315(f69(x68061),f315(f92(x68061),x68062)),f315(f72(x68061),f315(f92(x68061),x68062)))+~P1(f315(f315(f224(x68061),f315(f92(x68061),x68062)),f2(x68061)))
% 168.60/168.39 [6825]E(f315(f92(a901),x68251),f315(f92(a901),x68252))+~E(f315(f92(a1),x68252),f2(a1))+~P1(f315(f315(f223(a1),f315(f92(a1),x68251)),f2(a1)))+~P1(f315(a182,f315(f92(a1),x68251)))
% 168.60/168.39 [7717]~P110(x77172)+E(x77171,f177(f909(x77172,a899)))+~P1(f315(f54(x77172),x77171))+P1(f315(f315(f223(x77172),f14(x77172,f221(x77172),x77171)),f15(x77172,f222(x77172),x77171)))
% 168.60/168.39 [8036]~P6(x80361)+~P42(x80362)+P1(f315(f315(f317(a1),x80361),x80362))+~P1(f315(f315(f317(a901),f315(a93,x80361)),f315(f298(a1,a901,a93),x80362)))
% 168.60/168.39 [5942]~P143(x59422)+E(x59421,f2(a1))+E(f315(f72(x59422),f315(f91(x59422),f315(f72(a1),x59421))),f315(f91(x59422),x59421))+~P1(f315(f315(f224(a1),x59421),f2(a1)))
% 168.60/168.39 [6020]~P95(x60201)+~P97(x60201)+~P30(x60201,f315(f92(x60201),x60202))+P30(x60201,f315(f92(x60201),f315(f315(f73(a1),x60202),x60202)))
% 168.60/168.39 [6367]~P78(x63672)+E(x63671,f177(f909(x63672,a899)))+E(f17(x63672,f315(f298(x63672,x63672,f72(x63672)),x63671)),f315(f72(x63672),f16(x63672,x63671)))+~P1(f315(f54(x63672),x63671))
% 168.60/168.39 [6368]~P78(x63682)+E(x63681,f177(f909(x63682,a899)))+E(f16(x63682,f315(f298(x63682,x63682,f72(x63682)),x63681)),f315(f72(x63682),f17(x63682,x63681)))+~P1(f315(f54(x63682),x63681))
% 168.60/168.39 [6401]~P95(x64011)+~P97(x64011)+P30(x64011,f315(f92(x64011),x64012))+~P30(x64011,f315(f92(x64011),f315(f315(f73(a1),x64012),x64012)))
% 168.60/168.39 [6496]E(x64961,f2(a1))+E(f315(a44,f43(f315(f72(a1),x64961),f315(f72(a1),x64962))),f39(x64961,x64962))+P1(f315(f315(f223(a1),f2(a1)),x64962))+~P1(f315(f315(f223(a1),f2(a1)),x64961))
% 168.60/168.39 [8820]~P42(x88202)+~P42(x88201)+P1(f315(f315(f224(f909(a901,a899)),f315(f298(a1,a901,a93),x88201)),f315(f298(a1,a901,a93),x88202)))+~P1(f315(f315(f224(f909(a1,a899)),x88201),x88202))
% 168.60/168.39 [9052]~E(f712(x90522,x90521),f713(x90522,x90521))+~P1(f315(f126(x90521),f714(x90522,x90521)))+~P1(f315(f126(f902(x90521)),x90522))+P1(f315(f126(x90521),f315(f131(f902(x90521),f902(x90521),f123(x90521),f102(x90521)),x90522)))
% 168.60/168.39 [9138]~P42(x91382)+~P42(x91381)+~P1(f315(f315(f223(f909(a901,a899)),f315(f298(a1,a901,a93),x91381)),f315(f298(a1,a901,a93),x91382)))+P1(f315(f315(f223(f909(a1,a899)),x91381),x91382))
% 168.60/168.39 [9139]~P42(x91392)+~P42(x91391)+~P1(f315(f315(f224(f909(a901,a899)),f315(f298(a1,a901,a93),x91391)),f315(f298(a1,a901,a93),x91392)))+P1(f315(f315(f224(f909(a1,a899)),x91391),x91392))
% 168.60/168.39 [9145]~E(f712(x91452,x91451),f713(x91452,x91451))+~P1(f315(f126(f902(x91451)),x91452))+P1(f315(f126(x91451),f315(f131(f902(x91451),f902(x91451),f123(x91451),f102(x91451)),x91452)))+P1(f315(f315(f317(f902(x91451)),f714(x91452,x91451)),f315(f161(f902(x91451)),x91452)))
% 168.60/168.39 [9186]~P1(f315(f126(x91861),f714(x91862,x91861)))+~P1(f315(f126(f902(x91861)),x91862))+P1(f315(f126(x91861),f315(f131(f902(x91861),f902(x91861),f123(x91861),f102(x91861)),x91862)))+P1(f315(f315(f317(f902(x91861)),f713(x91862,x91861)),f315(f161(f902(x91861)),x91862)))
% 168.60/168.39 [9187]~P1(f315(f126(x91871),f714(x91872,x91871)))+~P1(f315(f126(f902(x91871)),x91872))+P1(f315(f126(x91871),f315(f131(f902(x91871),f902(x91871),f123(x91871),f102(x91871)),x91872)))+P1(f315(f315(f317(f902(x91871)),f712(x91872,x91871)),f315(f161(f902(x91871)),x91872)))
% 168.60/168.39 [9264]~P1(f315(f126(f902(x92641)),x92642))+P1(f315(f126(x92641),f315(f131(f902(x92641),f902(x92641),f123(x92641),f102(x92641)),x92642)))+P1(f315(f315(f317(f902(x92641)),f713(x92642,x92641)),f315(f161(f902(x92641)),x92642)))+P1(f315(f315(f317(f902(x92641)),f714(x92642,x92641)),f315(f161(f902(x92641)),x92642)))
% 168.60/168.39 [9265]~P1(f315(f126(f902(x92651)),x92652))+P1(f315(f126(x92651),f315(f131(f902(x92651),f902(x92651),f123(x92651),f102(x92651)),x92652)))+P1(f315(f315(f317(f902(x92651)),f712(x92652,x92651)),f315(f161(f902(x92651)),x92652)))+P1(f315(f315(f317(f902(x92651)),f714(x92652,x92651)),f315(f161(f902(x92651)),x92652)))
% 168.60/168.39 [9279]~E(f315(f315(f90(f909(x92791,a899)),f315(f161(x92791),f713(x92792,x92791))),f315(f161(x92791),f712(x92792,x92791))),f177(f909(x92791,a899)))+~P1(f315(f126(x92791),f714(x92792,x92791)))+~P1(f315(f126(f902(x92791)),x92792))+P1(f315(f126(x92791),f315(f131(f902(x92791),f902(x92791),f123(x92791),f102(x92791)),x92792)))
% 168.60/168.39 [9342]~E(f315(f315(f90(f909(x93421,a899)),f315(f161(x93421),f713(x93422,x93421))),f315(f161(x93421),f712(x93422,x93421))),f177(f909(x93421,a899)))+~P1(f315(f126(f902(x93421)),x93422))+P1(f315(f126(x93421),f315(f131(f902(x93421),f902(x93421),f123(x93421),f102(x93421)),x93422)))+P1(f315(f315(f317(f902(x93421)),f714(x93422,x93421)),f315(f161(f902(x93421)),x93422)))
% 168.60/168.39 [9629]E(x96291,f2(a1))+E(x96292,f2(a1))+E(f315(f315(f79(a1,f908(a1,a1)),f315(f315(a206,x96292),x96291)),f315(f315(f20(a1,a1,f908(a1,a1)),f315(f315(f10(a1,f909(a1,f908(a1,a1)),a1),f240(a1,a1)),f315(f29(a1),x96292))),f315(f29(a1),x96291))),f204(x96292,x96291))+P1(f315(f315(f224(a1),x96291),f2(a1)))
% 168.60/168.39 [8365]~P97(x83652)+~P114(x83652)+~P1(f315(f315(f223(x83652),f315(f92(x83652),x83651)),f71(x83652)))+P1(f315(f315(f223(a1),x83651),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))
% 168.60/168.39 [8366]~P97(x83662)+~P114(x83662)+~P1(f315(f315(f224(x83662),f315(f92(x83662),x83661)),f71(x83662)))+P1(f315(f315(f224(a1),x83661),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))
% 168.60/168.39 [8636]~P114(x86361)+~P97(x86361)+P1(f315(f315(f223(x86361),f315(f92(x86361),x86362)),f71(x86361)))+~P1(f315(f315(f223(a1),x86362),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))
% 168.60/168.39 [8637]~P114(x86371)+~P97(x86371)+P1(f315(f315(f224(x86371),f315(f92(x86371),x86372)),f71(x86371)))+~P1(f315(f315(f224(a1),x86372),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))
% 168.60/168.39 [8848]~P97(x88482)+~P114(x88482)+~P1(f315(f315(f223(x88482),f71(x88482)),f315(f92(x88482),x88481)))+P1(f315(f315(f223(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),x88481))
% 168.60/168.39 [8849]~P97(x88492)+~P114(x88492)+~P1(f315(f315(f224(x88492),f71(x88492)),f315(f92(x88492),x88491)))+P1(f315(f315(f224(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),x88491))
% 168.60/168.39 [9224]~P114(x92241)+~P97(x92241)+P1(f315(f315(f223(x92241),f71(x92241)),f315(f92(x92241),x92242)))+~P1(f315(f315(f223(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),x92242))
% 168.60/168.39 [9225]~P114(x92251)+~P97(x92251)+P1(f315(f315(f224(x92251),f71(x92251)),f315(f92(x92251),x92252)))+~P1(f315(f315(f224(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),x92252))
% 168.60/168.39 [9758]~P144(x97582)+E(x97581,f71(x97582))+E(x97581,f315(f72(x97582),f71(x97582)))+~E(f315(f315(f232(x97582),x97581),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),f71(x97582))
% 168.60/168.39 [10025]~P67(x100251)+~P97(x100251)+~P1(f315(f315(f224(x100251),f2(x100251)),x100252))+P1(f315(f315(f224(x100251),f2(x100251)),f315(f315(f279(x100251),x100252),f315(f92(x100251),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))))))
% 168.60/168.39 [10077]~P67(x100771)+~P97(x100771)+P1(f315(f315(f224(x100771),f2(x100771)),x100772))+~P1(f315(f315(f224(x100771),f2(x100771)),f315(f315(f279(x100771),x100772),f315(f92(x100771),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))))))
% 168.60/168.39 [10370]~P143(x103702)+E(x103701,f2(a1))+P1(f315(f315(f224(a1),x103701),f2(a1)))+E(f315(f315(f245(a1,a1,x103702),f315(f315(f9(a1,f909(a1,f909(x103702,x103702)),f909(a1,x103702)),f315(f315(f10(f909(f909(x103702,x103702),x103702),f909(f909(a1,f909(x103702,x103702)),f909(a1,x103702)),a1),f10(f909(x103702,x103702),x103702,a1)),f315(f315(f10(x103702,f909(f909(x103702,x103702),x103702),a1),f79(x103702,x103702)),f91(x103702)))),f315(f315(f9(a1,f909(x103702,x103702),f909(x103702,x103702)),f315(f315(f10(f909(x103702,f909(x103702,x103702)),f909(f909(x103702,x103702),f909(x103702,x103702)),a1),f20(x103702,x103702,x103702)),f315(f315(f9(a1,f909(x103702,x103702),f909(x103702,f909(x103702,x103702))),f315(f315(f10(f909(x103702,f909(x103702,x103702)),f909(f909(x103702,x103702),f909(x103702,f909(x103702,x103702))),a1),f10(x103702,f909(x103702,x103702),x103702)),f315(f315(f10(a899,f909(x103702,f909(x103702,x103702)),a1),f85(x103702)),f315(f315(f9(a1,a1,a899),a312),f2(a1))))),f315(f315(f20(x103702,x103702,x103702),f73(x103702)),f7(x103702))))),f315(f315(f9(x103702,x103702,x103702),f315(f315(f10(x103702,f909(x103702,x103702),x103702),f73(x103702)),f315(f315(f20(x103702,x103702,x103702),f73(x103702)),f7(x103702)))),f71(x103702))))),f39(x103701,f315(f92(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))))),f315(f91(x103702),x103701))
% 168.60/168.39 [5402]~P40(x54021,x54023)+~P53(x54021,x54023)+~P54(x54021,x54022,x54023)+P8(x54021,x54022,x54023)
% 168.60/168.39 [4937]~P95(x49373)+~P97(x49373)+E(x49371,x49372)+~E(f315(f92(x49373),x49371),f315(f92(x49373),x49372))
% 168.60/168.39 [5412]~P51(x54121,x54122)+~P52(x54121,x54122)+P16(x54121,x54122)+~P1(f315(f315(x54122,x54123),x54123))
% 168.60/168.39 [5922]P16(x59222,x59221)+E(f315(x59221,f788(x59221)),f315(x59221,f789(x59221)))+P1(f315(f315(x59221,f788(x59221)),f789(x59221)))+~P1(f315(f315(x59221,x59223),x59223))
% 168.60/168.39 [6129]~P1(f315(x61291,x61292))+~P1(f315(x61291,x61293))+~P1(f315(f315(f223(a901),x61293),f858(x61292,x61291)))+P1(f315(x61291,f2(a901)))
% 168.60/168.39 [6197]P16(x61971,x61972)+P1(f315(f315(x61972,f788(x61972)),f788(x61972)))+P1(f315(f315(x61972,f788(x61972)),f789(x61972)))+~P1(f315(f315(x61972,x61973),x61973))
% 168.60/168.39 [6198]P16(x61981,x61982)+P1(f315(f315(x61982,f788(x61982)),f789(x61982)))+P1(f315(f315(x61982,f789(x61982)),f789(x61982)))+~P1(f315(f315(x61982,x61983),x61983))
% 168.60/168.39 [6563]P150(x65632,x65633,x65631)+E(x65631,f2(a1))+P1(f315(f315(f223(a1),f2(a1)),f845(x65631,x65633,x65632)))+P1(f315(f315(f224(a1),x65631),f2(a1)))
% 168.60/168.39 [6564]P149(x65642,x65643,x65641)+E(x65641,f2(a1))+P1(f315(f315(f223(a1),f2(a1)),f849(x65641,x65643,x65642)))+P1(f315(f315(f224(a1),x65641),f2(a1)))
% 168.60/168.39 [6692]P149(x66921,x66922,x66923)+~P1(f315(x66921,x66922))+P1(f315(f315(f223(a1),f2(a1)),f849(x66923,x66922,x66921)))+P1(f315(f315(f224(a1),x66923),f2(a1)))
% 168.60/168.39 [6718]P150(x67181,x67182,x67183)+P1(f315(f315(f223(a1),f2(a1)),f845(x67183,x67182,x67181)))+~P1(f315(x67181,f2(a1)))+P1(f315(f315(f224(a1),x67183),f2(a1)))
% 168.60/168.39 [6750]P150(x67502,x67503,x67501)+E(x67501,f2(a1))+~P1(f315(x67502,f846(x67501,x67503,x67502)))+P1(f315(f315(f224(a1),x67501),f2(a1)))
% 168.60/168.39 [6751]P149(x67512,x67513,x67511)+E(x67511,f2(a1))+~P1(f315(x67512,f849(x67511,x67513,x67512)))+P1(f315(f315(f224(a1),x67511),f2(a1)))
% 168.60/168.39 [6853]~P110(x68531)+~P5(x68531)+~P1(f315(f315(f224(x68531),x68532),f30(x68531,x68533)))+P1(f315(f315(f224(x68531),x68532),f863(x68533,x68532,x68531)))
% 168.60/168.39 [6863]P149(x68631,x68632,x68633)+~P1(f315(x68631,x68632))+~P1(f315(x68631,f849(x68633,x68632,x68631)))+P1(f315(f315(f224(a1),x68633),f2(a1)))
% 168.60/168.39 [6896]P150(x68961,x68962,x68963)+~P1(f315(x68961,f846(x68963,x68962,x68961)))+~P1(f315(x68961,f2(a1)))+P1(f315(f315(f224(a1),x68963),f2(a1)))
% 168.60/168.39 [7150]P150(x71502,x71503,x71501)+E(x71501,f2(a1))+P1(f315(f315(f223(a1),f2(a1)),f845(x71501,x71503,x71502)))+P1(f315(f315(f224(a1),x71501),f844(x71501,x71503,x71502)))
% 168.60/168.39 [7151]P149(x71512,x71513,x71511)+E(x71511,f2(a1))+P1(f315(f315(f223(a1),f2(a1)),f849(x71511,x71513,x71512)))+P1(f315(f315(f224(a1),x71511),f848(x71511,x71513,x71512)))
% 168.60/168.39 [7271]P149(x72711,x72712,x72713)+~P1(f315(x72711,x72712))+P1(f315(f315(f223(a1),f2(a1)),f849(x72713,x72712,x72711)))+P1(f315(f315(f224(a1),x72713),f848(x72713,x72712,x72711)))
% 168.60/168.39 [7292]P150(x72921,x72922,x72923)+P1(f315(f315(f223(a1),f2(a1)),f845(x72923,x72922,x72921)))+P1(f315(f315(f224(a1),x72923),f844(x72923,x72922,x72921)))+~P1(f315(x72921,f2(a1)))
% 168.60/168.39 [7325]P150(x73252,x73253,x73251)+E(x73251,f2(a1))+~P1(f315(x73252,f846(x73251,x73253,x73252)))+P1(f315(f315(f224(a1),x73251),f844(x73251,x73253,x73252)))
% 168.60/168.39 [7326]P149(x73262,x73263,x73261)+E(x73261,f2(a1))+~P1(f315(x73262,f849(x73261,x73263,x73262)))+P1(f315(f315(f224(a1),x73261),f848(x73261,x73263,x73262)))
% 168.60/168.39 [7370]P150(x73702,x73703,x73701)+E(x73701,f2(a1))+P1(f315(f315(f223(a1),f2(a1)),f845(x73701,x73703,x73702)))+~P1(f315(x73702,f847(x73701,x73703,x73702)))
% 168.60/168.39 [7371]P149(x73712,x73713,x73711)+E(x73711,f2(a1))+P1(f315(f315(f223(a1),f2(a1)),f849(x73711,x73713,x73712)))+~P1(f315(x73712,f848(x73711,x73713,x73712)))
% 168.60/168.39 [7468]P149(x74681,x74682,x74683)+~P1(f315(x74681,x74682))+~P1(f315(x74681,f849(x74683,x74682,x74681)))+P1(f315(f315(f224(a1),x74683),f848(x74683,x74682,x74681)))
% 168.60/168.39 [7483]P150(x74831,x74832,x74833)+~P1(f315(x74831,f846(x74833,x74832,x74831)))+P1(f315(f315(f224(a1),x74833),f844(x74833,x74832,x74831)))+~P1(f315(x74831,f2(a1)))
% 168.60/168.39 [7486]P149(x74861,x74862,x74863)+~P1(f315(x74861,x74862))+P1(f315(f315(f223(a1),f2(a1)),f849(x74863,x74862,x74861)))+~P1(f315(x74861,f848(x74863,x74862,x74861)))
% 168.60/168.39 [7503]P150(x75031,x75032,x75033)+P1(f315(f315(f223(a1),f2(a1)),f845(x75033,x75032,x75031)))+~P1(f315(x75031,f847(x75033,x75032,x75031)))+~P1(f315(x75031,f2(a1)))
% 168.60/168.39 [7526]P150(x75262,x75263,x75261)+E(x75261,f2(a1))+~P1(f315(x75262,f846(x75261,x75263,x75262)))+~P1(f315(x75262,f847(x75261,x75263,x75262)))
% 168.60/168.39 [7527]P149(x75272,x75273,x75271)+E(x75271,f2(a1))+~P1(f315(x75272,f849(x75271,x75273,x75272)))+~P1(f315(x75272,f848(x75271,x75273,x75272)))
% 168.60/168.39 [7612]P149(x76121,x76122,x76123)+~P1(f315(x76121,x76122))+~P1(f315(x76121,f849(x76123,x76122,x76121)))+~P1(f315(x76121,f848(x76123,x76122,x76121)))
% 168.60/168.39 [7630]P150(x76301,x76302,x76303)+~P1(f315(x76301,f846(x76303,x76302,x76301)))+~P1(f315(x76301,f847(x76303,x76302,x76301)))+~P1(f315(x76301,f2(a1)))
% 168.60/168.39 [7676]P150(x76762,x76763,x76761)+E(x76761,f2(a1))+P1(f315(f315(f223(a1),f2(a1)),f845(x76761,x76763,x76762)))+P1(f315(f315(f223(a1),f844(x76761,x76763,x76762)),f2(a1)))
% 168.60/168.39 [7677]P149(x76772,x76773,x76771)+E(x76771,f2(a1))+P1(f315(f315(f223(a1),f2(a1)),f849(x76771,x76773,x76772)))+P1(f315(f315(f223(a1),f848(x76771,x76773,x76772)),f2(a1)))
% 168.60/168.39 [7678]~P143(x76781)+~P1(f315(f315(f317(x76781),x76783),f98(x76781)))+~P1(f315(f315(f317(x76781),x76782),f98(x76781)))+P1(f315(f315(f317(x76781),f315(f315(f3(x76781),x76782),x76783)),f98(x76781)))
% 168.60/168.39 [7679]~P143(x76791)+~P1(f315(f315(f317(x76791),x76793),f98(x76791)))+~P1(f315(f315(f317(x76791),x76792),f98(x76791)))+P1(f315(f315(f317(x76791),f315(f315(f74(x76791),x76792),x76793)),f98(x76791)))
% 168.60/168.39 [7680]~P147(x76801)+~P1(f315(f315(f317(x76801),x76803),f175(x76801)))+~P1(f315(f315(f317(x76801),x76802),f175(x76801)))+P1(f315(f315(f317(x76801),f315(f315(f74(x76801),x76802),x76803)),f175(x76801)))
% 168.60/168.39 [7681]~P143(x76811)+~P1(f315(f315(f317(x76811),x76813),f98(x76811)))+~P1(f315(f315(f317(x76811),x76812),f98(x76811)))+P1(f315(f315(f317(x76811),f315(f315(f73(x76811),x76812),x76813)),f98(x76811)))
% 168.60/168.39 [7682]~P147(x76821)+~P1(f315(f315(f317(x76821),x76823),f175(x76821)))+~P1(f315(f315(f317(x76821),x76822),f175(x76821)))+P1(f315(f315(f317(x76821),f315(f315(f73(x76821),x76822),x76823)),f175(x76821)))
% 168.60/168.39 [7683]~P91(x76831)+~P1(f315(f315(f223(x76831),x76833),f2(x76831)))+~P1(f315(f315(f223(x76831),x76832),f2(x76831)))+P1(f315(f315(f223(x76831),f315(f315(f73(x76831),x76832),x76833)),f2(x76831)))
% 168.60/168.39 [7684]~P91(x76841)+~P1(f315(f315(f223(x76841),x76843),f2(x76841)))+~P1(f315(f315(f224(x76841),x76842),f2(x76841)))+P1(f315(f315(f224(x76841),f315(f315(f73(x76841),x76842),x76843)),f2(x76841)))
% 168.60/168.39 [7685]~P91(x76851)+~P1(f315(f315(f223(x76851),x76852),f2(x76851)))+~P1(f315(f315(f224(x76851),x76853),f2(x76851)))+P1(f315(f315(f224(x76851),f315(f315(f73(x76851),x76852),x76853)),f2(x76851)))
% 168.60/168.39 [7686]~P91(x76861)+~P1(f315(f315(f224(x76861),x76863),f2(x76861)))+~P1(f315(f315(f224(x76861),x76862),f2(x76861)))+P1(f315(f315(f224(x76861),f315(f315(f73(x76861),x76862),x76863)),f2(x76861)))
% 168.60/168.39 [7713]P150(x77133,x77132,x77131)+E(x77131,f2(a1))+E(f315(f315(f73(a1),f315(f315(f74(a1),x77131),f846(x77131,x77132,x77133))),f845(x77131,x77132,x77133)),x77132)+P1(f315(f315(f224(a1),x77131),f2(a1)))
% 168.60/168.39 [7714]P149(x77143,x77142,x77141)+E(x77141,f2(a1))+E(f315(f315(f73(a1),f315(f315(f74(a1),x77141),f850(x77141,x77142,x77143))),f849(x77141,x77142,x77143)),x77142)+P1(f315(f315(f224(a1),x77141),f2(a1)))
% 168.60/168.39 [7797]P149(x77971,x77972,x77973)+~P1(f315(x77971,x77972))+P1(f315(f315(f223(a1),f2(a1)),f849(x77973,x77972,x77971)))+P1(f315(f315(f223(a1),f848(x77973,x77972,x77971)),f2(a1)))
% 168.60/168.39 [7828]P150(x78281,x78282,x78283)+P1(f315(f315(f223(a1),f2(a1)),f845(x78283,x78282,x78281)))+~P1(f315(x78281,f2(a1)))+P1(f315(f315(f223(a1),f844(x78283,x78282,x78281)),f2(a1)))
% 168.60/168.39 [7837]P149(x78373,x78372,x78371)+~P1(f315(x78373,x78372))+E(f315(f315(f73(a1),f315(f315(f74(a1),x78371),f850(x78371,x78372,x78373))),f849(x78371,x78372,x78373)),x78372)+P1(f315(f315(f224(a1),x78371),f2(a1)))
% 168.60/168.39 [7843]P150(x78432,x78433,x78431)+E(x78431,f2(a1))+~P1(f315(x78432,f846(x78431,x78433,x78432)))+P1(f315(f315(f223(a1),f844(x78431,x78433,x78432)),f2(a1)))
% 168.60/168.39 [7844]P149(x78442,x78443,x78441)+E(x78441,f2(a1))+~P1(f315(x78442,f849(x78441,x78443,x78442)))+P1(f315(f315(f223(a1),f848(x78441,x78443,x78442)),f2(a1)))
% 168.60/168.39 [7849]P150(x78493,x78492,x78491)+E(f315(f315(f73(a1),f315(f315(f74(a1),x78491),f846(x78491,x78492,x78493))),f845(x78491,x78492,x78493)),x78492)+~P1(f315(x78493,f2(a1)))+P1(f315(f315(f224(a1),x78491),f2(a1)))
% 168.60/168.39 [7905]P149(x79051,x79052,x79053)+~P1(f315(x79051,x79052))+~P1(f315(x79051,f849(x79053,x79052,x79051)))+P1(f315(f315(f223(a1),f848(x79053,x79052,x79051)),f2(a1)))
% 168.60/168.39 [7909]P150(x79091,x79092,x79093)+~P1(f315(x79091,f846(x79093,x79092,x79091)))+~P1(f315(x79091,f2(a1)))+P1(f315(f315(f223(a1),f844(x79093,x79092,x79091)),f2(a1)))
% 168.60/168.39 [7977]~P130(x79771)+~P1(f315(f315(f223(x79771),f315(f315(f74(x79771),x79773),x79772)),f2(x79771)))+P1(f315(f315(f223(x79771),x79772),f2(x79771)))+P1(f315(f315(f223(x79771),x79773),f2(x79771)))
% 168.60/168.39 [7978]~P67(x79781)+~P1(f315(f315(f223(x79781),f315(f315(f279(x79781),x79783),x79782)),f2(x79781)))+P1(f315(f315(f223(x79781),x79782),f2(x79781)))+P1(f315(f315(f223(x79781),x79783),f2(x79781)))
% 168.60/168.39 [7979]~P67(x79791)+~P1(f315(f315(f224(x79791),f315(f315(f279(x79791),x79793),x79792)),f2(x79791)))+P1(f315(f315(f224(x79791),x79792),f2(x79791)))+P1(f315(f315(f224(x79791),x79793),f2(x79791)))
% 168.60/168.39 [8092]P150(x80923,x80922,x80921)+E(x80921,f2(a1))+E(f315(f315(f73(a1),f315(f315(f74(a1),x80921),f846(x80921,x80922,x80923))),f845(x80921,x80922,x80923)),x80922)+P1(f315(f315(f224(a1),x80921),f844(x80921,x80922,x80923)))
% 168.60/168.39 [8093]P149(x80933,x80932,x80931)+E(x80931,f2(a1))+E(f315(f315(f73(a1),f315(f315(f74(a1),x80931),f850(x80931,x80932,x80933))),f849(x80931,x80932,x80933)),x80932)+P1(f315(f315(f224(a1),x80931),f848(x80931,x80932,x80933)))
% 168.60/168.39 [8106]P150(x81063,x81062,x81061)+E(x81061,f2(a1))+E(f315(f315(f73(a1),f315(f315(f74(a1),x81061),f847(x81061,x81062,x81063))),f844(x81061,x81062,x81063)),x81062)+P1(f315(f315(f223(a1),f2(a1)),f845(x81061,x81062,x81063)))
% 168.60/168.39 [8107]P149(x81073,x81072,x81071)+E(x81071,f2(a1))+E(f315(f315(f73(a1),f315(f315(f74(a1),x81071),f851(x81071,x81072,x81073))),f848(x81071,x81072,x81073)),x81072)+P1(f315(f315(f223(a1),f2(a1)),f849(x81071,x81072,x81073)))
% 168.60/168.39 [8149]P149(x81493,x81492,x81491)+~P1(f315(x81493,x81492))+E(f315(f315(f73(a1),f315(f315(f74(a1),x81491),f850(x81491,x81492,x81493))),f849(x81491,x81492,x81493)),x81492)+P1(f315(f315(f224(a1),x81491),f848(x81491,x81492,x81493)))
% 168.60/168.39 [8158]P150(x81583,x81582,x81581)+E(f315(f315(f73(a1),f315(f315(f74(a1),x81581),f846(x81581,x81582,x81583))),f845(x81581,x81582,x81583)),x81582)+P1(f315(f315(f224(a1),x81581),f844(x81581,x81582,x81583)))+~P1(f315(x81583,f2(a1)))
% 168.60/168.39 [8164]P149(x81643,x81642,x81641)+~P1(f315(x81643,x81642))+E(f315(f315(f73(a1),f315(f315(f74(a1),x81641),f851(x81641,x81642,x81643))),f848(x81641,x81642,x81643)),x81642)+P1(f315(f315(f223(a1),f2(a1)),f849(x81641,x81642,x81643)))
% 168.60/168.39 [8171]P150(x81713,x81712,x81711)+E(f315(f315(f73(a1),f315(f315(f74(a1),x81711),f847(x81711,x81712,x81713))),f844(x81711,x81712,x81713)),x81712)+P1(f315(f315(f223(a1),f2(a1)),f845(x81711,x81712,x81713)))+~P1(f315(x81713,f2(a1)))
% 168.60/168.39 [8182]P150(x81823,x81822,x81821)+E(x81821,f2(a1))+E(f315(f315(f73(a1),f315(f315(f74(a1),x81821),f846(x81821,x81822,x81823))),f845(x81821,x81822,x81823)),x81822)+~P1(f315(x81823,f847(x81821,x81822,x81823)))
% 168.60/168.39 [8183]P149(x81833,x81832,x81831)+E(x81831,f2(a1))+E(f315(f315(f73(a1),f315(f315(f74(a1),x81831),f850(x81831,x81832,x81833))),f849(x81831,x81832,x81833)),x81832)+~P1(f315(x81833,f848(x81831,x81832,x81833)))
% 168.60/168.39 [8184]P150(x81843,x81842,x81841)+E(x81841,f2(a1))+E(f315(f315(f73(a1),f315(f315(f74(a1),x81841),f847(x81841,x81842,x81843))),f844(x81841,x81842,x81843)),x81842)+~P1(f315(x81843,f846(x81841,x81842,x81843)))
% 168.60/168.39 [8185]P149(x81853,x81852,x81851)+E(x81851,f2(a1))+E(f315(f315(f73(a1),f315(f315(f74(a1),x81851),f851(x81851,x81852,x81853))),f848(x81851,x81852,x81853)),x81852)+~P1(f315(x81853,f849(x81851,x81852,x81853)))
% 168.60/168.39 [8245]P149(x82453,x82452,x82451)+~P1(f315(x82453,x82452))+E(f315(f315(f73(a1),f315(f315(f74(a1),x82451),f850(x82451,x82452,x82453))),f849(x82451,x82452,x82453)),x82452)+~P1(f315(x82453,f848(x82451,x82452,x82453)))
% 168.60/168.39 [8246]P149(x82463,x82462,x82461)+~P1(f315(x82463,x82462))+E(f315(f315(f73(a1),f315(f315(f74(a1),x82461),f851(x82461,x82462,x82463))),f848(x82461,x82462,x82463)),x82462)+~P1(f315(x82463,f849(x82461,x82462,x82463)))
% 168.60/168.39 [8259]P150(x82593,x82592,x82591)+E(f315(f315(f73(a1),f315(f315(f74(a1),x82591),f846(x82591,x82592,x82593))),f845(x82591,x82592,x82593)),x82592)+~P1(f315(x82593,f847(x82591,x82592,x82593)))+~P1(f315(x82593,f2(a1)))
% 168.60/168.39 [8260]P150(x82603,x82602,x82601)+E(f315(f315(f73(a1),f315(f315(f74(a1),x82601),f847(x82601,x82602,x82603))),f844(x82601,x82602,x82603)),x82602)+~P1(f315(x82603,f846(x82601,x82602,x82603)))+~P1(f315(x82603,f2(a1)))
% 168.60/168.39 [8358]P150(x83583,x83582,x83581)+E(x83581,f2(a1))+E(f315(f315(f73(a1),f315(f315(f74(a1),x83581),f846(x83581,x83582,x83583))),f845(x83581,x83582,x83583)),x83582)+P1(f315(f315(f223(a1),f844(x83581,x83582,x83583)),f2(a1)))
% 168.60/168.39 [8359]P149(x83593,x83592,x83591)+E(x83591,f2(a1))+E(f315(f315(f73(a1),f315(f315(f74(a1),x83591),f850(x83591,x83592,x83593))),f849(x83591,x83592,x83593)),x83592)+P1(f315(f315(f223(a1),f848(x83591,x83592,x83593)),f2(a1)))
% 168.60/168.39 [8398]P149(x83983,x83982,x83981)+~P1(f315(x83983,x83982))+E(f315(f315(f73(a1),f315(f315(f74(a1),x83981),f850(x83981,x83982,x83983))),f849(x83981,x83982,x83983)),x83982)+P1(f315(f315(f223(a1),f848(x83981,x83982,x83983)),f2(a1)))
% 168.60/168.39 [8403]P150(x84033,x84032,x84031)+E(f315(f315(f73(a1),f315(f315(f74(a1),x84031),f846(x84031,x84032,x84033))),f845(x84031,x84032,x84033)),x84032)+~P1(f315(x84033,f2(a1)))+P1(f315(f315(f223(a1),f844(x84031,x84032,x84033)),f2(a1)))
% 168.60/168.39 [8538]P150(x85383,x85382,x85381)+E(x85381,f2(a1))+E(f315(f315(f73(a1),f315(f315(f74(a1),x85381),f847(x85381,x85382,x85383))),f844(x85381,x85382,x85383)),x85382)+E(f315(f315(f73(a1),f315(f315(f74(a1),x85381),f846(x85381,x85382,x85383))),f845(x85381,x85382,x85383)),x85382)
% 168.60/168.39 [8539]P149(x85393,x85392,x85391)+E(x85391,f2(a1))+E(f315(f315(f73(a1),f315(f315(f74(a1),x85391),f851(x85391,x85392,x85393))),f848(x85391,x85392,x85393)),x85392)+E(f315(f315(f73(a1),f315(f315(f74(a1),x85391),f850(x85391,x85392,x85393))),f849(x85391,x85392,x85393)),x85392)
% 168.60/168.39 [8559]P149(x85593,x85592,x85591)+~P1(f315(x85593,x85592))+E(f315(f315(f73(a1),f315(f315(f74(a1),x85591),f851(x85591,x85592,x85593))),f848(x85591,x85592,x85593)),x85592)+E(f315(f315(f73(a1),f315(f315(f74(a1),x85591),f850(x85591,x85592,x85593))),f849(x85591,x85592,x85593)),x85592)
% 168.60/168.39 [8570]P150(x85703,x85702,x85701)+E(f315(f315(f73(a1),f315(f315(f74(a1),x85701),f847(x85701,x85702,x85703))),f844(x85701,x85702,x85703)),x85702)+E(f315(f315(f73(a1),f315(f315(f74(a1),x85701),f846(x85701,x85702,x85703))),f845(x85701,x85702,x85703)),x85702)+~P1(f315(x85703,f2(a1)))
% 168.60/168.39 [9232]~P130(x92321)+~E(x92323,f2(x92321))+~E(x92322,f2(x92321))+P1(f315(f315(f223(x92321),f315(f315(f73(x92321),f315(f315(f74(x92321),x92322),x92322)),f315(f315(f74(x92321),x92323),x92323))),f2(x92321)))
% 168.60/168.39 [10311]~P114(x103111)+~E(x103113,f2(x103111))+~E(x103112,f2(x103111))+P1(f315(f315(f223(x103111),f315(f315(f73(x103111),f315(f315(f232(x103111),x103112),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))))),f315(f315(f232(x103111),x103113),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))))),f2(x103111)))
% 168.60/168.39 [4885]~E(x48853,x48851)+~P125(x48852)+E(x48851,f2(x48852))+E(f315(f315(f279(x48852),x48853),x48851),f71(x48852))
% 168.60/168.39 [4938]~P81(x49381)+~E(x49383,f177(x49381))+~E(x49382,f177(x49381))+E(f315(f315(f99(x49381),x49382),x49383),f177(x49381))
% 168.60/168.39 [4939]~P102(x49391)+~E(x49393,f230(x49391))+~E(x49392,f230(x49391))+E(f315(f315(f90(x49391),x49392),x49393),f230(x49391))
% 168.60/168.39 [5036]~P125(x50363)+E(x50361,x50362)+E(x50362,f2(x50363))+~E(f315(f315(f279(x50363),x50361),x50362),f71(x50363))
% 168.60/168.39 [5054]~P134(x50542)+E(x50541,f2(x50542))+E(x50543,f2(x50542))+~E(f315(f315(f74(x50542),x50543),x50541),f2(x50542))
% 168.60/168.39 [5055]~P142(x50552)+E(x50551,f2(x50552))+E(x50553,f2(x50552))+~E(f315(f315(f74(x50552),x50553),x50551),f2(x50552))
% 168.60/168.39 [5431]~P123(x54313)+E(x54311,x54312)+E(x54311,f315(f72(x54313),x54312))+~E(f315(f315(f74(x54313),x54311),x54311),f315(f315(f74(x54313),x54312),x54312))
% 168.60/168.39 [5470]~P98(x54701)+E(f315(f72(x54701),x54702),x54703)+~E(f315(f315(f99(x54701),x54702),x54703),f230(x54701))+~E(f315(f315(f90(x54701),x54702),x54703),f177(x54701))
% 168.60/168.39 [5551]~P114(x55513)+E(x55511,x55512)+P1(f315(f315(f224(x55513),x55512),x55511))+P1(f315(f315(f224(x55513),x55511),x55512))
% 168.60/168.39 [5552]~P110(x55523)+E(x55521,x55522)+P1(f315(f315(f224(x55523),x55522),x55521))+P1(f315(f315(f224(x55523),x55521),x55522))
% 168.60/168.39 [5553]~E(x55532,x55533)+~P110(x55531)+P1(f315(f315(f224(x55531),x55532),x55533))+P1(f315(f315(f223(x55531),x55532),x55533))
% 168.60/168.39 [5817]~P111(x58173)+E(x58171,x58172)+~P1(f315(f315(f223(x58173),x58172),x58171))+P1(f315(f315(f224(x58173),x58172),x58171))
% 168.60/168.39 [5819]~P110(x58193)+E(x58191,x58192)+~P1(f315(f315(f223(x58193),x58191),x58192))+P1(f315(f315(f224(x58193),x58191),x58192))
% 168.60/168.39 [5825]~P111(x58253)+E(x58251,x58252)+~P1(f315(f315(f223(x58253),x58251),x58252))+P1(f315(f315(f224(x58253),x58251),x58252))
% 168.60/168.39 [5939]P149(x59391,x59392,x59393)+~P1(f315(x59391,x59392))+P1(f315(f315(f224(a1),x59393),f2(a1)))+P1(f315(f315(f224(a1),f2(a1)),x59393))
% 168.60/168.39 [5993]P150(x59931,x59932,x59933)+~P1(f315(x59931,f2(a1)))+P1(f315(f315(f224(a1),x59933),f2(a1)))+P1(f315(f315(f224(a1),f2(a1)),x59933))
% 168.60/168.39 [5998]~P80(x59981)+E(f315(f315(f99(x59981),x59982),f13(x59981,x59983)),x59982)+~P1(f315(f54(x59981),x59983))+~P1(f315(f315(f317(x59981),x59982),x59983))
% 168.60/168.39 [5999]~P80(x59991)+E(f315(f315(f90(x59991),x59992),f12(x59991,x59993)),x59992)+~P1(f315(f54(x59991),x59993))+~P1(f315(f315(f317(x59991),x59992),x59993))
% 168.60/168.39 [6037]~P80(x60371)+E(f315(f315(f99(x60371),x60372),f12(x60371,x60373)),f12(x60371,x60373))+~P1(f315(f54(x60371),x60373))+~P1(f315(f315(f317(x60371),x60372),x60373))
% 168.60/168.39 [6038]~P80(x60381)+E(f315(f315(f90(x60381),x60382),f13(x60381,x60383)),f13(x60381,x60383))+~P1(f315(f54(x60381),x60383))+~P1(f315(f315(f317(x60381),x60382),x60383))
% 168.60/168.39 [6039]~P110(x60391)+E(f315(f315(f221(x60391),x60392),f16(x60391,x60393)),f16(x60391,x60393))+~P1(f315(f54(x60391),x60393))+~P1(f315(f315(f317(x60391),x60392),x60393))
% 168.60/168.39 [6040]~P110(x60401)+E(f315(f315(f222(x60401),x60402),f17(x60401,x60403)),f17(x60401,x60403))+~P1(f315(f54(x60401),x60403))+~P1(f315(f315(f317(x60401),x60402),x60403))
% 168.60/168.39 [6079]E(x60791,x60792)+~P111(x60793)+~P1(f315(f315(f223(x60793),x60792),x60791))+~P1(f315(f315(f223(x60793),x60791),x60792))
% 168.60/168.39 [6226]~P108(x62261)+P1(f315(f315(f224(x62261),x62263),x62262))+~P1(f315(f315(f223(x62261),x62263),x62262))+P1(f315(f315(f223(x62261),x62262),x62263))
% 168.60/168.39 [6254]~P110(x62541)+~P1(f315(f54(x62541),x62543))+P1(f315(f315(f223(x62541),x62542),f17(x62541,x62543)))+~P1(f315(f315(f317(x62541),x62542),x62543))
% 168.60/168.39 [6302]~P110(x63021)+E(f315(f315(f221(x63021),x63022),f15(x63021,f222(x63021),x63023)),x63022)+~P1(f315(f54(x63021),x63023))+~P1(f315(f315(f317(x63021),x63022),x63023))
% 168.60/168.39 [6303]~P110(x63031)+E(f315(f315(f222(x63031),x63032),f14(x63031,f221(x63031),x63033)),x63032)+~P1(f315(f54(x63031),x63033))+~P1(f315(f315(f317(x63031),x63032),x63033))
% 168.60/168.39 [6448]E(x64481,x64482)+~E(f315(f315(f3(a901),x64481),x64483),f315(f315(f3(a901),x64482),x64483))+~P1(f315(f315(f223(a901),x64483),x64481))+~P1(f315(f315(f223(a901),x64483),x64482))
% 168.60/168.39 [6475]~P110(x64751)+~P1(f315(f54(x64751),x64752))+~P1(f315(f315(f317(x64751),x64753),x64752))+P1(f315(f315(f223(x64751),f16(x64751,x64752)),x64753))
% 168.60/168.39 [6541]P150(x65412,x65413,x65411)+E(x65411,f2(a1))+P1(f315(f315(f224(a1),x65411),f844(x65411,x65413,x65412)))+P1(f315(f315(f224(a1),f2(a1)),x65411))
% 168.60/168.39 [6542]P149(x65422,x65423,x65421)+E(x65421,f2(a1))+P1(f315(f315(f224(a1),x65421),f848(x65421,x65423,x65422)))+P1(f315(f315(f224(a1),f2(a1)),x65421))
% 168.60/168.39 [6543]~P110(x65431)+E(f315(f315(f221(x65431),x65432),f14(x65431,f221(x65431),x65433)),f14(x65431,f221(x65431),x65433))+~P1(f315(f54(x65431),x65433))+~P1(f315(f315(f317(x65431),x65432),x65433))
% 168.60/168.39 [6544]~P110(x65441)+E(f315(f315(f222(x65441),x65442),f15(x65441,f222(x65441),x65443)),f15(x65441,f222(x65441),x65443))+~P1(f315(f54(x65441),x65443))+~P1(f315(f315(f317(x65441),x65442),x65443))
% 168.60/168.39 [6550]~P1(f315(x65501,x65502))+P1(f315(x65501,f357(x65502,x65501,x65503)))+P1(f315(x65501,f2(a901)))+~P1(f315(f315(f224(a901),x65502),x65503))
% 168.60/168.39 [6610]~P1(f315(x66101,x66102))+~P1(f315(f54(x66103),x66102))+P1(f315(x66101,f433(x66101,x66102,x66103)))+P1(f315(x66101,f177(f909(x66103,a899))))
% 168.60/168.39 [6623]~P114(x66231)+~P97(x66231)+P1(f315(f315(f223(x66231),f315(f92(x66231),x66232)),f315(f92(x66231),x66233)))+~P1(f315(f315(f223(a1),x66232),x66233))
% 168.60/168.39 [6624]~P114(x66241)+~P97(x66241)+P1(f315(f315(f224(x66241),f315(f92(x66241),x66242)),f315(f92(x66241),x66243)))+~P1(f315(f315(f224(a1),x66242),x66243))
% 168.60/168.39 [6627]~P1(f315(x66271,x66273))+~P1(f315(f54(x66272),x66273))+P1(f315(f54(x66272),f433(x66271,x66273,x66272)))+P1(f315(x66271,f177(f909(x66272,a899))))
% 168.60/168.39 [6661]P149(x66611,x66612,x66613)+~P1(f315(x66611,x66612))+P1(f315(f315(f224(a1),x66613),f848(x66613,x66612,x66611)))+P1(f315(f315(f224(a1),f2(a1)),x66613))
% 168.60/168.39 [6699]P150(x66991,x66992,x66993)+P1(f315(f315(f224(a1),x66993),f844(x66993,x66992,x66991)))+~P1(f315(x66991,f2(a1)))+P1(f315(f315(f224(a1),f2(a1)),x66993))
% 168.60/168.39 [6729]~P109(x67291)+~P96(x67291)+E(f315(f315(f221(x67291),f315(f92(x67291),x67292)),f315(f92(x67291),x67293)),f315(f92(x67291),x67293))+P1(f315(f315(f223(x67291),f315(f92(x67291),x67292)),f315(f92(x67291),x67293)))
% 168.60/168.39 [6730]~P109(x67301)+~P96(x67301)+E(f315(f315(f222(x67301),f315(f92(x67301),x67302)),f315(f92(x67301),x67303)),f315(f92(x67301),x67302))+P1(f315(f315(f223(x67301),f315(f92(x67301),x67302)),f315(f92(x67301),x67303)))
% 168.60/168.39 [6790]P150(x67902,x67903,x67901)+E(x67901,f2(a1))+~P1(f315(x67902,f847(x67901,x67903,x67902)))+P1(f315(f315(f224(a1),f2(a1)),x67901))
% 168.60/168.39 [6791]P149(x67912,x67913,x67911)+E(x67911,f2(a1))+~P1(f315(x67912,f848(x67911,x67913,x67912)))+P1(f315(f315(f224(a1),f2(a1)),x67911))
% 168.60/168.39 [6795]P1(f315(x67951,x67952))+~P1(f315(f54(x67953),x67952))+P1(f315(x67951,f882(x67951,x67952,x67953)))+~P1(f315(x67951,f177(f909(x67953,a899))))
% 168.60/168.39 [6816]P1(f315(x68161,x68162))+P1(f315(f54(x68163),f882(x68161,x68162,x68163)))+~P1(f315(f54(x68163),x68162))+~P1(f315(x68161,f177(f909(x68163,a899))))
% 168.60/168.39 [6885]P149(x68851,x68852,x68853)+~P1(f315(x68851,x68852))+~P1(f315(x68851,f848(x68853,x68852,x68851)))+P1(f315(f315(f224(a1),f2(a1)),x68853))
% 168.60/168.39 [6915]P150(x69151,x69152,x69153)+~P1(f315(x69151,f847(x69153,x69152,x69151)))+~P1(f315(x69151,f2(a1)))+P1(f315(f315(f224(a1),f2(a1)),x69153))
% 168.60/168.39 [7023]~P97(x70233)+~P114(x70233)+~P1(f315(f315(f223(x70233),f315(f92(x70233),x70231)),f315(f92(x70233),x70232)))+P1(f315(f315(f223(a1),x70231),x70232))
% 168.60/168.39 [7024]~P97(x70243)+~P114(x70243)+~P1(f315(f315(f224(x70243),f315(f92(x70243),x70241)),f315(f92(x70243),x70242)))+P1(f315(f315(f224(a1),x70241),x70242))
% 168.60/168.39 [7053]~P110(x70531)+~P13(x70531,x70533)+P13(x70531,f315(f315(f140(x70531),x70532),x70533))+~P1(f315(f315(f223(x70531),x70532),f694(x70533,x70532,x70531)))
% 168.60/168.39 [7054]~P110(x70541)+~P13(x70541,x70543)+P13(x70541,f315(f315(f140(x70541),x70542),x70543))+~P1(f315(f315(f223(x70541),x70542),f696(x70543,x70542,x70541)))
% 168.60/168.39 [7055]~P110(x70551)+~P13(x70551,x70553)+P13(x70551,f315(f315(f140(x70551),x70552),x70553))+~P1(f315(f315(f223(x70551),x70552),f734(x70552,x70553,x70551)))
% 168.60/168.39 [7143]P150(x71432,x71433,x71431)+E(x71431,f2(a1))+P1(f315(f315(f224(a1),x71431),f2(a1)))+P1(f315(f315(f224(a1),f845(x71431,x71433,x71432)),x71431))
% 168.60/168.39 [7144]P149(x71442,x71443,x71441)+E(x71441,f2(a1))+P1(f315(f315(f224(a1),x71441),f2(a1)))+P1(f315(f315(f224(a1),f849(x71441,x71443,x71442)),x71441))
% 168.60/168.39 [7181]P150(x71812,x71813,x71811)+E(x71811,f2(a1))+P1(f315(f315(f223(a1),f844(x71811,x71813,x71812)),f2(a1)))+P1(f315(f315(f224(a1),f2(a1)),x71811))
% 168.60/168.39 [7182]P149(x71822,x71823,x71821)+E(x71821,f2(a1))+P1(f315(f315(f223(a1),f848(x71821,x71823,x71822)),f2(a1)))+P1(f315(f315(f224(a1),f2(a1)),x71821))
% 168.60/168.39 [7207]~P110(x72071)+~P13(x72071,x72073)+E(f315(f315(f137(x72071,x72071,f7(x72071)),x72072),f159(x72071,x72072,x72073)),x72073)+~P1(f315(f315(f317(x72071),x72072),f315(f161(x72071),x72073)))
% 168.60/168.39 [7254]P149(x72541,x72542,x72543)+~P1(f315(x72541,x72542))+P1(f315(f315(f224(a1),x72543),f2(a1)))+P1(f315(f315(f224(a1),f849(x72543,x72542,x72541)),x72543))
% 168.60/168.39 [7260]~P109(x72601)+~P96(x72601)+E(f315(f315(f221(x72601),f315(f92(x72601),x72602)),f315(f92(x72601),x72603)),f315(f92(x72601),x72602))+~P1(f315(f315(f223(x72601),f315(f92(x72601),x72602)),f315(f92(x72601),x72603)))
% 168.60/168.39 [7261]~P109(x72611)+~P96(x72611)+E(f315(f315(f222(x72611),f315(f92(x72611),x72612)),f315(f92(x72611),x72613)),f315(f92(x72611),x72613))+~P1(f315(f315(f223(x72611),f315(f92(x72611),x72612)),f315(f92(x72611),x72613)))
% 168.60/168.39 [7275]P150(x72751,x72752,x72753)+~P1(f315(x72751,f2(a1)))+P1(f315(f315(f224(a1),x72753),f2(a1)))+P1(f315(f315(f224(a1),f845(x72753,x72752,x72751)),x72753))
% 168.60/168.39 [7285]P149(x72851,x72852,x72853)+~P1(f315(x72851,x72852))+P1(f315(f315(f223(a1),f848(x72853,x72852,x72851)),f2(a1)))+P1(f315(f315(f224(a1),f2(a1)),x72853))
% 168.60/168.39 [7309]P150(x73091,x73092,x73093)+~P1(f315(x73091,f2(a1)))+P1(f315(f315(f223(a1),f844(x73093,x73092,x73091)),f2(a1)))+P1(f315(f315(f224(a1),f2(a1)),x73093))
% 168.60/168.39 [7337]~P1(f315(x73371,x73372))+P1(f315(x73371,f2(a901)))+~P1(f315(f315(f224(a901),x73372),x73373))+P1(f315(f315(f224(a901),f357(x73372,x73371,x73373)),x73373))
% 168.60/168.39 [7354]~P110(x73541)+~P13(x73541,x73543)+P13(x73541,f315(f315(f140(x73541),x73542),x73543))+P1(f315(f315(f317(x73541),f694(x73543,x73542,x73541)),f315(f161(x73541),x73543)))
% 168.60/168.39 [7355]~P110(x73551)+~P13(x73551,x73553)+P13(x73551,f315(f315(f140(x73551),x73552),x73553))+P1(f315(f315(f317(x73551),f696(x73553,x73552,x73551)),f315(f161(x73551),x73553)))
% 168.60/168.39 [7356]~P110(x73561)+~P13(x73561,x73563)+P13(x73561,f315(f315(f140(x73561),x73562),x73563))+P1(f315(f315(f317(x73561),f734(x73562,x73563,x73561)),f315(f161(x73561),x73563)))
% 168.60/168.39 [7472]~P110(x74721)+~P5(x74721)+~P1(f315(f315(f224(x74721),x74723),f30(x74721,x74722)))+P1(f315(f315(f317(x74721),f863(x74722,x74723,x74721)),x74722))
% 168.60/168.39 [7628]~P110(x76281)+~P5(x76281)+~P1(f315(f315(f224(x76281),f31(x76281,x76283)),x76282))+P1(f315(f315(f317(x76281),f364(x76282,x76283,x76281)),x76283))
% 168.60/168.39 [7629]~P110(x76291)+~P5(x76291)+~P1(f315(f315(f224(x76291),f31(x76291,x76293)),x76292))+P1(f315(f315(f224(x76291),f364(x76292,x76293,x76291)),x76292))
% 168.60/168.39 [7641]P150(x76412,x76413,x76411)+E(x76411,f2(a1))+P1(f315(f315(f224(a1),x76411),f844(x76411,x76413,x76412)))+P1(f315(f315(f224(a1),f845(x76411,x76413,x76412)),x76411))
% 168.60/168.39 [7642]P149(x76422,x76423,x76421)+E(x76421,f2(a1))+P1(f315(f315(f224(a1),x76421),f848(x76421,x76423,x76422)))+P1(f315(f315(f224(a1),f849(x76421,x76423,x76422)),x76421))
% 168.60/168.39 [7736]P150(x77363,x77362,x77361)+E(x77361,f2(a1))+E(f315(f315(f73(a1),f315(f315(f74(a1),x77361),f847(x77361,x77362,x77363))),f844(x77361,x77362,x77363)),x77362)+P1(f315(f315(f224(a1),f2(a1)),x77361))
% 168.60/168.39 [7737]P149(x77373,x77372,x77371)+E(x77371,f2(a1))+E(f315(f315(f73(a1),f315(f315(f74(a1),x77371),f851(x77371,x77372,x77373))),f848(x77371,x77372,x77373)),x77372)+P1(f315(f315(f224(a1),f2(a1)),x77371))
% 168.60/168.39 [7739]~P130(x77391)+~P1(f315(f315(f223(x77391),x77393),f2(x77391)))+P1(f315(f315(f223(x77391),f315(f315(f74(x77391),x77392),x77393)),f2(x77391)))+~P1(f315(f315(f223(x77391),f2(x77391)),x77392))
% 168.60/168.39 [7740]~P130(x77401)+~P1(f315(f315(f223(x77401),x77402),f2(x77401)))+P1(f315(f315(f223(x77401),f315(f315(f74(x77401),x77402),x77403)),f2(x77401)))+~P1(f315(f315(f223(x77401),f2(x77401)),x77403))
% 168.60/168.39 [7742]~P137(x77421)+~P1(f315(f315(f223(x77421),x77423),f2(x77421)))+P1(f315(f315(f223(x77421),f315(f315(f74(x77421),x77422),x77423)),f2(x77421)))+~P1(f315(f315(f223(x77421),f2(x77421)),x77422))
% 168.60/168.39 [7744]~P137(x77441)+~P1(f315(f315(f223(x77441),x77442),f2(x77441)))+P1(f315(f315(f223(x77441),f315(f315(f74(x77441),x77442),x77443)),f2(x77441)))+~P1(f315(f315(f223(x77441),f2(x77441)),x77443))
% 168.60/168.39 [7745]~P67(x77451)+~P1(f315(f315(f223(x77451),x77453),f2(x77451)))+P1(f315(f315(f223(x77451),f315(f315(f279(x77451),x77452),x77453)),f2(x77451)))+~P1(f315(f315(f223(x77451),f2(x77451)),x77452))
% 168.60/168.39 [7746]~P67(x77461)+~P1(f315(f315(f223(x77461),x77462),f2(x77461)))+P1(f315(f315(f223(x77461),f315(f315(f279(x77461),x77462),x77463)),f2(x77461)))+~P1(f315(f315(f223(x77461),f2(x77461)),x77463))
% 168.60/168.39 [7747]~P68(x77471)+~P1(f315(f315(f223(x77471),x77472),f2(x77471)))+P1(f315(f315(f223(x77471),f315(f315(f279(x77471),x77472),x77473)),f2(x77471)))+~P1(f315(f315(f224(x77471),f2(x77471)),x77473))
% 168.60/168.39 [7748]~P68(x77481)+~P1(f315(f315(f224(x77481),x77483),f2(x77481)))+P1(f315(f315(f223(x77481),f315(f315(f279(x77481),x77482),x77483)),f2(x77481)))+~P1(f315(f315(f223(x77481),f2(x77481)),x77482))
% 168.60/168.39 [7750]~P136(x77501)+~P1(f315(f315(f224(x77501),x77503),f2(x77501)))+P1(f315(f315(f224(x77501),f315(f315(f74(x77501),x77502),x77503)),f2(x77501)))+~P1(f315(f315(f224(x77501),f2(x77501)),x77502))
% 168.60/168.39 [7751]~P136(x77511)+~P1(f315(f315(f224(x77511),x77512),f2(x77511)))+P1(f315(f315(f224(x77511),f315(f315(f74(x77511),x77512),x77513)),f2(x77511)))+~P1(f315(f315(f224(x77511),f2(x77511)),x77513))
% 168.60/168.39 [7752]~P67(x77521)+~P1(f315(f315(f224(x77521),x77523),f2(x77521)))+P1(f315(f315(f224(x77521),f315(f315(f279(x77521),x77522),x77523)),f2(x77521)))+~P1(f315(f315(f224(x77521),f2(x77521)),x77522))
% 168.60/168.39 [7753]~P67(x77531)+~P1(f315(f315(f224(x77531),x77532),f2(x77531)))+P1(f315(f315(f224(x77531),f315(f315(f279(x77531),x77532),x77533)),f2(x77531)))+~P1(f315(f315(f224(x77531),f2(x77531)),x77533))
% 168.60/168.39 [7754]~P68(x77541)+~P1(f315(f315(f224(x77541),x77543),f2(x77541)))+P1(f315(f315(f224(x77541),f315(f315(f279(x77541),x77542),x77543)),f2(x77541)))+~P1(f315(f315(f224(x77541),f2(x77541)),x77542))
% 168.60/168.39 [7755]~P68(x77551)+~P1(f315(f315(f224(x77551),x77552),f2(x77551)))+P1(f315(f315(f224(x77551),f315(f315(f279(x77551),x77552),x77553)),f2(x77551)))+~P1(f315(f315(f224(x77551),f2(x77551)),x77553))
% 168.60/168.39 [7770]P149(x77701,x77702,x77703)+~P1(f315(x77701,x77702))+P1(f315(f315(f224(a1),x77703),f848(x77703,x77702,x77701)))+P1(f315(f315(f224(a1),f849(x77703,x77702,x77701)),x77703))
% 168.60/168.39 [7783]P150(x77831,x77832,x77833)+P1(f315(f315(f224(a1),x77833),f844(x77833,x77832,x77831)))+~P1(f315(x77831,f2(a1)))+P1(f315(f315(f224(a1),f845(x77833,x77832,x77831)),x77833))
% 168.60/168.39 [7835]P150(x78352,x78353,x78351)+E(x78351,f2(a1))+~P1(f315(x78352,f847(x78351,x78353,x78352)))+P1(f315(f315(f224(a1),f845(x78351,x78353,x78352)),x78351))
% 168.60/168.39 [7836]P149(x78362,x78363,x78361)+E(x78361,f2(a1))+~P1(f315(x78362,f848(x78361,x78363,x78362)))+P1(f315(f315(f224(a1),f849(x78361,x78363,x78362)),x78361))
% 168.60/168.39 [7846]P149(x78463,x78462,x78461)+~P1(f315(x78463,x78462))+E(f315(f315(f73(a1),f315(f315(f74(a1),x78461),f851(x78461,x78462,x78463))),f848(x78461,x78462,x78463)),x78462)+P1(f315(f315(f224(a1),f2(a1)),x78461))
% 168.60/168.39 [7861]P150(x78613,x78612,x78611)+E(f315(f315(f73(a1),f315(f315(f74(a1),x78611),f847(x78611,x78612,x78613))),f844(x78611,x78612,x78613)),x78612)+~P1(f315(x78613,f2(a1)))+P1(f315(f315(f224(a1),f2(a1)),x78611))
% 168.60/168.39 [7889]~P1(f315(x78891,x78893))+~P1(f315(f54(x78892),x78893))+P1(f315(f315(f317(x78892),f434(x78891,x78893,x78892)),f433(x78891,x78893,x78892)))+P1(f315(x78891,f177(f909(x78892,a899))))
% 168.60/168.39 [7900]P149(x79001,x79002,x79003)+~P1(f315(x79001,x79002))+~P1(f315(x79001,f848(x79003,x79002,x79001)))+P1(f315(f315(f224(a1),f849(x79003,x79002,x79001)),x79003))
% 168.60/168.39 [7906]P150(x79061,x79062,x79063)+~P1(f315(x79061,f847(x79063,x79062,x79061)))+~P1(f315(x79061,f2(a1)))+P1(f315(f315(f224(a1),f845(x79063,x79062,x79061)),x79063))
% 168.60/168.39 [8008]~P130(x80081)+~P1(f315(f315(f223(x80081),f315(f315(f74(x80081),x80083),x80082)),f2(x80081)))+P1(f315(f315(f223(x80081),x80082),f2(x80081)))+P1(f315(f315(f223(x80081),f2(x80081)),x80082))
% 168.60/168.39 [8009]~P130(x80091)+~P1(f315(f315(f223(x80091),f315(f315(f74(x80091),x80092),x80093)),f2(x80091)))+P1(f315(f315(f223(x80091),x80092),f2(x80091)))+P1(f315(f315(f223(x80091),f2(x80091)),x80092))
% 168.60/168.39 [8010]~P67(x80101)+~P1(f315(f315(f223(x80101),f315(f315(f279(x80101),x80103),x80102)),f2(x80101)))+P1(f315(f315(f223(x80101),x80102),f2(x80101)))+P1(f315(f315(f223(x80101),f2(x80101)),x80102))
% 168.60/168.39 [8011]~P67(x80111)+~P1(f315(f315(f223(x80111),f315(f315(f279(x80111),x80112),x80113)),f2(x80111)))+P1(f315(f315(f223(x80111),x80112),f2(x80111)))+P1(f315(f315(f223(x80111),f2(x80111)),x80112))
% 168.60/168.39 [8012]~P67(x80121)+~P1(f315(f315(f224(x80121),f315(f315(f279(x80121),x80123),x80122)),f2(x80121)))+P1(f315(f315(f224(x80121),x80122),f2(x80121)))+P1(f315(f315(f224(x80121),f2(x80121)),x80122))
% 168.60/168.39 [8013]~P67(x80131)+~P1(f315(f315(f224(x80131),f315(f315(f279(x80131),x80132),x80133)),f2(x80131)))+P1(f315(f315(f224(x80131),x80132),f2(x80131)))+P1(f315(f315(f224(x80131),f2(x80131)),x80132))
% 168.60/168.39 [8037]~P130(x80371)+~P1(f315(f315(f223(x80371),f315(f315(f74(x80371),x80372),x80373)),f2(x80371)))+P1(f315(f315(f223(x80371),f2(x80371)),x80372))+P1(f315(f315(f223(x80371),f2(x80371)),x80373))
% 168.60/168.39 [8038]~P67(x80381)+~P1(f315(f315(f223(x80381),f315(f315(f279(x80381),x80382),x80383)),f2(x80381)))+P1(f315(f315(f223(x80381),f2(x80381)),x80382))+P1(f315(f315(f223(x80381),f2(x80381)),x80383))
% 168.60/168.39 [8039]~P67(x80391)+~P1(f315(f315(f224(x80391),f315(f315(f279(x80391),x80392),x80393)),f2(x80391)))+P1(f315(f315(f224(x80391),f2(x80391)),x80392))+P1(f315(f315(f224(x80391),f2(x80391)),x80393))
% 168.60/168.39 [8061]P150(x80612,x80613,x80611)+E(x80611,f2(a1))+P1(f315(f315(f223(a1),f844(x80611,x80613,x80612)),f2(a1)))+P1(f315(f315(f224(a1),f845(x80611,x80613,x80612)),x80611))
% 168.60/168.39 [8062]P149(x80622,x80623,x80621)+E(x80621,f2(a1))+P1(f315(f315(f223(a1),f848(x80621,x80623,x80622)),f2(a1)))+P1(f315(f315(f224(a1),f849(x80621,x80623,x80622)),x80621))
% 168.60/168.39 [8069]~P128(x80691)+~P1(f315(f315(f224(x80691),x80692),f71(x80691)))+P1(f315(f315(f224(x80691),f315(f315(f232(x80691),x80692),f315(a101,x80693))),f71(x80691)))+~P1(f315(f315(f224(x80691),f2(x80691)),x80692))
% 168.60/168.39 [8123]~P110(x81231)+~E(x81233,f102(x81231))+~P13(x81231,f315(f157(x81231),x81233))+E(f315(f131(x81231,x81231,f315(f9(x81231,x81231,x81231),f222(x81231)),x81232),f315(f157(x81231),x81233)),x81232)
% 168.60/168.39 [8126]P149(x81261,x81262,x81263)+~P1(f315(x81261,x81262))+P1(f315(f315(f223(a1),f848(x81263,x81262,x81261)),f2(a1)))+P1(f315(f315(f224(a1),f849(x81263,x81262,x81261)),x81263))
% 168.60/168.39 [8133]P150(x81331,x81332,x81333)+~P1(f315(x81331,f2(a1)))+P1(f315(f315(f223(a1),f844(x81333,x81332,x81331)),f2(a1)))+P1(f315(f315(f224(a1),f845(x81333,x81332,x81331)),x81333))
% 168.60/168.39 [8353]P150(x83533,x83532,x83531)+E(x83531,f2(a1))+E(f315(f315(f73(a1),f315(f315(f74(a1),x83531),f847(x83531,x83532,x83533))),f844(x83531,x83532,x83533)),x83532)+P1(f315(f315(f224(a1),f845(x83531,x83532,x83533)),x83531))
% 168.60/168.39 [8354]P149(x83543,x83542,x83541)+E(x83541,f2(a1))+E(f315(f315(f73(a1),f315(f315(f74(a1),x83541),f851(x83541,x83542,x83543))),f848(x83541,x83542,x83543)),x83542)+P1(f315(f315(f224(a1),f849(x83541,x83542,x83543)),x83541))
% 168.60/168.39 [8389]P149(x83893,x83892,x83891)+~P1(f315(x83893,x83892))+E(f315(f315(f73(a1),f315(f315(f74(a1),x83891),f851(x83891,x83892,x83893))),f848(x83891,x83892,x83893)),x83892)+P1(f315(f315(f224(a1),f849(x83891,x83892,x83893)),x83891))
% 168.60/168.39 [8390]~P72(x83901)+~P77(x83901)+~P42(x83903)+E(f315(f315(f8(a901,x83901),f315(f315(f10(a1,x83901,a901),x83902),f89(a1))),f315(f298(a1,a901,a93),x83903)),f315(f315(f8(a1,x83901),x83902),x83903))
% 168.60/168.39 [8391]~P72(x83911)+~P77(x83911)+~P42(x83913)+E(f315(f315(f11(a901,x83911),f315(f315(f10(a1,x83911,a901),x83912),f89(a1))),f315(f298(a1,a901,a93),x83913)),f315(f315(f11(a1,x83911),x83912),x83913))
% 168.60/168.39 [8400]P150(x84003,x84002,x84001)+E(f315(f315(f73(a1),f315(f315(f74(a1),x84001),f847(x84001,x84002,x84003))),f844(x84001,x84002,x84003)),x84002)+~P1(f315(x84003,f2(a1)))+P1(f315(f315(f224(a1),f845(x84001,x84002,x84003)),x84001))
% 168.60/168.39 [8422]~E(x84222,f2(a901))+~E(f315(f239(a901,a901),x84223),f2(a901))+~E(x84221,f315(f315(f73(a901),f315(f315(f74(a901),f315(f239(a901,a901),x84223)),x84222)),f315(f244(a901,a901),x84223)))+P1(f315(f41(x84221,x84222),x84223))
% 168.60/168.39 [8479]P1(f315(x84791,x84792))+~P1(f315(f315(f317(x84793),f887(x84791,x84792,x84793)),f882(x84791,x84792,x84793)))+~P1(f315(f54(x84793),x84792))+~P1(f315(x84791,f177(f909(x84793,a899))))
% 168.60/168.39 [9104]P1(f315(x91041,x91042))+~P1(f315(f54(x91043),x91042))+~P1(f315(x91041,f315(f315(f297(x91043),f887(x91041,x91042,x91043)),f882(x91041,x91042,x91043))))+~P1(f315(x91041,f177(f909(x91043,a899))))
% 168.60/168.39 [9335]P1(f315(f315(f223(a1),x93351),f2(a1)))+~P1(f315(f315(f224(a1),f315(f315(f73(a1),f315(f315(f74(a1),x93353),x93351)),x93352)),f2(a1)))+~P1(f315(f315(f223(a1),f2(a1)),x93352))+~P1(f315(f315(f224(a1),f2(a1)),x93353))
% 168.60/168.39 [5887]~P80(x58872)+E(x58871,f177(f909(x58872,a899)))+~P1(f315(f54(x58872),x58871))+E(f12(x58872,f315(f315(f297(x58872),x58873),x58871)),f315(f315(f99(x58872),x58873),f12(x58872,x58871)))
% 168.60/168.39 [5888]~P80(x58882)+E(x58881,f177(f909(x58882,a899)))+~P1(f315(f54(x58882),x58881))+E(f13(x58882,f315(f315(f297(x58882),x58883),x58881)),f315(f315(f90(x58882),x58883),f13(x58882,x58881)))
% 168.60/168.39 [5889]~P110(x58892)+E(x58891,f177(f909(x58892,a899)))+~P1(f315(f54(x58892),x58891))+E(f16(x58892,f315(f315(f297(x58892),x58893),x58891)),f315(f315(f221(x58892),x58893),f16(x58892,x58891)))
% 168.60/168.39 [5890]~P110(x58902)+E(x58901,f177(f909(x58902,a899)))+~P1(f315(f54(x58902),x58901))+E(f17(x58902,f315(f315(f297(x58902),x58903),x58901)),f315(f315(f222(x58902),x58903),f17(x58902,x58901)))
% 168.60/168.39 [6222]~P130(x62221)+~E(x62223,f2(x62221))+~E(x62222,f2(x62221))+E(f315(f315(f73(x62221),f315(f315(f74(x62221),x62222),x62222)),f315(f315(f74(x62221),x62223),x62223)),f2(x62221))
% 168.60/168.39 [6295]~P99(x62952)+E(x62951,f177(f909(x62952,a899)))+~P1(f315(f54(x62952),x62951))+E(f315(f56(x62952,f74(x62952)),f315(f315(f297(x62952),x62953),x62951)),f315(f315(f74(x62952),x62953),f315(f56(x62952,f74(x62952)),x62951)))
% 168.60/168.39 [6424]~P110(x64242)+E(x64241,f177(f909(x64242,a899)))+~P1(f315(f54(x64242),x64241))+E(f14(x64242,f221(x64242),f315(f315(f297(x64242),x64243),x64241)),f315(f315(f221(x64242),x64243),f14(x64242,f221(x64242),x64241)))
% 168.60/168.39 [6425]~P110(x64252)+E(x64251,f177(f909(x64252,a899)))+~P1(f315(f54(x64252),x64251))+E(f15(x64252,f222(x64252),f315(f315(f297(x64252),x64253),x64251)),f315(f315(f222(x64252),x64253),f15(x64252,f222(x64252),x64251)))
% 168.60/168.39 [6949]~P70(x69491)+~P1(f315(f54(x69491),x69493))+E(f315(f56(x69491,f74(x69491)),f315(f315(f297(x69491),x69492),x69493)),f315(f315(f57(x69491,x69491,f74(x69491)),x69492),x69493))+P1(f315(f315(f317(x69491),x69492),x69493))
% 168.60/168.39 [7031]~E(f315(f315(f73(a1),x70312),f315(f315(f74(a1),x70313),x70311)),x70313)+~P1(f315(f315(f224(a1),f2(a1)),x70313))+P1(f315(f315(f223(a1),f71(a1)),x70311))+~P1(f315(f315(f224(a1),x70312),x70313))
% 168.60/168.39 [7060]~E(f315(f315(f73(a1),x70602),f315(f315(f74(a1),x70603),x70601)),x70603)+P1(f315(f315(f223(a1),x70601),f71(a1)))+~P1(f315(f315(f223(a1),f2(a1)),x70602))+~P1(f315(f315(f224(a1),f2(a1)),x70603))
% 168.60/168.39 [7078]E(x70781,f2(a901))+~P1(f315(f41(x70783,x70781),x70782))+~P1(f315(f315(f224(a901),f2(a901)),x70781))+P1(f315(f315(f224(a901),f315(f244(a901,a901),x70782)),x70781))
% 168.60/168.39 [7110]~P140(x71101)+~P1(f315(f315(f223(x71101),x71102),f2(x71101)))+~P1(f315(f315(f223(x71101),x71103),f2(x71101)))+E(f315(f315(f74(x71101),f315(f69(x71101),x71102)),f315(f69(x71101),x71103)),f315(f69(x71101),f315(f315(f74(x71101),x71102),x71103)))
% 168.60/168.39 [7158]~P140(x71581)+~P1(f315(f315(f223(x71581),x71582),f2(x71581)))+E(f315(f315(f74(x71581),f315(f69(x71581),x71582)),f315(f69(x71581),x71583)),f315(f69(x71581),f315(f315(f74(x71581),x71582),x71583)))+~P1(f315(f315(f223(x71581),f2(x71581)),x71583))
% 168.60/168.39 [7159]~P140(x71591)+~P1(f315(f315(f223(x71591),x71593),f2(x71591)))+E(f315(f315(f74(x71591),f315(f69(x71591),x71592)),f315(f69(x71591),x71593)),f315(f69(x71591),f315(f315(f74(x71591),x71592),x71593)))+~P1(f315(f315(f223(x71591),f2(x71591)),x71592))
% 168.60/168.39 [7215]~P140(x72151)+E(f315(f315(f74(x72151),f315(f69(x72151),x72152)),f315(f69(x72151),x72153)),f315(f69(x72151),f315(f315(f74(x72151),x72152),x72153)))+~P1(f315(f315(f223(x72151),f2(x72151)),x72152))+~P1(f315(f315(f223(x72151),f2(x72151)),x72153))
% 168.60/168.39 [7232]~P113(x72321)+~P1(f315(f315(f223(x72321),x72323),f2(x72321)))+~P1(f315(f315(f223(x72321),x72322),f2(x72321)))+P1(f315(f315(f223(x72321),f2(x72321)),f315(f315(f74(x72321),x72322),x72323)))
% 168.60/168.39 [7233]~P130(x72331)+~P1(f315(f315(f223(x72331),x72333),f2(x72331)))+~P1(f315(f315(f223(x72331),x72332),f2(x72331)))+P1(f315(f315(f223(x72331),f2(x72331)),f315(f315(f74(x72331),x72332),x72333)))
% 168.60/168.39 [7234]~P67(x72341)+~P1(f315(f315(f223(x72341),x72343),f2(x72341)))+~P1(f315(f315(f223(x72341),x72342),f2(x72341)))+P1(f315(f315(f223(x72341),f2(x72341)),f315(f315(f279(x72341),x72342),x72343)))
% 168.60/168.39 [7235]~P68(x72351)+~P1(f315(f315(f224(x72351),x72353),f2(x72351)))+~P1(f315(f315(f223(x72351),x72352),f2(x72351)))+P1(f315(f315(f223(x72351),f2(x72351)),f315(f315(f279(x72351),x72352),x72353)))
% 168.60/168.39 [7236]~P130(x72361)+~P1(f315(f315(f224(x72361),x72363),f2(x72361)))+~P1(f315(f315(f224(x72361),x72362),f2(x72361)))+P1(f315(f315(f224(x72361),f2(x72361)),f315(f315(f74(x72361),x72362),x72363)))
% 168.60/168.39 [7237]~P67(x72371)+~P1(f315(f315(f224(x72371),x72373),f2(x72371)))+~P1(f315(f315(f224(x72371),x72372),f2(x72371)))+P1(f315(f315(f224(x72371),f2(x72371)),f315(f315(f279(x72371),x72372),x72373)))
% 168.60/168.39 [7238]~P68(x72381)+~P1(f315(f315(f224(x72381),x72383),f2(x72381)))+~P1(f315(f315(f224(x72381),x72382),f2(x72381)))+P1(f315(f315(f224(x72381),f2(x72381)),f315(f315(f279(x72381),x72382),x72383)))
% 168.60/168.39 [7239]~P128(x72391)+~P1(f315(f315(f224(a901),f2(a901)),x72393))+~P1(f315(f315(f224(x72391),f71(x72391)),x72392))+P1(f315(f315(f224(x72391),f71(x72391)),f315(f315(f232(x72391),x72392),x72393)))
% 168.60/168.39 [7338]~P113(x73381)+~P1(f315(f315(f223(x73381),f2(x73381)),x73383))+~P1(f315(f315(f223(x73381),f2(x73381)),x73382))+P1(f315(f315(f223(x73381),f2(x73381)),f315(f315(f74(x73381),x73382),x73383)))
% 168.60/168.39 [7339]~P130(x73391)+~P1(f315(f315(f223(x73391),f2(x73391)),x73393))+~P1(f315(f315(f223(x73391),f2(x73391)),x73392))+P1(f315(f315(f223(x73391),f2(x73391)),f315(f315(f74(x73391),x73392),x73393)))
% 168.60/168.39 [7340]~P137(x73401)+~P1(f315(f315(f223(x73401),f2(x73401)),x73403))+~P1(f315(f315(f223(x73401),f2(x73401)),x73402))+P1(f315(f315(f223(x73401),f2(x73401)),f315(f315(f74(x73401),x73402),x73403)))
% 168.60/168.39 [7342]~P67(x73421)+~P1(f315(f315(f223(x73421),f2(x73421)),x73423))+~P1(f315(f315(f223(x73421),f2(x73421)),x73422))+P1(f315(f315(f223(x73421),f2(x73421)),f315(f315(f279(x73421),x73422),x73423)))
% 168.60/168.39 [7343]~P68(x73431)+~P1(f315(f315(f224(x73431),f2(x73431)),x73433))+~P1(f315(f315(f223(x73431),f2(x73431)),x73432))+P1(f315(f315(f223(x73431),f2(x73431)),f315(f315(f279(x73431),x73432),x73433)))
% 168.60/168.39 [7344]~P128(x73441)+~P1(f315(f315(f224(x73441),f71(x73441)),x73443))+~P1(f315(f315(f224(x73441),f71(x73441)),x73442))+P1(f315(f315(f224(x73441),f71(x73441)),f315(f315(f74(x73441),x73442),x73443)))
% 168.60/168.39 [7345]~P136(x73451)+~P1(f315(f315(f224(x73451),f2(x73451)),x73453))+~P1(f315(f315(f224(x73451),f2(x73451)),x73452))+P1(f315(f315(f224(x73451),f2(x73451)),f315(f315(f74(x73451),x73452),x73453)))
% 168.60/168.39 [7348]~P91(x73481)+~P1(f315(f315(f224(x73481),f2(x73481)),x73483))+~P1(f315(f315(f224(x73481),f2(x73481)),x73482))+P1(f315(f315(f224(x73481),f2(x73481)),f315(f315(f73(x73481),x73482),x73483)))
% 168.60/168.39 [7349]~P67(x73491)+~P1(f315(f315(f224(x73491),f2(x73491)),x73493))+~P1(f315(f315(f224(x73491),f2(x73491)),x73492))+P1(f315(f315(f224(x73491),f2(x73491)),f315(f315(f279(x73491),x73492),x73493)))
% 168.60/168.39 [7350]~P68(x73501)+~P1(f315(f315(f224(x73501),f2(x73501)),x73503))+~P1(f315(f315(f224(x73501),f2(x73501)),x73502))+P1(f315(f315(f224(x73501),f2(x73501)),f315(f315(f279(x73501),x73502),x73503)))
% 168.60/168.39 [7429]~P80(x74291)+~P1(f315(f54(x74291),x74293))+E(f12(x74291,f315(f315(f297(x74291),x74292),x74293)),x74292)+~E(f315(f315(f3(f909(x74291,a899)),x74293),f315(f315(f297(x74291),x74292),f177(f909(x74291,a899)))),f177(f909(x74291,a899)))
% 168.60/168.39 [7430]~P80(x74301)+~P1(f315(f54(x74301),x74303))+E(f13(x74301,f315(f315(f297(x74301),x74302),x74303)),x74302)+~E(f315(f315(f3(f909(x74301,a899)),x74303),f315(f315(f297(x74301),x74302),f177(f909(x74301,a899)))),f177(f909(x74301,a899)))
% 168.60/168.39 [7431]~P110(x74311)+~P1(f315(f54(x74311),x74313))+E(f16(x74311,f315(f315(f297(x74311),x74312),x74313)),x74312)+~E(f315(f315(f3(f909(x74311,a899)),x74313),f315(f315(f297(x74311),x74312),f177(f909(x74311,a899)))),f177(f909(x74311,a899)))
% 168.60/168.39 [7432]~P110(x74321)+~P1(f315(f54(x74321),x74323))+E(f17(x74321,f315(f315(f297(x74321),x74322),x74323)),x74322)+~E(f315(f315(f3(f909(x74321,a899)),x74323),f315(f315(f297(x74321),x74322),f177(f909(x74321,a899)))),f177(f909(x74321,a899)))
% 168.60/168.39 [7434]~P130(x74341)+P1(f315(f315(f223(x74341),x74342),f2(x74341)))+P1(f315(f315(f223(x74341),f2(x74341)),x74343))+~P1(f315(f315(f223(x74341),f2(x74341)),f315(f315(f74(x74341),x74343),x74342)))
% 168.60/168.39 [7435]~P130(x74351)+P1(f315(f315(f223(x74351),x74352),f2(x74351)))+P1(f315(f315(f223(x74351),f2(x74351)),x74353))+~P1(f315(f315(f223(x74351),f2(x74351)),f315(f315(f74(x74351),x74352),x74353)))
% 168.60/168.39 [7436]~P67(x74361)+P1(f315(f315(f223(x74361),x74362),f2(x74361)))+P1(f315(f315(f223(x74361),f2(x74361)),x74363))+~P1(f315(f315(f223(x74361),f2(x74361)),f315(f315(f279(x74361),x74363),x74362)))
% 168.60/168.39 [7437]~P67(x74371)+P1(f315(f315(f223(x74371),x74372),f2(x74371)))+P1(f315(f315(f223(x74371),f2(x74371)),x74373))+~P1(f315(f315(f223(x74371),f2(x74371)),f315(f315(f279(x74371),x74372),x74373)))
% 168.60/168.39 [7438]~P130(x74381)+P1(f315(f315(f223(x74381),x74382),f2(x74381)))+P1(f315(f315(f223(x74381),f2(x74381)),x74382))+~P1(f315(f315(f223(x74381),f2(x74381)),f315(f315(f74(x74381),x74383),x74382)))
% 168.60/168.39 [7439]~P130(x74391)+P1(f315(f315(f223(x74391),x74392),f2(x74391)))+P1(f315(f315(f223(x74391),f2(x74391)),x74392))+~P1(f315(f315(f223(x74391),f2(x74391)),f315(f315(f74(x74391),x74392),x74393)))
% 168.60/168.39 [7440]~P67(x74401)+P1(f315(f315(f223(x74401),x74402),f2(x74401)))+P1(f315(f315(f223(x74401),f2(x74401)),x74402))+~P1(f315(f315(f223(x74401),f2(x74401)),f315(f315(f279(x74401),x74403),x74402)))
% 168.60/168.39 [7441]~P67(x74411)+P1(f315(f315(f223(x74411),x74412),f2(x74411)))+P1(f315(f315(f223(x74411),f2(x74411)),x74412))+~P1(f315(f315(f223(x74411),f2(x74411)),f315(f315(f279(x74411),x74412),x74413)))
% 168.60/168.39 [7442]~P67(x74421)+P1(f315(f315(f224(x74421),x74422),f2(x74421)))+P1(f315(f315(f224(x74421),f2(x74421)),x74423))+~P1(f315(f315(f224(x74421),f2(x74421)),f315(f315(f279(x74421),x74423),x74422)))
% 168.60/168.39 [7443]~P67(x74431)+P1(f315(f315(f224(x74431),x74432),f2(x74431)))+P1(f315(f315(f224(x74431),f2(x74431)),x74433))+~P1(f315(f315(f224(x74431),f2(x74431)),f315(f315(f279(x74431),x74432),x74433)))
% 168.60/168.39 [7444]~P67(x74441)+P1(f315(f315(f224(x74441),x74442),f2(x74441)))+P1(f315(f315(f224(x74441),f2(x74441)),x74442))+~P1(f315(f315(f224(x74441),f2(x74441)),f315(f315(f279(x74441),x74443),x74442)))
% 168.60/168.39 [7445]~P67(x74451)+P1(f315(f315(f224(x74451),x74452),f2(x74451)))+P1(f315(f315(f224(x74451),f2(x74451)),x74452))+~P1(f315(f315(f224(x74451),f2(x74451)),f315(f315(f279(x74451),x74452),x74453)))
% 168.60/168.39 [7518]~P1(f315(f315(f275(a901),x75181),x75183))+P1(f315(f315(f275(a901),x75181),x75182))+~P1(f315(f315(f223(a901),x75182),x75183))+~P1(f315(f315(f275(a901),x75181),f315(f315(f3(a901),x75183),x75182)))
% 168.60/168.39 [7519]~P1(f315(f315(f275(a901),x75191),x75193))+P1(f315(f315(f275(a901),x75191),x75192))+~P1(f315(f315(f223(a901),x75193),x75192))+~P1(f315(f315(f275(a901),x75191),f315(f315(f3(a901),x75192),x75193)))
% 168.60/168.39 [7534]~E(f315(f315(f90(f909(x75341,a899)),f315(f161(x75341),x75342)),f315(f161(x75341),x75343)),f177(f909(x75341,a899)))+~P1(f315(f126(x75341),x75343))+~P1(f315(f126(x75341),x75342))+P1(f315(f126(x75341),f315(f315(f123(x75341),x75342),x75343)))
% 168.60/168.39 [7535]~P110(x75351)+~P1(f315(f54(x75351),x75353))+E(f14(x75351,f221(x75351),f315(f315(f297(x75351),x75352),x75353)),x75352)+~E(f315(f315(f3(f909(x75351,a899)),x75353),f315(f315(f297(x75351),x75352),f177(f909(x75351,a899)))),f177(f909(x75351,a899)))
% 168.60/168.39 [7536]~P110(x75361)+~P1(f315(f54(x75361),x75363))+E(f15(x75361,f222(x75361),f315(f315(f297(x75361),x75362),x75363)),x75362)+~E(f315(f315(f3(f909(x75361,a899)),x75363),f315(f315(f297(x75361),x75362),f177(f909(x75361,a899)))),f177(f909(x75361,a899)))
% 168.60/168.39 [7549]~P89(x75491)+~P1(f315(f315(f223(x75491),x75492),x75493))+~P1(f315(f315(f223(x75491),f315(f72(x75491),x75492)),x75493))+P1(f315(f315(f223(x75491),f315(f69(x75491),x75492)),x75493))
% 168.60/168.39 [7550]~P114(x75501)+~P1(f315(f315(f224(x75501),x75502),x75503))+~P1(f315(f315(f224(x75501),f315(f72(x75501),x75502)),x75503))+P1(f315(f315(f224(x75501),f315(f69(x75501),x75502)),x75503))
% 168.60/168.39 [7617]~P136(x76171)+P1(f315(f315(f224(x76171),f2(x76171)),x76172))+~P1(f315(f315(f224(x76171),f2(x76171)),x76173))+~P1(f315(f315(f224(x76171),f2(x76171)),f315(f315(f74(x76171),x76173),x76172)))
% 168.60/168.39 [7618]~P136(x76181)+P1(f315(f315(f224(x76181),f2(x76181)),x76182))+~P1(f315(f315(f224(x76181),f2(x76181)),x76183))+~P1(f315(f315(f224(x76181),f2(x76181)),f315(f315(f74(x76181),x76182),x76183)))
% 168.60/168.39 [7920]E(x79201,x79202)+~P1(f315(f54(x79203),x79201))+~P1(f315(f315(f223(a901),f315(f28(x79203),x79201)),f315(f28(x79203),x79202)))+~P1(f315(f315(f223(f909(x79203,a899)),x79202),x79201))
% 168.60/168.39 [8066]~P1(f315(f315(f224(a1),x80661),f2(a1)))+~P1(f315(f315(f224(a1),f2(a1)),x80662))+~P1(f315(f315(f223(a1),x80662),x80663))+P1(f315(f315(f223(a1),f315(f315(f29(a1),x80661),x80662)),f315(f315(f29(a1),x80661),x80663)))
% 168.60/168.39 [8076]~P1(f315(f315(f223(a1),f2(a1)),x80761))+~P1(f315(f315(f224(a1),f2(a1)),x80763))+~P1(f315(f315(f223(a1),x80763),x80762))+P1(f315(f315(f223(a1),f315(f315(f29(a1),x80761),x80762)),f315(f315(f29(a1),x80761),x80763)))
% 168.60/168.39 [8212]E(f315(x82121,f359(x82122,x82121,x82123)),x82122)+~P1(f315(f315(f223(a1),x82122),f315(x82121,x82123)))+P1(f315(f315(f224(a901),f360(x82122,x82121,x82123)),x82123))+~P1(f315(f315(f223(a1),f315(x82121,f2(a901))),x82122))
% 168.60/168.39 [8213]E(f315(x82131,f361(x82132,x82131,x82133)),x82132)+~P1(f315(f315(f223(a1),x82132),f315(x82131,x82133)))+P1(f315(f315(f224(a901),f362(x82132,x82131,x82133)),x82133))+~P1(f315(f315(f223(a1),f315(x82131,f2(a901))),x82132))
% 168.60/168.39 [8316]~P1(f315(f54(x83161),x83163))+~P1(f315(f315(f224(a901),f315(f28(x83161),x83162)),f315(f28(x83161),x83163)))+~P1(f315(f315(f223(f909(x83161,a899)),x83162),x83163))+P1(f315(f315(f224(f909(x83161,a899)),x83162),x83163))
% 168.60/168.39 [8343]E(f315(f315(f73(a1),f435(x83433,x83431,x83432)),f436(x83433,x83431,x83432)),x83431)+E(f315(f315(f3(a1),x83431),x83432),x83431)+~P1(f315(f315(f224(a1),f2(a1)),x83432))+~P1(f315(f315(f317(a1),f315(f315(f3(a1),x83431),f71(a1))),x83433))
% 168.60/168.39 [8344]E(f315(f315(f3(a1),f453(x83443,x83441,x83442)),f454(x83443,x83441,x83442)),x83441)+E(f315(f315(f73(a1),x83441),x83442),x83441)+~P1(f315(f315(f224(a1),f2(a1)),x83442))+~P1(f315(f315(f317(a1),f315(f315(f73(a1),x83441),f71(a1))),x83443))
% 168.60/168.39 [8395]~P1(f315(f315(f223(a901),x83953),x83951))+P1(f315(f315(f223(a901),x83951),x83952))+~P1(f315(f315(f223(a901),x83953),x83952))+~P1(f315(f315(f223(a901),f315(f315(f3(a901),x83951),x83953)),f315(f315(f3(a901),x83952),x83953)))
% 168.60/168.39 [8396]~P1(f315(f315(f223(a901),x83963),x83961))+P1(f315(f315(f224(a901),x83961),x83962))+~P1(f315(f315(f223(a901),x83963),x83962))+~P1(f315(f315(f224(a901),f315(f315(f3(a901),x83961),x83963)),f315(f315(f3(a901),x83962),x83963)))
% 168.60/168.39 [8415]~P110(x84152)+E(x84151,f102(x84152))+~P13(x84152,f315(f157(x84152),x84151))+E(f315(f131(x84152,x84152,f315(f9(x84152,x84152,x84152),f222(x84152)),x84153),f315(f157(x84152),x84151)),f315(f315(f222(x84152),f315(f315(f153(x84152),x84151),f2(a901))),x84153))
% 168.60/168.39 [8484]E(f315(f315(f3(a1),x84841),x84842),x84841)+~P1(f315(f315(f224(a1),f2(a1)),x84842))+P1(f315(f315(f317(a1),f435(x84843,x84841,x84842)),x84843))+~P1(f315(f315(f317(a1),f315(f315(f3(a1),x84841),f71(a1))),x84843))
% 168.60/168.39 [8485]E(f315(f315(f73(a1),x84851),x84852),x84851)+~P1(f315(f315(f224(a1),f2(a1)),x84852))+P1(f315(f315(f317(a1),f453(x84853,x84851,x84852)),x84853))+~P1(f315(f315(f317(a1),f315(f315(f73(a1),x84851),f71(a1))),x84853))
% 168.60/168.39 [8557]~P1(f315(f315(f223(a1),x85571),f315(x85572,x85573)))+P1(f315(f315(f224(a901),f360(x85571,x85572,x85573)),x85573))+P1(f315(f315(f223(a901),f359(x85571,x85572,x85573)),x85573))+~P1(f315(f315(f223(a1),f315(x85572,f2(a901))),x85571))
% 168.60/168.39 [8558]~P1(f315(f315(f223(a1),x85581),f315(x85582,x85583)))+P1(f315(f315(f224(a901),f362(x85581,x85582,x85583)),x85583))+P1(f315(f315(f223(a901),f361(x85581,x85582,x85583)),x85583))+~P1(f315(f315(f223(a1),f315(x85582,f2(a901))),x85581))
% 168.60/168.39 [8630]E(f315(f315(f3(a1),x86301),x86302),x86301)+~P1(f315(f315(f224(a1),f2(a1)),x86302))+P1(f315(f315(f317(a1),f436(x86303,x86301,x86302)),f291(a1,f71(a1),x86302)))+~P1(f315(f315(f317(a1),f315(f315(f3(a1),x86301),f71(a1))),x86303))
% 168.60/168.39 [8631]E(f315(f315(f73(a1),x86311),x86312),x86311)+~P1(f315(f315(f224(a1),f2(a1)),x86312))+P1(f315(f315(f317(a1),f454(x86313,x86311,x86312)),f291(a1,f71(a1),x86312)))+~P1(f315(f315(f317(a1),f315(f315(f73(a1),x86311),f71(a1))),x86313))
% 168.60/168.39 [8764]~P128(x87641)+~P1(f315(f315(f224(x87641),x87642),f71(x87641)))+~P1(f315(f315(f224(x87641),f2(x87641)),x87642))+P1(f315(f315(f224(x87641),f315(f315(f74(x87641),x87642),f315(f315(f232(x87641),x87642),x87643))),f315(f315(f232(x87641),x87642),x87643)))
% 168.60/168.39 [8857]~P1(f315(x88571,x88572))+P1(f315(x88571,f2(a901)))+~P1(f315(f315(f224(a901),x88572),x88573))+~P1(f315(x88571,f38(a901,f315(a101,f357(x88572,x88571,x88573)),x88573)))
% 168.60/168.39 [9009]E(f381(x90091,x90092,x90093),f2(a901))+P1(f315(f315(x90091,x90093),x90092))+P1(f315(f315(x90091,f381(x90091,x90092,x90093)),f38(a901,f380(x90091,x90092,x90093),f381(x90091,x90092,x90093))))+~P1(f315(f303(f908(a901,a901),a208),f315(f315(f240(a901,a901),x90093),x90092)))
% 168.60/168.39 [9046]~P25(x90461,x90461,x90462,x90463)+E(f315(f298(x90461,x90461,x90462),x90463),x90463)+~P1(f315(f54(x90461),x90463))+~P1(f315(f315(f223(f909(x90461,a899)),f315(f298(x90461,x90461,x90462),x90463)),x90463))
% 168.60/168.39 [9261]P1(f315(f315(x92611,x92612),x92613))+P1(f315(f315(f224(a1),f754(x92611,x92613,x92612)),f755(x92611,x92613,x92612)))+P1(f315(f315(x92611,f754(x92611,x92613,x92612)),f315(f315(f73(a1),f755(x92611,x92613,x92612)),f71(a1))))+~P1(f315(f303(f908(a1,a1),a122),f315(f315(f240(a1,a1),x92612),x92613)))
% 168.60/168.39 [9278]P1(f315(f315(x92781,x92782),x92783))+~P1(f315(f315(f224(a1),f390(x92781,x92783,x92782)),f2(a1)))+P1(f315(f315(x92781,f315(f72(a1),f388(x92781,x92783,x92782))),f315(f72(a1),f390(x92781,x92783,x92782))))+~P1(f315(f303(f908(a1,a1),a210),f315(f315(f240(a1,a1),x92782),x92783)))
% 168.60/168.39 [9469]P1(f315(f315(x94691,x94692),x94693))+P1(f315(f315(x94691,f315(f315(f73(a1),f659(x94691,x94693,x94692)),f71(a1))),f661(x94691,x94693,x94692)))+~P1(f315(f315(f223(a1),f659(x94691,x94693,x94692)),f661(x94691,x94693,x94692)))+~P1(f315(f303(f908(a1,a1),a171),f315(f315(f240(a1,a1),x94692),x94693)))
% 168.60/168.39 [9911]~P64(x99112)+~P64(x99111)+~P1(f315(f49(f908(x99111,x99112)),x99113))+P1(f315(f49(x99111),f315(f315(f10(f909(x99112,a899),a899,x99111),f49(x99112)),f315(f315(f10(f909(x99112,f908(x99111,x99112)),f909(x99112,a899),x99111),f315(f10(f908(x99111,x99112),a899,x99112),x99113)),f240(x99111,x99112)))))
% 168.60/168.39 [9912]~P64(x99122)+~P64(x99121)+~P1(f315(f50(f908(x99121,x99122)),x99123))+P1(f315(f50(x99121),f315(f315(f10(f909(x99122,a899),a899,x99121),f50(x99122)),f315(f315(f10(f909(x99122,f908(x99121,x99122)),f909(x99122,a899),x99121),f315(f10(f908(x99121,x99122),a899,x99122),x99123)),f240(x99121,x99122)))))
% 168.60/168.39 [10006]~P64(x100062)+~P64(x100061)+P1(f315(f49(f908(x100061,x100062)),x100063))+~P1(f315(f49(x100061),f315(f315(f10(f909(x100062,a899),a899,x100061),f49(x100062)),f315(f315(f10(f909(x100062,f908(x100061,x100062)),f909(x100062,a899),x100061),f315(f10(f908(x100061,x100062),a899,x100062),x100063)),f240(x100061,x100062)))))
% 168.60/168.39 [10007]~P64(x100072)+~P64(x100071)+P1(f315(f50(f908(x100071,x100072)),x100073))+~P1(f315(f50(x100071),f315(f315(f10(f909(x100072,a899),a899,x100071),f50(x100072)),f315(f315(f10(f909(x100072,f908(x100071,x100072)),f909(x100072,a899),x100071),f315(f10(f908(x100071,x100072),a899,x100072),x100073)),f240(x100071,x100072)))))
% 168.60/168.39 [10179]E(f315(x101791,f359(x101792,x101791,x101793)),x101792)+~P1(f315(f315(f223(a1),x101792),f315(x101791,x101793)))+~P1(f315(f315(f223(a1),f315(f69(a1),f315(f315(f3(a1),f315(x101791,f315(f315(f73(a901),f360(x101792,x101791,x101793)),f71(a901)))),f315(x101791,f360(x101792,x101791,x101793))))),f71(a1)))+~P1(f315(f315(f223(a1),f315(x101791,f2(a901))),x101792))
% 168.60/168.39 [10180]E(f315(x101801,f361(x101802,x101801,x101803)),x101802)+~P1(f315(f315(f223(a1),x101802),f315(x101801,x101803)))+~P1(f315(f315(f223(a1),f315(f69(a1),f315(f315(f3(a1),f315(x101801,f315(f315(f73(a901),f362(x101802,x101801,x101803)),f71(a901)))),f315(x101801,f362(x101802,x101801,x101803))))),f71(a1)))+~P1(f315(f315(f223(a1),f315(x101801,f2(a901))),x101802))
% 168.60/168.39 [10183]~P1(f315(f315(f223(a1),x101831),f315(x101832,x101833)))+~P1(f315(f315(f223(a1),f315(f69(a1),f315(f315(f3(a1),f315(x101832,f315(f315(f73(a901),f360(x101831,x101832,x101833)),f71(a901)))),f315(x101832,f360(x101831,x101832,x101833))))),f71(a1)))+P1(f315(f315(f223(a901),f359(x101831,x101832,x101833)),x101833))+~P1(f315(f315(f223(a1),f315(x101832,f2(a901))),x101831))
% 168.60/168.39 [10184]~P1(f315(f315(f223(a1),x101841),f315(x101842,x101843)))+~P1(f315(f315(f223(a1),f315(f69(a1),f315(f315(f3(a1),f315(x101842,f315(f315(f73(a901),f362(x101841,x101842,x101843)),f71(a901)))),f315(x101842,f362(x101841,x101842,x101843))))),f71(a1)))+P1(f315(f315(f223(a901),f361(x101841,x101842,x101843)),x101843))+~P1(f315(f315(f223(a1),f315(x101842,f2(a901))),x101841))
% 168.60/168.39 [10241]E(x102411,x102412)+~E(f315(f131(f902(x102413),f902(x102413),f123(x102413),f102(x102413)),x102411),f315(f131(f902(x102413),f902(x102413),f123(x102413),f102(x102413)),x102412))+~E(f315(f178(f902(f902(x102413))),x102411),f315(f178(f902(f902(x102413))),x102412))+~P1(f315(f315(f245(f902(x102413),f902(x102413),a899),f315(f315(f9(f902(x102413),f909(f902(x102413),a901),f909(f902(x102413),a899)),f315(f315(f10(f909(a901,a899),f909(f909(f902(x102413),a901),f909(f902(x102413),a899)),f902(x102413)),f10(a901,a899,f902(x102413))),f315(f315(f10(a901,f909(a901,a899),f902(x102413)),a312),f178(f902(x102413))))),f178(f902(x102413)))),f684(x102411,x102412,x102413)))
% 168.60/168.39 [10242]E(x102421,x102422)+~E(f315(f131(f902(x102423),f902(x102423),f123(x102423),f102(x102423)),x102421),f315(f131(f902(x102423),f902(x102423),f123(x102423),f102(x102423)),x102422))+~E(f315(f178(f902(f902(x102423))),x102421),f315(f178(f902(f902(x102423))),x102422))+~P1(f315(f315(f245(f902(x102423),f902(x102423),a899),f315(f315(f9(f902(x102423),f909(f902(x102423),a901),f909(f902(x102423),a899)),f315(f315(f10(f909(a901,a899),f909(f909(f902(x102423),a901),f909(f902(x102423),a899)),f902(x102423)),f10(a901,a899,f902(x102423))),f315(f315(f10(a901,f909(a901,a899),f902(x102423)),a312),f178(f902(x102423))))),f178(f902(x102423)))),f685(x102422,x102421,x102423)))
% 168.60/168.39 [6937]~E(f71(a901),f2(a901))+~P1(f315(f54(x69371),x69373))+~P1(f315(f54(x69371),x69372))+E(f315(f315(f73(a901),f315(f28(x69371),x69372)),f315(f28(x69371),x69373)),f315(f28(x69371),f315(f315(f99(f909(x69371,a899)),x69372),x69373)))
% 168.60/168.39 [7357]~P104(x73571)+~P1(f315(f54(x73571),x73572))+~P1(f315(f315(f317(x73571),x73573),x73572))+P1(f315(f315(f223(x73571),f315(f56(x73571,f90(x73571)),x73572)),x73573))
% 168.60/168.39 [7358]~P110(x73581)+~P1(f315(f54(x73581),x73582))+~P1(f315(f315(f317(x73581),x73583),x73582))+P1(f315(f315(f223(x73581),f315(f56(x73581,f221(x73581)),x73582)),x73583))
% 168.60/168.39 [7611]~P1(f315(f54(x76111),x76113))+~P1(f315(f54(x76111),x76112))+~E(f315(f315(f90(f909(x76111,a899)),x76112),x76113),f177(f909(x76111,a899)))+E(f315(f315(f73(a901),f315(f28(x76111),x76112)),f315(f28(x76111),x76113)),f315(f28(x76111),f315(f315(f99(f909(x76111,a899)),x76112),x76113)))
% 168.60/168.39 [8401]~P39(x84011,x84013)+~P39(x84011,x84012)+~E(f315(f315(f90(f909(x84011,a899)),f315(f252(x84011,x84011),x84012)),f315(f272(x84011,x84011),x84013)),f177(f909(x84011,a899)))+P39(x84011,f315(f315(f99(f909(f908(x84011,x84011),a899)),x84012),x84013))
% 168.60/168.39 [8496]E(x84961,f315(f315(f29(a901),x84962),x84963))+~P1(f315(f315(f224(a901),f2(a901)),x84963))+~P1(f315(f315(f224(a901),x84962),f315(f315(f74(a901),x84963),f315(a101,x84961))))+~P1(f315(f315(f223(a901),f315(f315(f74(a901),x84963),x84961)),x84962))
% 168.60/168.39 [8628]~P1(f315(f54(x86281),x86282))+~P1(f315(f54(x86281),x86283))+E(f315(f315(f73(a901),f315(f28(x86281),x86282)),f315(f28(x86281),x86283)),f315(f28(x86281),f315(f315(f99(f909(x86281,a899)),x86282),x86283)))+P1(f315(f315(f317(x86281),f809(x86283,x86282,x86281)),f315(f315(f90(f909(x86281,a899)),x86282),x86283)))
% 168.60/168.39 [9021]~P130(x90212)+~E(x90211,f2(x90212))+~E(x90213,f2(x90212))+~P1(f315(f315(f224(x90212),f2(x90212)),f315(f315(f73(x90212),f315(f315(f74(x90212),x90213),x90213)),f315(f315(f74(x90212),x90211),x90211))))
% 168.60/168.39 [9550]~P39(x95501,x95503)+~P39(x95501,x95502)+P39(x95501,f315(f315(f99(f909(f908(x95501,x95501),a899)),x95502),x95503))+~P1(f315(f315(f223(f909(f908(x95501,x95501),a899)),f315(f315(f277(x95501,x95501,x95501),x95502),x95503)),x95502))
% 168.60/168.39 [9687]~P1(f315(x96871,x96873))+~P1(f315(f54(x96872),x96873))+P1(f315(x96871,f177(f909(x96872,a899))))+~P1(f315(x96871,f315(f315(f3(f909(x96872,a899)),f433(x96871,x96873,x96872)),f315(f315(f297(x96872),f434(x96871,x96873,x96872)),f177(f909(x96872,a899))))))
% 168.60/168.39 [8804]~P1(f315(f315(f224(a1),f2(a1)),x88043))+P1(f315(f315(f223(a1),f2(a1)),x88041))+~P1(f315(f315(f224(a1),x88042),x88043))+~P1(f315(f315(f223(a1),f2(a1)),f315(f315(f73(a1),f315(f315(f74(a1),x88043),x88041)),x88042)))
% 168.60/168.39 [8828]~P80(x88281)+~P1(f315(f54(x88281),x88282))+E(f315(f315(f3(f909(x88281,a899)),x88282),f315(f315(f297(x88281),x88283),f177(f909(x88281,a899)))),f177(f909(x88281,a899)))+E(f315(f315(f99(x88281),x88283),f12(x88281,f315(f315(f3(f909(x88281,a899)),x88282),f315(f315(f297(x88281),x88283),f177(f909(x88281,a899)))))),f12(x88281,f315(f315(f297(x88281),x88283),x88282)))
% 168.60/168.39 [8829]~P80(x88291)+~P1(f315(f54(x88291),x88292))+E(f315(f315(f3(f909(x88291,a899)),x88292),f315(f315(f297(x88291),x88293),f177(f909(x88291,a899)))),f177(f909(x88291,a899)))+E(f315(f315(f90(x88291),x88293),f13(x88291,f315(f315(f3(f909(x88291,a899)),x88292),f315(f315(f297(x88291),x88293),f177(f909(x88291,a899)))))),f13(x88291,f315(f315(f297(x88291),x88293),x88292)))
% 168.60/168.39 [8830]~P110(x88301)+~P1(f315(f54(x88301),x88302))+E(f315(f315(f3(f909(x88301,a899)),x88302),f315(f315(f297(x88301),x88303),f177(f909(x88301,a899)))),f177(f909(x88301,a899)))+E(f315(f315(f221(x88301),x88303),f16(x88301,f315(f315(f3(f909(x88301,a899)),x88302),f315(f315(f297(x88301),x88303),f177(f909(x88301,a899)))))),f16(x88301,f315(f315(f297(x88301),x88303),x88302)))
% 168.60/168.39 [8831]~P110(x88311)+~P1(f315(f54(x88311),x88312))+E(f315(f315(f3(f909(x88311,a899)),x88312),f315(f315(f297(x88311),x88313),f177(f909(x88311,a899)))),f177(f909(x88311,a899)))+E(f315(f315(f222(x88311),x88313),f17(x88311,f315(f315(f3(f909(x88311,a899)),x88312),f315(f315(f297(x88311),x88313),f177(f909(x88311,a899)))))),f17(x88311,f315(f315(f297(x88311),x88313),x88312)))
% 168.60/168.39 [8903]~P110(x89031)+~P1(f315(f54(x89031),x89032))+E(f315(f315(f3(f909(x89031,a899)),x89032),f315(f315(f297(x89031),x89033),f177(f909(x89031,a899)))),f177(f909(x89031,a899)))+E(f315(f315(f221(x89031),x89033),f14(x89031,f221(x89031),f315(f315(f3(f909(x89031,a899)),x89032),f315(f315(f297(x89031),x89033),f177(f909(x89031,a899)))))),f14(x89031,f221(x89031),f315(f315(f297(x89031),x89033),x89032)))
% 168.60/168.39 [8904]~P110(x89041)+~P1(f315(f54(x89041),x89042))+E(f315(f315(f3(f909(x89041,a899)),x89042),f315(f315(f297(x89041),x89043),f177(f909(x89041,a899)))),f177(f909(x89041,a899)))+E(f315(f315(f222(x89041),x89043),f15(x89041,f222(x89041),f315(f315(f3(f909(x89041,a899)),x89042),f315(f315(f297(x89041),x89043),f177(f909(x89041,a899)))))),f15(x89041,f222(x89041),f315(f315(f297(x89041),x89043),x89042)))
% 168.60/168.39 [9488]E(x94881,x94882)+~E(f315(f131(f902(x94883),f902(x94883),f123(x94883),f102(x94883)),x94881),f315(f131(f902(x94883),f902(x94883),f123(x94883),f102(x94883)),x94882))+~E(f315(f178(f902(f902(x94883))),x94881),f315(f178(f902(f902(x94883))),x94882))+P1(f315(f315(f317(f908(f902(x94883),f902(x94883))),f684(x94881,x94882,x94883)),f315(f161(f908(f902(x94883),f902(x94883))),f315(f315(f170(f902(x94883),f902(x94883)),x94882),x94881))))
% 168.60/168.39 [9489]E(x94891,x94892)+~E(f315(f131(f902(x94893),f902(x94893),f123(x94893),f102(x94893)),x94891),f315(f131(f902(x94893),f902(x94893),f123(x94893),f102(x94893)),x94892))+~E(f315(f178(f902(f902(x94893))),x94891),f315(f178(f902(f902(x94893))),x94892))+P1(f315(f315(f317(f908(f902(x94893),f902(x94893))),f685(x94892,x94891,x94893)),f315(f161(f908(f902(x94893),f902(x94893))),f315(f315(f170(f902(x94893),f902(x94893)),x94891),x94892))))
% 168.60/168.39 [10350]~P101(x103502)+E(x103501,f177(f909(x103502,a899)))+~P1(f315(f54(x103502),x103501))+E(f13(x103502,f315(f250(x103502),f315(f315(f10(f909(x103502,a899),a899,x103502),f80(x103502)),f315(f315(f9(x103502,f909(x103502,a899),f909(x103502,a899)),f315(f315(f10(f909(x103502,f909(a899,a899)),f909(f909(x103502,a899),f909(x103502,a899)),x103502),f20(x103502,a899,a899)),f315(f315(f10(f909(x103502,a899),f909(x103502,f909(a899,a899)),x103502),f315(f10(a899,f909(a899,a899),x103502),a313)),f315(f315(f9(x103502,f909(x103502,x103502),f909(x103502,a899)),f315(f315(f10(f909(x103502,a899),f909(f909(x103502,x103502),f909(x103502,a899)),x103502),f10(x103502,a899,x103502)),a312)),f315(f99(x103502),x103503))))),f315(f315(f9(x103502,f909(x103502,a899),a899),f317(x103502)),x103501))))),f315(f315(f99(x103502),x103503),f13(x103502,x103501)))
% 168.60/168.39 [10351]~P101(x103512)+E(x103511,f177(f909(x103512,a899)))+~P1(f315(f54(x103512),x103511))+E(f12(x103512,f315(f250(x103512),f315(f315(f10(f909(x103512,a899),a899,x103512),f80(x103512)),f315(f315(f9(x103512,f909(x103512,a899),f909(x103512,a899)),f315(f315(f10(f909(x103512,f909(a899,a899)),f909(f909(x103512,a899),f909(x103512,a899)),x103512),f20(x103512,a899,a899)),f315(f315(f10(f909(x103512,a899),f909(x103512,f909(a899,a899)),x103512),f315(f10(a899,f909(a899,a899),x103512),a313)),f315(f315(f9(x103512,f909(x103512,x103512),f909(x103512,a899)),f315(f315(f10(f909(x103512,a899),f909(f909(x103512,x103512),f909(x103512,a899)),x103512),f10(x103512,a899,x103512)),a312)),f315(f90(x103512),x103513))))),f315(f315(f9(x103512,f909(x103512,a899),a899),f317(x103512)),x103511))))),f315(f315(f90(x103512),x103513),f12(x103512,x103511)))
% 168.60/168.39 [10352]~P79(x103522)+E(x103521,f177(f909(x103522,a899)))+~P1(f315(f54(x103522),x103521))+E(f16(x103522,f315(f250(x103522),f315(f315(f10(f909(x103522,a899),a899,x103522),f80(x103522)),f315(f315(f9(x103522,f909(x103522,a899),f909(x103522,a899)),f315(f315(f10(f909(x103522,f909(a899,a899)),f909(f909(x103522,a899),f909(x103522,a899)),x103522),f20(x103522,a899,a899)),f315(f315(f10(f909(x103522,a899),f909(x103522,f909(a899,a899)),x103522),f315(f10(a899,f909(a899,a899),x103522),a313)),f315(f315(f9(x103522,f909(x103522,x103522),f909(x103522,a899)),f315(f315(f10(f909(x103522,a899),f909(f909(x103522,x103522),f909(x103522,a899)),x103522),f10(x103522,a899,x103522)),a312)),f315(f73(x103522),x103523))))),f315(f315(f9(x103522,f909(x103522,a899),a899),f317(x103522)),x103521))))),f315(f315(f73(x103522),x103523),f16(x103522,x103521)))
% 168.60/168.39 [10353]~P79(x103532)+E(x103531,f177(f909(x103532,a899)))+~P1(f315(f54(x103532),x103531))+E(f17(x103532,f315(f250(x103532),f315(f315(f10(f909(x103532,a899),a899,x103532),f80(x103532)),f315(f315(f9(x103532,f909(x103532,a899),f909(x103532,a899)),f315(f315(f10(f909(x103532,f909(a899,a899)),f909(f909(x103532,a899),f909(x103532,a899)),x103532),f20(x103532,a899,a899)),f315(f315(f10(f909(x103532,a899),f909(x103532,f909(a899,a899)),x103532),f315(f10(a899,f909(a899,a899),x103532),a313)),f315(f315(f9(x103532,f909(x103532,x103532),f909(x103532,a899)),f315(f315(f10(f909(x103532,a899),f909(f909(x103532,x103532),f909(x103532,a899)),x103532),f10(x103532,a899,x103532)),a312)),f315(f73(x103532),x103533))))),f315(f315(f9(x103532,f909(x103532,a899),a899),f317(x103532)),x103531))))),f315(f315(f73(x103532),x103533),f17(x103532,x103531)))
% 168.60/168.39 [10354]~P110(x103542)+E(x103541,f177(f909(x103542,a899)))+~P1(f315(f54(x103542),x103541))+E(f15(x103542,f222(x103542),f315(f250(x103542),f315(f315(f10(f909(x103542,a899),a899,x103542),f80(x103542)),f315(f315(f9(x103542,f909(x103542,a899),f909(x103542,a899)),f315(f315(f10(f909(x103542,f909(a899,a899)),f909(f909(x103542,a899),f909(x103542,a899)),x103542),f20(x103542,a899,a899)),f315(f315(f10(f909(x103542,a899),f909(x103542,f909(a899,a899)),x103542),f315(f10(a899,f909(a899,a899),x103542),a313)),f315(f315(f9(x103542,f909(x103542,x103542),f909(x103542,a899)),f315(f315(f10(f909(x103542,a899),f909(f909(x103542,x103542),f909(x103542,a899)),x103542),f10(x103542,a899,x103542)),a312)),f315(f221(x103542),x103543))))),f315(f315(f9(x103542,f909(x103542,a899),a899),f317(x103542)),x103541))))),f315(f315(f221(x103542),x103543),f15(x103542,f222(x103542),x103541)))
% 168.60/168.39 [10355]~P110(x103552)+E(x103551,f177(f909(x103552,a899)))+~P1(f315(f54(x103552),x103551))+E(f14(x103552,f221(x103552),f315(f250(x103552),f315(f315(f10(f909(x103552,a899),a899,x103552),f80(x103552)),f315(f315(f9(x103552,f909(x103552,a899),f909(x103552,a899)),f315(f315(f10(f909(x103552,f909(a899,a899)),f909(f909(x103552,a899),f909(x103552,a899)),x103552),f20(x103552,a899,a899)),f315(f315(f10(f909(x103552,a899),f909(x103552,f909(a899,a899)),x103552),f315(f10(a899,f909(a899,a899),x103552),a313)),f315(f315(f9(x103552,f909(x103552,x103552),f909(x103552,a899)),f315(f315(f10(f909(x103552,a899),f909(f909(x103552,x103552),f909(x103552,a899)),x103552),f10(x103552,a899,x103552)),a312)),f315(f222(x103552),x103553))))),f315(f315(f9(x103552,f909(x103552,a899),a899),f317(x103552)),x103551))))),f315(f315(f222(x103552),x103553),f14(x103552,f221(x103552),x103551)))
% 168.60/168.39 [10070]~P114(x100701)+~E(x100703,f2(x100701))+~E(x100702,f2(x100701))+E(f315(f315(f73(x100701),f315(f315(f232(x100701),x100702),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))))),f315(f315(f232(x100701),x100703),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))))),f2(x100701))
% 168.60/168.39 [10222]~P128(x102221)+~P1(f315(f315(f223(x102221),f2(x102221)),x102223))+P1(f315(f315(f223(x102221),x102222),x102223))+~P1(f315(f315(f223(x102221),f315(f315(f232(x102221),x102222),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))))),f315(f315(f232(x102221),x102223),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))))))
% 168.60/168.39 [10279]~P114(x102792)+~E(x102791,f2(x102792))+~E(x102793,f2(x102792))+~P1(f315(f315(f224(x102792),f2(x102792)),f315(f315(f73(x102792),f315(f315(f232(x102792),x102793),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86))))),f315(f315(f232(x102792),x102791),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))))))
% 168.60/168.39 [6814]~P7(x68143,x68142)+~P1(f315(x68141,x68144))+~P1(f315(f315(f317(x68143),x68144),f258(x68143,x68142)))+P1(f315(x68141,f803(x68141,x68142,x68143)))
% 168.60/168.39 [8739]P26(x87391,x87392,f807(x87393,x87392,x87394,x87391),x87394,x87393)+~E(f315(f28(x87391),x87394),f315(f28(x87392),x87393))+~P1(f315(f54(x87392),x87393))+~P1(f315(f54(x87391),x87394))
% 168.60/168.39 [9451]E(x94511,x94512)+~E(f638(x94511,x94512,x94514,x94513),f639(x94511,x94512,x94514,x94513))+P1(f315(f315(f317(f908(f902(x94513),f902(x94513))),f315(f315(f240(f902(x94513),f902(x94513)),x94512),x94511)),f136(x94513,x94514)))+P1(f315(f315(f317(f908(f902(x94513),f902(x94513))),f315(f315(f240(f902(x94513),f902(x94513)),x94511),x94512)),f136(x94513,x94514)))
% 168.60/168.39 [4923]~P65(x49232)+~E(x49234,f2(x49232))+~E(x49231,f2(x49232))+E(x49231,f315(f315(f279(x49232),x49233),x49234))
% 168.60/168.39 [4924]~P65(x49241)+~E(x49243,f2(x49241))+~E(x49244,f2(x49241))+E(f315(f315(f279(x49241),x49242),x49243),x49244)
% 168.60/168.39 [5044]~P65(x50442)+E(x50441,f2(x50442))+~E(x50443,f2(x50442))+~E(x50441,f315(f315(f279(x50442),x50444),x50443))
% 168.60/168.39 [5045]~P65(x50452)+E(x50451,f2(x50452))+~E(x50453,f2(x50452))+~E(f315(f315(f279(x50452),x50454),x50453),x50451)
% 168.60/168.39 [5228]~P125(x52282)+E(x52281,f2(x52282))+~E(f315(f315(f279(x52282),x52283),x52281),x52284)+E(x52283,f315(f315(f74(x52282),x52284),x52281))
% 168.60/168.39 [5230]~P125(x52302)+E(x52301,f2(x52302))+~E(f315(f315(f74(x52302),x52303),x52301),x52304)+E(x52303,f315(f315(f279(x52302),x52304),x52301))
% 168.60/168.39 [5231]~P65(x52312)+E(x52311,f2(x52312))+~E(f315(f315(f279(x52312),x52313),x52311),x52314)+E(x52313,f315(f315(f74(x52312),x52314),x52311))
% 168.60/168.39 [5232]~P65(x52322)+E(x52321,f2(x52322))+~E(f315(f315(f74(x52322),x52323),x52321),x52324)+E(x52323,f315(f315(f279(x52322),x52324),x52321))
% 168.60/168.39 [5233]~P125(x52332)+E(x52331,f2(x52332))+~E(x52333,f315(f315(f279(x52332),x52334),x52331))+E(f315(f315(f74(x52332),x52333),x52331),x52334)
% 168.60/168.39 [5235]~P125(x52352)+E(x52351,f2(x52352))+~E(x52353,f315(f315(f74(x52352),x52354),x52351))+E(f315(f315(f279(x52352),x52353),x52351),x52354)
% 168.60/168.39 [5236]~P65(x52362)+E(x52361,f2(x52362))+~E(x52363,f315(f315(f279(x52362),x52364),x52361))+E(f315(f315(f74(x52362),x52363),x52361),x52364)
% 168.60/168.39 [5237]~P65(x52372)+E(x52371,f2(x52372))+~E(x52373,f315(f315(f74(x52372),x52374),x52371))+E(f315(f315(f279(x52372),x52373),x52371),x52374)
% 168.60/168.39 [5261]~P65(x52612)+~E(x52611,f2(x52612))+~E(f315(f315(f74(x52612),x52611),x52614),x52613)+E(x52611,f315(f315(f279(x52612),x52613),x52614))
% 168.60/168.39 [5262]~P65(x52621)+~E(x52624,f2(x52621))+~E(x52622,f315(f315(f74(x52621),x52624),x52623))+E(f315(f315(f279(x52621),x52622),x52623),x52624)
% 168.60/168.39 [5337]~E(x53373,x53374)+~E(x53372,x53373)+~P111(x53371)+E(f291(x53371,x53372,x53373),f315(f315(f297(x53371),x53374),f177(f909(x53371,a899))))
% 168.60/168.39 [5541]~E(f103(x55412,x55411),x55413)+~E(f133(x55412,x55411),x55414)+E(x55411,f102(x55412))+E(f315(f315(f123(x55412),x55413),f315(f315(f140(x55412),x55414),f102(x55412))),x55411)
% 168.60/168.39 [6188]~P128(x61883)+E(x61881,x61882)+~E(f315(f315(f232(x61883),x61884),x61881),f315(f315(f232(x61883),x61884),x61882))+~P1(f315(f315(f224(x61883),f71(x61883)),x61884))
% 168.60/168.39 [6189]E(x61891,x61892)+~E(f315(f315(f297(x61893),x61894),x61891),f315(f315(f297(x61893),x61894),x61892))+P1(f315(f315(f317(x61893),x61894),x61892))+P1(f315(f315(f317(x61893),x61894),x61891))
% 168.60/168.39 [6232]E(f315(x62321,x62322),f71(a901))+~E(f315(f315(f11(x62323,a901),x62321),x62324),f71(a901))+~P1(f315(f54(x62323),x62324))+~P1(f315(f315(f317(x62323),x62322),x62324))
% 168.60/168.39 [6233]E(f315(x62331,x62332),f2(a901))+~E(f315(f315(f8(x62333,a901),x62331),x62334),f2(a901))+~P1(f315(f54(x62333),x62334))+~P1(f315(f315(f317(x62333),x62332),x62334))
% 168.60/168.39 [6459]~P111(x64591)+~P1(f315(f315(f223(x64591),x64594),x64593))+P1(f315(f315(f223(x64591),x64592),x64593))+~P1(f315(f315(f223(x64591),x64592),x64594))
% 168.60/168.39 [6460]~P108(x64601)+~P1(f315(f315(f223(x64601),x64602),x64604))+P1(f315(f315(f223(x64601),x64602),x64603))+~P1(f315(f315(f223(x64601),x64604),x64603))
% 168.60/168.39 [6461]~P111(x64611)+~P1(f315(f315(f224(x64611),x64614),x64613))+P1(f315(f315(f224(x64611),x64612),x64613))+~P1(f315(f315(f223(x64611),x64612),x64614))
% 168.60/168.39 [6462]~P111(x64621)+~P1(f315(f315(f224(x64621),x64622),x64624))+P1(f315(f315(f224(x64621),x64622),x64623))+~P1(f315(f315(f223(x64621),x64624),x64623))
% 168.60/168.39 [6463]~P111(x64631)+~P1(f315(f315(f224(x64631),x64634),x64633))+P1(f315(f315(f224(x64631),x64632),x64633))+~P1(f315(f315(f224(x64631),x64632),x64634))
% 168.60/168.39 [6464]~P108(x64641)+~P1(f315(f315(f224(x64641),x64642),x64644))+P1(f315(f315(f224(x64641),x64642),x64643))+~P1(f315(f315(f223(x64641),x64644),x64643))
% 168.60/168.39 [6465]~P108(x64651)+~P1(f315(f315(f224(x64651),x64654),x64653))+P1(f315(f315(f224(x64651),x64652),x64653))+~P1(f315(f315(f223(x64651),x64652),x64654))
% 168.60/168.39 [6466]~P108(x64661)+~P1(f315(f315(f224(x64661),x64662),x64664))+P1(f315(f315(f224(x64661),x64662),x64663))+~P1(f315(f315(f224(x64661),x64664),x64663))
% 168.60/168.39 [6467]~P121(x64671)+~P1(f315(f315(f275(x64671),x64672),x64674))+P1(f315(f315(f275(x64671),x64672),x64673))+~P1(f315(f315(f275(x64671),x64674),x64673))
% 168.60/168.39 [6551]~P37(x65514,x65513,x65512)+E(x65511,f739(x65512,x65513,x65514))+~P1(f315(x65513,x65511))+~P1(f315(f315(f317(x65514),x65511),f315(f161(x65514),x65512)))
% 168.60/168.39 [6552]~P37(x65524,x65523,x65522)+E(x65521,f749(x65522,x65523,x65524))+~P1(f315(x65523,x65521))+~P1(f315(f315(f317(x65524),x65521),f315(f161(x65524),x65522)))
% 168.60/168.39 [6705]~P5(x67051)+~P1(f315(f315(f223(x67051),x67052),f31(x67051,x67054)))+P1(f315(f315(f223(x67051),x67052),x67053))+~P1(f315(f315(f317(x67051),x67053),x67054))
% 168.60/168.39 [6856]~P110(x68561)+~P13(x68561,f315(f315(f140(x68561),x68562),x68564))+~P1(f315(f315(f317(x68561),x68563),f315(f161(x68561),x68564)))+P1(f315(f315(f223(x68561),x68562),x68563))
% 168.60/168.39 [6947]~P5(x69471)+~P1(f315(f315(f223(x69471),f30(x69471,x69474)),x69473))+P1(f315(f315(f223(x69471),x69472),x69473))+~P1(f315(f315(f317(x69471),x69472),x69474))
% 168.60/168.39 [7092]~P62(x70921)+P1(f315(f315(f275(x70921),x70922),f38(x70921,x70923,x70924)))+~P1(f315(f315(f275(x70921),x70922),x70924))+~P1(f315(f315(f275(x70921),x70922),x70923))
% 168.60/168.39 [7360]~P110(x73601)+E(f315(f315(f99(f909(x73601,a899)),f315(f290(x73601,x73602),x73603)),f315(f290(x73601,x73603),x73604)),f315(f290(x73601,x73602),x73604))+~P1(f315(f315(f223(x73601),x73603),x73604))+~P1(f315(f315(f223(x73601),x73602),x73603))
% 168.60/168.39 [7404]P37(x74041,x74042,x74043)+~E(f751(x74043,x74042,x74041,x74044),x74044)+~P1(f315(x74042,x74044))+~P1(f315(f315(f317(x74041),x74044),f315(f161(x74041),x74043)))
% 168.60/168.39 [7405]P37(x74051,x74052,x74053)+~E(f758(x74053,x74052,x74051,x74054),x74054)+~P1(f315(x74052,x74054))+~P1(f315(f315(f317(x74051),x74054),f315(f161(x74051),x74053)))
% 168.60/168.39 [7448]~P62(x74481)+~P1(f315(f315(f275(x74481),x74482),f38(x74481,x74483,x74484)))+P1(f315(f315(f275(x74481),x74482),x74483))+~P1(f315(f315(f275(x74481),x74482),x74484))
% 168.60/168.39 [7482]~P110(x74821)+E(f315(f315(f99(f909(x74821,a899)),f315(f290(x74821,x74822),x74823)),f291(x74821,x74823,x74824)),f291(x74821,x74822,x74824))+~P1(f315(f315(f223(x74821),x74823),x74824))+~P1(f315(f315(f223(x74821),x74822),x74823))
% 168.60/168.39 [7544]~P110(x75441)+E(f315(f315(f99(f909(x75441,a899)),f294(x75441,x75442,x75443)),f315(f290(x75441,x75443),x75444)),f294(x75441,x75442,x75444))+~P1(f315(f315(f223(x75441),x75443),x75444))+~P1(f315(f315(f224(x75441),x75442),x75443))
% 168.60/168.39 [7561]~P110(x75611)+E(f315(f315(f99(f909(x75611,a899)),f291(x75611,x75612,x75613)),f294(x75611,x75613,x75614)),f315(f290(x75611,x75612),x75614))+~P1(f315(f315(f223(x75611),x75612),x75613))+~P1(f315(f315(f224(x75611),x75613),x75614))
% 168.60/168.39 [7592]~P110(x75921)+E(f315(f315(f99(f909(x75921,a899)),f291(x75921,x75922,x75923)),f293(x75921,x75923,x75924)),f291(x75921,x75922,x75924))+~P1(f315(f315(f223(x75921),x75923),x75924))+~P1(f315(f315(f223(x75921),x75922),x75923))
% 168.60/168.39 [7593]~P110(x75931)+E(f315(f315(f99(f909(x75931,a899)),f294(x75931,x75932,x75933)),f291(x75931,x75933,x75934)),f293(x75931,x75932,x75934))+~P1(f315(f315(f223(x75931),x75933),x75934))+~P1(f315(f315(f224(x75931),x75932),x75933))
% 168.60/168.39 [7594]~P110(x75941)+E(f315(f315(f99(f909(x75941,a899)),f293(x75941,x75942,x75943)),f294(x75941,x75943,x75944)),f294(x75941,x75942,x75944))+~P1(f315(f315(f223(x75941),x75942),x75943))+~P1(f315(f315(f224(x75941),x75943),x75944))
% 168.60/168.39 [7595]~P110(x75951)+E(f315(f315(f99(f909(x75951,a899)),f293(x75951,x75952,x75953)),f293(x75951,x75953,x75954)),f293(x75951,x75952,x75954))+~P1(f315(f315(f223(x75951),x75953),x75954))+~P1(f315(f315(f223(x75951),x75952),x75953))
% 168.60/168.39 [8385]P25(x83851,x83852,f495(x83853,x83852,x83854,x83851),x83854)+~P1(f315(f54(x83852),x83853))+~P1(f315(f54(x83851),x83854))+~P1(f315(f315(f223(a901),f315(f28(x83851),x83854)),f315(f28(x83852),x83853)))
% 168.60/168.39 [8406]P37(x84061,x84062,x84063)+~P1(f315(x84062,x84064))+P1(f315(x84062,f751(x84063,x84062,x84061,x84064)))+~P1(f315(f315(f317(x84061),x84064),f315(f161(x84061),x84063)))
% 168.60/168.39 [8407]P37(x84071,x84072,x84073)+~P1(f315(x84072,x84074))+P1(f315(x84072,f758(x84073,x84072,x84071,x84074)))+~P1(f315(f315(f317(x84071),x84074),f315(f161(x84071),x84073)))
% 168.60/168.39 [8461]~P77(x84611)+~E(f315(x84613,f881(x84613,x84614,x84612,x84611)),f71(x84611))+E(f315(f315(f315(f58(x84611,x84612,f74(x84611)),x84613),f71(x84611)),x84614),f71(x84611))+~P1(f315(f54(x84612),x84614))
% 168.60/168.39 [8728]~P128(x87281)+~P1(f315(f315(f223(x87281),f2(x87281)),x87283))+P1(f315(f315(f223(x87281),x87282),x87283))+~P1(f315(f315(f223(x87281),f315(f315(f232(x87281),x87282),f315(a101,x87284))),f315(f315(f232(x87281),x87283),f315(a101,x87284))))
% 168.60/168.39 [9047]P37(x90471,x90472,x90473)+~P1(f315(x90472,x90474))+~P1(f315(f315(f317(x90471),x90474),f315(f161(x90471),x90473)))+P1(f315(f315(f317(x90471),f751(x90473,x90472,x90471,x90474)),f315(f161(x90471),x90473)))
% 168.60/168.39 [9048]P37(x90481,x90482,x90483)+~P1(f315(x90482,x90484))+~P1(f315(f315(f317(x90481),x90484),f315(f161(x90481),x90483)))+P1(f315(f315(f317(x90481),f758(x90483,x90482,x90481,x90484)),f315(f161(x90481),x90483)))
% 168.60/168.39 [9124]~P77(x91241)+E(f315(f315(f315(f58(x91241,x91242,f74(x91241)),x91243),f71(x91241)),x91244),f71(x91241))+~P1(f315(f54(x91242),x91244))+P1(f315(f315(f317(x91242),f881(x91243,x91244,x91242,x91241)),x91244))
% 168.60/168.39 [9625]~P1(f315(f315(f275(a901),x96251),x96253))+~P1(f315(f315(f275(a901),x96251),x96252))+~P1(f315(f315(f275(a901),x96254),x96253))+~P1(f315(f315(f224(f909(a901,a899)),f278(a901,f275(a901),x96251,x96253)),f278(a901,f275(a901),x96252,x96254)))
% 168.60/168.39 [9630]~P1(f315(f315(f223(a1),x96304),f2(a1)))+P1(f315(f315(f223(a1),f315(f315(f73(a1),f315(f315(f74(a1),x96301),f38(a1,x96302,x96303))),x96304)),f2(a1)))+~P1(f315(f315(f224(a1),f2(a1)),x96303))+~P1(f315(f315(f224(a1),x96301),x96304))
% 168.60/168.39 [10063]~P1(f315(f54(x100631),x100632))+~P1(f315(f315(f317(x100631),x100634),x100632))+~P1(f315(f315(f317(x100631),x100633),x100632))+P1(f315(f315(f224(a901),f315(f28(x100631),f315(f315(f3(f909(x100631,a899)),f315(f315(f3(f909(x100631,a899)),x100632),f315(f315(f297(x100631),x100633),f177(f909(x100631,a899))))),f315(f315(f297(x100631),x100634),f177(f909(x100631,a899)))))),f315(f28(x100631),x100632)))
% 168.60/168.39 [7005]~P148(x70053)+~P124(x70053)+P1(f315(x70051,f837(x70052,x70051,x70053)))+~P1(f315(x70051,f315(f315(f74(x70053),x70052),x70054)))
% 168.60/168.39 [7064]~P104(x70641)+~P1(f315(f315(f223(x70641),x70642),x70644))+~P1(f315(f315(f223(x70641),x70642),x70643))+P1(f315(f315(f223(x70641),x70642),f315(f315(f90(x70641),x70643),x70644)))
% 168.60/168.39 [7067]~P110(x70671)+~P1(f315(f315(f223(x70671),x70672),x70674))+~P1(f315(f315(f223(x70671),x70672),x70673))+P1(f315(f315(f223(x70671),x70672),f315(f315(f221(x70671),x70673),x70674)))
% 168.60/168.39 [7068]~P110(x70681)+~P1(f315(f315(f224(x70681),x70682),x70684))+~P1(f315(f315(f224(x70681),x70682),x70683))+P1(f315(f315(f224(x70681),x70682),f315(f315(f221(x70681),x70683),x70684)))
% 168.60/168.39 [7069]~P116(x70691)+~P1(f315(f315(f275(x70691),x70692),x70694))+~P1(f315(f315(f275(x70691),x70692),x70693))+P1(f315(f315(f275(x70691),x70692),f315(f315(f3(x70691),x70693),x70694)))
% 168.60/168.39 [7070]~P121(x70701)+~P1(f315(f315(f275(x70701),x70702),x70704))+~P1(f315(f315(f275(x70701),x70702),x70703))+P1(f315(f315(f275(x70701),x70702),f315(f315(f73(x70701),x70703),x70704)))
% 168.60/168.39 [7090]~P66(x70902)+E(x70901,f2(x70902))+E(f315(f315(f279(x70902),f315(f315(f232(x70902),x70901),x70903)),f315(f315(f232(x70902),x70901),x70904)),f315(f315(f232(x70902),x70901),f315(f315(f3(a901),x70903),x70904)))+~P1(f315(f315(f223(a901),x70904),x70903))
% 168.60/168.39 [7137]~P110(x71371)+~P13(x71371,f315(f315(f140(x71371),x71373),x71374))+P13(x71371,f315(f315(f140(x71371),x71372),f315(f315(f140(x71371),x71373),x71374)))+~P1(f315(f315(f223(x71371),x71372),x71373))
% 168.60/168.39 [7174]~P91(x71741)+~P1(f315(f315(f223(x71741),f2(x71741)),x71744))+~P1(f315(f315(f223(x71741),x71742),x71743))+P1(f315(f315(f223(x71741),x71742),f315(f315(f73(x71741),x71743),x71744)))
% 168.60/168.39 [7175]~P91(x71751)+~P1(f315(f315(f223(x71751),f2(x71751)),x71753))+~P1(f315(f315(f223(x71751),x71752),x71754))+P1(f315(f315(f223(x71751),x71752),f315(f315(f73(x71751),x71753),x71754)))
% 168.60/168.39 [7176]~P128(x71761)+~P1(f315(f315(f224(x71761),f2(x71761)),x71763))+~P1(f315(f315(f224(x71761),x71762),x71764))+P1(f315(f315(f224(x71761),x71762),f315(f315(f73(x71761),x71763),x71764)))
% 168.60/168.39 [7177]~P91(x71771)+~P1(f315(f315(f223(x71771),x71772),x71774))+~P1(f315(f315(f224(x71771),f2(x71771)),x71773))+P1(f315(f315(f224(x71771),x71772),f315(f315(f73(x71771),x71773),x71774)))
% 168.60/168.39 [7178]~P91(x71781)+~P1(f315(f315(f223(x71781),f2(x71781)),x71783))+~P1(f315(f315(f224(x71781),x71782),x71784))+P1(f315(f315(f224(x71781),x71782),f315(f315(f73(x71781),x71783),x71784)))
% 168.60/168.39 [7219]~P110(x72191)+P1(f315(f315(f223(x72191),x72192),x72193))+P1(f315(f315(f223(x72191),x72192),x72194))+~P1(f315(f315(f223(x72191),x72192),f315(f315(f222(x72191),x72194),x72193)))
% 168.60/168.39 [7220]~P110(x72201)+P1(f315(f315(f224(x72201),x72202),x72203))+P1(f315(f315(f224(x72201),x72202),x72204))+~P1(f315(f315(f224(x72201),x72202),f315(f315(f222(x72201),x72204),x72203)))
% 168.60/168.39 [7516]~P111(x75162)+~P64(x75161)+~P1(f315(f315(f224(f909(x75161,x75162)),x75163),x75164))+P1(f315(f315(f223(f909(x75161,x75162)),x75163),x75164))
% 168.60/168.39 [7882]~P68(x78821)+~P1(f315(f315(f224(x78821),x78824),f2(x78821)))+~P1(f315(f315(f223(x78821),x78823),f315(f315(f279(x78821),x78822),x78824)))+P1(f315(f315(f223(x78821),x78822),f315(f315(f74(x78821),x78823),x78824)))
% 168.60/168.39 [7883]~P68(x78831)+~P1(f315(f315(f224(x78831),x78834),f2(x78831)))+~P1(f315(f315(f223(x78831),x78833),f315(f315(f74(x78831),x78832),x78834)))+P1(f315(f315(f223(x78831),x78832),f315(f315(f279(x78831),x78833),x78834)))
% 168.60/168.39 [7884]~P68(x78841)+~P1(f315(f315(f224(x78841),x78844),f2(x78841)))+~P1(f315(f315(f224(x78841),x78843),f315(f315(f279(x78841),x78842),x78844)))+P1(f315(f315(f224(x78841),x78842),f315(f315(f74(x78841),x78843),x78844)))
% 168.60/168.39 [7885]~P68(x78851)+~P1(f315(f315(f224(x78851),x78854),f2(x78851)))+~P1(f315(f315(f224(x78851),x78853),f315(f315(f74(x78851),x78852),x78854)))+P1(f315(f315(f224(x78851),x78852),f315(f315(f279(x78851),x78853),x78854)))
% 168.60/168.39 [7991]~P113(x79911)+~P1(f315(f315(f223(x79911),x79912),f2(x79911)))+~P1(f315(f315(f223(x79911),x79914),x79913))+P1(f315(f315(f223(x79911),f315(f315(f74(x79911),x79912),x79913)),f315(f315(f74(x79911),x79912),x79914)))
% 168.60/168.39 [7992]~P130(x79921)+~P1(f315(f315(f224(x79921),x79922),f2(x79921)))+~P1(f315(f315(f223(x79921),x79924),x79923))+P1(f315(f315(f223(x79921),f315(f315(f74(x79921),x79922),x79923)),f315(f315(f74(x79921),x79922),x79924)))
% 168.60/168.39 [7993]~P113(x79931)+~P1(f315(f315(f223(x79931),x79933),f2(x79931)))+~P1(f315(f315(f223(x79931),x79934),x79932))+P1(f315(f315(f223(x79931),f315(f315(f74(x79931),x79932),x79933)),f315(f315(f74(x79931),x79934),x79933)))
% 168.60/168.39 [7994]~P67(x79941)+~P1(f315(f315(f223(x79941),x79943),f2(x79941)))+~P1(f315(f315(f223(x79941),x79944),x79942))+P1(f315(f315(f223(x79941),f315(f315(f279(x79941),x79942),x79943)),f315(f315(f279(x79941),x79944),x79943)))
% 168.60/168.39 [7998]~P130(x79981)+~P1(f315(f315(f224(x79981),x79983),f2(x79981)))+~P1(f315(f315(f224(x79981),x79984),x79982))+P1(f315(f315(f224(x79981),f315(f315(f74(x79981),x79982),x79983)),f315(f315(f74(x79981),x79984),x79983)))
% 168.60/168.39 [7999]~P130(x79991)+~P1(f315(f315(f224(x79991),x79992),f2(x79991)))+~P1(f315(f315(f224(x79991),x79994),x79993))+P1(f315(f315(f224(x79991),f315(f315(f74(x79991),x79992),x79993)),f315(f315(f74(x79991),x79992),x79994)))
% 168.60/168.39 [8000]~P68(x80001)+~P1(f315(f315(f224(x80001),x80003),f2(x80001)))+~P1(f315(f315(f224(x80001),x80004),x80002))+P1(f315(f315(f224(x80001),f315(f315(f279(x80001),x80002),x80003)),f315(f315(f279(x80001),x80004),x80003)))
% 168.60/168.39 [8001]~P128(x80011)+~P1(f315(f315(f224(x80011),f71(x80011)),x80012))+~P1(f315(f315(f223(a901),x80013),x80014))+P1(f315(f315(f223(x80011),f315(f315(f232(x80011),x80012),x80013)),f315(f315(f232(x80011),x80012),x80014)))
% 168.60/168.39 [8002]~P128(x80021)+~P1(f315(f315(f223(x80021),f71(x80021)),x80022))+~P1(f315(f315(f223(a901),x80023),x80024))+P1(f315(f315(f223(x80021),f315(f315(f232(x80021),x80022),x80023)),f315(f315(f232(x80021),x80022),x80024)))
% 168.60/168.39 [8004]~P128(x80041)+~P1(f315(f315(f224(x80041),f71(x80041)),x80042))+~P1(f315(f315(f224(a901),x80043),x80044))+P1(f315(f315(f224(x80041),f315(f315(f232(x80041),x80042),x80043)),f315(f315(f232(x80041),x80042),x80044)))
% 168.60/168.39 [8031]P1(f315(f315(f224(a901),f2(a901)),f315(x80311,x80312)))+~P1(f315(f54(x80313),x80314))+~P1(f315(f315(f317(x80313),x80312),x80314))+~P1(f315(f315(f224(a901),f2(a901)),f315(f315(f11(x80313,a901),x80311),x80314)))
% 168.60/168.39 [8040]~P130(x80401)+~P1(f315(f315(f224(x80401),f2(x80401)),x80402))+~P1(f315(f315(f223(x80401),x80403),x80404))+P1(f315(f315(f223(x80401),f315(f315(f74(x80401),x80402),x80403)),f315(f315(f74(x80401),x80402),x80404)))
% 168.60/168.39 [8041]~P139(x80411)+~P1(f315(f315(f223(x80411),x80413),x80414))+~P1(f315(f315(f223(x80411),f2(x80411)),x80412))+P1(f315(f315(f223(x80411),f315(f315(f74(x80411),x80412),x80413)),f315(f315(f74(x80411),x80412),x80414)))
% 168.60/168.39 [8042]~P138(x80421)+~P1(f315(f315(f223(x80421),x80423),x80424))+~P1(f315(f315(f223(x80421),f2(x80421)),x80422))+P1(f315(f315(f223(x80421),f315(f315(f74(x80421),x80422),x80423)),f315(f315(f74(x80421),x80422),x80424)))
% 168.60/168.39 [8043]~P139(x80431)+~P1(f315(f315(f223(x80431),x80432),x80434))+~P1(f315(f315(f223(x80431),f2(x80431)),x80433))+P1(f315(f315(f223(x80431),f315(f315(f74(x80431),x80432),x80433)),f315(f315(f74(x80431),x80434),x80433)))
% 168.60/168.39 [8044]~P67(x80441)+~P1(f315(f315(f223(x80441),x80442),x80444))+~P1(f315(f315(f223(x80441),f2(x80441)),x80443))+P1(f315(f315(f223(x80441),f315(f315(f279(x80441),x80442),x80443)),f315(f315(f279(x80441),x80444),x80443)))
% 168.60/168.39 [8045]~P128(x80451)+~P1(f315(f315(f223(x80451),x80452),x80454))+~P1(f315(f315(f223(x80451),f2(x80451)),x80452))+P1(f315(f315(f223(x80451),f315(f315(f232(x80451),x80452),x80453)),f315(f315(f232(x80451),x80454),x80453)))
% 168.60/168.39 [8047]~P122(x80471)+~P1(f315(f315(f224(x80471),x80473),x80474))+~P1(f315(f315(f224(x80471),f2(x80471)),x80472))+P1(f315(f315(f224(x80471),f315(f315(f74(x80471),x80472),x80473)),f315(f315(f74(x80471),x80472),x80474)))
% 168.60/168.39 [8048]~P136(x80481)+~P1(f315(f315(f224(x80481),x80483),x80484))+~P1(f315(f315(f224(x80481),f2(x80481)),x80482))+P1(f315(f315(f224(x80481),f315(f315(f74(x80481),x80482),x80483)),f315(f315(f74(x80481),x80482),x80484)))
% 168.60/168.39 [8049]~P130(x80491)+~P1(f315(f315(f224(x80491),x80492),x80494))+~P1(f315(f315(f224(x80491),f2(x80491)),x80493))+P1(f315(f315(f224(x80491),f315(f315(f74(x80491),x80492),x80493)),f315(f315(f74(x80491),x80494),x80493)))
% 168.60/168.39 [8050]~P136(x80501)+~P1(f315(f315(f224(x80501),x80502),x80504))+~P1(f315(f315(f224(x80501),f2(x80501)),x80503))+P1(f315(f315(f224(x80501),f315(f315(f74(x80501),x80502),x80503)),f315(f315(f74(x80501),x80504),x80503)))
% 168.60/168.39 [8051]~P130(x80511)+~P1(f315(f315(f224(x80511),x80513),x80514))+~P1(f315(f315(f224(x80511),f2(x80511)),x80512))+P1(f315(f315(f224(x80511),f315(f315(f74(x80511),x80512),x80513)),f315(f315(f74(x80511),x80512),x80514)))
% 168.60/168.39 [8052]~P68(x80521)+~P1(f315(f315(f224(x80521),x80522),x80524))+~P1(f315(f315(f224(x80521),f2(x80521)),x80523))+P1(f315(f315(f224(x80521),f315(f315(f279(x80521),x80522),x80523)),f315(f315(f279(x80521),x80524),x80523)))
% 168.60/168.39 [8094]~P109(x80942)+P1(f315(f315(f224(f909(x80941,x80942)),x80944),x80943))+~P1(f315(f315(f223(f909(x80941,x80942)),x80944),x80943))+P1(f315(f315(f223(f909(x80941,x80942)),x80943),x80944))
% 168.60/168.39 [8135]P1(f315(f315(f317(x81351),x81352),x81353))+P1(f315(f315(f317(x81351),x81352),x81354))+~P1(f315(f315(f223(f909(x81351,a899)),x81354),x81353))+P1(f315(f315(f224(f909(x81351,a899)),x81354),f315(f315(f297(x81351),x81352),x81353)))
% 168.60/168.39 [8248]~P123(x82482)+E(x82481,f2(x82482))+P1(f315(f315(f275(x82482),x82483),x82484))+~P1(f315(f315(f275(x82482),f315(f315(f74(x82482),x82483),x82481)),f315(f315(f74(x82482),x82484),x82481)))
% 168.60/168.39 [8249]~P123(x82492)+E(x82491,f2(x82492))+P1(f315(f315(f275(x82492),x82493),x82494))+~P1(f315(f315(f275(x82492),f315(f315(f74(x82492),x82491),x82493)),f315(f315(f74(x82492),x82491),x82494)))
% 168.60/168.39 [8298]P1(f315(f315(f317(x82981),x82982),x82983))+P1(f315(f315(f317(x82981),x82982),x82984))+~P1(f315(f315(f224(f909(x82981,a899)),x82984),f315(f315(f297(x82981),x82982),x82983)))+P1(f315(f315(f223(f909(x82981,a899)),x82984),x82983))
% 168.60/168.39 [8363]~P130(x83631)+P1(f315(f315(f224(x83631),x83633),x83632))+P1(f315(f315(f224(x83631),x83632),x83633))+~P1(f315(f315(f224(x83631),f315(f315(f74(x83631),x83634),x83632)),f315(f315(f74(x83631),x83634),x83633)))
% 168.60/168.39 [8364]~P130(x83641)+P1(f315(f315(f224(x83641),x83643),x83642))+P1(f315(f315(f224(x83641),x83642),x83643))+~P1(f315(f315(f224(x83641),f315(f315(f74(x83641),x83642),x83644)),f315(f315(f74(x83641),x83643),x83644)))
% 168.60/168.39 [8375]~P130(x83751)+P1(f315(f315(f224(x83751),x83754),f2(x83751)))+P1(f315(f315(f224(x83751),x83752),x83753))+~P1(f315(f315(f224(x83751),f315(f315(f74(x83751),x83752),x83754)),f315(f315(f74(x83751),x83753),x83754)))
% 168.60/168.39 [8376]~P130(x83761)+P1(f315(f315(f224(x83761),x83764),f2(x83761)))+P1(f315(f315(f224(x83761),x83762),x83763))+~P1(f315(f315(f224(x83761),f315(f315(f74(x83761),x83764),x83762)),f315(f315(f74(x83761),x83764),x83763)))
% 168.60/168.39 [8379]~P130(x83791)+P1(f315(f315(f224(x83791),x83792),x83793))+P1(f315(f315(f224(x83791),f2(x83791)),x83794))+~P1(f315(f315(f224(x83791),f315(f315(f74(x83791),x83794),x83793)),f315(f315(f74(x83791),x83794),x83792)))
% 168.60/168.39 [8380]~P130(x83801)+P1(f315(f315(f224(x83801),x83802),x83803))+P1(f315(f315(f224(x83801),f2(x83801)),x83804))+~P1(f315(f315(f224(x83801),f315(f315(f74(x83801),x83803),x83804)),f315(f315(f74(x83801),x83802),x83804)))
% 168.60/168.39 [8393]~P130(x83931)+P1(f315(f315(f224(x83931),x83932),f2(x83931)))+P1(f315(f315(f224(x83931),f2(x83931)),x83932))+~P1(f315(f315(f224(x83931),f315(f315(f74(x83931),x83933),x83932)),f315(f315(f74(x83931),x83934),x83932)))
% 168.60/168.39 [8394]~P130(x83941)+P1(f315(f315(f224(x83941),x83942),f2(x83941)))+P1(f315(f315(f224(x83941),f2(x83941)),x83942))+~P1(f315(f315(f224(x83941),f315(f315(f74(x83941),x83942),x83943)),f315(f315(f74(x83941),x83942),x83944)))
% 168.60/168.39 [8423]~P130(x84231)+~P1(f315(f315(f224(x84231),x84234),f2(x84231)))+P1(f315(f315(f223(x84231),x84232),x84233))+~P1(f315(f315(f223(x84231),f315(f315(f74(x84231),x84234),x84233)),f315(f315(f74(x84231),x84234),x84232)))
% 168.60/168.39 [8424]~P130(x84241)+~P1(f315(f315(f224(x84241),x84244),f2(x84241)))+P1(f315(f315(f224(x84241),x84242),x84243))+~P1(f315(f315(f224(x84241),f315(f315(f74(x84241),x84244),x84243)),f315(f315(f74(x84241),x84244),x84242)))
% 168.60/168.39 [8435]~P128(x84353)+~P1(f315(f315(f224(x84353),f71(x84353)),x84354))+P1(f315(f315(f223(a901),x84351),x84352))+~P1(f315(f315(f223(x84353),f315(f315(f232(x84353),x84354),x84351)),f315(f315(f232(x84353),x84354),x84352)))
% 168.60/168.39 [8437]~P128(x84373)+~P1(f315(f315(f224(x84373),f71(x84373)),x84374))+P1(f315(f315(f224(a901),x84371),x84372))+~P1(f315(f315(f224(x84373),f315(f315(f232(x84373),x84374),x84371)),f315(f315(f232(x84373),x84374),x84372)))
% 168.60/168.39 [8447]~P130(x84471)+P1(f315(f315(f223(x84471),x84472),x84473))+~P1(f315(f315(f224(x84471),f2(x84471)),x84474))+~P1(f315(f315(f223(x84471),f315(f315(f74(x84471),x84474),x84472)),f315(f315(f74(x84471),x84474),x84473)))
% 168.60/168.39 [8448]~P136(x84481)+P1(f315(f315(f223(x84481),x84482),x84483))+~P1(f315(f315(f224(x84481),f2(x84481)),x84484))+~P1(f315(f315(f223(x84481),f315(f315(f74(x84481),x84484),x84482)),f315(f315(f74(x84481),x84484),x84483)))
% 168.60/168.39 [8449]~P136(x84491)+P1(f315(f315(f223(x84491),x84492),x84493))+~P1(f315(f315(f224(x84491),f2(x84491)),x84494))+~P1(f315(f315(f223(x84491),f315(f315(f74(x84491),x84492),x84494)),f315(f315(f74(x84491),x84493),x84494)))
% 168.60/168.39 [8450]~P130(x84501)+P1(f315(f315(f224(x84501),x84502),x84503))+~P1(f315(f315(f224(x84501),f2(x84501)),x84504))+~P1(f315(f315(f224(x84501),f315(f315(f74(x84501),x84504),x84502)),f315(f315(f74(x84501),x84504),x84503)))
% 168.60/168.39 [8451]~P136(x84511)+P1(f315(f315(f224(x84511),x84512),x84513))+~P1(f315(f315(f223(x84511),f2(x84511)),x84514))+~P1(f315(f315(f224(x84511),f315(f315(f74(x84511),x84514),x84512)),f315(f315(f74(x84511),x84514),x84513)))
% 168.60/168.39 [8452]~P132(x84521)+P1(f315(f315(f224(x84521),x84522),x84523))+~P1(f315(f315(f223(x84521),f2(x84521)),x84524))+~P1(f315(f315(f224(x84521),f315(f315(f74(x84521),x84524),x84522)),f315(f315(f74(x84521),x84524),x84523)))
% 168.60/168.39 [8453]~P128(x84531)+~P1(f315(f315(f223(x84531),f2(x84531)),x84533))+P1(f315(f315(f224(x84531),x84532),x84533))+~P1(f315(f315(f224(x84531),f315(f315(f232(x84531),x84532),x84534)),f315(f315(f232(x84531),x84533),x84534)))
% 168.60/168.39 [8454]~P136(x84541)+P1(f315(f315(f224(x84541),x84542),x84543))+~P1(f315(f315(f223(x84541),f2(x84541)),x84544))+~P1(f315(f315(f224(x84541),f315(f315(f74(x84541),x84542),x84544)),f315(f315(f74(x84541),x84543),x84544)))
% 168.60/168.39 [8455]~P132(x84551)+P1(f315(f315(f224(x84551),x84552),x84553))+~P1(f315(f315(f223(x84551),f2(x84551)),x84554))+~P1(f315(f315(f224(x84551),f315(f315(f74(x84551),x84552),x84554)),f315(f315(f74(x84551),x84553),x84554)))
% 168.60/168.39 [8499]P1(f315(f315(f317(x84991),x84992),x84993))+~P1(f315(f315(f223(f909(x84991,a899)),x84993),x84994))+~P1(f315(f315(f224(f909(x84991,a899)),x84993),x84994))+P1(f315(f315(f224(f909(x84991,a899)),x84993),f315(f315(f297(x84991),x84992),x84994)))
% 168.60/168.39 [8531]~P148(x85311)+~P124(x85311)+P1(f315(f315(f275(x85311),x85312),f315(f315(f73(x85311),f837(x85312,x85313,x85311)),f2(x85311))))+~P1(f315(x85313,f315(f315(f74(x85311),x85312),x85314)))
% 168.60/168.39 [8878]E(f315(f315(f3(a1),f439(x88781,x88782,x88783,x88784)),f440(x88781,x88782,x88783,x88784)),x88784)+~P1(f315(f315(f224(a1),f2(a1)),x88783))+~P1(f315(f315(f223(a1),x88781),x88784))+P1(f315(f315(f223(a1),x88781),f315(f315(f73(a1),x88784),x88783)))
% 168.60/168.39 [8879]E(f315(f315(f3(a1),f461(x88791,x88792,x88793,x88794)),f462(x88791,x88792,x88793,x88794)),x88794)+~P1(f315(f315(f224(a1),f2(a1)),x88793))+~P1(f315(f315(f224(a1),x88791),x88794))+P1(f315(f315(f224(a1),x88791),f315(f315(f73(a1),x88794),x88793)))
% 168.60/168.39 [9029]~E(f315(f315(f153(x90291),x90293),f660(x90294,x90293,x90291,x90292)),f315(f315(f153(x90291),x90294),f660(x90294,x90293,x90291,x90292)))+E(f315(f315(f164(x90291),x90292),x90293),f315(f315(f164(x90291),x90292),x90294))+~P1(f315(f315(f223(a901),x90292),f315(f178(f902(x90291)),x90293)))+~P1(f315(f315(f223(a901),x90292),f315(f178(f902(x90291)),x90294)))
% 168.60/168.39 [9092]~P1(f315(f315(f224(a1),f2(a1)),x90923))+~P1(f315(f315(f223(a1),x90921),x90924))+P1(f315(f315(f317(a1),f439(x90921,x90922,x90923,x90924)),x90922))+P1(f315(f315(f223(a1),x90921),f315(f315(f73(a1),x90924),x90923)))
% 168.60/168.39 [9093]~P1(f315(f315(f224(a1),f2(a1)),x90933))+~P1(f315(f315(f224(a1),x90931),x90934))+P1(f315(f315(f317(a1),f461(x90931,x90932,x90933,x90934)),x90932))+P1(f315(f315(f224(a1),x90931),f315(f315(f73(a1),x90934),x90933)))
% 168.60/168.39 [9133]~P104(x91331)+~P1(f315(f54(x91331),x91333))+~P1(f315(f315(f317(x91331),x91334),x91333))+P1(f315(f315(f223(x91331),f315(f315(f57(x91331,x91331,f90(x91331)),x91332),x91333)),f315(f315(f90(x91331),x91334),x91332)))
% 168.60/168.39 [9134]~P110(x91341)+~P1(f315(f54(x91341),x91343))+~P1(f315(f315(f317(x91341),x91344),x91343))+P1(f315(f315(f223(x91341),f315(f315(f57(x91341,x91341,f221(x91341)),x91342),x91343)),f315(f315(f221(x91341),x91344),x91342)))
% 168.60/168.39 [9178]E(f315(f315(f164(x91781),x91782),x91783),f315(f315(f164(x91781),x91782),x91784))+P1(f315(f315(f224(a901),f660(x91783,x91784,x91781,x91782)),x91782))+~P1(f315(f315(f223(a901),x91782),f315(f178(f902(x91781)),x91783)))+~P1(f315(f315(f223(a901),x91782),f315(f178(f902(x91781)),x91784)))
% 168.60/168.39 [9183]~P1(f315(f315(f224(a1),f2(a1)),x91833))+~P1(f315(f315(f223(a1),x91831),x91832))+P1(f315(f315(f317(a1),f440(x91831,x91834,x91833,x91832)),f291(a1,f71(a1),x91833)))+P1(f315(f315(f223(a1),x91831),f315(f315(f73(a1),x91832),x91833)))
% 168.60/168.39 [9184]~P1(f315(f315(f224(a1),f2(a1)),x91843))+~P1(f315(f315(f224(a1),x91841),x91842))+P1(f315(f315(f317(a1),f462(x91841,x91844,x91843,x91842)),f291(a1,f71(a1),x91843)))+P1(f315(f315(f224(a1),x91841),f315(f315(f73(a1),x91842),x91843)))
% 168.60/168.39 [9509]~P103(x95091)+~P1(f315(f54(x95091),x95094))+P1(f315(f315(f317(x95091),f886(x95092,x95093,x95094,x95091)),x95094))+P1(f315(f315(f223(x95091),f315(f315(f57(x95091,x95091,f99(x95091)),x95092),x95094)),f315(f315(f99(x95091),x95093),x95092)))
% 168.60/168.39 [9510]~P110(x95101)+~P1(f315(f54(x95101),x95104))+P1(f315(f315(f317(x95101),f587(x95102,x95103,x95104,x95101)),x95104))+P1(f315(f315(f223(x95101),f315(f315(f57(x95101,x95101,f222(x95101)),x95102),x95104)),f315(f315(f222(x95101),x95103),x95102)))
% 168.60/168.39 [9646]~P103(x96461)+~P1(f315(f54(x96461),x96463))+~P1(f315(f315(f223(x96461),f886(x96462,x96464,x96463,x96461)),x96464))+P1(f315(f315(f223(x96461),f315(f315(f57(x96461,x96461,f99(x96461)),x96462),x96463)),f315(f315(f99(x96461),x96464),x96462)))
% 168.60/168.39 [9647]~P110(x96471)+~P1(f315(f54(x96471),x96473))+~P1(f315(f315(f223(x96471),f587(x96472,x96474,x96473,x96471)),x96474))+P1(f315(f315(f223(x96471),f315(f315(f57(x96471,x96471,f222(x96471)),x96472),x96473)),f315(f315(f222(x96471),x96474),x96472)))
% 168.60/168.39 [9649]~P1(f315(f315(f223(a1),f2(a1)),x96494))+~P1(f315(f315(f224(a1),f2(a1)),x96493))+~P1(f315(f315(f224(a1),x96494),x96491))+P1(f315(f315(f224(a1),f315(f315(f73(a1),f315(f315(f74(a1),x96491),f38(a1,x96492,x96493))),x96494)),f315(f315(f74(a1),x96491),x96493)))
% 168.60/168.39 [10035]E(x100351,x100352)+P1(f315(f315(f317(f908(f902(x100353),f902(x100353))),f315(f315(f240(f902(x100353),f902(x100353)),x100352),x100351)),f136(x100353,x100354)))+P1(f315(f315(f317(f908(f902(x100353),f902(x100353))),f315(f315(f240(f902(x100353),f902(x100353)),x100351),x100352)),f136(x100353,x100354)))+~P1(f315(f315(f317(f908(x100353,x100353)),f315(f315(f240(x100353,x100353),f638(x100351,x100352,x100354,x100353)),f639(x100351,x100352,x100354,x100353))),x100354))
% 168.60/168.39 [10036]E(x100361,x100362)+P1(f315(f315(f317(f908(f902(x100363),f902(x100363))),f315(f315(f240(f902(x100363),f902(x100363)),x100362),x100361)),f136(x100363,x100364)))+P1(f315(f315(f317(f908(f902(x100363),f902(x100363))),f315(f315(f240(f902(x100363),f902(x100363)),x100361),x100362)),f136(x100363,x100364)))+~P1(f315(f315(f317(f908(x100363,x100363)),f315(f315(f240(x100363,x100363),f639(x100361,x100362,x100364,x100363)),f638(x100361,x100362,x100364,x100363))),x100364))
% 168.60/168.39 [7583]~P103(x75831)+~P1(f315(f315(f223(x75831),x75833),x75834))+~P1(f315(f315(f223(x75831),x75832),x75834))+P1(f315(f315(f223(x75831),f315(f315(f99(x75831),x75832),x75833)),x75834))
% 168.60/168.39 [7586]~P110(x75861)+~P1(f315(f315(f223(x75861),x75863),x75864))+~P1(f315(f315(f223(x75861),x75862),x75864))+P1(f315(f315(f223(x75861),f315(f315(f222(x75861),x75862),x75863)),x75864))
% 168.60/168.39 [7587]~P110(x75871)+~P1(f315(f315(f224(x75871),x75873),x75874))+~P1(f315(f315(f224(x75871),x75872),x75874))+P1(f315(f315(f224(x75871),f315(f315(f222(x75871),x75872),x75873)),x75874))
% 168.60/168.39 [7825]~P62(x78251)+E(f315(f315(f73(x78251),f315(f315(f29(x78251),x78252),x78253)),f315(f315(f29(x78251),x78254),x78253)),f315(f315(f29(x78251),f315(f315(f73(x78251),x78252),x78254)),x78253))+~P1(f315(f315(f275(x78251),x78253),x78254))+~P1(f315(f315(f275(x78251),x78253),x78252))
% 168.60/168.39 [7907]~E(x79071,x79073)+E(f128(a901,f315(f290(a901,x79071),x79072)),f315(f315(f140(a901),x79073),x79074))+~E(f128(a901,f315(f290(a901,f315(f315(f73(a901),x79071),f71(a901))),x79072)),x79074)+~P1(f315(f315(f224(a901),x79071),x79072))
% 168.60/168.39 [7915]~P110(x79151)+P1(f315(f315(f223(x79151),x79152),x79153))+P1(f315(f315(f223(x79151),x79154),x79153))+~P1(f315(f315(f223(x79151),f315(f315(f221(x79151),x79154),x79152)),x79153))
% 168.60/168.39 [7916]~P110(x79161)+P1(f315(f315(f224(x79161),x79162),x79163))+P1(f315(f315(f224(x79161),x79164),x79163))+~P1(f315(f315(f224(x79161),f315(f315(f221(x79161),x79164),x79162)),x79163))
% 168.60/168.39 [8194]~P67(x81941)+~P1(f315(f315(f224(x81941),f2(x81941)),x81943))+~P1(f315(f315(f223(x81941),x81942),f315(f315(f279(x81941),x81944),x81943)))+P1(f315(f315(f223(x81941),f315(f315(f74(x81941),x81942),x81943)),x81944))
% 168.60/168.39 [8195]~P68(x81951)+~P1(f315(f315(f224(x81951),f2(x81951)),x81953))+~P1(f315(f315(f223(x81951),x81952),f315(f315(f279(x81951),x81954),x81953)))+P1(f315(f315(f223(x81951),f315(f315(f74(x81951),x81952),x81953)),x81954))
% 168.60/168.39 [8196]~P67(x81961)+~P1(f315(f315(f224(x81961),f2(x81961)),x81963))+~P1(f315(f315(f223(x81961),x81962),f315(f315(f74(x81961),x81964),x81963)))+P1(f315(f315(f223(x81961),f315(f315(f279(x81961),x81962),x81963)),x81964))
% 168.60/168.39 [8198]~P68(x81981)+~P1(f315(f315(f224(x81981),f2(x81981)),x81983))+~P1(f315(f315(f223(x81981),x81982),f315(f315(f74(x81981),x81984),x81983)))+P1(f315(f315(f223(x81981),f315(f315(f279(x81981),x81982),x81983)),x81984))
% 168.60/168.39 [8199]~P67(x81991)+~P1(f315(f315(f224(x81991),f2(x81991)),x81993))+~P1(f315(f315(f224(x81991),x81992),f315(f315(f279(x81991),x81994),x81993)))+P1(f315(f315(f224(x81991),f315(f315(f74(x81991),x81992),x81993)),x81994))
% 168.60/168.39 [8200]~P68(x82001)+~P1(f315(f315(f224(x82001),f2(x82001)),x82003))+~P1(f315(f315(f224(x82001),x82002),f315(f315(f279(x82001),x82004),x82003)))+P1(f315(f315(f224(x82001),f315(f315(f74(x82001),x82002),x82003)),x82004))
% 168.60/168.39 [8201]~P67(x82011)+~P1(f315(f315(f224(x82011),f2(x82011)),x82013))+~P1(f315(f315(f224(x82011),x82012),f315(f315(f74(x82011),x82014),x82013)))+P1(f315(f315(f224(x82011),f315(f315(f279(x82011),x82012),x82013)),x82014))
% 168.60/168.39 [8203]~P68(x82031)+~P1(f315(f315(f224(x82031),f2(x82031)),x82033))+~P1(f315(f315(f224(x82031),x82032),f315(f315(f74(x82031),x82034),x82033)))+P1(f315(f315(f224(x82031),f315(f315(f279(x82031),x82032),x82033)),x82034))
% 168.60/168.39 [8333]~P67(x83331)+~P1(f315(f315(f224(x83331),f2(x83331)),x83334))+P1(f315(f315(f223(x83331),x83332),f315(f315(f74(x83331),x83333),x83334)))+~P1(f315(f315(f223(x83331),f315(f315(f279(x83331),x83332),x83334)),x83333))
% 168.60/168.39 [8334]~P67(x83341)+~P1(f315(f315(f224(x83341),f2(x83341)),x83344))+P1(f315(f315(f223(x83341),x83342),f315(f315(f279(x83341),x83343),x83344)))+~P1(f315(f315(f223(x83341),f315(f315(f74(x83341),x83342),x83344)),x83343))
% 168.60/168.39 [8336]~P68(x83361)+~P1(f315(f315(f224(x83361),f2(x83361)),x83364))+P1(f315(f315(f223(x83361),x83362),f315(f315(f74(x83361),x83363),x83364)))+~P1(f315(f315(f223(x83361),f315(f315(f279(x83361),x83362),x83364)),x83363))
% 168.60/168.39 [8337]~P68(x83371)+~P1(f315(f315(f224(x83371),f2(x83371)),x83374))+P1(f315(f315(f223(x83371),x83372),f315(f315(f279(x83371),x83373),x83374)))+~P1(f315(f315(f223(x83371),f315(f315(f74(x83371),x83372),x83374)),x83373))
% 168.60/168.39 [8338]~P67(x83381)+~P1(f315(f315(f224(x83381),f2(x83381)),x83384))+P1(f315(f315(f224(x83381),x83382),f315(f315(f74(x83381),x83383),x83384)))+~P1(f315(f315(f224(x83381),f315(f315(f279(x83381),x83382),x83384)),x83383))
% 168.60/168.39 [8339]~P67(x83391)+~P1(f315(f315(f224(x83391),f2(x83391)),x83394))+P1(f315(f315(f224(x83391),x83392),f315(f315(f279(x83391),x83393),x83394)))+~P1(f315(f315(f224(x83391),f315(f315(f74(x83391),x83392),x83394)),x83393))
% 168.60/168.39 [8341]~P68(x83411)+~P1(f315(f315(f224(x83411),f2(x83411)),x83414))+P1(f315(f315(f224(x83411),x83412),f315(f315(f74(x83411),x83413),x83414)))+~P1(f315(f315(f224(x83411),f315(f315(f279(x83411),x83412),x83414)),x83413))
% 168.60/168.39 [8342]~P68(x83421)+~P1(f315(f315(f224(x83421),f2(x83421)),x83424))+P1(f315(f315(f224(x83421),x83422),f315(f315(f279(x83421),x83423),x83424)))+~P1(f315(f315(f224(x83421),f315(f315(f74(x83421),x83422),x83424)),x83423))
% 168.60/168.39 [8502]~P68(x85021)+~P1(f315(f315(f224(x85021),x85023),f2(x85021)))+~P1(f315(f315(f223(x85021),f315(f315(f279(x85021),x85024),x85023)),x85022))+P1(f315(f315(f223(x85021),f315(f315(f74(x85021),x85022),x85023)),x85024))
% 168.60/168.39 [8503]~P68(x85031)+~P1(f315(f315(f224(x85031),x85033),f2(x85031)))+~P1(f315(f315(f223(x85031),f315(f315(f74(x85031),x85034),x85033)),x85032))+P1(f315(f315(f223(x85031),f315(f315(f279(x85031),x85032),x85033)),x85034))
% 168.60/168.39 [8504]~P68(x85041)+~P1(f315(f315(f224(x85041),x85043),f2(x85041)))+~P1(f315(f315(f224(x85041),f315(f315(f279(x85041),x85044),x85043)),x85042))+P1(f315(f315(f224(x85041),f315(f315(f74(x85041),x85042),x85043)),x85044))
% 168.60/168.39 [8505]~P68(x85051)+~P1(f315(f315(f224(x85051),x85053),f2(x85051)))+~P1(f315(f315(f224(x85051),f315(f315(f74(x85051),x85054),x85053)),x85052))+P1(f315(f315(f224(x85051),f315(f315(f279(x85051),x85052),x85053)),x85054))
% 168.60/168.39 [8517]~P1(f315(x85171,x85174))+~P1(f315(f315(f224(a901),x85172),f315(f315(f74(a901),x85173),f315(a101,x85174))))+P1(f315(x85171,f315(f315(f29(a901),x85172),x85173)))+~P1(f315(f315(f223(a901),f315(f315(f74(a901),x85173),x85174)),x85172))
% 168.60/168.39 [8726]~P103(x87261)+~P1(f315(f54(x87261),x87264))+~P1(f315(f315(f317(x87261),x87262),x87264))+P1(f315(f315(f223(x87261),f315(f315(f99(x87261),x87262),x87263)),f315(f315(f57(x87261,x87261,f99(x87261)),x87263),x87264)))
% 168.60/168.39 [8727]~P110(x87271)+~P1(f315(f54(x87271),x87274))+~P1(f315(f315(f317(x87271),x87272),x87274))+P1(f315(f315(f223(x87271),f315(f315(f222(x87271),x87272),x87273)),f315(f315(f57(x87271,x87271,f222(x87271)),x87273),x87274)))
% 168.60/168.39 [8880]~P1(f315(f54(x88801),x88802))+E(f315(f28(x88801),f315(f315(f3(f909(x88801,a899)),x88802),f315(f315(f297(x88801),x88803),x88804))),f315(f315(f3(a901),f315(f28(x88801),f315(f315(f3(f909(x88801,a899)),x88802),x88804))),f71(a901)))+P1(f315(f315(f317(x88801),x88803),x88804))+~P1(f315(f315(f317(x88801),x88803),x88802))
% 168.60/168.39 [8957]E(f315(f315(f73(a1),f446(x89571,x89572,x89573,x89574)),f447(x89571,x89572,x89573,x89574)),x89574)+~P1(f315(f315(f224(a1),f2(a1)),x89573))+~P1(f315(f315(f223(a1),x89574),x89571))+P1(f315(f315(f223(a1),f315(f315(f3(a1),x89574),x89573)),x89571))
% 168.60/168.39 [8958]E(f315(f315(f73(a1),f463(x89581,x89582,x89583,x89584)),f464(x89581,x89582,x89583,x89584)),x89584)+~P1(f315(f315(f224(a1),f2(a1)),x89583))+~P1(f315(f315(f224(a1),x89584),x89581))+P1(f315(f315(f224(a1),f315(f315(f3(a1),x89584),x89583)),x89581))
% 168.60/168.39 [9163]~P1(f315(f315(f224(a1),f2(a1)),x91633))+~P1(f315(f315(f223(a1),x91634),x91631))+P1(f315(f315(f317(a1),f446(x91631,x91632,x91633,x91634)),x91632))+P1(f315(f315(f223(a1),f315(f315(f3(a1),x91634),x91633)),x91631))
% 168.60/168.39 [9164]~P1(f315(f315(f224(a1),f2(a1)),x91643))+~P1(f315(f315(f224(a1),x91644),x91641))+P1(f315(f315(f317(a1),f463(x91641,x91642,x91643,x91644)),x91642))+P1(f315(f315(f224(a1),f315(f315(f3(a1),x91644),x91643)),x91641))
% 168.60/168.39 [9250]~P1(f315(f315(f224(a1),f2(a1)),x92502))+~P1(f315(f315(f223(a1),x92501),x92503))+P1(f315(f315(f317(a1),f447(x92503,x92504,x92502,x92501)),f291(a1,f71(a1),x92502)))+P1(f315(f315(f223(a1),f315(f315(f3(a1),x92501),x92502)),x92503))
% 168.60/168.39 [9251]~P1(f315(f315(f224(a1),f2(a1)),x92512))+~P1(f315(f315(f224(a1),x92511),x92513))+P1(f315(f315(f317(a1),f464(x92513,x92514,x92512,x92511)),f291(a1,f71(a1),x92512)))+P1(f315(f315(f224(a1),f315(f315(f3(a1),x92511),x92512)),x92513))
% 168.60/168.39 [9269]~P1(f315(f315(f223(a1),f2(a1)),x92694))+~P1(f315(f315(f224(a1),f2(a1)),x92693))+~P1(f315(f315(f224(a1),x92694),x92691))+P1(f315(f315(f223(a1),f2(a1)),f315(f315(f73(a1),f315(f315(f74(a1),x92691),f38(a1,x92692,x92693))),x92694)))
% 168.60/168.39 [9298]E(x92981,x92982)+~P41(x92983,x92984)+~P1(f315(f315(f317(f908(x92983,x92983)),f315(f315(f240(x92983,x92983),x92982),x92981)),x92984))+~P1(f315(f315(f317(f908(x92983,x92983)),f315(f315(f240(x92983,x92983),x92981),x92982)),x92984))
% 168.60/168.39 [9331]~P104(x93311)+~P1(f315(f54(x93311),x93314))+~P1(f315(f315(f223(x93311),x93312),f884(x93313,x93312,x93314,x93311)))+P1(f315(f315(f223(x93311),f315(f315(f90(x93311),x93312),x93313)),f315(f315(f57(x93311,x93311,f90(x93311)),x93313),x93314)))
% 168.60/168.39 [9332]~P110(x93321)+~P1(f315(f54(x93321),x93324))+~P1(f315(f315(f223(x93321),x93322),f334(x93323,x93322,x93324,x93321)))+P1(f315(f315(f223(x93321),f315(f315(f221(x93321),x93322),x93323)),f315(f315(f57(x93321,x93321,f221(x93321)),x93323),x93324)))
% 168.60/168.39 [9349]~P1(f315(f315(f223(a1),x93494),f2(a1)))+~P1(f315(f315(f224(a1),f2(a1)),x93492))+~P1(f315(f315(f224(a1),x93491),x93494))+P1(f315(f315(f224(a1),f315(f315(f74(a1),x93491),x93492)),f315(f315(f73(a1),f315(f315(f74(a1),x93491),f38(a1,x93493,x93492))),x93494)))
% 168.60/168.39 [9375]P1(f315(f54(x93751),x93752))+~P1(f315(f54(x93751),x93753))+~P1(f315(f315(f317(f909(x93751,a899)),x93752),f315(f315(f53(x93751),x93753),x93754)))+~P1(f315(f315(f223(f909(f908(x93751,x93751),a899)),x93754),f315(f315(f242(x93751,x93751),x93753),f315(f18(f909(x93751,a899),x93751),x93753))))
% 168.60/168.39 [9399]~P104(x93991)+~P1(f315(f54(x93991),x93994))+P1(f315(f315(f317(x93991),f884(x93992,x93993,x93994,x93991)),x93994))+P1(f315(f315(f223(x93991),f315(f315(f90(x93991),x93993),x93992)),f315(f315(f57(x93991,x93991,f90(x93991)),x93992),x93994)))
% 168.60/168.39 [9400]~P110(x94001)+~P1(f315(f54(x94001),x94004))+P1(f315(f315(f317(x94001),f334(x94002,x94003,x94004,x94001)),x94004))+P1(f315(f315(f223(x94001),f315(f315(f221(x94001),x94003),x94002)),f315(f315(f57(x94001,x94001,f221(x94001)),x94002),x94004)))
% 168.60/168.39 [9813]~P1(f315(f54(x98132),x98134))+~P1(f315(f54(x98131),x98133))+~P1(f315(f315(f223(a901),f315(f28(x98132),x98134)),f315(f28(x98131),x98133)))+P1(f315(f315(f223(f909(x98131,a899)),f315(f298(x98132,x98131,f495(x98133,x98131,x98134,x98132)),x98134)),x98133))
% 168.60/168.39 [9450]~P1(f315(f315(f317(x94501),x94502),x94504))+P1(f315(f315(f317(x94501),x94502),x94503))+~P1(f315(f315(f224(f909(x94501,a899)),x94504),f315(f315(f297(x94501),x94502),x94503)))+P1(f315(f315(f224(f909(x94501,a899)),f315(f315(f3(f909(x94501,a899)),x94504),f315(f315(f297(x94501),x94502),f177(f909(x94501,a899))))),x94503))
% 168.60/168.39 [9627]~P1(f315(f315(f317(x96271),x96272),x96274))+P1(f315(f315(f317(x96271),x96272),x96273))+P1(f315(f315(f224(f909(x96271,a899)),x96274),f315(f315(f297(x96271),x96272),x96273)))+~P1(f315(f315(f224(f909(x96271,a899)),f315(f315(f3(f909(x96271,a899)),x96274),f315(f315(f297(x96271),x96272),f177(f909(x96271,a899))))),x96273))
% 168.60/168.39 [9652]P1(f315(f315(f317(x96521),x96522),x96523))+~P1(f315(f315(f223(f909(x96521,a899)),x96524),x96523))+P1(f315(f315(f224(f909(x96521,a899)),x96524),f315(f315(f297(x96521),x96522),x96523)))+~P1(f315(f315(f224(f909(x96521,a899)),f315(f315(f3(f909(x96521,a899)),x96524),f315(f315(f297(x96521),x96522),f177(f909(x96521,a899))))),x96523))
% 168.60/168.39 [9657]~P1(f315(f315(f317(x96571),x96573),x96572))+~P1(f315(f315(f224(f909(x96571,a899)),x96572),x96574))+P1(f315(f315(f224(f909(x96571,a899)),x96572),f315(f315(f297(x96571),x96573),x96574)))+~P1(f315(f315(f224(f909(x96571,a899)),f315(f315(f3(f909(x96571,a899)),x96572),f315(f315(f297(x96571),x96573),f177(f909(x96571,a899))))),x96574))
% 168.60/168.39 [9673]~P1(f315(f315(f223(f909(x96731,a899)),x96732),x96734))+~P1(f315(f315(f224(f909(x96731,a899)),x96732),x96734))+P1(f315(f315(f224(f909(x96731,a899)),x96732),f315(f315(f297(x96731),x96733),x96734)))+~P1(f315(f315(f224(f909(x96731,a899)),f315(f315(f3(f909(x96731,a899)),x96732),f315(f315(f297(x96731),x96733),f177(f909(x96731,a899))))),x96734))
% 168.60/168.39 [9718]~P111(x97182)+~P64(x97181)+~P1(f315(f315(f223(f909(x97181,x97182)),x97183),x97184))+P1(f315(f50(x97181),f315(f315(f20(x97181,x97182,a899),f315(f315(f10(x97182,f909(x97182,a899),x97181),f223(x97182)),x97183)),x97184)))
% 168.60/168.39 [9861]~P111(x98612)+~P64(x98611)+P1(f315(f315(f223(f909(x98611,x98612)),x98613),x98614))+~P1(f315(f50(x98611),f315(f315(f20(x98611,x98612,a899),f315(f315(f10(x98612,f909(x98612,a899),x98611),f223(x98612)),x98613)),x98614)))
% 168.60/168.39 [10026]E(f315(f315(f153(x100261),f315(f315(f153(f902(x100261)),f168(x100261,x100262)),x100263)),x100264),f315(f315(f153(x100261),f315(f315(f153(f902(x100261)),x100262),x100264)),x100263))+~P1(f315(f315(f224(a901),x100263),f315(f178(f902(f902(x100261))),f168(x100261,x100262))))+~P13(a901,f315(f157(a901),f315(f315(f143(f902(x100261),a901),f178(f902(x100261))),x100262)))+~P1(f315(f315(f224(a901),x100264),f315(f178(f902(f902(x100261))),f315(f125(f902(x100261),f315(f315(f10(a901,a899,f902(x100261)),f315(f224(a901),x100263)),f178(f902(x100261)))),x100262))))
% 168.60/168.39 [10047]~P1(f315(f315(f317(f908(a901,a901)),x100474),x100471))+~P1(f315(f315(f317(f908(f908(a901,a901),f908(a901,a901))),f315(f315(f240(f908(a901,a901),f908(a901,a901)),x100474),x100472)),a26))+~P1(f315(f315(f317(f908(f909(f908(a901,a901),a899),f909(f908(a901,a901),a899))),f315(f315(f240(f909(f908(a901,a901),a899),f909(f908(a901,a901),a899)),x100471),x100473)),a62))+P1(f315(f315(f317(f908(f909(f908(a901,a901),a899),f909(f908(a901,a901),a899))),f315(f315(f240(f909(f908(a901,a901),a899),f909(f908(a901,a901),a899)),x100471),f315(f315(f297(f908(a901,a901)),x100472),x100473))),a62))
% 168.60/168.39 [10048]~P1(f315(f315(f317(f908(a901,a901)),x100484),x100481))+~P1(f315(f315(f317(f908(f908(a901,a901),f908(a901,a901))),f315(f315(f240(f908(a901,a901),f908(a901,a901)),x100484),x100482)),a64))+~P1(f315(f315(f317(f908(f909(f908(a901,a901),a899),f909(f908(a901,a901),a899))),f315(f315(f240(f909(f908(a901,a901),a899),f909(f908(a901,a901),a899)),x100481),x100483)),a65))+P1(f315(f315(f317(f908(f909(f908(a901,a901),a899),f909(f908(a901,a901),a899))),f315(f315(f240(f909(f908(a901,a901),a899),f909(f908(a901,a901),a899)),x100481),f315(f315(f297(f908(a901,a901)),x100482),x100483))),a65))
% 168.60/168.39 [9938]~P111(x99382)+~P64(x99381)+~P1(f315(f315(f224(f909(x99381,x99382)),x99383),x99384))+P1(f315(f49(x99381),f315(f315(f10(a899,a899,x99381),a310),f315(f315(f20(x99381,x99382,a899),f315(f315(f10(x99382,f909(x99382,a899),x99381),a312),x99383)),x99384))))
% 168.60/168.39 [10059]~P1(f315(f315(f317(f908(a901,a901)),x100594),x100593))+~P1(f315(f315(f317(f908(f908(a901,a901),f908(a901,a901))),f315(f315(f240(f908(a901,a901),f908(a901,a901)),x100591),x100594)),a26))+~P1(f315(f315(f317(f908(f909(f908(a901,a901),a899),f909(f908(a901,a901),a899))),f315(f315(f240(f909(f908(a901,a901),a899),f909(f908(a901,a901),a899)),x100592),x100593)),a27))+P1(f315(f315(f317(f908(f909(f908(a901,a901),a899),f909(f908(a901,a901),a899))),f315(f315(f240(f909(f908(a901,a901),a899),f909(f908(a901,a901),a899)),f315(f315(f297(f908(a901,a901)),x100591),x100592)),x100593)),a27))
% 168.60/168.39 [10060]~P1(f315(f315(f317(f908(a901,a901)),x100604),x100603))+~P1(f315(f315(f317(f908(f908(a901,a901),f908(a901,a901))),f315(f315(f240(f908(a901,a901),f908(a901,a901)),x100601),x100604)),a64))+~P1(f315(f315(f317(f908(f909(f908(a901,a901),a899),f909(f908(a901,a901),a899))),f315(f315(f240(f909(f908(a901,a901),a899),f909(f908(a901,a901),a899)),x100602),x100603)),a63))+P1(f315(f315(f317(f908(f909(f908(a901,a901),a899),f909(f908(a901,a901),a899))),f315(f315(f240(f909(f908(a901,a901),a899),f909(f908(a901,a901),a899)),f315(f315(f297(f908(a901,a901)),x100601),x100602)),x100603)),a63))
% 168.60/168.39 [6138]~P7(x61384,x61381)+~P1(f315(f315(x61381,x61382),x61385))+P1(f315(f315(x61381,x61382),x61383))+~P1(f315(f315(x61381,x61385),x61383))
% 168.60/168.39 [6139]~P51(x61394,x61391)+~P1(f315(f315(x61391,x61392),x61395))+P1(f315(f315(x61391,x61392),x61393))+~P1(f315(f315(x61391,x61395),x61393))
% 168.60/168.39 [6140]~P16(x61404,x61401)+~P1(f315(f315(x61401,x61402),x61405))+P1(f315(f315(x61401,x61402),x61403))+~P1(f315(f315(x61401,x61405),x61403))
% 168.60/168.39 [8865]~P7(x88654,x88653)+~P1(f315(x88651,x88655))+P1(f315(x88652,f816(x88652,x88651,x88653,x88654)))+P1(f315(x88651,f815(x88652,x88651,x88653,x88654)))
% 168.60/168.39 [9100]~P7(x91004,x91003)+~P1(f315(x91002,x91005))+~P1(f315(x91001,f815(x91001,x91002,x91003,x91004)))+P1(f315(x91001,f816(x91001,x91002,x91003,x91004)))
% 168.60/168.39 [9282]~P7(x92824,x92823)+~P1(f315(x92821,x92825))+P1(f315(f315(f317(x92824),f816(x92822,x92821,x92823,x92824)),f258(x92824,x92823)))+P1(f315(x92821,f815(x92822,x92821,x92823,x92824)))
% 168.60/168.39 [9408]~P7(x94081,x94084)+~P1(f315(x94083,x94085))+~P1(f315(x94082,f815(x94082,x94083,x94084,x94081)))+P1(f315(f315(f317(x94081),f816(x94082,x94083,x94084,x94081)),f258(x94081,x94084)))
% 168.60/168.39 [9707]~P40(x97071,x97074)+P1(f315(f315(f317(f908(f902(x97071),f902(x97071))),f315(f315(f240(f902(x97071),f902(x97071)),x97072),x97073)),f136(x97071,x97074)))+~P1(f315(f315(f317(f908(f902(x97071),f902(x97071))),f315(f315(f240(f902(x97071),f902(x97071)),x97072),x97075)),f136(x97071,x97074)))+~P1(f315(f315(f317(f908(f902(x97071),f902(x97071))),f315(f315(f240(f902(x97071),f902(x97071)),x97075),x97073)),f136(x97071,x97074)))
% 168.60/168.39 [5361]~P69(x53615)+E(x53611,x53612)+~E(x53613,x53614)+~E(f315(f315(f3(x53615),x53613),x53614),f315(f315(f3(x53615),x53611),x53612))
% 168.60/168.39 [6255]~P18(x62555,x62551,x62553)+E(f315(f315(x62551,x62552),f315(x62553,x62554)),f315(x62553,x62554))+~P1(f315(f54(x62555),x62554))+~P1(f315(f315(f317(x62555),x62552),x62554))
% 168.60/168.39 [6450]~P82(x64501)+~E(f315(f315(f3(x64501),x64504),x64505),f315(f315(f3(x64501),x64502),x64503))+~P1(f315(f315(f223(x64501),x64504),x64505))+P1(f315(f315(f223(x64501),x64502),x64503))
% 168.60/168.39 [6452]~P82(x64521)+~E(f315(f315(f3(x64521),x64524),x64525),f315(f315(f3(x64521),x64522),x64523))+~P1(f315(f315(f224(x64521),x64524),x64525))+P1(f315(f315(f224(x64521),x64522),x64523))
% 168.60/168.39 [7449]~E(x74492,f315(f315(f140(x74491),x74494),x74495))+P1(f315(f315(f317(f902(x74491)),x74492),f150(x74491,x74493)))+~P1(f315(f315(f317(f902(x74491)),x74495),f150(x74491,x74493)))+~P1(f315(f315(f317(x74491),x74494),x74493))
% 168.60/168.39 [7856]~E(f315(f178(f902(x78561)),x78563),f315(f178(f902(x78562)),x78564))+~E(f315(f315(f143(f908(x78561,x78562),x78562),f244(x78561,x78562)),x78565),x78564)+~E(f315(f315(f143(f908(x78561,x78562),x78561),f239(x78561,x78562)),x78565),x78563)+E(f315(f315(f170(x78561,x78562),x78563),x78564),x78565)
% 168.60/168.39 [8190]~P111(x81901)+P1(f315(f315(f224(f909(x81901,a899)),f291(x81901,x81902,x81903)),f291(x81901,x81904,x81905)))+~P1(f315(f315(f223(x81901),x81904),x81905))+P1(f315(f315(f223(x81901),x81902),x81903))
% 168.60/168.39 [8291]~P111(x82911)+P1(f315(f315(f223(f909(x82911,a899)),f291(x82911,x82912,x82913)),f291(x82911,x82914,x82915)))+~P1(f315(f315(f223(x82911),x82913),x82915))+~P1(f315(f315(f223(x82911),x82914),x82912))
% 168.60/168.39 [8409]~P110(x84091)+P1(f315(f315(f223(x84091),x84092),x84093))+P1(f315(f315(f223(x84091),x84094),x84093))+~P1(f315(f315(f223(f909(x84091,a899)),f315(f290(x84091,x84093),x84092)),f315(f290(x84091,x84094),x84095)))
% 168.60/168.39 [8410]~P110(x84101)+P1(f315(f315(f223(x84101),x84102),x84103))+P1(f315(f315(f223(x84101),x84102),x84104))+~P1(f315(f315(f223(f909(x84101,a899)),f315(f290(x84101,x84103),x84102)),f315(f290(x84101,x84105),x84104)))
% 168.60/168.39 [8643]~P111(x86431)+~P1(f315(f315(f223(f909(x86431,a899)),f291(x86431,x86434,x86432)),f291(x86431,x86435,x86433)))+P1(f315(f315(f223(x86431),x86432),x86433))+~P1(f315(f315(f223(x86431),x86434),x86432))
% 168.60/168.39 [8644]~P111(x86441)+~P1(f315(f315(f224(f909(x86441,a899)),f291(x86441,x86444,x86442)),f291(x86441,x86445,x86443)))+P1(f315(f315(f223(x86441),x86442),x86443))+~P1(f315(f315(f223(x86441),x86444),x86442))
% 168.60/168.39 [8645]~P111(x86451)+~P1(f315(f315(f223(f909(x86451,a899)),f291(x86451,x86453,x86454)),f291(x86451,x86452,x86455)))+P1(f315(f315(f223(x86451),x86452),x86453))+~P1(f315(f315(f223(x86451),x86453),x86454))
% 168.60/168.39 [8646]~P111(x86461)+~P1(f315(f315(f224(f909(x86461,a899)),f291(x86461,x86463,x86464)),f291(x86461,x86462,x86465)))+P1(f315(f315(f223(x86461),x86462),x86463))+~P1(f315(f315(f223(x86461),x86463),x86464))
% 168.60/168.39 [6137]~P18(x61372,x61375,x61373)+E(x61371,f177(f909(x61372,a899)))+~P1(f315(f54(x61372),x61371))+E(f315(x61373,f315(f315(f297(x61372),x61374),x61371)),f315(f315(x61375,x61374),f315(x61373,x61371)))
% 168.60/168.39 [6935]~E(x69351,x69352)+~E(f315(f315(f90(f909(x69353,a899)),x69354),x69355),f177(f909(x69353,a899)))+~P1(f315(f315(f317(x69353),x69352),x69355))+~P1(f315(f315(f317(x69353),x69351),x69354))
% 168.60/168.39 [7016]~P19(x70162,x70165,x70161)+~P1(f315(f54(x70162),x70164))+E(f315(x70161,f315(f315(f297(x70162),x70163),x70164)),f315(f315(f57(x70162,x70162,x70165),x70163),x70164))+P1(f315(f315(f317(x70162),x70163),x70164))
% 168.60/168.39 [7086]~P72(x70862)+~P1(f315(f54(x70861),x70865))+E(f315(f315(f8(x70861,x70862),x70863),f315(f315(f297(x70861),x70864),x70865)),f315(f315(f73(x70862),f315(x70863,x70864)),f315(f315(f8(x70861,x70862),x70863),x70865)))+P1(f315(f315(f317(x70861),x70864),x70865))
% 168.60/168.39 [7088]~P77(x70882)+~P1(f315(f54(x70881),x70885))+E(f315(f315(f11(x70881,x70882),x70883),f315(f315(f297(x70881),x70884),x70885)),f315(f315(f74(x70882),f315(x70883,x70884)),f315(f315(f11(x70881,x70882),x70883),x70885)))+P1(f315(f315(f317(x70881),x70884),x70885))
% 168.60/168.39 [7496]~P121(x74961)+~P1(f315(f54(x74964),x74965))+~P1(f315(f315(f317(x74964),x74963),x74965))+P1(f315(f315(f275(x74961),f315(x74962,x74963)),f315(f315(f11(x74964,x74961),x74962),x74965)))
% 168.60/168.39 [7596]~P19(x75962,x75965,x75961)+~P1(f315(f54(x75962),x75964))+E(f315(x75961,f315(f315(f297(x75962),x75963),x75964)),x75963)+~E(f315(f315(f3(f909(x75962,a899)),x75964),f315(f315(f297(x75962),x75963),f177(f909(x75962,a899)))),f177(f909(x75962,a899)))
% 168.60/168.39 [7928]~P121(x79281)+~P1(f315(f315(f275(x79281),x79282),x79284))+~P1(f315(f315(f223(a901),x79283),x79285))+P1(f315(f315(f275(x79281),f315(f315(f232(x79281),x79282),x79283)),f315(f315(f232(x79281),x79284),x79285)))
% 168.60/168.39 [7956]~P62(x79561)+E(f315(f315(f29(x79561),f315(f315(f74(x79561),x79562),x79563)),f315(f315(f74(x79561),x79564),x79565)),f315(f315(f74(x79561),f315(f315(f29(x79561),x79562),x79564)),f315(f315(f29(x79561),x79563),x79565)))+~P1(f315(f315(f275(x79561),x79565),x79563))+~P1(f315(f315(f275(x79561),x79564),x79562))
% 168.60/168.39 [7960]~P103(x79601)+~P1(f315(f315(f223(x79601),x79603),x79605))+~P1(f315(f315(f223(x79601),x79602),x79604))+P1(f315(f315(f223(x79601),f315(f315(f99(x79601),x79602),x79603)),f315(f315(f99(x79601),x79604),x79605)))
% 168.60/168.39 [7961]~P104(x79611)+~P1(f315(f315(f223(x79611),x79613),x79615))+~P1(f315(f315(f223(x79611),x79612),x79614))+P1(f315(f315(f223(x79611),f315(f315(f90(x79611),x79612),x79613)),f315(f315(f90(x79611),x79614),x79615)))
% 168.60/168.39 [7962]~P88(x79621)+~P1(f315(f315(f223(x79621),x79623),x79625))+~P1(f315(f315(f223(x79621),x79622),x79624))+P1(f315(f315(f223(x79621),f315(f315(f73(x79621),x79622),x79623)),f315(f315(f73(x79621),x79624),x79625)))
% 168.60/168.39 [7963]~P110(x79631)+~P1(f315(f315(f223(x79631),x79633),x79635))+~P1(f315(f315(f223(x79631),x79632),x79634))+P1(f315(f315(f223(x79631),f315(f315(f221(x79631),x79632),x79633)),f315(f315(f221(x79631),x79634),x79635)))
% 168.60/168.39 [7964]~P110(x79641)+~P1(f315(f315(f223(x79641),x79643),x79645))+~P1(f315(f315(f223(x79641),x79642),x79644))+P1(f315(f315(f223(x79641),f315(f315(f222(x79641),x79642),x79643)),f315(f315(f222(x79641),x79644),x79645)))
% 168.60/168.39 [7965]~P86(x79651)+~P1(f315(f315(f223(x79651),x79653),x79655))+~P1(f315(f315(f224(x79651),x79652),x79654))+P1(f315(f315(f224(x79651),f315(f315(f73(x79651),x79652),x79653)),f315(f315(f73(x79651),x79654),x79655)))
% 168.60/168.39 [7966]~P86(x79661)+~P1(f315(f315(f223(x79661),x79662),x79664))+~P1(f315(f315(f224(x79661),x79663),x79665))+P1(f315(f315(f224(x79661),f315(f315(f73(x79661),x79662),x79663)),f315(f315(f73(x79661),x79664),x79665)))
% 168.60/168.39 [7967]~P86(x79671)+~P1(f315(f315(f224(x79671),x79673),x79675))+~P1(f315(f315(f224(x79671),x79672),x79674))+P1(f315(f315(f224(x79671),f315(f315(f73(x79671),x79672),x79673)),f315(f315(f73(x79671),x79674),x79675)))
% 168.60/168.39 [7968]~P121(x79681)+~P1(f315(f315(f275(x79681),x79683),x79685))+~P1(f315(f315(f275(x79681),x79682),x79684))+P1(f315(f315(f275(x79681),f315(f315(f74(x79681),x79682),x79683)),f315(f315(f74(x79681),x79684),x79685)))
% 168.60/168.39 [8105]~P145(x81055)+E(x81051,x81052)+E(x81053,x81054)+~E(f315(f315(f73(x81055),f315(f315(f74(x81055),x81053),x81051)),f315(f315(f74(x81055),x81054),x81052)),f315(f315(f73(x81055),f315(f315(f74(x81055),x81053),x81052)),f315(f315(f74(x81055),x81054),x81051)))
% 168.60/168.39 [8242]P28(x82421,x82422,x82423)+~P29(x82421,x82424,x82425)+~P28(x82421,x82422,f541(x82425,x82424,x82421,x82422))+~P1(f315(f315(f317(f900(x82421)),x82423),x82425))
% 168.60/168.39 [8311]~P110(x83114)+~P1(f315(f126(x83111),x83113))+P1(f315(f315(f317(x83111),x83112),f315(f161(x83111),x83113)))+P1(f315(f126(x83111),f315(f315(f137(x83111,x83114,x83115),x83112),x83113)))
% 168.60/168.39 [8456]~P69(x84561)+E(f315(f315(f3(x84561),f315(f315(f8(a901,x84561),x84562),f315(f290(a901,x84563),x84564))),f315(f315(f8(a901,x84561),x84562),f315(f290(a901,x84563),x84565))),f315(f315(f8(a901,x84561),x84562),f315(f290(a901,x84565),x84564)))+~P1(f315(f315(f223(a901),x84565),x84564))+~P1(f315(f315(f223(a901),x84563),x84565))
% 168.60/168.39 [8457]~P72(x84571)+E(f315(f315(f73(x84571),f315(f315(f8(a901,x84571),x84572),f315(f290(a901,x84573),x84574))),f315(f315(f8(a901,x84571),x84572),f315(f290(a901,x84574),x84575))),f315(f315(f8(a901,x84571),x84572),f315(f290(a901,x84573),x84575)))+~P1(f315(f315(f223(a901),x84574),x84575))+~P1(f315(f315(f223(a901),x84573),x84574))
% 168.60/168.39 [8786]~P66(x87862)+E(x87861,f2(x87862))+E(x87863,f2(x87862))+E(f315(f315(f279(x87862),f315(f315(f3(x87862),f315(f315(f74(x87862),x87864),x87861)),f315(f315(f74(x87862),x87865),x87863))),f315(f315(f74(x87862),x87863),x87861)),f315(f315(f3(x87862),f315(f315(f279(x87862),x87864),x87863)),f315(f315(f279(x87862),x87865),x87861)))
% 168.60/168.39 [8787]~P66(x87872)+E(x87871,f2(x87872))+E(x87873,f2(x87872))+E(f315(f315(f279(x87872),f315(f315(f73(x87872),f315(f315(f74(x87872),x87874),x87871)),f315(f315(f74(x87872),x87875),x87873))),f315(f315(f74(x87872),x87873),x87871)),f315(f315(f73(x87872),f315(f315(f279(x87872),x87874),x87873)),f315(f315(f279(x87872),x87875),x87871)))
% 168.60/168.39 [8796]~E(x87962,f315(x87963,x87961))+E(x87961,f490(x87962,x87963,x87964,x87965))+~P25(x87965,x87964,x87963,f230(f909(x87965,a899)))+~P1(f315(f315(f317(x87964),x87962),f315(f298(x87965,x87964,x87963),f230(f909(x87965,a899)))))
% 168.60/168.39 [9013]~P114(x90131)+~P1(f315(f315(f224(x90131),f315(f69(x90131),x90132)),x90134))+P1(f315(f315(f224(x90131),f315(f315(f74(x90131),f315(f69(x90131),x90132)),f315(f69(x90131),x90133))),f315(f315(f74(x90131),x90134),x90135)))+~P1(f315(f315(f224(x90131),f315(f69(x90131),x90133)),x90135))
% 168.60/168.39 [9031]~P29(x90311,x90315,x90314)+P28(x90311,x90312,x90313)+P1(f315(f315(f317(f900(x90311)),f541(x90314,x90315,x90311,x90312)),x90315))+~P1(f315(f315(f317(f900(x90311)),x90313),x90314))
% 168.60/168.39 [9125]~P25(x91251,x91253,x91255,x91252)+~P1(f315(f54(x91253),x91254))+P1(f315(f315(f223(a901),f315(f28(x91251),x91252)),f315(f28(x91253),x91254)))+~P1(f315(f315(f223(f909(x91253,a899)),f315(f298(x91251,x91253,x91255),x91252)),x91254))
% 168.60/168.39 [9192]~P72(x91922)+~P25(x91921,x91921,x91924,x91925)+~P1(f315(f54(x91921),x91925))+E(f315(f315(f8(x91921,x91922),f315(f66(x91921,x91922,x91921,x91923),x91924)),x91925),f315(f315(f8(x91921,x91922),x91923),f315(f298(x91921,x91921,x91924),x91925)))
% 168.60/168.39 [9193]~P77(x91932)+~P25(x91931,x91931,x91934,x91935)+~P1(f315(f54(x91931),x91935))+E(f315(f315(f11(x91931,x91932),f315(f66(x91931,x91932,x91931,x91933),x91934)),x91935),f315(f315(f11(x91931,x91932),x91933),f315(f298(x91931,x91931,x91934),x91935)))
% 168.60/168.39 [9311]~P39(x93111,x93112)+~P1(f315(f315(f317(x93111),x93113),x93114))+~P1(f315(f315(f317(x93111),x93115),x93114))+~P1(f315(f315(f317(f908(x93111,x93111)),f315(f315(f240(x93111,x93111),x93115),f582(x93112,x93111,x93114))),x93112))
% 168.60/168.39 [9348]~P25(x93482,x93483,x93485,x93481)+E(x93481,f177(f909(x93482,a899)))+E(f315(f298(x93483,x93482,f493(x93484,x93483,x93482,x93481)),x93484),x93481)+~P1(f315(f315(f223(f909(x93483,a899)),f315(f298(x93482,x93483,x93485),x93481)),x93484))
% 168.60/168.39 [9842]~P110(x98425)+~P5(x98425)+P1(f315(f315(f317(x98421),f418(x98422,x98423,x98421,x98424,x98425)),x98423))+~P1(f315(f315(f224(x98425),x98424),f315(f315(f33(x98421,x98425),x98423),x98422)))
% 168.60/168.39 [9847]~P110(x98471)+~P5(x98471)+P1(f315(f315(f224(x98471),x98472),f315(x98473,f418(x98473,x98474,x98475,x98472,x98471))))+~P1(f315(f315(f224(x98471),x98472),f315(f315(f33(x98475,x98471),x98474),x98473)))
% 168.60/168.39 [9925]~P70(x99251)+~P1(f315(f59(x99251,x99251,f74(x99251),x99252,x99253),x99255))+P1(f315(f315(f317(x99251),x99252),x99253))+P1(f315(f59(x99251,x99251,f74(x99251),x99254,f315(f315(f297(x99251),x99252),x99253)),f315(f315(f74(x99251),x99254),x99255)))
% 168.60/168.39 [10137]~P72(x101372)+~P1(f315(f54(x101371),x101375))+E(f315(f315(f8(x101371,x101372),f315(f315(f9(x101371,x101372,x101372),f315(f315(f20(x101371,x101372,f909(x101372,x101372)),f315(f315(f10(a899,f909(x101372,f909(x101372,x101372)),x101371),f85(x101372)),f315(a312,x101373))),x101374)),f2(x101372))),x101375),f2(x101372))+P1(f315(f315(f317(x101371),x101373),x101375))
% 168.60/168.39 [10138]~P77(x101382)+~P1(f315(f54(x101381),x101385))+E(f315(f315(f11(x101381,x101382),f315(f315(f9(x101381,x101382,x101382),f315(f315(f20(x101381,x101382,f909(x101382,x101382)),f315(f315(f10(a899,f909(x101382,f909(x101382,x101382)),x101381),f85(x101382)),f315(a312,x101383))),x101384)),f71(x101382))),x101385),f71(x101382))+P1(f315(f315(f317(x101381),x101383),x101385))
% 168.60/168.39 [10139]~P72(x101392)+~P1(f315(f54(x101391),x101395))+E(f315(f315(f8(x101391,x101392),f315(f315(f9(x101391,x101392,x101392),f315(f315(f20(x101391,x101392,f909(x101392,x101392)),f315(f315(f10(a899,f909(x101392,f909(x101392,x101392)),x101391),f85(x101392)),f315(a312,x101393))),x101394)),f2(x101392))),x101395),f315(x101394,x101393))+~P1(f315(f315(f317(x101391),x101393),x101395))
% 168.60/168.39 [10140]~P77(x101402)+~P1(f315(f54(x101401),x101405))+E(f315(f315(f11(x101401,x101402),f315(f315(f9(x101401,x101402,x101402),f315(f315(f20(x101401,x101402,f909(x101402,x101402)),f315(f315(f10(a899,f909(x101402,f909(x101402,x101402)),x101401),f85(x101402)),f315(a312,x101403))),x101404)),f71(x101402))),x101405),f315(x101404,x101403))+~P1(f315(f315(f317(x101401),x101403),x101405))
% 168.60/168.39 [10197]~P72(x101972)+~P1(f315(f54(x101971),x101975))+E(f315(f315(f8(x101971,x101972),f315(f315(f9(x101971,x101972,x101972),f315(f315(f20(x101971,x101972,f909(x101972,x101972)),f315(f315(f10(a899,f909(x101972,f909(x101972,x101972)),x101971),f85(x101972)),f315(f315(f9(x101971,x101971,a899),a312),x101973))),x101974)),f2(x101972))),x101975),f2(x101972))+P1(f315(f315(f317(x101971),x101973),x101975))
% 168.60/168.39 [10198]~P77(x101982)+~P1(f315(f54(x101981),x101985))+E(f315(f315(f11(x101981,x101982),f315(f315(f9(x101981,x101982,x101982),f315(f315(f20(x101981,x101982,f909(x101982,x101982)),f315(f315(f10(a899,f909(x101982,f909(x101982,x101982)),x101981),f85(x101982)),f315(f315(f9(x101981,x101981,a899),a312),x101983))),x101984)),f71(x101982))),x101985),f71(x101982))+P1(f315(f315(f317(x101981),x101983),x101985))
% 168.60/168.39 [10200]~P72(x102002)+~P1(f315(f54(x102001),x102005))+E(f315(f315(f8(x102001,x102002),f315(f315(f9(x102001,x102002,x102002),f315(f315(f20(x102001,x102002,f909(x102002,x102002)),f315(f315(f10(a899,f909(x102002,f909(x102002,x102002)),x102001),f85(x102002)),f315(f315(f9(x102001,x102001,a899),a312),x102003))),x102004)),f2(x102002))),x102005),f315(x102004,x102003))+~P1(f315(f315(f317(x102001),x102003),x102005))
% 168.60/168.39 [10201]~P77(x102012)+~P1(f315(f54(x102011),x102015))+E(f315(f315(f11(x102011,x102012),f315(f315(f9(x102011,x102012,x102012),f315(f315(f20(x102011,x102012,f909(x102012,x102012)),f315(f315(f10(a899,f909(x102012,f909(x102012,x102012)),x102011),f85(x102012)),f315(f315(f9(x102011,x102011,a899),a312),x102013))),x102014)),f71(x102012))),x102015),f315(x102014,x102013))+~P1(f315(f315(f317(x102011),x102013),x102015))
% 168.60/168.39 [7959]~P69(x79592)+~P1(f315(f54(x79591),x79594))+E(f315(f315(f8(x79591,x79592),x79593),f315(f315(f3(f909(x79591,a899)),x79594),f315(f315(f297(x79591),x79595),f177(f909(x79591,a899))))),f315(f315(f8(x79591,x79592),x79593),x79594))+P1(f315(f315(f317(x79591),x79595),x79594))
% 168.60/168.39 [8464]~P112(x84642)+~P1(f315(f54(x84641),x84644))+E(f315(f315(f8(x84641,x84642),x84643),f315(f315(f3(f909(x84641,a899)),x84644),f315(f315(f297(x84641),x84645),f177(f909(x84641,a899))))),f315(f315(f3(x84642),f315(f315(f8(x84641,x84642),x84643),x84644)),f315(x84643,x84645)))+~P1(f315(f315(f317(x84641),x84645),x84644))
% 168.60/168.39 [8465]~P69(x84652)+~P1(f315(f54(x84651),x84654))+E(f315(f315(f8(x84651,x84652),x84653),f315(f315(f3(f909(x84651,a899)),x84654),f315(f315(f297(x84651),x84655),f177(f909(x84651,a899))))),f315(f315(f3(x84652),f315(f315(f8(x84651,x84652),x84653),x84654)),f315(x84653,x84655)))+~P1(f315(f315(f317(x84651),x84655),x84654))
% 168.60/168.39 [8477]~P121(x84771)+~P1(f315(f315(f223(a901),x84773),x84775))+~P1(f315(f315(f275(x84771),f315(f315(f232(x84771),x84772),x84775)),x84774))+P1(f315(f315(f275(x84771),f315(f315(f232(x84771),x84772),x84773)),x84774))
% 168.60/168.39 [8495]~P69(x84951)+~P1(f315(f54(x84952),x84954))+E(f315(f315(f3(x84951),f315(f315(f8(x84952,x84951),x84953),x84954)),f315(f315(f8(x84952,x84951),x84953),x84955)),f315(f315(f8(x84952,x84951),x84953),f315(f315(f3(f909(x84952,a899)),x84954),x84955)))+~P1(f315(f315(f223(f909(x84952,a899)),x84955),x84954))
% 168.60/168.39 [8514]P1(f315(f54(x85141),f315(x85142,x85143)))+~P1(f315(f54(x85144),x85145))+~P1(f315(f315(f317(x85144),x85143),x85145))+~P1(f315(f54(x85141),f315(f315(f33(x85144,f909(x85141,a899)),x85145),x85142)))
% 168.60/168.39 [8969]~P8(x89691,x89695,x89694)+~E(f315(f273(x89691,x89691,x89694),f315(f315(f297(x89691),x89692),f177(f909(x89691,a899)))),f315(f273(x89691,x89691,x89694),f315(f315(f297(x89691),x89693),f177(f909(x89691,a899)))))+~P1(f315(f315(f317(x89691),x89693),x89695))+P1(f315(f315(f317(f908(x89691,x89691)),f315(f315(f240(x89691,x89691),x89692),x89693)),x89694))
% 168.60/168.39 [9267]~P1(f315(x92671,x92675))+P1(f315(x92671,f889(x92671,x92672,x92673,x92674)))+P1(f315(x92671,f880(x92671,x92672,x92673,x92674)))+~P1(f315(f315(f317(x92674),x92675),f315(f315(f99(f909(x92674,a899)),x92673),x92672)))
% 168.60/168.39 [9455]~P1(f315(x94551,x94555))+P1(f315(x94551,f880(x94551,x94552,x94553,x94554)))+P1(f315(f315(f317(x94554),f889(x94551,x94552,x94553,x94554)),x94552))+~P1(f315(f315(f317(x94554),x94555),f315(f315(f99(f909(x94554,a899)),x94553),x94552)))
% 168.60/168.39 [9456]~P1(f315(x94561,x94565))+P1(f315(x94561,f889(x94561,x94562,x94563,x94564)))+P1(f315(f315(f317(x94564),f880(x94561,x94562,x94563,x94564)),x94563))+~P1(f315(f315(f317(x94564),x94565),f315(f315(f99(f909(x94564,a899)),x94563),x94562)))
% 168.60/168.39 [9460]P1(f315(x94601,x94602))+~P1(f315(x94601,f356(x94601,x94603,x94604,x94605)))+~P1(f315(x94601,f345(x94601,x94603,x94604,x94605)))+~P1(f315(f315(f317(x94605),x94602),f315(f315(f99(f909(x94605,a899)),x94604),x94603)))
% 168.60/168.39 [9465]~P40(x94651,x94654)+~P1(f315(f315(f317(f908(x94651,x94651)),f315(f315(f240(x94651,x94651),x94652),x94655)),x94654))+P1(f315(f315(f317(f908(x94651,x94651)),f315(f315(f240(x94651,x94651),x94652),x94653)),x94654))+~P1(f315(f315(f317(f908(x94651,x94651)),f315(f315(f240(x94651,x94651),x94655),x94653)),x94654))
% 168.60/168.39 [9504]E(x95041,x95042)+~P1(f315(f315(f317(f908(x95043,x95043)),f315(f315(f240(x95043,x95043),x95041),x95042)),f295(x95043,x95045)))+P1(f315(f315(f317(x95043),x95041),x95044))+~P1(f315(f315(f223(f909(f908(x95043,x95043),a899)),x95045),f315(f315(f242(x95043,x95043),x95044),f315(f18(f909(x95043,a899),x95043),x95044))))
% 168.60/168.39 [9522]P1(f315(x95221,x95222))+~P1(f315(x95221,f345(x95221,x95224,x95225,x95223)))+P1(f315(f315(f317(x95223),f356(x95221,x95224,x95225,x95223)),x95224))+~P1(f315(f315(f317(x95223),x95222),f315(f315(f99(f909(x95223,a899)),x95225),x95224)))
% 168.60/168.39 [9523]P1(f315(x95231,x95232))+~P1(f315(x95231,f356(x95231,x95234,x95235,x95233)))+P1(f315(f315(f317(x95233),f345(x95231,x95234,x95235,x95233)),x95235))+~P1(f315(f315(f317(x95233),x95232),f315(f315(f99(f909(x95233,a899)),x95235),x95234)))
% 168.60/168.39 [9591]P1(f315(x95911,x95912))+P1(f315(f315(f317(x95913),f356(x95911,x95914,x95915,x95913)),x95914))+P1(f315(f315(f317(x95913),f345(x95911,x95914,x95915,x95913)),x95915))+~P1(f315(f315(f317(x95913),x95912),f315(f315(f99(f909(x95913,a899)),x95915),x95914)))
% 168.60/168.39 [9593]~P1(f315(x95932,x95935))+P1(f315(f315(f317(x95931),f889(x95932,x95933,x95934,x95931)),x95933))+P1(f315(f315(f317(x95931),f880(x95932,x95933,x95934,x95931)),x95934))+~P1(f315(f315(f317(x95931),x95935),f315(f315(f99(f909(x95931,a899)),x95934),x95933)))
% 168.60/168.39 [9749]~P8(x97491,x97495,x97494)+~P1(f315(f315(f317(x97491),x97493),x97495))+P1(f315(f315(f317(f908(x97491,x97491)),f315(f315(f240(x97491,x97491),x97492),x97493)),x97494))+~P1(f315(f315(f223(f909(x97491,a899)),f315(f273(x97491,x97491,x97494),f315(f315(f297(x97491),x97493),f177(f909(x97491,a899))))),f315(f273(x97491,x97491,x97494),f315(f315(f297(x97491),x97492),f177(f909(x97491,a899))))))
% 168.60/168.39 [9876]~P110(x98765)+~P5(x98765)+P1(f315(f315(f317(x98761),f420(x98762,x98763,x98764,x98761,x98765)),x98764))+~P1(f315(f315(f224(x98765),f315(f315(f32(x98761,x98765),x98764),x98763)),x98762))
% 168.60/168.39 [9908]~P88(x99085)+~P85(x99085)+P1(f315(f315(f317(x99081),f677(x99082,x99083,x99084,x99081,x99085)),f315(f161(x99081),x99084)))+P1(f315(f315(f223(x99085),f315(f154(x99085),f315(f315(f143(x99081,x99085),x99083),x99084))),f315(f154(x99085),f315(f315(f143(x99081,x99085),x99082),x99084))))
% 168.60/168.39 [10016]~P110(x100161)+~P5(x100161)+P1(f315(f315(f224(x100161),f315(x100162,f420(x100163,x100162,x100164,x100165,x100161))),x100163))+~P1(f315(f315(f224(x100161),f315(f315(f32(x100165,x100161),x100164),x100162)),x100163))
% 168.60/168.39 [10155]~P88(x101551)+~P85(x101551)+~P1(f315(f315(f223(x101551),f315(x101553,f677(x101555,x101553,x101554,x101552,x101551))),f315(x101555,f677(x101555,x101553,x101554,x101552,x101551))))+P1(f315(f315(f223(x101551),f315(f154(x101551),f315(f315(f143(x101552,x101551),x101553),x101554))),f315(f154(x101551),f315(f315(f143(x101552,x101551),x101555),x101554))))
% 168.60/168.39 [8809]~P72(x88091)+~P1(f315(f54(x88094),x88095))+~P1(f315(f315(f317(x88094),x88093),x88095))+E(f315(f315(f73(x88091),f315(x88092,x88093)),f315(f315(f8(x88094,x88091),x88092),f315(f315(f3(f909(x88094,a899)),x88095),f315(f315(f297(x88094),x88093),f177(f909(x88094,a899)))))),f315(f315(f8(x88094,x88091),x88092),x88095))
% 168.60/168.39 [8810]~P77(x88101)+~P1(f315(f54(x88104),x88105))+~P1(f315(f315(f317(x88104),x88103),x88105))+E(f315(f315(f74(x88101),f315(x88102,x88103)),f315(f315(f11(x88104,x88101),x88102),f315(f315(f3(f909(x88104,a899)),x88105),f315(f315(f297(x88104),x88103),f177(f909(x88104,a899)))))),f315(f315(f11(x88104,x88101),x88102),x88105))
% 168.60/168.39 [8870]~P19(x88701,x88704,x88705)+~P1(f315(f54(x88701),x88702))+E(f315(f315(f3(f909(x88701,a899)),x88702),f315(f315(f297(x88701),x88703),f177(f909(x88701,a899)))),f177(f909(x88701,a899)))+E(f315(f315(x88704,x88703),f315(x88705,f315(f315(f3(f909(x88701,a899)),x88702),f315(f315(f297(x88701),x88703),f177(f909(x88701,a899)))))),f315(x88705,f315(f315(f297(x88701),x88703),x88702)))
% 168.60/168.39 [9246]~P77(x92461)+~P1(f315(f54(x92462),x92465))+~P1(f315(f54(x92462),x92464))+E(f315(f315(f74(x92461),f315(f315(f11(x92462,x92461),x92463),f315(f315(f99(f909(x92462,a899)),x92464),x92465))),f315(f315(f11(x92462,x92461),x92463),f315(f315(f90(f909(x92462,a899)),x92464),x92465))),f315(f315(f74(x92461),f315(f315(f11(x92462,x92461),x92463),x92464)),f315(f315(f11(x92462,x92461),x92463),x92465)))
% 168.60/168.39 [9247]~P72(x92471)+~P1(f315(f54(x92472),x92475))+~P1(f315(f54(x92472),x92474))+E(f315(f315(f73(x92471),f315(f315(f8(x92472,x92471),x92473),f315(f315(f99(f909(x92472,a899)),x92474),x92475))),f315(f315(f8(x92472,x92471),x92473),f315(f315(f90(f909(x92472,a899)),x92474),x92475))),f315(f315(f73(x92471),f315(f315(f8(x92472,x92471),x92473),x92474)),f315(f315(f8(x92472,x92471),x92473),x92475)))
% 168.60/168.39 [9388]~P69(x93881)+~P1(f315(f54(x93882),x93885))+~P1(f315(f54(x93882),x93884))+E(f315(f315(f3(x93881),f315(f315(f73(x93881),f315(f315(f8(x93882,x93881),x93883),x93884)),f315(f315(f8(x93882,x93881),x93883),x93885))),f315(f315(f8(x93882,x93881),x93883),f315(f315(f90(f909(x93882,a899)),x93884),x93885))),f315(f315(f8(x93882,x93881),x93883),f315(f315(f99(f909(x93882,a899)),x93884),x93885)))
% 168.60/168.39 [9607]~P25(x96071,x96072,x96073,x96075)+~P25(x96071,x96072,x96073,x96074)+P25(x96071,x96072,x96073,f315(f315(f99(f909(x96071,a899)),x96074),x96075))+~E(f315(f315(f90(f909(x96072,a899)),f315(f298(x96071,x96072,x96073),f315(f315(f3(f909(x96071,a899)),x96074),x96075))),f315(f298(x96071,x96072,x96073),f315(f315(f3(f909(x96071,a899)),x96075),x96074))),f177(f909(x96072,a899)))
% 168.60/168.39 [9724]E(x97241,f2(a1))+~P1(f315(f315(f224(a1),f2(a1)),x97243))+~P1(f315(f42(x97242,x97241),f315(f315(f240(a1,a1),x97244),x97245)))+P1(f315(f42(x97242,f315(f315(f74(a1),x97241),x97243)),f315(f315(f240(a1,a1),f315(f315(f29(a1),x97244),x97243)),f315(f315(f73(a1),f315(f315(f74(a1),x97241),f38(a1,x97244,x97243))),x97245))))
% 168.60/168.39 [9732]~P1(f315(f315(f224(a901),f2(a901)),x97323))+~P1(f315(f315(f224(a901),f2(a901)),x97322))+~P1(f315(f41(x97321,x97322),f315(f315(f240(a901,a901),x97324),x97325)))+P1(f315(f41(x97321,f315(f315(f74(a901),x97322),x97323)),f315(f315(f240(a901,a901),f315(f315(f29(a901),x97324),x97323)),f315(f315(f73(a901),f315(f315(f74(a901),x97322),f38(a901,x97324,x97323))),x97325))))
% 168.60/168.39 [9781]~P77(x97811)+~P1(f315(f54(x97812),x97815))+~P1(f315(f54(x97812),x97814))+E(f315(f315(f74(x97811),f315(f315(f315(f58(x97811,x97812,f74(x97811)),x97813),f71(x97811)),f315(f315(f99(f909(x97812,a899)),x97814),x97815))),f315(f315(f315(f58(x97811,x97812,f74(x97811)),x97813),f71(x97811)),f315(f315(f90(f909(x97812,a899)),x97814),x97815))),f315(f315(f74(x97811),f315(f315(f315(f58(x97811,x97812,f74(x97811)),x97813),f71(x97811)),x97814)),f315(f315(f315(f58(x97811,x97812,f74(x97811)),x97813),f71(x97811)),x97815)))
% 168.60/168.39 [9783]~E(f315(f315(f164(x97831),x97835),x97832),f315(f315(f164(x97831),x97835),x97833))+P1(f315(f315(f317(f908(f902(x97831),f902(x97831))),f315(f315(f240(f902(x97831),f902(x97831)),x97832),x97833)),f136(x97831,x97834)))+~P1(f315(f315(f224(a901),x97835),f315(f315(f221(a901),f315(f178(f902(x97831)),x97832)),f315(f178(f902(x97831)),x97833))))+~P1(f315(f315(f317(f908(x97831,x97831)),f315(f315(f240(x97831,x97831),f315(f315(f153(x97831),x97832),x97835)),f315(f315(f153(x97831),x97833),x97835))),x97834))
% 168.60/168.39 [9897]~P88(x98975)+~P147(x98975)+P1(f315(f315(f317(x98971),f335(x98972,x98973,x98974,x98971,x98975)),x98974))+P1(f315(f315(f223(x98975),f315(f315(f8(x98971,x98975),x98973),x98974)),f315(f315(f74(x98975),f315(f89(x98975),f315(f28(x98971),x98974))),x98972)))
% 168.60/168.39 [10073]~P88(x100731)+~P147(x100731)+~P1(f315(f315(f223(x100731),f315(x100733,f335(x100735,x100733,x100734,x100732,x100731))),x100735))+P1(f315(f315(f223(x100731),f315(f315(f8(x100732,x100731),x100733),x100734)),f315(f315(f74(x100731),f315(f89(x100731),f315(f28(x100732),x100734))),x100735)))
% 168.60/168.39 [8838]E(f315(f315(f123(x88381),x88382),x88383),f315(f315(f123(x88381),x88384),x88385))+~E(f315(f315(f164(x88381),f315(f178(f902(x88381)),x88382)),x88384),x88382)+~E(f315(f315(f123(x88381),f315(f315(f127(x88381),f315(f178(f902(x88381)),x88382)),x88384)),x88385),x88383)+P1(f315(f315(f223(a901),f315(f178(f902(x88381)),x88384)),f315(f178(f902(x88381)),x88382)))
% 168.60/168.39 [8968]E(f315(f315(f123(x89681),x89682),x89683),f315(f315(f123(x89681),x89684),x89685))+~E(f315(f315(f164(x89681),f315(f178(f902(x89681)),x89682)),x89684),x89682)+~E(x89683,f315(f315(f123(x89681),f315(f315(f127(x89681),f315(f178(f902(x89681)),x89682)),x89684)),x89685))+~P1(f315(f315(f223(a901),f315(f178(f902(x89681)),x89682)),f315(f178(f902(x89681)),x89684)))
% 168.60/168.40 [10218]~P1(f315(x102185,x102184))+~P1(f315(f54(x102182),f315(f250(x102182),x102185)))+P1(f315(f54(x102181),f315(f250(x102181),f315(f315(f9(x102181,x102182,a899),x102183),x102184))))+~P1(f315(f54(x102181),f315(f250(x102181),f315(f315(f10(f909(x102182,a899),a899,x102181),f80(x102182)),f315(f315(f10(f909(x102182,a899),f909(x102182,a899),x102181),f315(f20(x102182,a899,a899),f315(f315(f10(a899,f909(a899,a899),x102182),a313),x102185))),x102183)))))
% 168.60/168.40 [10294]~P1(f315(f54(x102942),x102945))+~P1(f315(f315(f317(x102942),x102944),x102945))+P1(f315(f54(x102941),f315(f250(x102941),f315(f315(f9(x102941,x102942,a899),x102943),x102944))))+~P1(f315(f54(x102941),f315(f250(x102941),f315(f315(f10(f909(x102942,a899),a899,x102941),f80(x102942)),f315(f315(f10(f909(x102942,a899),f909(x102942,a899),x102941),f315(f20(x102942,a899,a899),f315(f315(f10(a899,f909(a899,a899),x102942),a313),f315(f315(f9(x102942,f909(x102942,a899),a899),f317(x102942)),x102945)))),x102943)))))
% 168.60/168.40 [8624]~P20(x86245,x86241,x86246,x86242)+E(f315(f66(x86241,x86241,x86241,f315(x86242,x86243)),f315(x86242,x86244)),f315(f66(x86241,x86241,x86241,f315(x86242,x86244)),f315(x86242,x86243)))+~P1(f315(f54(x86245),x86244))+~P1(f315(f54(x86245),x86243))
% 168.60/168.40 [8015]~P25(x80151,x80152,x80154,x80153)+~E(f315(x80154,x80156),x80155)+E(f315(f70(x80151,x80152,x80153,x80154),x80155),x80156)+~P1(f315(f315(f317(x80151),x80156),x80153))
% 168.60/168.40 [8016]~P25(x80161,x80162,x80164,x80163)+~E(f315(x80164,x80166),x80165)+E(f315(f84(x80161,x80162,x80163,x80164),x80165),x80166)+~P1(f315(f315(f317(x80161),x80166),x80163))
% 168.60/168.40 [8211]~P21(x82116,x82111,x82114,x82112)+E(f315(f66(x82111,x82111,x82111,f315(x82112,x82113)),f315(x82114,x82115)),f315(x82112,x82113))+~P1(f315(f54(x82116),x82113))+~P1(f315(f315(f317(x82116),x82115),x82113))
% 168.60/168.40 [9339]E(x93391,x93392)+~E(f315(f84(x93393,x93394,x93395,x93396),x93391),f315(f84(x93393,x93394,x93395,x93396),x93392))+~P1(f315(f315(f317(x93394),x93392),f315(f298(x93393,x93394,x93396),x93395)))+~P1(f315(f315(f317(x93394),x93391),f315(f298(x93393,x93394,x93396),x93395)))
% 168.60/168.40 [9439]~P20(x94393,x94391,x94396,x94392)+E(f315(f66(x94391,x94391,x94391,f315(x94392,f315(f315(f3(f909(x94393,a899)),x94394),f315(f315(f297(x94393),x94395),f177(f909(x94393,a899)))))),f315(x94396,x94395)),f315(x94392,x94394))+~P1(f315(f54(x94393),x94394))+~P1(f315(f315(f317(x94393),x94395),x94394))
% 168.60/168.40 [7093]~P63(x70931)+~E(f38(x70931,x70933,x70934),f38(x70931,x70936,x70934))+~E(f38(x70931,x70932,x70934),f38(x70931,x70935,x70934))+E(f38(x70931,f315(f315(f3(x70931),x70932),x70933),x70934),f38(x70931,f315(f315(f3(x70931),x70935),x70936),x70934))
% 168.60/168.40 [7094]~P62(x70941)+~E(f38(x70941,x70943,x70944),f38(x70941,x70946,x70944))+~E(f38(x70941,x70942,x70944),f38(x70941,x70945,x70944))+E(f38(x70941,f315(f315(f74(x70941),x70942),x70943),x70944),f38(x70941,f315(f315(f74(x70941),x70945),x70946),x70944))
% 168.60/168.40 [7095]~P62(x70951)+~E(f38(x70951,x70953,x70954),f38(x70951,x70956,x70954))+~E(f38(x70951,x70952,x70954),f38(x70951,x70955,x70954))+E(f38(x70951,f315(f315(f73(x70951),x70952),x70953),x70954),f38(x70951,f315(f315(f73(x70951),x70955),x70956),x70954))
% 168.60/168.40 [7910]~P17(x79101,x79102,x79103)+~P1(f315(f54(x79101),x79106))+E(f315(f315(f57(x79101,x79102,x79103),x79104),f315(f315(f297(x79101),x79105),x79106)),f315(f315(f57(x79101,x79102,x79103),f315(f315(x79103,x79105),x79104)),x79106))+P1(f315(f315(f317(x79101),x79105),x79106))
% 168.60/168.40 [7974]~P5(x79741)+P1(f315(f315(f223(x79741),x79742),f315(x79743,x79744)))+~P1(f315(f315(f317(x79745),x79744),x79746))+~P1(f315(f315(f223(x79741),x79742),f315(f315(f32(x79745,x79741),x79746),x79743)))
% 168.60/168.40 [8132]~P17(x81321,x81322,x81323)+~P1(f315(f54(x81321),x81326))+E(f315(f315(f57(x81321,x81322,x81323),x81324),f315(f315(f297(x81321),x81325),x81326)),f315(f315(x81323,x81325),f315(f315(f57(x81321,x81322,x81323),x81324),x81326)))+P1(f315(f315(f317(x81321),x81325),x81326))
% 168.60/168.40 [8229]~P110(x82293)+~P1(f315(x82292,x82295))+~P13(x82293,f315(f315(f143(x82291,x82293),x82294),x82296))+E(f315(f125(x82291,x82292),f315(f315(f137(x82291,x82293,x82294),x82295),x82296)),f315(f315(f137(x82291,x82293,x82294),x82295),f315(f125(x82291,x82292),x82296)))
% 168.60/168.40 [8253]E(x82531,x82532)+E(x82533,f2(a1))+~P1(f315(f42(x82534,x82533),f315(f315(f240(a1,a1),x82535),x82532)))+~P1(f315(f42(x82534,x82533),f315(f315(f240(a1,a1),x82536),x82531)))
% 168.60/168.40 [8254]E(x82541,x82542)+E(x82543,f2(a1))+~P1(f315(f42(x82544,x82543),f315(f315(f240(a1,a1),x82542),x82545)))+~P1(f315(f42(x82544,x82543),f315(f315(f240(a1,a1),x82541),x82546)))
% 168.60/168.40 [8277]~P20(x82772,x82775,x82776,x82771)+~P1(f315(f54(x82772),x82774))+E(f315(x82771,f315(f315(f297(x82772),x82773),x82774)),f315(f66(x82775,x82775,x82775,f315(x82771,x82774)),f315(x82776,x82773)))+P1(f315(f315(f317(x82772),x82773),x82774))
% 168.60/168.40 [8498]~P21(x84985,x84981,x84986,x84982)+E(f315(f66(x84981,x84981,x84981,f315(x84982,x84983)),f315(x84982,x84984)),f315(x84982,x84983))+~P1(f315(f54(x84985),x84983))+~P1(f315(f315(f223(f909(x84985,a899)),x84984),x84983))
% 168.60/168.40 [9654]~P25(x96541,x96542,x96544,x96543)+~P1(f315(f315(f317(x96542),x96545),f315(f298(x96541,x96542,x96544),x96543)))+P1(f315(f315(f317(x96541),f315(f70(x96541,x96542,x96543,x96544),x96545)),x96546))+~P1(f315(f315(f223(f909(x96541,a899)),x96543),x96546))
% 168.60/168.40 [10027]~P72(x100272)+~E(f576(x100271,x100273,x100275,x100276,x100274,x100272),f577(x100271,x100273,x100275,x100276,x100274,x100272))+~P1(f315(f54(x100274),x100276))+E(f315(f315(f8(x100271,x100272),x100273),f315(f298(x100274,x100271,x100275),x100276)),f315(f315(f8(x100274,x100272),f315(f66(x100271,x100272,x100274,x100273),x100275)),x100276))
% 168.60/168.40 [10055]~P72(x100556)+E(f315(x100551,f576(x100552,x100553,x100551,x100554,x100555,x100556)),f315(x100551,f577(x100552,x100553,x100551,x100554,x100555,x100556)))+E(f315(f315(f8(x100552,x100556),x100553),f315(f298(x100555,x100552,x100551),x100554)),f315(f315(f8(x100555,x100556),f315(f66(x100552,x100556,x100555,x100553),x100551)),x100554))+~P1(f315(f54(x100555),x100554))
% 168.60/168.40 [10105]~P72(x101052)+~E(f315(x101053,f315(x101055,f577(x101051,x101053,x101055,x101056,x101054,x101052))),f2(x101052))+~P1(f315(f54(x101054),x101056))+E(f315(f315(f8(x101051,x101052),x101053),f315(f298(x101054,x101051,x101055),x101056)),f315(f315(f8(x101054,x101052),f315(f66(x101051,x101052,x101054,x101053),x101055)),x101056))
% 168.60/168.40 [10163]~P72(x101632)+~P1(f315(f54(x101634),x101636))+E(f315(f315(f8(x101631,x101632),x101633),f315(f298(x101634,x101631,x101635),x101636)),f315(f315(f8(x101634,x101632),f315(f66(x101631,x101632,x101634,x101633),x101635)),x101636))+P1(f315(f315(f317(x101634),f577(x101631,x101633,x101635,x101636,x101634,x101632)),x101636))
% 168.60/168.40 [10164]~P72(x101642)+~P1(f315(f54(x101644),x101646))+E(f315(f315(f8(x101641,x101642),x101643),f315(f298(x101644,x101641,x101645),x101646)),f315(f315(f8(x101644,x101642),f315(f66(x101641,x101642,x101644,x101643),x101645)),x101646))+P1(f315(f315(f317(x101644),f576(x101641,x101643,x101645,x101646,x101644,x101642)),x101646))
% 168.60/168.40 [10293]~P77(x102931)+~P1(f315(f54(x102932),x102936))+E(f315(f315(f315(f58(x102931,x102932,f74(x102931)),f315(f315(f20(x102932,f909(x102933,a899),x102931),f315(f315(f9(x102932,x102931,f909(f909(x102933,a899),x102931)),f315(f315(f10(f909(x102933,x102931),f909(x102931,f909(f909(x102933,a899),x102931)),x102932),f58(x102931,x102933,f74(x102931))),x102934)),f71(x102931))),x102935)),f71(x102931)),x102936),f315(f315(f315(f58(x102931,f908(x102932,x102933),f74(x102931)),f315(f245(x102932,x102933,x102931),x102934)),f71(x102931)),f315(f315(f242(x102932,x102933),x102936),x102935)))+P1(f315(f315(f317(x102932),f531(x102934,x102935,x102933,x102936,x102932,x102931)),x102936))
% 168.60/168.40 [10315]~P77(x103151)+~P1(f315(f54(x103152),x103156))+E(f315(f315(f315(f58(x103151,x103152,f74(x103151)),f315(f315(f20(x103152,f909(x103153,a899),x103151),f315(f315(f9(x103152,x103151,f909(f909(x103153,a899),x103151)),f315(f315(f10(f909(x103153,x103151),f909(x103151,f909(f909(x103153,a899),x103151)),x103152),f58(x103151,x103153,f74(x103151))),x103154)),f71(x103151))),x103155)),f71(x103151)),x103156),f315(f315(f315(f58(x103151,f908(x103152,x103153),f74(x103151)),f315(f245(x103152,x103153,x103151),x103154)),f71(x103151)),f315(f315(f242(x103152,x103153),x103156),x103155)))+~P1(f315(f54(x103153),f315(x103155,f531(x103154,x103155,x103153,x103156,x103152,x103151))))
% 168.60/168.40 [8408]~P21(x84082,x84085,x84086,x84081)+~P1(f315(f54(x84082),x84084))+~P1(f315(f54(x84082),x84083))+E(f315(x84081,f315(f315(f99(f909(x84082,a899)),x84083),x84084)),f315(f66(x84085,x84085,x84085,f315(x84081,x84083)),f315(x84081,x84084)))
% 168.60/168.40 [8625]~P5(x86251)+P1(f315(f315(f223(x86251),f315(x86252,x86253)),x86254))+~P1(f315(f315(f317(x86255),x86253),x86256))+~P1(f315(f315(f223(x86251),f315(f315(f33(x86255,x86251),x86256),x86252)),x86254))
% 168.60/168.40 [9055]~P25(x90552,x90551,x90553,x90556)+E(f315(f315(f3(f909(x90551,a899)),f315(f298(x90552,x90551,x90553),x90554)),f315(f298(x90552,x90551,x90553),x90555)),f315(f298(x90552,x90551,x90553),f315(f315(f3(f909(x90552,a899)),x90554),x90555)))+~P1(f315(f315(f223(f909(x90552,a899)),x90555),x90556))+~P1(f315(f315(f223(f909(x90552,a899)),x90554),x90556))
% 168.60/168.40 [9056]~P25(x90562,x90561,x90563,x90566)+E(f315(f315(f90(f909(x90561,a899)),f315(f298(x90562,x90561,x90563),x90564)),f315(f298(x90562,x90561,x90563),x90565)),f315(f298(x90562,x90561,x90563),f315(f315(f90(f909(x90562,a899)),x90564),x90565)))+~P1(f315(f315(f223(f909(x90562,a899)),x90565),x90566))+~P1(f315(f315(f223(f909(x90562,a899)),x90564),x90566))
% 168.60/168.40 [9313]E(x93131,x93132)+~P56(x93133,x93134,x93135)+~P1(f315(f315(f317(f908(x93133,x93134)),f315(f315(f240(x93133,x93134),x93136),x93132)),x93135))+~P1(f315(f315(f317(f908(x93133,x93134)),f315(f315(f240(x93133,x93134),x93136),x93131)),x93135))
% 168.60/168.40 [10101]~P70(x101011)+~E(f315(x101013,f885(x101014,x101016,x101013,x101015,x101012,x101011)),f315(x101016,f885(x101014,x101016,x101013,x101015,x101012,x101011)))+~P1(f315(f54(x101012),x101015))+E(f315(f315(f315(f58(x101011,x101012,f74(x101011)),x101013),x101014),x101015),f315(f315(f315(f58(x101011,x101012,f74(x101011)),x101016),x101014),x101015))
% 168.60/168.40 [10161]~P70(x101611)+~P1(f315(f54(x101612),x101615))+E(f315(f315(f315(f58(x101611,x101612,f74(x101611)),x101613),x101614),x101615),f315(f315(f315(f58(x101611,x101612,f74(x101611)),x101616),x101614),x101615))+P1(f315(f315(f317(x101612),f885(x101614,x101613,x101616,x101615,x101612,x101611)),x101615))
% 168.60/168.40 [8852]~P70(x88521)+~P1(f315(f54(x88522),x88526))+P1(f315(f315(f317(x88522),x88525),x88526))+E(f315(f315(f315(f58(x88521,x88522,f74(x88521)),x88523),x88524),f315(f315(f297(x88522),x88525),x88526)),f315(f315(f74(x88521),f315(x88523,x88525)),f315(f315(f315(f58(x88521,x88522,f74(x88521)),x88523),x88524),x88526)))
% 168.60/168.40 [8905]~P8(x89051,x89056,x89053)+~P11(x89051,f909(x89052,a899),x89053,x89055)+~P1(f315(f315(f317(x89051),x89054),x89056))+E(f315(f315(f33(x89051,f909(x89052,a899)),f315(f273(x89051,x89051,x89053),f315(f315(f297(x89051),x89054),f177(f909(x89051,a899))))),x89055),f315(x89055,x89054))
% 168.60/168.40 [9032]~P17(x90323,x90324,x90321)+~P1(f315(f54(x90323),x90326))+~P1(f315(f315(f317(x90323),x90322),x90326))+E(f315(f315(x90321,x90322),f315(f315(f57(x90323,x90324,x90321),x90325),f315(f315(f3(f909(x90323,a899)),x90326),f315(f315(f297(x90323),x90322),f177(f909(x90323,a899)))))),f315(f315(f57(x90323,x90324,x90321),x90325),x90326))
% 168.60/168.40 [9323]~P20(x93233,x93231,x93236,x93232)+~P1(f315(f54(x93233),x93235))+~P1(f315(f54(x93233),x93234))+E(f315(f66(x93231,x93231,x93231,f315(x93232,f315(f315(f99(f909(x93233,a899)),x93234),x93235))),f315(x93232,f315(f315(f90(f909(x93233,a899)),x93234),x93235))),f315(f66(x93231,x93231,x93231,f315(x93232,x93234)),f315(x93232,x93235)))
% 168.60/168.40 [9677]~E(x96773,f315(f315(f148(x96771,x96772),x96775),x96776))+P1(f315(f315(f317(f908(f902(x96771),f902(x96771))),f315(f315(f240(f902(x96771),f902(x96771)),x96772),x96773)),f146(x96771,x96774)))+~P1(f315(f315(f224(a901),x96775),f315(f178(f902(x96771)),x96772)))+~P1(f315(f315(f317(f908(x96771,x96771)),f315(f315(f240(x96771,x96771),f315(f315(f153(x96771),x96772),x96775)),x96776)),x96774))
% 168.60/168.40 [10177]~P72(x101772)+~P1(f315(f54(x101771),x101776))+P1(f315(f315(f317(x101771),f532(x101774,x101775,x101773,x101776,x101771,x101772)),x101776))+E(f315(f315(f8(x101771,x101772),f315(f315(f20(x101771,f909(x101773,a899),x101772),f315(f315(f10(f909(x101773,x101772),f909(f909(x101773,a899),x101772),x101771),f8(x101773,x101772)),x101774)),x101775)),x101776),f315(f315(f8(f908(x101771,x101773),x101772),f315(f245(x101771,x101773,x101772),x101774)),f315(f315(f242(x101771,x101773),x101776),x101775)))
% 168.60/168.40 [10178]~P77(x101782)+~P1(f315(f54(x101781),x101786))+P1(f315(f315(f317(x101781),f530(x101784,x101785,x101783,x101786,x101781,x101782)),x101786))+E(f315(f315(f11(x101781,x101782),f315(f315(f20(x101781,f909(x101783,a899),x101782),f315(f315(f10(f909(x101783,x101782),f909(f909(x101783,a899),x101782),x101781),f11(x101783,x101782)),x101784)),x101785)),x101786),f315(f315(f11(f908(x101781,x101783),x101782),f315(f245(x101781,x101783,x101782),x101784)),f315(f315(f242(x101781,x101783),x101786),x101785)))
% 168.60/168.40 [10216]~P72(x102162)+~P1(f315(f54(x102161),x102166))+~P1(f315(f54(x102163),f315(x102165,f532(x102164,x102165,x102163,x102166,x102161,x102162))))+E(f315(f315(f8(x102161,x102162),f315(f315(f20(x102161,f909(x102163,a899),x102162),f315(f315(f10(f909(x102163,x102162),f909(f909(x102163,a899),x102162),x102161),f8(x102163,x102162)),x102164)),x102165)),x102166),f315(f315(f8(f908(x102161,x102163),x102162),f315(f245(x102161,x102163,x102162),x102164)),f315(f315(f242(x102161,x102163),x102166),x102165)))
% 168.60/168.40 [10217]~P77(x102172)+~P1(f315(f54(x102171),x102176))+~P1(f315(f54(x102173),f315(x102175,f530(x102174,x102175,x102173,x102176,x102171,x102172))))+E(f315(f315(f11(x102171,x102172),f315(f315(f20(x102171,f909(x102173,a899),x102172),f315(f315(f10(f909(x102173,x102172),f909(f909(x102173,a899),x102172),x102171),f11(x102173,x102172)),x102174)),x102175)),x102176),f315(f315(f11(f908(x102171,x102173),x102172),f315(f245(x102171,x102173,x102172),x102174)),f315(f315(f242(x102171,x102173),x102176),x102175)))
% 168.60/168.40 [10199]~P77(x101992)+~P1(f315(f54(x101991),x101996))+P1(f315(f315(f317(x101991),x101993),x101996))+E(f315(f315(f11(x101991,x101992),f315(f315(f9(x101991,x101992,x101992),f315(f315(f20(x101991,x101992,f909(x101992,x101992)),f315(f315(f10(a899,f909(x101992,f909(x101992,x101992)),x101991),f85(x101992)),f315(f315(f9(x101991,x101991,a899),a312),x101993))),x101994)),x101995)),x101996),f315(f315(f232(x101992),x101995),f315(f28(x101991),x101996)))
% 168.60/168.40 [10202]~P77(x102022)+~P1(f315(f54(x102021),x102026))+~P1(f315(f315(f317(x102021),x102023),x102026))+E(f315(f315(f11(x102021,x102022),f315(f315(f9(x102021,x102022,x102022),f315(f315(f20(x102021,x102022,f909(x102022,x102022)),f315(f315(f10(a899,f909(x102022,f909(x102022,x102022)),x102021),f85(x102022)),f315(f315(f9(x102021,x102021,a899),a312),x102023))),x102024)),x102025)),x102026),f315(f315(f74(x102022),f315(x102024,x102023)),f315(f315(f232(x102022),x102025),f315(f315(f3(a901),f315(f28(x102021),x102026)),f71(a901)))))
% 168.60/168.40 [10280]~P1(f315(f54(x102801),x102805))+~P1(f315(f54(x102802),x102803))+P1(f315(f315(f317(x102802),f543(x102806,x102804,x102803,x102802,x102805,x102801)),x102803))+E(f315(f315(f8(x102801,a901),f315(f315(f10(f909(x102802,a899),a901,x102801),f28(x102802)),f315(f315(f10(f909(x102802,a899),f909(x102802,a899),x102801),f250(x102802)),f315(f315(f10(f909(x102802,a899),f909(x102802,a899),x102801),f315(f20(x102802,a899,a899),f315(f315(f10(a899,f909(a899,a899),x102802),a313),f315(f315(f9(x102802,f909(x102802,a899),a899),f317(x102802)),x102803)))),x102804)))),x102805),f315(f315(f74(a901),x102806),f315(f28(x102802),x102803)))
% 168.60/168.40 [10281]~P1(f315(f54(x102811),x102815))+~P1(f315(f54(x102812),x102813))+P1(f315(f315(f317(x102812),f547(x102816,x102814,x102813,x102812,x102815,x102811)),x102813))+E(f315(f315(f8(x102811,a901),f315(f315(f10(f909(x102812,a899),a901,x102811),f28(x102812)),f315(f315(f10(f909(x102812,a899),f909(x102812,a899),x102811),f250(x102812)),f315(f315(f10(f909(x102812,a899),f909(x102812,a899),x102811),f315(f20(x102812,a899,a899),f315(f315(f10(a899,f909(a899,a899),x102812),a313),f315(f315(f9(x102812,f909(x102812,a899),a899),f317(x102812)),x102813)))),x102814)))),x102815),f315(f315(f8(x102812,a901),x102816),x102813))
% 168.60/168.40 [10328]~P1(f315(f54(x103282),x103283))+~P1(f315(f54(x103281),x103285))+~E(f315(f28(x103281),f315(f250(x103281),f315(f315(f20(x103281,a899,a899),f315(f315(f10(a899,f909(a899,a899),x103281),a313),f315(f315(f9(x103281,f909(x103281,a899),a899),f317(x103281)),x103285))),f315(f315(f9(x103281,x103282,a899),x103284),f543(x103286,x103284,x103283,x103282,x103285,x103281))))),x103286)+E(f315(f315(f8(x103281,a901),f315(f315(f10(f909(x103282,a899),a901,x103281),f28(x103282)),f315(f315(f10(f909(x103282,a899),f909(x103282,a899),x103281),f250(x103282)),f315(f315(f10(f909(x103282,a899),f909(x103282,a899),x103281),f315(f20(x103282,a899,a899),f315(f315(f10(a899,f909(a899,a899),x103282),a313),f315(f315(f9(x103282,f909(x103282,a899),a899),f317(x103282)),x103283)))),x103284)))),x103285),f315(f315(f74(a901),x103286),f315(f28(x103282),x103283)))
% 168.60/168.40 [10330]~P1(f315(f54(x103302),x103303))+~P1(f315(f54(x103301),x103305))+~E(f315(f28(x103301),f315(f250(x103301),f315(f315(f20(x103301,a899,a899),f315(f315(f10(a899,f909(a899,a899),x103301),a313),f315(f315(f9(x103301,f909(x103301,a899),a899),f317(x103301)),x103305))),f315(f315(f9(x103301,x103302,a899),x103304),f547(x103306,x103304,x103303,x103302,x103305,x103301))))),f315(x103306,f547(x103306,x103304,x103303,x103302,x103305,x103301)))+E(f315(f315(f8(x103301,a901),f315(f315(f10(f909(x103302,a899),a901,x103301),f28(x103302)),f315(f315(f10(f909(x103302,a899),f909(x103302,a899),x103301),f250(x103302)),f315(f315(f10(f909(x103302,a899),f909(x103302,a899),x103301),f315(f20(x103302,a899,a899),f315(f315(f10(a899,f909(a899,a899),x103302),a313),f315(f315(f9(x103302,f909(x103302,a899),a899),f317(x103302)),x103303)))),x103304)))),x103305),f315(f315(f8(x103302,a901),x103306),x103303))
% 168.60/168.40 [9953]E(x99531,x99532)+~P17(x99533,x99534,x99535)+~P1(f315(f59(x99533,x99534,x99535,x99536,x99537),x99532))+~P1(f315(f59(x99533,x99534,x99535,x99536,x99537),x99531))
% 168.60/168.40 [9753]P1(f315(x97531,x97532))+~P1(f315(f315(f317(x97537),x97532),f315(x97536,x97534)))+~P1(f315(x97531,f425(x97531,x97536,x97535,x97533,x97537)))+~P1(f315(f315(f317(x97533),x97534),x97535))
% 168.60/168.40 [10191]~P17(x101917,x101916,x101911)+E(f315(f315(x101911,x101912),f832(x101912,x101913,x101914,x101915,x101911,x101916,x101917)),x101913)+~P1(f315(f59(x101917,x101916,x101911,x101915,x101914),x101913))+~P1(f315(f315(f317(x101917),x101912),x101914))
% 168.60/168.40 [10258]~P17(x102581,x102582,x102583)+~P1(f315(f59(x102581,x102582,x102583,x102584,x102585),x102587))+P1(f315(f59(x102581,x102582,x102583,x102584,f315(f315(f3(f909(x102581,a899)),x102585),f315(f315(f297(x102581),x102586),f177(f909(x102581,a899))))),f832(x102586,x102587,x102585,x102584,x102583,x102582,x102581)))+~P1(f315(f315(f317(x102581),x102586),x102585))
% 168.60/168.40 [9395]P26(x93951,x93952,x93953,x93954,x93955)+~P26(x93951,x93952,x93953,x93956,x93957)+~E(f315(f298(x93951,x93952,x93953),x93954),x93955)+~P1(f315(f315(f223(f909(x93951,a899)),x93954),x93956))
% 168.60/168.40 [9645]~P26(x96451,x96452,x96453,x96455,x96457)+~P26(x96451,x96452,x96453,x96454,x96456)+P26(x96451,x96452,x96453,f315(f315(f99(f909(x96451,a899)),x96454),x96455),f315(f315(f99(f909(x96452,a899)),x96456),x96457))+~E(f315(f315(f90(f909(x96452,a899)),x96456),x96457),f177(f909(x96452,a899)))
% 168.60/168.40 [9650]~P70(x96501)+~P25(x96505,x96502,x96506,x96507)+~P1(f315(f54(x96505),x96507))+E(f315(f315(f315(f58(x96501,x96502,f74(x96501)),x96503),x96504),f315(f298(x96505,x96502,x96506),x96507)),f315(f315(f315(f58(x96501,x96505,f74(x96501)),f315(f66(x96502,x96501,x96505,x96503),x96506)),x96504),x96507))
% 168.60/168.40 [9776]~E(f315(f315(f297(x97761),x97765),x97766),f315(f315(f297(x97761),x97762),x97763))+~P1(f315(f59(x97761,x97761,x97764,x97762,x97763),x97767))+P1(f315(f315(f317(x97761),x97762),x97763))+P1(f315(f55(x97761,x97764,f315(f315(f297(x97761),x97765),x97766)),x97767))
% 168.60/168.40 [9860]P1(f315(x98601,x98602))+~P1(f315(f315(f317(x98603),x98602),f315(x98604,x98607)))+~P1(f315(f315(f317(x98606),x98607),x98605))+P1(f315(f315(f317(x98603),f425(x98601,x98604,x98605,x98606,x98603)),f315(f315(f33(x98606,f909(x98603,a899)),x98605),x98604)))
% 168.60/168.40 [9877]~P25(x98772,x98771,x98775,x98774)+~P25(x98771,x98773,x98776,f315(f298(x98772,x98771,x98775),x98774))+E(f315(f315(f66(x98771,x98772,x98773,f70(x98772,x98771,x98774,x98775)),f70(x98771,x98773,f315(f298(x98772,x98771,x98775),x98774),x98776)),x98777),f315(f70(x98772,x98773,x98774,f315(f66(x98771,x98773,x98772,x98776),x98775)),x98777))+~P1(f315(f315(f317(x98773),x98777),f315(f298(x98771,x98773,x98776),f315(f298(x98772,x98771,x98775),x98774))))
% 168.60/168.40 [9878]~P25(x98782,x98781,x98785,x98784)+~P25(x98781,x98783,x98786,f315(f298(x98782,x98781,x98785),x98784))+E(f315(f315(f66(x98781,x98782,x98783,f84(x98782,x98781,x98784,x98785)),f84(x98781,x98783,f315(f298(x98782,x98781,x98785),x98784),x98786)),x98787),f315(f84(x98782,x98783,x98784,f315(f66(x98781,x98783,x98782,x98786),x98785)),x98787))+~P1(f315(f315(f317(x98783),x98787),f315(f298(x98781,x98783,x98786),f315(f298(x98782,x98781,x98785),x98784))))
% 168.60/168.40 [10192]~P17(x101927,x101926,x101921)+E(f315(f315(x101921,x101922),f875(x101923,x101924,x101922,x101925,x101921,x101926,x101927)),x101923)+P1(f315(f315(f317(x101927),x101922),x101924))+~P1(f315(f59(x101927,x101926,x101921,x101925,f315(f315(f297(x101927),x101922),x101924)),x101923))
% 168.60/168.40 [10257]~P17(x102571,x102574,x102575)+P1(f315(f59(x102571,x102574,x102575,x102576,x102573),f875(x102577,x102573,x102572,x102576,x102575,x102574,x102571)))+P1(f315(f315(f317(x102571),x102572),x102573))+~P1(f315(f59(x102571,x102574,x102575,x102576,f315(f315(f297(x102571),x102572),x102573)),x102577))
% 168.60/168.40 [9935]E(x99351,f2(a1))+~P1(f315(f42(x99353,x99351),f315(f315(f240(a1,a1),x99355),x99357)))+~P1(f315(f42(x99352,x99351),f315(f315(f240(a1,a1),x99354),x99356)))+P1(f315(f42(f315(f315(f73(a1),x99352),x99353),x99351),f315(f315(f240(a1,a1),f315(f315(f73(a1),f315(f315(f73(a1),x99354),x99355)),f315(f315(f29(a1),f315(f315(f73(a1),x99356),x99357)),x99351))),f38(a1,f315(f315(f73(a1),x99356),x99357),x99351))))
% 168.60/168.40 [9937]~P1(f315(f315(f224(a901),f2(a901)),x99373))+~P1(f315(f41(x99372,x99373),f315(f315(f240(a901,a901),x99375),x99377)))+~P1(f315(f41(x99371,x99373),f315(f315(f240(a901,a901),x99374),x99376)))+P1(f315(f41(f315(f315(f73(a901),x99371),x99372),x99373),f315(f315(f240(a901,a901),f315(f315(f73(a901),f315(f315(f73(a901),x99374),x99375)),f315(f315(f29(a901),f315(f315(f73(a901),x99376),x99377)),x99373))),f38(a901,f315(f315(f73(a901),x99376),x99377),x99373))))
% 168.60/168.40 [10327]~P72(x103272)+~P1(f315(f54(x103273),x103275))+~P1(f315(f54(x103271),x103277))+E(f315(f315(f8(x103271,x103272),f315(f315(f20(x103271,f909(x103273,a899),x103272),f315(f315(f10(f909(x103273,x103272),f909(f909(x103273,a899),x103272),x103271),f8(x103273,x103272)),x103274)),f315(f315(f10(f909(x103273,a899),f909(x103273,a899),x103271),f250(x103273)),f315(f315(f10(f909(x103273,a899),f909(x103273,a899),x103271),f315(f20(x103273,a899,a899),f315(f315(f10(a899,f909(a899,a899),x103273),a313),f315(f315(f9(x103273,f909(x103273,a899),a899),f317(x103273)),x103275)))),x103276)))),x103277),f315(f315(f8(x103273,x103272),f315(f315(f20(x103273,f909(x103271,a899),x103272),f315(f315(f10(f909(x103271,x103272),f909(f909(x103271,a899),x103272),x103273),f8(x103271,x103272)),f315(f9(x103271,x103273,x103272),x103274))),f315(f315(f10(f909(x103271,a899),f909(x103271,a899),x103273),f250(x103271)),f315(f315(f10(f909(x103271,a899),f909(x103271,a899),x103273),f315(f20(x103271,a899,a899),f315(f315(f10(a899,f909(a899,a899),x103271),a313),f315(f315(f9(x103271,f909(x103271,a899),a899),f317(x103271)),x103277)))),f315(f9(x103271,x103273,a899),x103276))))),x103275))
% 168.60/168.40 [10278]~P22(x102788,x102787,x102786,x102785,x102781)+~E(f315(x102782,f838(x102784,x102782,x102783,x102781,x102785,x102786,x102787)),f315(x102784,f838(x102784,x102782,x102783,x102781,x102785,x102786,x102787)))+E(f315(f315(x102781,x102782),x102783),f315(f315(x102781,x102784),x102783))+~P1(f315(f54(x102787),x102783))
% 168.60/168.40 [9812]~P23(x98127,x98126,x98121,x98128,x98122,x98124)+E(f315(f315(x98121,f315(x98122,x98123)),f315(x98124,x98125)),f315(x98124,x98125))+~P1(f315(f54(x98126),x98125))+~P1(f315(f315(f317(x98126),x98123),x98125))
% 168.60/168.40 [9816]~P12(x98166,x98161,x98162,x98168,x98163,x98164)+~P8(x98166,x98167,x98168)+P11(x98161,x98162,x98163,f315(x98164,x98165))+~P1(f315(f315(f317(x98166),x98165),x98167))
% 168.60/168.40 [10300]~P22(x103008,x103005,x103007,x103006,x103001)+E(f315(f315(x103001,x103002),x103003),f315(f315(x103001,x103004),x103003))+~P1(f315(f54(x103005),x103003))+P1(f315(f315(f317(x103005),f838(x103002,x103004,x103003,x103001,x103006,x103007,x103005)),x103003))
% 168.60/168.40 [10377]~P1(f315(f315(x103771,x103776),x103775))+P1(f315(f315(x103771,f823(x103771,x103774,x103775,x103776,x103773,x103772,x103777,x103778)),f831(x103771,x103774,x103775,x103776,x103773,x103772,x103777,x103778)))+P1(f315(f315(x103771,x103772),x103773))+~P1(f315(f315(f317(f908(f908(x103778,x103777),f908(x103778,x103777))),f315(f315(f240(f908(x103778,x103777),f908(x103778,x103777)),f315(f315(f240(x103778,x103777),x103772),x103773)),f315(f315(f240(x103778,x103777),x103776),x103775))),f295(f908(x103778,x103777),x103774)))
% 168.60/168.40 [10378]~P1(f315(f315(x103781,x103786),x103785))+P1(f315(f315(x103781,f822(x103781,x103784,x103783,x103782,x103785,x103786,x103787,x103788)),f824(x103781,x103784,x103783,x103782,x103785,x103786,x103787,x103788)))+P1(f315(f315(x103781,x103782),x103783))+~P1(f315(f315(f317(f908(f908(x103788,x103787),f908(x103788,x103787))),f315(f315(f240(f908(x103788,x103787),f908(x103788,x103787)),f315(f315(f240(x103788,x103787),x103786),x103785)),f315(f315(f240(x103788,x103787),x103782),x103783))),f295(f908(x103788,x103787),x103784)))
% 168.60/168.40 [10388]~P1(f315(f315(x103881,f825(x103881,x103886,x103885,x103884,x103883,x103882,x103887,x103888)),f830(x103881,x103886,x103885,x103884,x103883,x103882,x103887,x103888)))+P1(f315(f315(x103881,x103882),x103883))+~P1(f315(f315(x103881,x103884),x103885))+~P1(f315(f315(f317(f908(f908(x103888,x103887),f908(x103888,x103887))),f315(f315(f240(f908(x103888,x103887),f908(x103888,x103887)),f315(f315(f240(x103888,x103887),x103882),x103883)),f315(f315(f240(x103888,x103887),x103884),x103885))),f295(f908(x103888,x103887),x103886)))
% 168.60/168.40 [10389]~P1(f315(f315(x103891,f826(x103891,x103896,x103893,x103892,x103895,x103894,x103897,x103898)),f827(x103891,x103896,x103893,x103892,x103895,x103894,x103897,x103898)))+P1(f315(f315(x103891,x103892),x103893))+~P1(f315(f315(x103891,x103894),x103895))+~P1(f315(f315(f317(f908(f908(x103898,x103897),f908(x103898,x103897))),f315(f315(f240(f908(x103898,x103897),f908(x103898,x103897)),f315(f315(f240(x103898,x103897),x103894),x103895)),f315(f315(f240(x103898,x103897),x103892),x103893))),f295(f908(x103898,x103897),x103896)))
% 168.60/168.40 [10402]~P1(f315(f315(x104021,x104026),x104027))+P1(f315(f315(x104021,x104022),x104023))+P1(f315(f315(f317(f908(f908(x104024,x104025),f908(x104024,x104025))),f315(f315(f240(f908(x104024,x104025),f908(x104024,x104025)),f315(f315(f240(x104024,x104025),x104026),x104027)),f315(f315(f240(x104024,x104025),f822(x104021,x104028,x104023,x104022,x104027,x104026,x104025,x104024)),f824(x104021,x104028,x104023,x104022,x104027,x104026,x104025,x104024)))),f295(f908(x104024,x104025),x104028)))+~P1(f315(f315(f317(f908(f908(x104024,x104025),f908(x104024,x104025))),f315(f315(f240(f908(x104024,x104025),f908(x104024,x104025)),f315(f315(f240(x104024,x104025),x104026),x104027)),f315(f315(f240(x104024,x104025),x104022),x104023))),f295(f908(x104024,x104025),x104028)))
% 168.60/168.40 [10404]~P1(f315(f315(x104041,x104048),x104047))+P1(f315(f315(x104041,x104042),x104043))+P1(f315(f315(f317(f908(f908(x104044,x104045),f908(x104044,x104045))),f315(f315(f240(f908(x104044,x104045),f908(x104044,x104045)),f315(f315(f240(x104044,x104045),f823(x104041,x104046,x104047,x104048,x104043,x104042,x104045,x104044)),f831(x104041,x104046,x104047,x104048,x104043,x104042,x104045,x104044))),f315(f315(f240(x104044,x104045),x104048),x104047))),f295(f908(x104044,x104045),x104046)))+~P1(f315(f315(f317(f908(f908(x104044,x104045),f908(x104044,x104045))),f315(f315(f240(f908(x104044,x104045),f908(x104044,x104045)),f315(f315(f240(x104044,x104045),x104042),x104043)),f315(f315(f240(x104044,x104045),x104048),x104047))),f295(f908(x104044,x104045),x104046)))
% 168.60/168.40 [9422]~P20(x94227,x94221,x94228,x94223)+~P1(f315(f54(x94227),x94225))+~P1(f315(f54(x94227),x94224))+E(f315(f66(x94221,x94221,x94222,f315(x94223,x94224)),f315(f66(x94221,x94221,x94222,f315(x94223,x94225)),x94226)),f315(f66(x94221,x94221,x94222,f315(x94223,x94225)),f315(f66(x94221,x94221,x94222,f315(x94223,x94224)),x94226)))
% 168.60/168.40 [9431]~P36(x94311,x94312,x94313,x94314,x94317)+P36(x94311,x94312,x94313,f315(f315(f148(x94311,x94314),x94315),x94316),f315(f315(f148(x94312,x94317),x94315),x94318))+~P1(f315(f315(x94313,x94316),x94318))+~P1(f315(f315(f224(a901),x94315),f315(f178(f902(x94311)),x94314)))
% 168.60/168.40 [9432]~P36(x94321,x94322,x94323,x94324,x94327)+P36(x94321,x94322,x94323,f315(f315(f148(x94321,x94324),x94325),x94326),f315(f315(f148(x94322,x94327),x94325),x94328))+~P1(f315(f315(x94323,x94326),x94328))+~P1(f315(f315(f224(a901),x94325),f315(f178(f902(x94322)),x94327)))
% 168.60/168.40 [9511]~P25(x95112,x95112,x95115,x95116)+~P22(x95113,x95112,x95117,x95118,x95111)+~P1(f315(f54(x95112),x95116))+E(f315(f315(x95111,f315(f66(x95112,x95113,x95112,x95114),x95115)),x95116),f315(f315(x95111,x95114),f315(f298(x95112,x95112,x95115),x95116)))
% 168.60/168.40 [9777]P26(x97771,x97772,x97773,x97774,x97775)+~P26(x97772,x97776,x97777,x97775,x97778)+~P26(x97771,x97776,f315(f66(x97772,x97776,x97771,x97777),x97773),x97774,x97778)+~P1(f315(f315(f223(f909(x97772,a899)),f315(f298(x97771,x97772,x97773),x97774)),x97775))
% 168.60/168.40 [9814]~P24(x98147,x98142,x98145,x98148,x98146,x98141)+~P1(f315(f54(x98142),x98144))+E(f315(x98141,f315(f315(f297(x98142),x98143),x98144)),f315(f315(x98145,f315(x98146,x98143)),f315(x98141,x98144)))+P1(f315(f315(f317(x98142),x98143),x98144))
% 168.60/168.40 [9825]~P23(x98256,x98255,x98251,x98257,x98258,x98252)+E(f315(f315(x98251,f315(x98252,x98253)),f315(x98252,x98254)),f315(x98252,x98254))+~P1(f315(f54(x98255),x98254))+~P1(f315(f315(f223(f909(x98255,a899)),x98253),x98254))
% 168.60/168.40 [9409]P1(f315(f315(f317(f908(f902(x94091),f902(x94091))),f315(f315(f240(f902(x94091),f902(x94091)),x94092),x94093)),f146(x94091,x94094)))+~E(x94093,f315(f315(f123(x94091),x94095),f315(f315(f140(x94091),x94096),x94097)))+~E(x94092,f315(f315(f123(x94091),x94095),f315(f315(f140(x94091),x94098),x94097)))+~P1(f315(f315(f317(f908(x94091,x94091)),f315(f315(f240(x94091,x94091),x94098),x94096)),x94094))
% 168.60/168.40 [9819]~P23(x98196,x98192,x98195,x98197,x98198,x98191)+~P1(f315(f54(x98192),x98194))+~P1(f315(f54(x98192),x98193))+E(f315(x98191,f315(f315(f99(f909(x98192,a899)),x98193),x98194)),f315(f315(x98195,f315(x98191,x98193)),f315(x98191,x98194)))
% 168.60/168.40 [10367]~P25(x103674,x103672,x103675,x103678)+E(f315(f315(f32(x103671,f909(x103672,a899)),x103673),f315(f315(f10(f909(x103674,a899),f909(x103672,a899),x103671),f298(x103674,x103672,x103675)),x103676)),f315(f298(x103674,x103672,x103675),f315(f315(f32(x103671,f909(x103674,a899)),x103673),x103676)))+~P1(f315(f315(f317(x103671),x103677),x103673))+P1(f315(f315(f317(x103671),f498(x103677,x103676,x103673,x103671,x103678,x103675,x103672,x103674)),x103673))
% 168.60/168.40 [10393]~P25(x103934,x103932,x103935,x103937)+E(f315(f315(f32(x103931,f909(x103932,a899)),x103933),f315(f315(f10(f909(x103934,a899),f909(x103932,a899),x103931),f298(x103934,x103932,x103935)),x103936)),f315(f298(x103934,x103932,x103935),f315(f315(f32(x103931,f909(x103934,a899)),x103933),x103936)))+~P1(f315(f315(f317(x103931),x103938),x103933))+~P1(f315(f315(f223(f909(x103934,a899)),f315(x103936,f498(x103938,x103936,x103933,x103931,x103937,x103935,x103932,x103934))),x103937))
% 168.60/168.40 [10405]~P1(f315(f315(x104051,x104058),x104057))+P1(f315(f315(x104051,x104052),x104053))+~P1(f315(f315(f317(f908(f908(x104054,x104055),f908(x104054,x104055))),f315(f315(f240(f908(x104054,x104055),f908(x104054,x104055)),f315(f315(f240(x104054,x104055),x104052),x104053)),f315(f315(f240(x104054,x104055),x104058),x104057))),f295(f908(x104054,x104055),x104056)))+P1(f315(f315(f317(f908(f908(x104054,x104055),f908(x104054,x104055))),f315(f315(f240(f908(x104054,x104055),f908(x104054,x104055)),f315(f315(f240(x104054,x104055),f825(x104051,x104056,x104057,x104058,x104053,x104052,x104055,x104054)),f830(x104051,x104056,x104057,x104058,x104053,x104052,x104055,x104054))),f315(f315(f240(x104054,x104055),f823(x104051,x104056,x104057,x104058,x104053,x104052,x104055,x104054)),f831(x104051,x104056,x104057,x104058,x104053,x104052,x104055,x104054)))),x104056))
% 168.60/168.40 [10406]~P1(f315(f315(x104061,x104068),x104067))+P1(f315(f315(x104061,x104062),x104063))+~P1(f315(f315(f317(f908(f908(x104064,x104065),f908(x104064,x104065))),f315(f315(f240(f908(x104064,x104065),f908(x104064,x104065)),f315(f315(f240(x104064,x104065),x104068),x104067)),f315(f315(f240(x104064,x104065),x104062),x104063))),f295(f908(x104064,x104065),x104066)))+P1(f315(f315(f317(f908(f908(x104064,x104065),f908(x104064,x104065))),f315(f315(f240(f908(x104064,x104065),f908(x104064,x104065)),f315(f315(f240(x104064,x104065),f822(x104061,x104066,x104063,x104062,x104067,x104068,x104065,x104064)),f824(x104061,x104066,x104063,x104062,x104067,x104068,x104065,x104064))),f315(f315(f240(x104064,x104065),f826(x104061,x104066,x104063,x104062,x104067,x104068,x104065,x104064)),f827(x104061,x104066,x104063,x104062,x104067,x104068,x104065,x104064)))),x104066))
% 168.60/168.40 [9887]~P24(x98877,x98875,x98871,x98878,x98872,x98874)+~P1(f315(f54(x98875),x98876))+~P1(f315(f315(f317(x98875),x98873),x98876))+E(f315(f315(x98871,f315(x98872,x98873)),f315(x98874,f315(f315(f3(f909(x98875,a899)),x98876),f315(f315(f297(x98875),x98873),f177(f909(x98875,a899)))))),f315(x98874,x98876))
% 168.60/168.40 [9895]~P24(x98956,x98953,x98951,x98957,x98958,x98952)+~P1(f315(f54(x98953),x98955))+~P1(f315(f54(x98953),x98954))+E(f315(f315(x98951,f315(x98952,f315(f315(f99(f909(x98953,a899)),x98954),x98955))),f315(x98952,f315(f315(f90(f909(x98953,a899)),x98954),x98955))),f315(f315(x98951,f315(x98952,x98954)),f315(x98952,x98955)))
% 168.60/168.40 [9977]P44(x99771,x99772,x99773,x99774,x99775,f315(f315(x99773,x99776),x99777))+~P44(x99771,x99772,x99773,x99774,f315(f315(f3(f909(x99771,a899)),x99775),f315(f315(f297(x99771),x99778),f177(f909(x99771,a899)))),x99779)+~E(f315(f315(x99773,x99776),x99777),f315(f315(x99773,x99778),x99779))+~P1(f315(f315(f317(x99771),x99778),x99775))
% 168.60/168.40 [9919]~P12(x99196,x99197,x99198,x99199,x991910,x99191)+E(f315(f315(x99191,x99192),x99193),f315(f315(x99191,x99194),x99195))+~P1(f315(f315(f317(f908(x99197,x99197)),f315(f315(f240(x99197,x99197),x99193),x99195)),x991910))+~P1(f315(f315(f317(f908(x99196,x99196)),f315(f315(f240(x99196,x99196),x99192),x99194)),x99199))
% 168.60/168.40 [9513]~P80(x95132)+E(x95131,f177(f909(x95132,a899)))+~P1(f315(f54(x95132),x95131))+P1(f315(f315(f317(x95132),f12(x95132,x95131)),x95131))+~P1(f315(f315(f317(x95132),f315(f315(f99(x95132),f497(x95131,x95132)),f513(x95131,x95132))),f315(f315(f297(x95132),f497(x95131,x95132)),f315(f315(f297(x95132),f513(x95131,x95132)),f177(f909(x95132,a899))))))
% 168.60/168.40 [9514]~P80(x95142)+E(x95141,f177(f909(x95142,a899)))+~P1(f315(f54(x95142),x95141))+P1(f315(f315(f317(x95142),f13(x95142,x95141)),x95141))+~P1(f315(f315(f317(x95142),f315(f315(f90(x95142),f611(x95141,x95142)),f631(x95141,x95142))),f315(f315(f297(x95142),f611(x95141,x95142)),f315(f315(f297(x95142),f631(x95141,x95142)),f177(f909(x95142,a899))))))
% 168.60/168.40 [9547]~P70(x95472)+E(x95471,f177(f909(x95472,a899)))+~P1(f315(f54(x95472),x95471))+P1(f315(f315(f317(x95472),f315(f56(x95472,f74(x95472)),x95471)),x95471))+~P1(f315(f315(f317(x95472),f315(f315(f74(x95472),f841(x95471,x95472)),f852(x95471,x95472))),f315(f315(f297(x95472),f841(x95471,x95472)),f315(f315(f297(x95472),f852(x95471,x95472)),f177(f909(x95472,a899))))))
% 168.60/168.40 [9552]~P110(x95522)+E(x95521,f177(f909(x95522,a899)))+~P1(f315(f54(x95522),x95521))+P1(f315(f315(f317(x95522),f14(x95522,f221(x95522),x95521)),x95521))+~P1(f315(f315(f317(x95522),f315(f315(f221(x95522),f896(x95521,x95522)),f897(x95521,x95522))),f315(f315(f297(x95522),f896(x95521,x95522)),f315(f315(f297(x95522),f897(x95521,x95522)),f177(f909(x95522,a899))))))
% 168.60/168.40 [9553]~P110(x95532)+E(x95531,f177(f909(x95532,a899)))+~P1(f315(f54(x95532),x95531))+P1(f315(f315(f317(x95532),f15(x95532,f222(x95532),x95531)),x95531))+~P1(f315(f315(f317(x95532),f315(f315(f222(x95532),f404(x95531,x95532)),f408(x95531,x95532))),f315(f315(f297(x95532),f404(x95531,x95532)),f315(f315(f297(x95532),f408(x95531,x95532)),f177(f909(x95532,a899))))))
% 168.60/168.40 [6646]~P91(x66462)+E(x66461,f2(x66462))+~E(f315(f315(f73(x66462),x66463),x66461),f2(x66462))+~P1(f315(f315(f223(x66462),f2(x66462)),x66463))+~P1(f315(f315(f223(x66462),f2(x66462)),x66461))
% 168.60/168.40 [6647]~P91(x66472)+E(x66471,f2(x66472))+~E(f315(f315(f73(x66472),x66471),x66473),f2(x66472))+~P1(f315(f315(f223(x66472),f2(x66472)),x66473))+~P1(f315(f315(f223(x66472),f2(x66472)),x66471))
% 168.60/168.40 [7194]~P110(x71942)+~P13(x71942,x71941)+E(x71941,f102(x71942))+~P1(f315(f315(f317(x71942),x71943),f315(f161(x71942),f690(x71941,x71942))))+P1(f315(f315(f223(x71942),f709(x71941,x71942)),x71943))
% 168.60/168.40 [7365]~P110(x73651)+E(f16(x73651,x73652),x73653)+~P1(f315(f54(x73651),x73652))+~P1(f315(f315(f223(x73651),x73653),f337(x73653,x73652,x73651)))+~P1(f315(f315(f317(x73651),x73653),x73652))
% 168.60/168.40 [7398]~P110(x73981)+~P13(x73981,x73982)+~P13(x73981,x73983)+P13(x73981,f315(f315(f123(x73981),x73982),x73983))+P1(f315(f315(f317(x73981),f697(x73983,x73982,x73981)),f315(f161(x73981),x73982)))
% 168.60/168.40 [7399]~P110(x73991)+~P13(x73991,x73992)+~P13(x73991,x73993)+P13(x73991,f315(f315(f123(x73991),x73992),x73993))+P1(f315(f315(f317(x73991),f698(x73993,x73992,x73991)),f315(f161(x73991),x73993)))
% 168.60/168.40 [7462]~P110(x74621)+E(f16(x74621,x74622),x74623)+~P1(f315(f54(x74621),x74622))+P1(f315(f315(f317(x74621),f337(x74623,x74622,x74621)),x74622))+~P1(f315(f315(f317(x74621),x74623),x74622))
% 168.60/168.40 [7463]~P110(x74631)+E(f17(x74631,x74632),x74633)+~P1(f315(f54(x74631),x74632))+P1(f315(f315(f317(x74631),f583(x74633,x74632,x74631)),x74632))+~P1(f315(f315(f317(x74631),x74633),x74632))
% 168.60/168.40 [8035]~P110(x80351)+E(f17(x80351,x80352),x80353)+~P1(f315(f54(x80351),x80352))+~P1(f315(f315(f317(x80351),x80353),x80352))+~P1(f315(f315(f223(x80351),f583(x80353,x80352,x80351)),x80353))
% 168.60/168.40 [8356]~P110(x83561)+~P13(x83561,x83562)+~P13(x83561,x83563)+P13(x83561,f315(f315(f123(x83561),x83562),x83563))+~P1(f315(f315(f223(x83561),f697(x83563,x83562,x83561)),f698(x83563,x83562,x83561)))
% 168.60/168.40 [9148]~P80(x91482)+E(x91481,f177(f909(x91482,a899)))+~E(f315(f315(f99(x91482),f315(x91483,f504(x91481,x91483,x91482))),f315(x91483,f514(x91481,x91483,x91482))),f315(x91483,f315(f315(f99(x91482),f504(x91481,x91483,x91482)),f514(x91481,x91483,x91482))))+E(f12(x91482,f315(f298(x91482,x91482,x91483),x91481)),f315(x91483,f12(x91482,x91481)))+~P1(f315(f54(x91482),x91481))
% 168.60/168.40 [9149]~P80(x91492)+E(x91491,f177(f909(x91492,a899)))+~E(f315(f315(f90(x91492),f315(x91493,f505(x91491,x91493,x91492))),f315(x91493,f512(x91491,x91493,x91492))),f315(x91493,f315(f315(f90(x91492),f505(x91491,x91493,x91492)),f512(x91491,x91493,x91492))))+E(f13(x91492,f315(f298(x91492,x91492,x91493),x91491)),f315(x91493,f13(x91492,x91491)))+~P1(f315(f54(x91492),x91491))
% 168.60/168.40 [9150]~P110(x91502)+E(x91501,f177(f909(x91502,a899)))+~E(f315(f315(f221(x91502),f315(x91503,f506(x91501,x91503,x91502))),f315(x91503,f511(x91501,x91503,x91502))),f315(x91503,f315(f315(f221(x91502),f506(x91501,x91503,x91502)),f511(x91501,x91503,x91502))))+E(f16(x91502,f315(f298(x91502,x91502,x91503),x91501)),f315(x91503,f16(x91502,x91501)))+~P1(f315(f54(x91502),x91501))
% 168.60/168.40 [9151]~P110(x91512)+E(x91511,f177(f909(x91512,a899)))+~E(f315(f315(f222(x91512),f315(x91513,f507(x91511,x91513,x91512))),f315(x91513,f510(x91511,x91513,x91512))),f315(x91513,f315(f315(f222(x91512),f507(x91511,x91513,x91512)),f510(x91511,x91513,x91512))))+E(f17(x91512,f315(f298(x91512,x91512,x91513),x91511)),f315(x91513,f17(x91512,x91511)))+~P1(f315(f54(x91512),x91511))
% 168.60/168.40 [9219]~P110(x92192)+E(x92191,f177(f909(x92192,a899)))+~E(f315(f315(f221(x92192),f315(x92193,f508(x92191,x92193,x92192))),f315(x92193,f509(x92191,x92193,x92192))),f315(x92193,f315(f315(f221(x92192),f508(x92191,x92193,x92192)),f509(x92191,x92193,x92192))))+E(f14(x92192,f221(x92192),f315(f298(x92192,x92192,x92193),x92191)),f315(x92193,f14(x92192,f221(x92192),x92191)))+~P1(f315(f54(x92192),x92191))
% 168.60/168.40 [9220]~P110(x92202)+E(x92201,f177(f909(x92202,a899)))+~E(f315(f315(f222(x92202),f315(x92203,f496(x92201,x92203,x92202))),f315(x92203,f499(x92201,x92203,x92202))),f315(x92203,f315(f315(f222(x92202),f496(x92201,x92203,x92202)),f499(x92201,x92203,x92202))))+E(f15(x92202,f222(x92202),f315(f298(x92202,x92202,x92203),x92201)),f315(x92203,f15(x92202,f222(x92202),x92201)))+~P1(f315(f54(x92202),x92201))
% 168.60/168.40 [6663]~P70(x66632)+E(x66631,f177(f909(x66632,a899)))+~P1(f315(f54(x66632),x66631))+E(f315(f56(x66632,f74(x66632)),f315(f315(f297(x66632),x66633),x66631)),f315(f315(f74(x66632),x66633),f315(f56(x66632,f74(x66632)),x66631)))+P1(f315(f315(f317(x66632),x66633),x66631))
% 168.60/168.40 [7200]~P80(x72002)+E(f315(f315(f99(x72002),f12(x72002,x72001)),f12(x72002,x72003)),f12(x72002,x72003))+E(x72001,f177(f909(x72002,a899)))+~P1(f315(f54(x72002),x72003))+~P1(f315(f315(f223(f909(x72002,a899)),x72001),x72003))
% 168.60/168.40 [7201]~P80(x72012)+E(f315(f315(f90(x72012),f13(x72012,x72011)),f13(x72012,x72013)),f13(x72012,x72013))+E(x72011,f177(f909(x72012,a899)))+~P1(f315(f54(x72012),x72013))+~P1(f315(f315(f223(f909(x72012,a899)),x72011),x72013))
% 168.60/168.40 [7202]~P110(x72022)+E(f315(f315(f221(x72022),f16(x72022,x72021)),f16(x72022,x72023)),f16(x72022,x72023))+E(x72021,f177(f909(x72022,a899)))+~P1(f315(f54(x72022),x72023))+~P1(f315(f315(f223(f909(x72022,a899)),x72021),x72023))
% 168.60/168.40 [7203]~P110(x72032)+E(f315(f315(f222(x72032),f17(x72032,x72031)),f17(x72032,x72033)),f17(x72032,x72033))+E(x72031,f177(f909(x72032,a899)))+~P1(f315(f54(x72032),x72033))+~P1(f315(f315(f223(f909(x72032,a899)),x72031),x72033))
% 168.60/168.40 [7510]~P110(x75102)+E(x75101,f177(f909(x75102,a899)))+~P1(f315(f54(x75102),x75103))+P1(f315(f315(f223(x75102),f16(x75102,x75103)),f16(x75102,x75101)))+~P1(f315(f315(f223(f909(x75102,a899)),x75101),x75103))
% 168.60/168.40 [7511]~P110(x75112)+E(x75111,f177(f909(x75112,a899)))+~P1(f315(f54(x75112),x75113))+P1(f315(f315(f223(x75112),f17(x75112,x75111)),f17(x75112,x75113)))+~P1(f315(f315(f223(f909(x75112,a899)),x75111),x75113))
% 168.60/168.40 [7565]~P80(x75651)+E(f12(x75651,x75652),x75653)+~P1(f315(f54(x75651),x75652))+~E(f315(f315(f3(f909(x75651,a899)),x75652),f315(f315(f297(x75651),x75653),f177(f909(x75651,a899)))),f177(f909(x75651,a899)))+~P1(f315(f315(f317(x75651),x75653),x75652))
% 168.60/168.40 [7566]~P80(x75661)+E(f13(x75661,x75662),x75663)+~P1(f315(f54(x75661),x75662))+~E(f315(f315(f3(f909(x75661,a899)),x75662),f315(f315(f297(x75661),x75663),f177(f909(x75661,a899)))),f177(f909(x75661,a899)))+~P1(f315(f315(f317(x75661),x75663),x75662))
% 168.60/168.40 [7567]~P110(x75671)+E(f16(x75671,x75672),x75673)+~P1(f315(f54(x75671),x75672))+~E(f315(f315(f3(f909(x75671,a899)),x75672),f315(f315(f297(x75671),x75673),f177(f909(x75671,a899)))),f177(f909(x75671,a899)))+~P1(f315(f315(f317(x75671),x75673),x75672))
% 168.60/168.40 [7568]~P110(x75681)+E(f17(x75681,x75682),x75683)+~P1(f315(f54(x75681),x75682))+~E(f315(f315(f3(f909(x75681,a899)),x75682),f315(f315(f297(x75681),x75683),f177(f909(x75681,a899)))),f177(f909(x75681,a899)))+~P1(f315(f315(f317(x75681),x75683),x75682))
% 168.60/168.40 [7664]~P110(x76641)+E(f14(x76641,f221(x76641),x76642),x76643)+~P1(f315(f54(x76641),x76642))+~E(f315(f315(f3(f909(x76641,a899)),x76642),f315(f315(f297(x76641),x76643),f177(f909(x76641,a899)))),f177(f909(x76641,a899)))+~P1(f315(f315(f317(x76641),x76643),x76642))
% 168.60/168.40 [7665]~P110(x76651)+E(f15(x76651,f222(x76651),x76652),x76653)+~P1(f315(f54(x76651),x76652))+~E(f315(f315(f3(f909(x76651,a899)),x76652),f315(f315(f297(x76651),x76653),f177(f909(x76651,a899)))),f177(f909(x76651,a899)))+~P1(f315(f315(f317(x76651),x76653),x76652))
% 168.60/168.40 [7700]~P104(x77002)+E(x77001,f177(f909(x77002,a899)))+~P1(f315(f54(x77002),x77001))+~P1(f315(f315(f223(x77002),x77003),f784(x77003,x77001,x77002)))+P1(f315(f315(f223(x77002),x77003),f315(f56(x77002,f90(x77002)),x77001)))
% 168.60/168.40 [7701]~P110(x77012)+E(x77011,f177(f909(x77012,a899)))+~P1(f315(f54(x77012),x77011))+~P1(f315(f315(f223(x77012),x77013),f891(x77013,x77011,x77012)))+P1(f315(f315(f223(x77012),x77013),f315(f56(x77012,f221(x77012)),x77011)))
% 168.60/168.40 [7702]~P110(x77022)+E(x77021,f177(f909(x77022,a899)))+~P1(f315(f54(x77022),x77021))+~P1(f315(f315(f224(x77022),x77023),f893(x77023,x77021,x77022)))+P1(f315(f315(f224(x77022),x77023),f315(f56(x77022,f221(x77022)),x77021)))
% 168.60/168.40 [7789]~P104(x77892)+E(x77891,f177(f909(x77892,a899)))+~P1(f315(f54(x77892),x77891))+P1(f315(f315(f317(x77892),f784(x77893,x77891,x77892)),x77891))+P1(f315(f315(f223(x77892),x77893),f315(f56(x77892,f90(x77892)),x77891)))
% 168.60/168.40 [7790]~P110(x77902)+E(x77901,f177(f909(x77902,a899)))+~P1(f315(f54(x77902),x77901))+P1(f315(f315(f317(x77902),f891(x77903,x77901,x77902)),x77901))+P1(f315(f315(f223(x77902),x77903),f315(f56(x77902,f221(x77902)),x77901)))
% 168.60/168.40 [7791]~P110(x77912)+E(x77911,f177(f909(x77912,a899)))+~P1(f315(f54(x77912),x77911))+P1(f315(f315(f317(x77912),f893(x77913,x77911,x77912)),x77911))+P1(f315(f315(f224(x77912),x77913),f315(f56(x77912,f221(x77912)),x77911)))
% 168.60/168.40 [7912]~P110(x79122)+E(x79121,f177(f909(x79122,a899)))+E(f315(f315(f221(x79122),f14(x79122,f221(x79122),x79121)),f14(x79122,f221(x79122),x79123)),f14(x79122,f221(x79122),x79123))+~P1(f315(f54(x79122),x79123))+~P1(f315(f315(f223(f909(x79122,a899)),x79121),x79123))
% 168.60/168.40 [7913]~P110(x79132)+E(x79131,f177(f909(x79132,a899)))+E(f315(f315(f222(x79132),f15(x79132,f222(x79132),x79131)),f15(x79132,f222(x79132),x79133)),f15(x79132,f222(x79132),x79133))+~P1(f315(f54(x79132),x79133))+~P1(f315(f315(f223(f909(x79132,a899)),x79131),x79133))
% 168.60/168.40 [8113]~E(f876(x81131,x81133,x81132),f877(x81131,x81133,x81132))+~E(f315(f28(x81132),f878(x81131,x81133,x81132)),x81131)+E(f315(f315(f74(a901),x81131),f315(f28(f909(x81132,a899)),x81133)),f315(f28(x81132),f30(f909(x81132,a899),x81133)))+~P1(f315(f54(x81132),f30(f909(x81132,a899),x81133)))+~P1(f315(f54(f909(x81132,a899)),x81133))
% 168.60/168.40 [8296]~P110(x82962)+E(x82961,f177(f909(x82962,a899)))+~P1(f315(f54(x82962),x82963))+P1(f315(f315(f223(x82962),f315(f56(x82962,f221(x82962)),x82963)),f315(f56(x82962,f221(x82962)),x82961)))+~P1(f315(f315(f223(f909(x82962,a899)),x82961),x82963))
% 168.60/168.40 [8595]~E(f876(x85951,x85953,x85952),f877(x85951,x85953,x85952))+E(f315(f315(f74(a901),x85951),f315(f28(f909(x85952,a899)),x85953)),f315(f28(x85952),f30(f909(x85952,a899),x85953)))+P1(f315(f315(f317(f909(x85952,a899)),f878(x85951,x85953,x85952)),x85953))+~P1(f315(f54(x85952),f30(f909(x85952,a899),x85953)))+~P1(f315(f54(f909(x85952,a899)),x85953))
% 168.60/168.40 [8621]~E(f315(f28(x86212),f878(x86211,x86213,x86212)),x86211)+E(f315(f315(f74(a901),x86211),f315(f28(f909(x86212,a899)),x86213)),f315(f28(x86212),f30(f909(x86212,a899),x86213)))+P1(f315(f315(f317(f909(x86212,a899)),f877(x86211,x86213,x86212)),x86213))+~P1(f315(f54(x86212),f30(f909(x86212,a899),x86213)))+~P1(f315(f54(f909(x86212,a899)),x86213))
% 168.60/168.40 [8622]~E(f315(f28(x86222),f878(x86221,x86223,x86222)),x86221)+E(f315(f315(f74(a901),x86221),f315(f28(f909(x86222,a899)),x86223)),f315(f28(x86222),f30(f909(x86222,a899),x86223)))+P1(f315(f315(f317(f909(x86222,a899)),f876(x86221,x86223,x86222)),x86223))+~P1(f315(f54(x86222),f30(f909(x86222,a899),x86223)))+~P1(f315(f54(f909(x86222,a899)),x86223))
% 168.60/168.40 [8647]~E(f315(f28(x86472),f878(x86471,x86473,x86472)),x86471)+~E(f315(f315(f90(f909(x86472,a899)),f877(x86471,x86473,x86472)),f876(x86471,x86473,x86472)),f177(f909(x86472,a899)))+E(f315(f315(f74(a901),x86471),f315(f28(f909(x86472,a899)),x86473)),f315(f28(x86472),f30(f909(x86472,a899),x86473)))+~P1(f315(f54(f909(x86472,a899)),x86473))+~P1(f315(f54(x86472),f30(f909(x86472,a899),x86473)))
% 168.60/168.40 [8911]E(f315(f315(f74(a901),x89111),f315(f28(f909(x89112,a899)),x89113)),f315(f28(x89112),f30(f909(x89112,a899),x89113)))+P1(f315(f315(f317(f909(x89112,a899)),f878(x89111,x89113,x89112)),x89113))+P1(f315(f315(f317(f909(x89112,a899)),f877(x89111,x89113,x89112)),x89113))+~P1(f315(f54(f909(x89112,a899)),x89113))+~P1(f315(f54(x89112),f30(f909(x89112,a899),x89113)))
% 168.60/168.40 [8912]E(f315(f315(f74(a901),x89121),f315(f28(f909(x89122,a899)),x89123)),f315(f28(x89122),f30(f909(x89122,a899),x89123)))+P1(f315(f315(f317(f909(x89122,a899)),f878(x89121,x89123,x89122)),x89123))+P1(f315(f315(f317(f909(x89122,a899)),f876(x89121,x89123,x89122)),x89123))+~P1(f315(f54(f909(x89122,a899)),x89123))+~P1(f315(f54(x89122),f30(f909(x89122,a899),x89123)))
% 168.60/168.40 [8938]~E(f315(f315(f90(f909(x89382,a899)),f877(x89381,x89383,x89382)),f876(x89381,x89383,x89382)),f177(f909(x89382,a899)))+E(f315(f315(f74(a901),x89381),f315(f28(f909(x89382,a899)),x89383)),f315(f28(x89382),f30(f909(x89382,a899),x89383)))+~P1(f315(f54(f909(x89382,a899)),x89383))+P1(f315(f315(f317(f909(x89382,a899)),f878(x89381,x89383,x89382)),x89383))+~P1(f315(f54(x89382),f30(f909(x89382,a899),x89383)))
% 168.60/168.40 [9194]~P99(x91942)+E(x91941,f177(f909(x91942,a899)))+~E(f315(f315(f74(x91942),f315(x91943,f515(x91941,x91943,x91942))),f315(x91943,f516(x91941,x91943,x91942))),f315(x91943,f315(f315(f74(x91942),f515(x91941,x91943,x91942)),f516(x91941,x91943,x91942))))+~P1(f315(f54(x91942),x91941))+E(f315(f56(x91942,f74(x91942)),f315(f298(x91942,x91942,x91943),x91941)),f315(x91943,f315(f56(x91942,f74(x91942)),x91941)))
% 168.60/168.40 [10135]P1(f315(f315(x101351,x101352),x101353))+P1(f315(f315(f224(a1),f375(x101351,x101353,x101352)),f376(x101351,x101353,x101352)))+P1(f315(f315(f223(a1),f376(x101351,x101353,x101352)),f2(a1)))+P1(f315(f315(x101351,f375(x101351,x101353,x101352)),f315(f315(f74(a1),f315(f92(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),f376(x101351,x101353,x101352))))+~P1(f315(f303(f908(a1,a1),a51),f315(f315(f240(a1,a1),x101352),x101353)))
% 168.60/168.40 [10141]P1(f315(f315(x101411,x101412),x101413))+P1(f315(f315(f223(a1),f374(x101411,x101413,x101412)),f2(a1)))+P1(f315(f315(x101411,f372(x101411,x101413,x101412)),f315(f315(f74(a1),f315(f92(a1),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),f374(x101411,x101413,x101412))))+P1(f315(f315(f223(a1),f2(a1)),f315(f315(f73(a1),f372(x101411,x101413,x101412)),f374(x101411,x101413,x101412))))+~P1(f315(f303(f908(a1,a1),a45),f315(f315(f240(a1,a1),x101412),x101413)))
% 168.60/168.40 [8084]~P114(x80841)+~P1(f315(f315(f223(x80841),x80842),f71(x80841)))+~P1(f315(f315(f223(x80841),f2(x80841)),x80842))+~P1(f315(f315(f223(x80841),f2(x80841)),x80843))+P1(f315(f315(f223(x80841),f315(f315(f74(x80841),x80842),x80843)),x80843))
% 168.60/168.40 [8085]~P114(x80851)+~P1(f315(f315(f223(x80851),x80853),f71(x80851)))+~P1(f315(f315(f223(x80851),f2(x80851)),x80853))+~P1(f315(f315(f223(x80851),f2(x80851)),x80852))+P1(f315(f315(f223(x80851),f315(f315(f74(x80851),x80852),x80853)),x80852))
% 168.60/168.40 [8441]~P110(x84412)+E(x84411,f177(f909(x84412,a899)))+~P1(f315(f54(x84412),x84411))+P1(f315(f315(f317(x84412),f892(x84413,x84411,x84412)),x84411))+~P1(f315(f315(f223(x84412),f315(f56(x84412,f221(x84412)),x84411)),x84413))
% 168.60/168.40 [8442]~P110(x84422)+E(x84421,f177(f909(x84422,a899)))+~P1(f315(f54(x84422),x84421))+P1(f315(f315(f317(x84422),f895(x84423,x84421,x84422)),x84421))+~P1(f315(f315(f224(x84422),f315(f56(x84422,f221(x84422)),x84421)),x84423))
% 168.60/168.40 [8443]~P110(x84432)+E(x84431,f177(f909(x84432,a899)))+~P1(f315(f54(x84432),x84431))+P1(f315(f315(f223(x84432),f892(x84433,x84431,x84432)),x84433))+~P1(f315(f315(f223(x84432),f315(f56(x84432,f221(x84432)),x84431)),x84433))
% 168.60/168.40 [8444]~P110(x84442)+E(x84441,f177(f909(x84442,a899)))+~P1(f315(f54(x84442),x84441))+P1(f315(f315(f224(x84442),f895(x84443,x84441,x84442)),x84443))+~P1(f315(f315(f224(x84442),f315(f56(x84442,f221(x84442)),x84441)),x84443))
% 168.60/168.40 [8530]~P1(f315(x85301,x85303))+P1(f315(x85301,f458(x85301,x85302)))+P1(f315(x85301,f456(x85301,x85302)))+~P1(f315(f315(f224(a1),f2(a1)),x85302))+P1(f315(x85301,f315(f315(f3(a1),f456(x85301,x85302)),f315(f315(f74(a1),f459(x85301,x85302)),x85302))))
% 168.60/168.40 [8748]~P1(f315(x87481,x87483))+P1(f315(x87481,f456(x87481,x87482)))+~P1(f315(f315(f224(a1),f2(a1)),x87482))+P1(f315(f315(f317(a1),f458(x87481,x87482)),f291(a1,f71(a1),x87482)))+P1(f315(x87481,f315(f315(f3(a1),f456(x87481,x87482)),f315(f315(f74(a1),f459(x87481,x87482)),x87482))))
% 168.60/168.40 [8960]~P1(f315(x89601,x89603))+~P1(f315(x89601,f456(x89601,x89602)))+P1(f315(x89601,f458(x89601,x89602)))+~P1(f315(f315(f224(a1),f2(a1)),x89602))+~P1(f315(x89601,f315(f315(f3(a1),f456(x89601,x89602)),f315(f315(f74(a1),f459(x89601,x89602)),x89602))))
% 168.60/168.40 [9085]~P1(f315(x90851,x90853))+~P1(f315(x90851,f456(x90851,x90852)))+~P1(f315(f315(f224(a1),f2(a1)),x90852))+P1(f315(f315(f317(a1),f458(x90851,x90852)),f291(a1,f71(a1),x90852)))+~P1(f315(x90851,f315(f315(f3(a1),f456(x90851,x90852)),f315(f315(f74(a1),f459(x90851,x90852)),x90852))))
% 168.60/168.40 [8866]~P80(x88661)+~P1(f315(f54(x88661),x88662))+E(f315(f315(f3(f909(x88661,a899)),x88662),f315(f315(f297(x88661),x88663),f177(f909(x88661,a899)))),f177(f909(x88661,a899)))+~P1(f315(f315(f317(x88661),x88663),x88662))+E(f315(f315(f99(x88661),x88663),f12(x88661,f315(f315(f3(f909(x88661,a899)),x88662),f315(f315(f297(x88661),x88663),f177(f909(x88661,a899)))))),f12(x88661,x88662))
% 168.60/168.40 [8867]~P80(x88671)+~P1(f315(f54(x88671),x88672))+E(f315(f315(f3(f909(x88671,a899)),x88672),f315(f315(f297(x88671),x88673),f177(f909(x88671,a899)))),f177(f909(x88671,a899)))+~P1(f315(f315(f317(x88671),x88673),x88672))+E(f315(f315(f90(x88671),x88673),f13(x88671,f315(f315(f3(f909(x88671,a899)),x88672),f315(f315(f297(x88671),x88673),f177(f909(x88671,a899)))))),f13(x88671,x88672))
% 168.60/168.40 [8868]~P110(x88681)+~P1(f315(f54(x88681),x88682))+E(f315(f315(f3(f909(x88681,a899)),x88682),f315(f315(f297(x88681),x88683),f177(f909(x88681,a899)))),f177(f909(x88681,a899)))+~P1(f315(f315(f317(x88681),x88683),x88682))+E(f315(f315(f221(x88681),x88683),f16(x88681,f315(f315(f3(f909(x88681,a899)),x88682),f315(f315(f297(x88681),x88683),f177(f909(x88681,a899)))))),f16(x88681,x88682))
% 168.60/168.40 [8869]~P110(x88691)+~P1(f315(f54(x88691),x88692))+E(f315(f315(f3(f909(x88691,a899)),x88692),f315(f315(f297(x88691),x88693),f177(f909(x88691,a899)))),f177(f909(x88691,a899)))+~P1(f315(f315(f317(x88691),x88693),x88692))+E(f315(f315(f222(x88691),x88693),f17(x88691,f315(f315(f3(f909(x88691,a899)),x88692),f315(f315(f297(x88691),x88693),f177(f909(x88691,a899)))))),f17(x88691,x88692))
% 168.60/168.40 [8931]~P110(x89311)+~P1(f315(f54(x89311),x89312))+E(f315(f315(f3(f909(x89311,a899)),x89312),f315(f315(f297(x89311),x89313),f177(f909(x89311,a899)))),f177(f909(x89311,a899)))+~P1(f315(f315(f317(x89311),x89313),x89312))+E(f315(f315(f221(x89311),x89313),f14(x89311,f221(x89311),f315(f315(f3(f909(x89311,a899)),x89312),f315(f315(f297(x89311),x89313),f177(f909(x89311,a899)))))),f14(x89311,f221(x89311),x89312))
% 168.60/168.40 [8932]~P110(x89321)+~P1(f315(f54(x89321),x89322))+E(f315(f315(f3(f909(x89321,a899)),x89322),f315(f315(f297(x89321),x89323),f177(f909(x89321,a899)))),f177(f909(x89321,a899)))+~P1(f315(f315(f317(x89321),x89323),x89322))+E(f315(f315(f222(x89321),x89323),f15(x89321,f222(x89321),f315(f315(f3(f909(x89321,a899)),x89322),f315(f315(f297(x89321),x89323),f177(f909(x89321,a899)))))),f15(x89321,f222(x89321),x89322))
% 168.60/168.40 [8947]~P80(x89471)+~P1(f315(f54(x89471),x89473))+~P1(f315(f54(x89471),x89472))+E(f315(f315(f90(f909(x89471,a899)),x89472),x89473),f177(f909(x89471,a899)))+E(f315(f315(f99(x89471),f12(x89471,f315(f315(f99(f909(x89471,a899)),x89472),x89473))),f12(x89471,f315(f315(f90(f909(x89471,a899)),x89472),x89473))),f315(f315(f99(x89471),f12(x89471,x89472)),f12(x89471,x89473)))
% 168.60/168.40 [8948]~P80(x89481)+~P1(f315(f54(x89481),x89483))+~P1(f315(f54(x89481),x89482))+E(f315(f315(f90(f909(x89481,a899)),x89482),x89483),f177(f909(x89481,a899)))+E(f315(f315(f90(x89481),f13(x89481,f315(f315(f99(f909(x89481,a899)),x89482),x89483))),f13(x89481,f315(f315(f90(f909(x89481,a899)),x89482),x89483))),f315(f315(f90(x89481),f13(x89481,x89482)),f13(x89481,x89483)))
% 168.60/168.40 [8949]~P110(x89491)+~P1(f315(f54(x89491),x89493))+~P1(f315(f54(x89491),x89492))+E(f315(f315(f90(f909(x89491,a899)),x89492),x89493),f177(f909(x89491,a899)))+E(f315(f315(f221(x89491),f16(x89491,f315(f315(f99(f909(x89491,a899)),x89492),x89493))),f16(x89491,f315(f315(f90(f909(x89491,a899)),x89492),x89493))),f315(f315(f221(x89491),f16(x89491,x89492)),f16(x89491,x89493)))
% 168.60/168.40 [8950]~P110(x89501)+~P1(f315(f54(x89501),x89503))+~P1(f315(f54(x89501),x89502))+E(f315(f315(f90(f909(x89501,a899)),x89502),x89503),f177(f909(x89501,a899)))+E(f315(f315(f222(x89501),f17(x89501,f315(f315(f99(f909(x89501,a899)),x89502),x89503))),f17(x89501,f315(f315(f90(f909(x89501,a899)),x89502),x89503))),f315(f315(f222(x89501),f17(x89501,x89502)),f17(x89501,x89503)))
% 168.60/168.40 [9166]~P110(x91661)+~P1(f315(f54(x91661),x91663))+~P1(f315(f54(x91661),x91662))+E(f315(f315(f90(f909(x91661,a899)),x91662),x91663),f177(f909(x91661,a899)))+E(f315(f315(f221(x91661),f14(x91661,f221(x91661),f315(f315(f99(f909(x91661,a899)),x91662),x91663))),f14(x91661,f221(x91661),f315(f315(f90(f909(x91661,a899)),x91662),x91663))),f315(f315(f221(x91661),f14(x91661,f221(x91661),x91662)),f14(x91661,f221(x91661),x91663)))
% 168.60/168.40 [9167]~P110(x91671)+~P1(f315(f54(x91671),x91673))+~P1(f315(f54(x91671),x91672))+E(f315(f315(f90(f909(x91671,a899)),x91672),x91673),f177(f909(x91671,a899)))+E(f315(f315(f222(x91671),f15(x91671,f222(x91671),f315(f315(f99(f909(x91671,a899)),x91672),x91673))),f15(x91671,f222(x91671),f315(f315(f90(f909(x91671,a899)),x91672),x91673))),f315(f315(f222(x91671),f15(x91671,f222(x91671),x91672)),f15(x91671,f222(x91671),x91673)))
% 168.60/168.40 [9974]~P128(x99743)+E(x99741,x99742)+~P1(f315(f315(f223(x99743),f2(x99743)),x99742))+~P1(f315(f315(f223(x99743),f2(x99743)),x99741))+~E(f315(f315(f232(x99743),x99741),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))),f315(f315(f232(x99743),x99742),f315(f92(a901),f315(f315(f73(a1),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)),f315(f315(f3(a1),f315(f315(f73(a1),a76),a76)),a86)))))
% 168.60/168.40 [5977]~P62(x59772)+E(x59771,f2(x59772))+~E(f315(f315(f29(x59772),x59773),x59771),x59774)+E(x59773,f315(f315(f74(x59772),x59774),x59771))+~P1(f315(f315(f275(x59772),x59771),x59773))
% 168.60/168.40 [5978]~P62(x59782)+E(x59781,f2(x59782))+~E(x59783,f315(f315(f74(x59782),x59784),x59781))+E(f315(f315(f29(x59782),x59783),x59781),x59784)+~P1(f315(f315(f275(x59782),x59781),x59783))
% 168.60/168.40 [6454]E(f763(x64541,x64542,x64543),x64544)+E(f315(x64541,x64544),f2(a901))+~E(f315(f315(f8(x64543,a901),x64541),x64542),f71(a901))+~P1(f315(f54(x64543),x64542))+~P1(f315(f315(f317(x64543),x64544),x64542))
% 168.60/168.40 [6520]E(f740(x65201,x65202,x65203),x65204)+E(f315(x65201,x65204),f2(a901))+~E(f315(f315(f8(x65203,a901),x65201),x65202),f315(a101,f2(a901)))+~P1(f315(f54(x65203),x65202))+~P1(f315(f315(f317(x65203),x65204),x65202))
% 168.60/168.40 [6632]~P110(x66321)+~P5(x66321)+P1(f315(f315(f224(x66321),x66322),f30(x66321,x66323)))+~P1(f315(f315(f224(x66321),x66322),x66324))+~P1(f315(f315(f317(x66321),x66324),x66323))
% 168.60/168.40 [6809]~P110(x68091)+~P5(x68091)+~P1(f315(f315(f224(x68091),x68094),x68093))+P1(f315(f315(f224(x68091),f31(x68091,x68092)),x68093))+~P1(f315(f315(f317(x68091),x68094),x68092))
% 168.60/168.40 [7077]~P128(x70773)+E(x70771,x70772)+~E(f315(f315(f232(x70773),x70771),f315(a101,x70774)),f315(f315(f232(x70773),x70772),f315(a101,x70774)))+~P1(f315(f315(f223(x70773),f2(x70773)),x70772))+~P1(f315(f315(f223(x70773),f2(x70773)),x70771))
% 168.60/168.40 [7291]~E(f776(x72912,x72913,x72911,x72914),x72914)+~E(f315(x72912,x72914),f71(a901))+E(f315(f315(f8(x72911,a901),x72912),x72913),f71(a901))+~P1(f315(f54(x72911),x72913))+~P1(f315(f315(f317(x72911),x72914),x72913))
% 168.60/168.40 [7298]~P121(x72984)+~P134(x72984)+E(f315(x72981,f650(x72981,x72982,x72983,x72984)),f2(x72984))+~E(f315(f315(f11(x72983,x72984),x72981),x72982),f2(x72984))+~P1(f315(f54(x72983),x72982))
% 168.60/168.40 [7388]~E(f750(x73882,x73883,x73881,x73884),x73884)+~E(f315(x73882,x73884),f315(a101,f2(a901)))+E(f315(f315(f8(x73881,a901),x73882),x73883),f315(a101,f2(a901)))+~P1(f315(f54(x73881),x73883))+~P1(f315(f315(f317(x73881),x73884),x73883))
% 168.60/168.40 [8125]~E(f315(x81252,x81254),f71(a901))+~E(f315(x81252,f776(x81252,x81253,x81251,x81254)),f2(a901))+E(f315(f315(f8(x81251,a901),x81252),x81253),f71(a901))+~P1(f315(f54(x81251),x81253))+~P1(f315(f315(f317(x81251),x81254),x81253))
% 168.60/168.40 [8163]~E(f315(x81632,x81634),f315(a101,f2(a901)))+~E(f315(x81632,f750(x81632,x81633,x81631,x81634)),f2(a901))+E(f315(f315(f8(x81631,a901),x81632),x81633),f315(a101,f2(a901)))+~P1(f315(f54(x81631),x81633))+~P1(f315(f315(f317(x81631),x81634),x81633))
% 168.60/168.40 [8251]~P148(x82512)+~P124(x82512)+~P1(f315(x82511,x82514))+~P1(f315(f315(f275(x82512),x82513),f315(f315(f73(x82512),x82514),f2(x82512))))+P1(f315(x82511,f315(f315(f74(x82512),x82513),f840(x82513,x82511,x82512))))
% 168.60/168.40 [8715]~P110(x87151)+~P13(x87151,x87154)+P13(x87151,x87152)+~E(x87152,f315(f315(f140(x87151),x87153),x87154))+~P1(f315(f315(f223(x87151),x87153),f711(x87152,x87151,x87154,x87153)))
% 168.60/168.40 [8752]E(x87521,x87522)+E(f315(f315(f3(a1),f437(x87523,x87522,x87524,x87521)),f438(x87523,x87522,x87524,x87521)),x87521)+~E(f315(f315(f73(a1),x87521),x87524),x87522)+~P1(f315(f315(f224(a1),f2(a1)),x87524))+~P1(f315(f315(f317(a1),x87522),x87523))
% 168.60/168.40 [8753]E(x87531,x87532)+E(f315(f315(f73(a1),f449(x87533,x87532,x87534,x87531)),f450(x87533,x87532,x87534,x87531)),x87531)+~E(f315(f315(f3(a1),x87531),x87534),x87532)+~P1(f315(f315(f224(a1),f2(a1)),x87534))+~P1(f315(f315(f317(a1),x87532),x87533))
% 168.60/168.40 [8945]E(f315(x89451,f368(x89452,x89451,x89453,x89454)),x89452)+P1(f315(f315(f223(a901),x89454),f365(x89452,x89451,x89453,x89454)))+~P1(f315(f315(f223(a1),x89452),f315(x89451,x89453)))+~P1(f315(f315(f224(a901),x89454),x89453))+~P1(f315(f315(f223(a1),f315(x89451,x89454)),x89452))
% 168.60/168.40 [8946]~P110(x89461)+~P13(x89461,x89463)+P13(x89461,x89462)+~E(x89462,f315(f315(f140(x89461),x89464),x89463))+P1(f315(f315(f317(x89461),f711(x89462,x89461,x89463,x89464)),f315(f161(x89461),x89463)))
% 168.60/168.40 [8964]~P121(x89644)+~P134(x89644)+~E(f315(f315(f11(x89641,x89644),x89642),x89643),f2(x89644))+~P1(f315(f54(x89641),x89643))+P1(f315(f315(f317(x89641),f650(x89642,x89643,x89641,x89644)),x89643))
% 168.60/168.40 [9002]~E(f315(x90022,x90024),f71(a901))+E(f315(f315(f8(x90021,a901),x90022),x90023),f71(a901))+~P1(f315(f54(x90021),x90023))+~P1(f315(f315(f317(x90021),x90024),x90023))+P1(f315(f315(f317(x90021),f776(x90022,x90023,x90021,x90024)),x90023))
% 168.60/168.40 [9014]E(x90141,x90142)+~E(f315(f315(f73(a1),x90142),x90144),x90141)+~P1(f315(f315(f224(a1),f2(a1)),x90144))+~P1(f315(f315(f317(a1),x90141),x90143))+P1(f315(f315(f317(a1),f437(x90143,x90141,x90144,x90142)),x90143))
% 168.60/168.40 [9015]E(x90151,x90152)+~E(f315(f315(f3(a1),x90152),x90154),x90151)+~P1(f315(f315(f224(a1),f2(a1)),x90154))+~P1(f315(f315(f317(a1),x90151),x90153))+P1(f315(f315(f317(a1),f449(x90153,x90151,x90154,x90152)),x90153))
% 168.60/168.40 [9017]~E(f315(x90172,x90174),f315(a101,f2(a901)))+E(f315(f315(f8(x90171,a901),x90172),x90173),f315(a101,f2(a901)))+~P1(f315(f54(x90171),x90173))+~P1(f315(f315(f317(x90171),x90174),x90173))+P1(f315(f315(f317(x90171),f750(x90172,x90173,x90171,x90174)),x90173))
% 168.60/168.40 [9022]P60(x90222,x90223,x90224,x90221)+E(x90221,f177(f909(x90222,a899)))+~P1(f315(f54(x90222),x90224))+~P1(f315(f54(x90222),x90221))+P1(f315(f315(f317(x90222),f779(x90223,x90221,x90224,x90222)),x90224))
% 168.60/168.40 [9023]P60(x90232,x90233,x90234,x90231)+E(x90231,f177(f909(x90232,a899)))+~P1(f315(f54(x90232),x90234))+~P1(f315(f54(x90232),x90231))+P1(f315(f315(f317(x90232),f503(x90231,x90234,x90233,x90232)),x90234))
% 168.60/168.40 [9024]P60(x90242,x90243,x90244,x90241)+E(x90241,f177(f909(x90242,a899)))+~P1(f315(f54(x90242),x90244))+~P1(f315(f54(x90242),x90241))+P1(f315(f315(f317(x90242),f780(x90241,x90244,x90243,x90242)),x90244))
% 168.60/168.40 [9098]E(x90981,x90982)+~E(f315(f315(f73(a1),x90982),x90984),x90981)+~P1(f315(f315(f224(a1),f2(a1)),x90984))+~P1(f315(f315(f317(a1),x90981),x90983))+P1(f315(f315(f317(a1),f438(x90983,x90981,x90984,x90982)),f291(a1,f71(a1),x90984)))
% 168.60/168.40 [9099]E(x90991,x90992)+~E(f315(f315(f3(a1),x90992),x90994),x90991)+~P1(f315(f315(f224(a1),f2(a1)),x90994))+~P1(f315(f315(f317(a1),x90991),x90993))+P1(f315(f315(f317(a1),f450(x90993,x90991,x90994,x90992)),f291(a1,f71(a1),x90994)))
% 168.60/168.40 [9172]P1(f315(f315(f223(a901),x91721),f368(x91722,x91723,x91724,x91721)))+~P1(f315(f315(f223(a1),x91722),f315(x91723,x91724)))+P1(f315(f315(f223(a901),x91721),f365(x91722,x91723,x91724,x91721)))+~P1(f315(f315(f224(a901),x91721),x91724))+~P1(f315(f315(f223(a1),f315(x91723,x91721)),x91722))
% 168.60/168.40 [9286]E(f315(x92861,f368(x92862,x92861,x92863,x92864)),x92862)+~P1(f315(f315(f223(a1),x92862),f315(x92861,x92863)))+P1(f315(f315(f224(a901),f365(x92862,x92861,x92863,x92864)),x92863))+~P1(f315(f315(f224(a901),x92864),x92863))+~P1(f315(f315(f223(a1),f315(x92861,x92864)),x92862))
% 168.60/168.40 [9401]~P1(f315(f315(f275(a901),x94014),x94011))+~P1(f315(f315(f275(a901),x94014),x94013))+~P1(f315(f315(f275(a901),x94012),x94011))+P1(f315(f315(f275(a901),x94011),x94012))+P1(f315(f315(f224(f909(a901,a899)),f278(a901,f275(a901),x94013,x94012)),f278(a901,f275(a901),x94014,x94011)))
% 168.60/168.40 [9402]~P1(f315(f315(f275(a901),x94022),x94021))+~P1(f315(f315(f275(a901),x94023),x94024))+~P1(f315(f315(f275(a901),x94022),x94024))+P1(f315(f315(f275(a901),x94021),x94022))+P1(f315(f315(f224(f909(a901,a899)),f278(a901,f275(a901),x94021,x94023)),f278(a901,f275(a901),x94022,x94024)))
% 168.60/168.40 [9419]~P1(f315(f315(f223(a1),x94192),f315(x94193,x94194)))+P1(f315(f315(f223(a901),x94191),f365(x94192,x94193,x94194,x94191)))+P1(f315(f315(f223(a901),f368(x94192,x94193,x94194,x94191)),x94194))+~P1(f315(f315(f224(a901),x94191),x94194))+~P1(f315(f315(f223(a1),f315(x94193,x94191)),x94192))
% 168.60/168.40 [9420]~P1(f315(f315(f223(a1),x94202),f315(x94203,x94204)))+P1(f315(f315(f223(a901),x94201),f368(x94202,x94203,x94204,x94201)))+P1(f315(f315(f224(a901),f365(x94202,x94203,x94204,x94201)),x94204))+~P1(f315(f315(f224(a901),x94201),x94204))+~P1(f315(f315(f223(a1),f315(x94203,x94201)),x94202))
% 168.60/168.40 [9528]~P1(f315(f315(f223(a1),x95281),f315(x95282,x95283)))+P1(f315(f315(f224(a901),f365(x95281,x95282,x95283,x95284)),x95283))+~P1(f315(f315(f224(a901),x95284),x95283))+~P1(f315(f315(f223(a1),f315(x95282,x95284)),x95281))+P1(f315(f315(f223(a901),f368(x95281,x95282,x95283,x95284)),x95283))
% 168.60/168.40 [9622]E(x96221,f177(f909(x96222,a899)))+~P1(f315(f54(x96222),x96224))+~P1(f315(f54(x96222),x96221))+P1(f315(f315(f317(f908(f909(x96222,a899),f909(x96222,a899))),f315(f315(f240(f909(x96222,a899),f909(x96222,a899)),x96224),x96221)),f306(x96222,x96223)))+P1(f315(f315(f317(x96222),f384(x96223,x96221,x96224,x96222)),x96224))
% 168.60/168.40 [9623]E(x96231,f177(f909(x96232,a899)))+~P1(f315(f54(x96232),x96234))+~P1(f315(f54(x96232),x96231))+P1(f315(f315(f317(f908(f909(x96232,a899),f909(x96232,a899))),f315(f315(f240(f909(x96232,a899),f909(x96232,a899)),x96234),x96231)),f306(x96232,x96233)))+P1(f315(f315(f317(x96232),f588(x96233,x96231,x96234,x96232)),x96234))
% 168.60/168.40 [10295]E(f315(x102951,f368(x102952,x102951,x102953,x102954)),x102952)+~P1(f315(f315(f223(a1),x102952),f315(x102951,x102953)))+~P1(f315(f315(f223(a1),f315(f69(a1),f315(f315(f3(a1),f315(x102951,f315(f315(f73(a901),f365(x102952,x102951,x102953,x102954)),f71(a901)))),f315(x102951,f365(x102952,x102951,x102953,x102954))))),f71(a1)))+~P1(f315(f315(f224(a901),x102954),x102953))+~P1(f315(f315(f223(a1),f315(x102951,x102954)),x102952))
% 168.60/168.40 [10296]~P1(f315(f315(f223(a1),x102962),f315(x102963,x102964)))+P1(f315(f315(f223(a901),x102961),f368(x102962,x102963,x102964,x102961)))+~P1(f315(f315(f223(a1),f315(f69(a1),f315(f315(f3(a1),f315(x102963,f315(f315(f73(a901),f365(x102962,x102963,x102964,x102961)),f71(a901)))),f315(x102963,f365(x102962,x102963,x102964,x102961))))),f71(a1)))+~P1(f315(f315(f224(a901),x102961),x102964))+~P1(f315(f315(f223(a1),f315(x102963,x102961)),x102962))
% 168.60/168.40 [10297]~P1(f315(f315(f223(a1),x102971),f315(x102972,x102973)))+~P1(f315(f315(f223(a1),f315(f69(a1),f315(f315(f3(a1),f315(x102972,f315(f315(f73(a901),f365(x102971,x102972,x102973,x102974)),f71(a901)))),f315(x102972,f365(x102971,x102972,x102973,x102974))))),f71(a1)))+~P1(f315(f315(f224(a901),x102974),x102973))+~P1(f315(f315(f223(a1),f315(x102972,x102974)),x102971))+P1(f315(f315(f223(a901),f368(x102971,x102972,x102973,x102974)),x102973))
% 168.60/168.40 [7351]~P67(x73511)+P1(f315(f315(f224(x73511),x73512),f2(x73511)))+~P1(f315(f315(f223(x73511),x73513),f2(x73511)))+P1(f315(f315(f224(x73511),f2(x73511)),x73512))+P1(f315(f315(f223(x73511),x73513),f315(f315(f279(x73511),x73514),x73512)))
% 168.60/168.40 [7352]~P67(x73521)+P1(f315(f315(f224(x73521),x73522),f2(x73521)))+~P1(f315(f315(f224(x73521),x73523),f2(x73521)))+P1(f315(f315(f224(x73521),f2(x73521)),x73522))+P1(f315(f315(f224(x73521),x73523),f315(f315(f279(x73521),x73524),x73522)))
% 168.60/168.40 [7602]~P67(x76021)+P1(f315(f315(f223(x76021),x76022),f2(x76021)))+P1(f315(f315(f224(x76021),x76023),f2(x76021)))+P1(f315(f315(f224(x76021),f2(x76021)),x76023))+~P1(f315(f315(f223(x76021),x76022),f315(f315(f279(x76021),x76024),x76023)))
% 168.60/168.40 [7603]~P67(x76031)+P1(f315(f315(f224(x76031),x76032),f2(x76031)))+P1(f315(f315(f224(x76031),x76033),f2(x76031)))+P1(f315(f315(f224(x76031),f2(x76031)),x76033))+~P1(f315(f315(f224(x76031),x76032),f315(f315(f279(x76031),x76034),x76033)))
% 168.60/168.40 [7721]E(x77211,x77212)+~E(f315(f315(f153(x77213),x77214),x77211),f315(f315(f153(x77213),x77214),x77212))+~P1(f315(f126(x77213),x77214))+~P1(f315(f315(f224(a901),x77212),f315(f178(f902(x77213)),x77214)))+~P1(f315(f315(f224(a901),x77211),f315(f178(f902(x77213)),x77214)))
% 168.60/168.40 [8086]~P67(x80861)+~P1(f315(f315(f223(x80861),x80863),f2(x80861)))+P1(f315(f315(f224(x80861),f2(x80861)),x80862))+~P1(f315(f315(f223(x80861),x80864),f315(f315(f74(x80861),x80863),x80862)))+P1(f315(f315(f223(x80861),x80863),f315(f315(f279(x80861),x80864),x80862)))
% 168.60/168.40 [8087]~P67(x80871)+~P1(f315(f315(f224(x80871),x80873),f2(x80871)))+P1(f315(f315(f224(x80871),f2(x80871)),x80872))+~P1(f315(f315(f224(x80871),x80874),f315(f315(f74(x80871),x80873),x80872)))+P1(f315(f315(f224(x80871),x80873),f315(f315(f279(x80871),x80874),x80872)))
% 168.60/168.40 [8088]~P67(x80881)+~P1(f315(f315(f224(x80881),x80882),f2(x80881)))+P1(f315(f315(f224(x80881),f2(x80881)),x80882))+~P1(f315(f315(f223(x80881),x80884),f315(f315(f74(x80881),x80883),x80882)))+P1(f315(f315(f223(x80881),x80883),f315(f315(f279(x80881),x80884),x80882)))
% 168.60/168.40 [8089]~P67(x80891)+~P1(f315(f315(f224(x80891),x80892),f2(x80891)))+P1(f315(f315(f224(x80891),f2(x80891)),x80892))+~P1(f315(f315(f223(x80891),x80894),f315(f315(f279(x80891),x80893),x80892)))+P1(f315(f315(f223(x80891),x80893),f315(f315(f74(x80891),x80894),x80892)))
% 168.60/168.40 [8090]~P67(x80901)+~P1(f315(f315(f224(x80901),x80902),f2(x80901)))+P1(f315(f315(f224(x80901),f2(x80901)),x80902))+~P1(f315(f315(f224(x80901),x80904),f315(f315(f74(x80901),x80903),x80902)))+P1(f315(f315(f224(x80901),x80903),f315(f315(f279(x80901),x80904),x80902)))
% 168.60/168.40 [8091]~P67(x80911)+~P1(f315(f315(f224(x80911),x80912),f2(x80911)))+P1(f315(f315(f224(x80911),f2(x80911)),x80912))+~P1(f315(f315(f224(x80911),x80914),f315(f315(f279(x80911),x80913),x80912)))+P1(f315(f315(f224(x80911),x80913),f315(f315(f74(x80911),x80914),x80912)))
% 168.60/168.40 [8218]~P62(x82181)+~P1(f315(f315(f275(x82181),x82183),x82184))+~P1(f315(f315(f275(x82181),x82183),x82182))+~P1(f315(f315(f275(x82181),x82182),x82184))+P1(f315(f315(f275(x82181),f315(f315(f29(x82181),x82182),x82183)),f315(f315(f29(x82181),x82184),x82183)))
% 168.60/168.40 [8233]~P110(x82331)+~P13(x82331,x82332)+~P1(f315(f315(f223(a901),x82333),x82334))+P1(f315(f315(f223(x82331),f315(f315(f153(x82331),x82332),x82333)),f315(f315(f153(x82331),x82332),x82334)))+~P1(f315(f315(f224(a901),x82334),f315(f178(f902(x82331)),x82332)))
% 168.60/168.40 [8287]~P128(x82871)+~P1(f315(f315(f223(x82871),x82872),f71(x82871)))+~P1(f315(f315(f223(x82871),f2(x82871)),x82872))+~P1(f315(f315(f223(a901),x82874),x82873))+P1(f315(f315(f223(x82871),f315(f315(f232(x82871),x82872),x82873)),f315(f315(f232(x82871),x82872),x82874)))
% 168.60/168.40 [8288]~P128(x82881)+~P1(f315(f315(f224(x82881),x82882),f71(x82881)))+~P1(f315(f315(f224(x82881),f2(x82881)),x82882))+~P1(f315(f315(f224(a901),x82884),x82883))+P1(f315(f315(f224(x82881),f315(f315(f232(x82881),x82882),x82883)),f315(f315(f232(x82881),x82882),x82884)))
% 168.60/168.40 [8289]~P128(x82891)+~P1(f315(f315(f223(x82891),f2(x82891)),x82892))+~P1(f315(f315(f224(a901),f2(a901)),x82893))+~P1(f315(f315(f224(x82891),x82892),x82894))+P1(f315(f315(f224(x82891),f315(f315(f232(x82891),x82892),x82893)),f315(f315(f232(x82891),x82894),x82893)))
% 168.60/168.40 [8307]~P110(x83071)+~P13(x83071,f315(f157(x83071),x83072))+~P1(f315(f315(f223(a901),x83074),x83073))+P1(f315(f315(f223(x83071),f315(f315(f153(x83071),x83072),x83073)),f315(f315(f153(x83071),x83072),x83074)))+~P1(f315(f315(f224(a901),x83073),f315(f178(f902(x83071)),x83072)))
% 168.60/168.40 [8537]~P62(x85371)+P1(f315(f315(f275(x85371),x85372),x85373))+~P1(f315(f315(f275(x85371),x85374),x85373))+~P1(f315(f315(f275(x85371),x85374),x85372))+~P1(f315(f315(f275(x85371),f315(f315(f29(x85371),x85372),x85374)),f315(f315(f29(x85371),x85373),x85374)))
% 168.60/168.40 [8552]~P67(x85521)+~P1(f315(f315(f223(x85521),x85522),f2(x85521)))+~P1(f315(f315(f223(x85521),x85523),x85524))+~P1(f315(f315(f224(x85521),f2(x85521)),f315(f315(f74(x85521),x85523),x85524)))+P1(f315(f315(f223(x85521),f315(f315(f279(x85521),x85522),x85523)),f315(f315(f279(x85521),x85522),x85524)))
% 168.60/168.40 [8553]~P68(x85531)+~P1(f315(f315(f224(x85531),x85532),f2(x85531)))+~P1(f315(f315(f224(x85531),x85533),x85534))+~P1(f315(f315(f224(x85531),f2(x85531)),f315(f315(f74(x85531),x85533),x85534)))+P1(f315(f315(f224(x85531),f315(f315(f279(x85531),x85532),x85533)),f315(f315(f279(x85531),x85532),x85534)))
% 168.60/168.40 [8562]~P68(x85621)+~P1(f315(f315(f223(x85621),x85624),x85623))+~P1(f315(f315(f223(x85621),f2(x85621)),x85622))+~P1(f315(f315(f224(x85621),f2(x85621)),f315(f315(f74(x85621),x85623),x85624)))+P1(f315(f315(f223(x85621),f315(f315(f279(x85621),x85622),x85623)),f315(f315(f279(x85621),x85622),x85624)))
% 168.60/168.40 [8563]~P68(x85631)+~P1(f315(f315(f224(x85631),x85634),x85633))+~P1(f315(f315(f224(x85631),f2(x85631)),x85632))+~P1(f315(f315(f224(x85631),f2(x85631)),f315(f315(f74(x85631),x85633),x85634)))+P1(f315(f315(f224(x85631),f315(f315(f279(x85631),x85632),x85633)),f315(f315(f279(x85631),x85632),x85634)))
% 168.60/168.40 [8663]P1(f315(x86631,x86632))+~P1(f315(f54(x86634),x86632))+P1(f315(x86631,f486(x86631,x86633,x86632,x86634)))+~P1(f315(x86631,f177(f909(x86634,a899))))+~P1(f315(f315(f223(f909(x86634,a899)),x86632),x86633))
% 168.60/168.40 [8672]P1(f315(x86721,x86722))+P1(f315(f54(x86723),f486(x86721,x86724,x86722,x86723)))+~P1(f315(f54(x86723),x86722))+~P1(f315(x86721,f177(f909(x86723,a899))))+~P1(f315(f315(f223(f909(x86723,a899)),x86722),x86724))
% 168.60/168.40 [8940]E(f315(f315(f73(a1),f451(x89401,x89402,x89403,x89404)),f452(x89401,x89402,x89403,x89404)),x89404)+~P1(f315(f315(f224(a1),f2(a1)),x89403))+~P1(f315(f315(f224(a1),x89402),x89404))+~P1(f315(f315(f317(a1),x89402),x89401))+P1(f315(f315(f224(a1),x89402),f315(f315(f3(a1),x89404),x89403)))
% 168.60/168.40 [9154]~P1(f315(f315(f224(a1),f2(a1)),x91543))+~P1(f315(f315(f224(a1),x91542),x91544))+~P1(f315(f315(f317(a1),x91542),x91541))+P1(f315(f315(f317(a1),f451(x91541,x91542,x91543,x91544)),x91541))+P1(f315(f315(f224(a1),x91542),f315(f315(f3(a1),x91544),x91543)))
% 168.60/168.40 [9165]P1(f315(x91651,x91652))+~P1(f315(f54(x91653),x91652))+P1(f315(f315(f317(x91653),f480(x91651,x91654,x91652,x91653)),x91654))+~P1(f315(x91651,f177(f909(x91653,a899))))+~P1(f315(f315(f223(f909(x91653,a899)),x91652),x91654))
% 168.60/168.40 [9182]E(f315(f315(f73(a1),f441(x91821,x91822,x91823,x91824)),f442(x91821,x91822,x91823,x91824)),x91824)+~P1(f315(f315(f224(a1),f2(a1)),x91823))+~P1(f315(f315(f223(a1),x91822),x91824))+P1(f315(f315(f223(a1),x91822),f315(f315(f3(a1),x91824),x91823)))+~P1(f315(f315(f317(a1),f315(f315(f3(a1),x91822),f71(a1))),x91821))
% 168.60/168.40 [9236]~P1(f315(f315(f224(a1),f2(a1)),x92363))+~P1(f315(f315(f224(a1),x92361),x92362))+~P1(f315(f315(f317(a1),x92361),x92364))+P1(f315(f315(f317(a1),f452(x92364,x92361,x92363,x92362)),f291(a1,f71(a1),x92363)))+P1(f315(f315(f224(a1),x92361),f315(f315(f3(a1),x92362),x92363)))
% 168.60/168.40 [9262]~P72(x92622)+~E(f759(x92623,x92624,x92621,x92622),f760(x92623,x92624,x92621,x92622))+~P1(f315(f54(x92621),f761(x92623,x92624,x92621,x92622)))+E(f315(f315(f8(f909(x92621,a899),x92622),f315(f8(x92621,x92622),x92623)),x92624),f315(f315(f8(x92621,x92622),x92623),f30(f909(x92621,a899),x92624)))+~P1(f315(f54(f909(x92621,a899)),x92624))
% 168.60/168.40 [9266]~P72(x92662)+~E(f315(x92663,f762(x92663,x92664,x92661,x92662)),f2(x92662))+~P1(f315(f54(x92661),f761(x92663,x92664,x92661,x92662)))+E(f315(f315(f8(f909(x92661,a899),x92662),f315(f8(x92661,x92662),x92663)),x92664),f315(f315(f8(x92661,x92662),x92663),f30(f909(x92661,a899),x92664)))+~P1(f315(f54(f909(x92661,a899)),x92664))
% 168.60/168.40 [9330]~P1(f315(f315(f224(a1),f2(a1)),x93303))+~P1(f315(f315(f223(a1),x93302),x93304))+P1(f315(f315(f317(a1),f441(x93301,x93302,x93303,x93304)),x93301))+P1(f315(f315(f223(a1),x93302),f315(f315(f3(a1),x93304),x93303)))+~P1(f315(f315(f317(a1),f315(f315(f3(a1),x93302),f71(a1))),x93301))
% 168.60/168.40 [9376]~P1(f315(f315(f224(a1),f2(a1)),x93763))+~P1(f315(f315(f223(a1),x93761),x93762))+P1(f315(f315(f317(a1),f442(x93764,x93761,x93763,x93762)),f291(a1,f71(a1),x93763)))+P1(f315(f315(f223(a1),x93761),f315(f315(f3(a1),x93762),x93763)))+~P1(f315(f315(f317(a1),f315(f315(f3(a1),x93761),f71(a1))),x93764))
% 168.60/168.40 [9397]~P72(x93972)+~E(f759(x93973,x93974,x93971,x93972),f760(x93973,x93974,x93971,x93972))+E(f315(f315(f8(f909(x93971,a899),x93972),f315(f8(x93971,x93972),x93973)),x93974),f315(f315(f8(x93971,x93972),x93973),f30(f909(x93971,a899),x93974)))+P1(f315(f315(f317(f909(x93971,a899)),f761(x93973,x93974,x93971,x93972)),x93974))+~P1(f315(f54(f909(x93971,a899)),x93974))
% 168.60/168.40 [9404]~P72(x94042)+~E(f315(x94043,f762(x94043,x94044,x94041,x94042)),f2(x94042))+E(f315(f315(f8(f909(x94041,a899),x94042),f315(f8(x94041,x94042),x94043)),x94044),f315(f315(f8(x94041,x94042),x94043),f30(f909(x94041,a899),x94044)))+P1(f315(f315(f317(f909(x94041,a899)),f761(x94043,x94044,x94041,x94042)),x94044))+~P1(f315(f54(f909(x94041,a899)),x94044))
% 168.60/168.40 [9505]~P72(x95052)+~P1(f315(f54(x95051),f761(x95053,x95054,x95051,x95052)))+E(f315(f315(f8(f909(x95051,a899),x95052),f315(f8(x95051,x95052),x95053)),x95054),f315(f315(f8(x95051,x95052),x95053),f30(f909(x95051,a899),x95054)))+P1(f315(f315(f317(f909(x95051,a899)),f760(x95053,x95054,x95051,x95052)),x95054))+~P1(f315(f54(f909(x95051,a899)),x95054))
% 168.60/168.40 [9506]~P72(x95062)+~P1(f315(f54(x95061),f761(x95063,x95064,x95061,x95062)))+E(f315(f315(f8(f909(x95061,a899),x95062),f315(f8(x95061,x95062),x95063)),x95064),f315(f315(f8(x95061,x95062),x95063),f30(f909(x95061,a899),x95064)))+P1(f315(f315(f317(f909(x95061,a899)),f759(x95063,x95064,x95061,x95062)),x95064))+~P1(f315(f54(f909(x95061,a899)),x95064))
% 168.60/168.40 [9586]~P72(x95862)+E(f315(f315(f8(f909(x95861,a899),x95862),f315(f8(x95861,x95862),x95863)),x95864),f315(f315(f8(x95861,x95862),x95863),f30(f909(x95861,a899),x95864)))+P1(f315(f315(f317(f909(x95861,a899)),f761(x95863,x95864,x95861,x95862)),x95864))+P1(f315(f315(f317(f909(x95861,a899)),f760(x95863,x95864,x95861,x95862)),x95864))+~P1(f315(f54(f909(x95861,a899)),x95864))
% 168.60/168.40 [9587]~P72(x95872)+E(f315(f315(f8(f909(x95871,a899),x95872),f315(f8(x95871,x95872),x95873)),x95874),f315(f315(f8(x95871,x95872),x95873),f30(f909(x95871,a899),x95874)))+P1(f315(f315(f317(f909(x95871,a899)),f761(x95873,x95874,x95871,x95872)),x95874))+P1(f315(f315(f317(f909(x95871,a899)),f759(x95873,x95874,x95871,x95872)),x95874))+~P1(f315(f54(f909(x95871,a899)),x95874))
% 168.60/168.40 [9608]~P72(x96082)+P1(f315(f315(f317(x96081),f762(x96083,x96084,x96081,x96082)),f760(x96083,x96084,x96081,x96082)))+~P1(f315(f54(x96081),f761(x96083,x96084,x96081,x96082)))+E(f315(f315(f8(f909(x96081,a899),x96082),f315(f8(x96081,x96082),x96083)),x96084),f315(f315(f8(x96081,x96082),x96083),f30(f909(x96081,a899),x96084)))+~P1(f315(f54(f909(x96081,a899)),x96084))
% 168.60/168.40 [9609]~P72(x96092)+P1(f315(f315(f317(x96091),f762(x96093,x96094,x96091,x96092)),f759(x96093,x96094,x96091,x96092)))+~P1(f315(f54(x96091),f761(x96093,x96094,x96091,x96092)))+E(f315(f315(f8(f909(x96091,a899),x96092),f315(f8(x96091,x96092),x96093)),x96094),f315(f315(f8(x96091,x96092),x96093),f30(f909(x96091,a899),x96094)))+~P1(f315(f54(f909(x96091,a899)),x96094))
% 168.60/168.40 [9626]P1(f315(x96261,x96262))+~P1(f315(f315(f317(x96263),f480(x96261,x96264,x96262,x96263)),f486(x96261,x96264,x96262,x96263)))+~P1(f315(f54(x96263),x96262))+~P1(f315(x96261,f177(f909(x96263,a899))))+~P1(f315(f315(f223(f909(x96263,a899)),x96262),x96264))
% 168.60/168.40 [9663]~P72(x96632)+P1(f315(f315(f317(x96631),f762(x96633,x96634,x96631,x96632)),f760(x96633,x96634,x96631,x96632)))+E(f315(f315(f8(f909(x96631,a899),x96632),f315(f8(x96631,x96632),x96633)),x96634),f315(f315(f8(x96631,x96632),x96633),f30(f909(x96631,a899),x96634)))+P1(f315(f315(f317(f909(x96631,a899)),f761(x96633,x96634,x96631,x96632)),x96634))+~P1(f315(f54(f909(x96631,a899)),x96634))
% 168.60/168.40 [9664]~P72(x96642)+P1(f315(f315(f317(x96641),f762(x96643,x96644,x96641,x96642)),f759(x96643,x96644,x96641,x96642)))+E(f315(f315(f8(f909(x96641,a899),x96642),f315(f8(x96641,x96642),x96643)),x96644),f315(f315(f8(x96641,x96642),x96643),f30(f909(x96641,a899),x96644)))+P1(f315(f315(f317(f909(x96641,a899)),f761(x96643,x96644,x96641,x96642)),x96644))+~P1(f315(f54(f909(x96641,a899)),x96644))
% 168.60/168.40 [9839]P1(f315(x98391,x98392))+~P1(f315(f54(x98393),x98392))+~P1(f315(x98391,f315(f315(f297(x98393),f480(x98391,x98394,x98392,x98393)),f486(x98391,x98394,x98392,x98393))))+~P1(f315(x98391,f177(f909(x98393,a899))))+~P1(f315(f315(f223(f909(x98393,a899)),x98392),x98394))
% 168.60/168.40 [7857]~P67(x78571)+P1(f315(f315(f224(x78571),x78572),f2(x78571)))+~P1(f315(f315(f223(x78571),f2(x78571)),x78574))+P1(f315(f315(f224(x78571),f2(x78571)),x78572))+P1(f315(f315(f223(x78571),f315(f315(f279(x78571),x78573),x78572)),x78574))
% 168.60/168.40 [7858]~P67(x78581)+P1(f315(f315(f224(x78581),x78582),f2(x78581)))+P1(f315(f315(f224(x78581),f2(x78581)),x78582))+~P1(f315(f315(f224(x78581),f2(x78581)),x78584))+P1(f315(f315(f224(x78581),f315(f315(f279(x78581),x78583),x78582)),x78584))
% 168.60/168.40 [8138]~P1(f315(f315(f223(a1),x81384),f2(a1)))+~E(x81382,f315(f315(f73(a1),f315(f315(f74(a1),x81381),x81383)),x81384))+P1(f315(f315(f224(a1),f2(a1)),x81381))+~P1(f315(f315(f224(a1),x81381),x81384))+P1(f315(f42(x81382,x81381),f315(f315(f240(a1,a1),x81383),x81384)))
% 168.60/168.40 [8173]~P1(f315(x81731,x81734))+P1(f315(x81731,f332(x81732,x81731,x81733)))+~P1(f315(f315(f223(a1),f2(a1)),x81732))+~P1(f315(f315(f224(a1),f2(a1)),x81733))+P1(f315(x81731,f315(f315(f3(a1),x81734),f315(f315(f74(a1),x81732),x81733))))
% 168.60/168.40 [8174]~P1(f315(x81741,x81744))+P1(f315(x81741,f336(x81742,x81741,x81743)))+~P1(f315(f315(f223(a1),f2(a1)),x81742))+~P1(f315(f315(f224(a1),f2(a1)),x81743))+P1(f315(x81741,f315(f315(f73(a1),x81744),f315(f315(f74(a1),x81742),x81743))))
% 168.60/168.40 [8175]~P67(x81751)+P1(f315(f315(f224(x81751),x81752),f2(x81751)))+P1(f315(f315(f224(x81751),f2(x81751)),x81752))+P1(f315(f315(f223(x81751),f2(x81751)),x81753))+~P1(f315(f315(f223(x81751),f315(f315(f279(x81751),x81754),x81752)),x81753))
% 168.60/168.40 [8176]~P67(x81761)+P1(f315(f315(f224(x81761),x81762),f2(x81761)))+P1(f315(f315(f224(x81761),f2(x81761)),x81762))+P1(f315(f315(f224(x81761),f2(x81761)),x81763))+~P1(f315(f315(f224(x81761),f315(f315(f279(x81761),x81764),x81762)),x81763))
% 168.60/168.40 [8228]~E(x82281,f315(f315(f73(a1),f315(f315(f74(a1),x82282),x82283)),x82284))+~P1(f315(f315(f223(a1),f2(a1)),x82284))+~P1(f315(f315(f224(a1),f2(a1)),x82282))+~P1(f315(f315(f224(a1),x82284),x82282))+P1(f315(f42(x82281,x82282),f315(f315(f240(a1,a1),x82283),x82284)))
% 168.60/168.40 [8346]~P67(x83461)+P1(f315(f315(f224(x83461),x83462),f2(x83461)))+~P1(f315(f315(f223(x83461),f2(x83461)),x83464))+~P1(f315(f315(f223(x83461),x83463),f315(f315(f74(x83461),x83464),x83462)))+P1(f315(f315(f223(x83461),f315(f315(f279(x83461),x83463),x83462)),x83464))
% 168.60/168.40 [8347]~P67(x83471)+P1(f315(f315(f224(x83471),x83472),f2(x83471)))+~P1(f315(f315(f224(x83471),f2(x83471)),x83474))+~P1(f315(f315(f224(x83471),x83473),f315(f315(f74(x83471),x83474),x83472)))+P1(f315(f315(f224(x83471),f315(f315(f279(x83471),x83473),x83472)),x83474))
% 168.60/168.40 [8431]~P67(x84311)+P1(f315(f315(f224(x84311),x84312),f2(x84311)))+~P1(f315(f315(f223(x84311),x84313),f2(x84311)))+P1(f315(f315(f223(x84311),x84313),f315(f315(f279(x84311),x84314),x84312)))+~P1(f315(f315(f223(x84311),f315(f315(f74(x84311),x84313),x84312)),x84314))
% 168.60/168.40 [8432]~P67(x84321)+P1(f315(f315(f224(x84321),x84322),f2(x84321)))+~P1(f315(f315(f224(x84321),x84323),f2(x84321)))+P1(f315(f315(f224(x84321),x84323),f315(f315(f279(x84321),x84324),x84322)))+~P1(f315(f315(f224(x84321),f315(f315(f74(x84321),x84323),x84322)),x84324))
% 168.60/168.40 [8584]~P67(x85841)+~P1(f315(f315(f224(x85841),x85842),f2(x85841)))+P1(f315(f315(f224(x85841),f2(x85841)),x85842))+~P1(f315(f315(f223(x85841),f315(f315(f279(x85841),x85844),x85842)),x85843))+P1(f315(f315(f223(x85841),f315(f315(f74(x85841),x85843),x85842)),x85844))
% 168.60/168.40 [8585]~P67(x85851)+~P1(f315(f315(f224(x85851),x85852),f2(x85851)))+P1(f315(f315(f224(x85851),f2(x85851)),x85852))+~P1(f315(f315(f223(x85851),f315(f315(f74(x85851),x85854),x85852)),x85853))+P1(f315(f315(f223(x85851),f315(f315(f279(x85851),x85853),x85852)),x85854))
% 168.60/168.40 [8586]~P67(x85861)+~P1(f315(f315(f224(x85861),x85862),f2(x85861)))+P1(f315(f315(f224(x85861),f2(x85861)),x85862))+~P1(f315(f315(f224(x85861),f315(f315(f279(x85861),x85864),x85862)),x85863))+P1(f315(f315(f224(x85861),f315(f315(f74(x85861),x85863),x85862)),x85864))
% 168.60/168.40 [8587]~P67(x85871)+~P1(f315(f315(f224(x85871),x85872),f2(x85871)))+P1(f315(f315(f224(x85871),f2(x85871)),x85872))+~P1(f315(f315(f224(x85871),f315(f315(f74(x85871),x85874),x85872)),x85873))+P1(f315(f315(f224(x85871),f315(f315(f279(x85871),x85873),x85872)),x85874))
% 168.60/168.40 [8603]~P67(x86031)+~P1(f315(f315(f223(x86031),f2(x86031)),x86034))+P1(f315(f315(f224(x86031),f2(x86031)),x86032))+~P1(f315(f315(f223(x86031),f315(f315(f74(x86031),x86034),x86032)),x86033))+P1(f315(f315(f223(x86031),f315(f315(f279(x86031),x86033),x86032)),x86034))
% 168.60/168.40 [8604]~P67(x86041)+~P1(f315(f315(f224(x86041),f2(x86041)),x86044))+P1(f315(f315(f224(x86041),f2(x86041)),x86042))+~P1(f315(f315(f224(x86041),f315(f315(f74(x86041),x86044),x86042)),x86043))+P1(f315(f315(f224(x86041),f315(f315(f279(x86041),x86043),x86042)),x86044))
% 168.60/168.40 [8680]~P67(x86801)+~P1(f315(f315(f224(x86801),x86804),f2(x86801)))+~P1(f315(f315(f223(x86801),x86803),f315(f315(f74(x86801),x86802),x86804)))+P1(f315(f315(f223(x86801),x86802),f315(f315(f279(x86801),x86803),x86804)))+~P1(f315(f315(f223(x86801),f315(f315(f74(x86801),x86802),x86804)),x86803))
% 168.60/168.40 [8681]~P67(x86811)+~P1(f315(f315(f223(x86811),x86812),f2(x86811)))+~P1(f315(f315(f223(x86811),x86813),f315(f315(f74(x86811),x86812),x86814)))+P1(f315(f315(f223(x86811),x86812),f315(f315(f279(x86811),x86813),x86814)))+~P1(f315(f315(f223(x86811),f315(f315(f74(x86811),x86812),x86814)),x86813))
% 168.60/168.40 [8682]~P67(x86821)+~P1(f315(f315(f224(x86821),x86824),f2(x86821)))+~P1(f315(f315(f224(x86821),x86823),f315(f315(f74(x86821),x86822),x86824)))+P1(f315(f315(f224(x86821),x86822),f315(f315(f279(x86821),x86823),x86824)))+~P1(f315(f315(f224(x86821),f315(f315(f74(x86821),x86822),x86824)),x86823))
% 168.60/168.40 [8683]~P67(x86831)+~P1(f315(f315(f224(x86831),x86832),f2(x86831)))+~P1(f315(f315(f224(x86831),x86833),f315(f315(f74(x86831),x86832),x86834)))+P1(f315(f315(f224(x86831),x86832),f315(f315(f279(x86831),x86833),x86834)))+~P1(f315(f315(f224(x86831),f315(f315(f74(x86831),x86832),x86834)),x86833))
% 168.60/168.40 [8805]~P67(x88051)+~P1(f315(f315(f224(x88051),x88053),f2(x88051)))+~P1(f315(f315(f223(x88051),x88052),f315(f315(f74(x88051),x88054),x88053)))+~P1(f315(f315(f223(x88051),f315(f315(f74(x88051),x88054),x88053)),x88052))+P1(f315(f315(f223(x88051),f315(f315(f279(x88051),x88052),x88053)),x88054))
% 168.60/168.40 [8806]~P67(x88061)+~P1(f315(f315(f224(x88061),x88063),f2(x88061)))+~P1(f315(f315(f224(x88061),x88062),f315(f315(f74(x88061),x88064),x88063)))+~P1(f315(f315(f224(x88061),f315(f315(f74(x88061),x88064),x88063)),x88062))+P1(f315(f315(f224(x88061),f315(f315(f279(x88061),x88062),x88063)),x88064))
% 168.60/168.40 [8823]~P67(x88231)+~P1(f315(f315(f223(x88231),f2(x88231)),x88234))+~P1(f315(f315(f223(x88231),x88232),f315(f315(f74(x88231),x88234),x88233)))+~P1(f315(f315(f223(x88231),f315(f315(f74(x88231),x88234),x88233)),x88232))+P1(f315(f315(f223(x88231),f315(f315(f279(x88231),x88232),x88233)),x88234))
% 168.60/168.40 [8824]~P67(x88241)+~P1(f315(f315(f224(x88241),f2(x88241)),x88244))+~P1(f315(f315(f224(x88241),x88242),f315(f315(f74(x88241),x88244),x88243)))+~P1(f315(f315(f224(x88241),f315(f315(f74(x88241),x88244),x88243)),x88242))+P1(f315(f315(f224(x88241),f315(f315(f279(x88241),x88242),x88243)),x88244))
% 168.60/168.40 [9007]E(f315(f315(f3(a1),f457(x90071,x90072,x90073,x90074)),f455(x90071,x90072,x90073,x90074)),x90074)+~P1(f315(f315(f224(a1),f2(a1)),x90073))+~P1(f315(f315(f317(a1),x90072),x90071))+~P1(f315(f315(f224(a1),x90074),x90072))+P1(f315(f315(f224(a1),f315(f315(f73(a1),x90074),x90073)),x90072))
% 168.60/168.40 [9079]~P1(f315(x90791,x90792))+~P1(f315(f315(f223(a1),f2(a1)),x90793))+~P1(f315(f315(f224(a1),f2(a1)),x90794))+~P1(f315(x90791,f315(f315(f3(a1),f332(x90793,x90791,x90794)),x90794)))+P1(f315(x90791,f315(f315(f3(a1),x90792),f315(f315(f74(a1),x90793),x90794))))
% 168.60/168.40 [9080]~P1(f315(x90801,x90802))+~P1(f315(f315(f223(a1),f2(a1)),x90803))+~P1(f315(f315(f224(a1),f2(a1)),x90804))+~P1(f315(x90801,f315(f315(f73(a1),f336(x90803,x90801,x90804)),x90804)))+P1(f315(x90801,f315(f315(f73(a1),x90802),f315(f315(f74(a1),x90803),x90804))))
% 168.60/168.40 [9230]~P1(f315(f315(f224(a1),f2(a1)),x92303))+~P1(f315(f315(f317(a1),x92302),x92301))+~P1(f315(f315(f224(a1),x92304),x92302))+P1(f315(f315(f317(a1),f457(x92301,x92302,x92303,x92304)),x92301))+P1(f315(f315(f224(a1),f315(f315(f73(a1),x92304),x92303)),x92302))
% 168.60/168.40 [9249]E(f315(f315(f3(a1),f443(x92491,x92492,x92493,x92494)),f444(x92491,x92492,x92493,x92494)),x92494)+~P1(f315(f315(f224(a1),f2(a1)),x92493))+~P1(f315(f315(f223(a1),x92494),x92492))+~P1(f315(f315(f317(a1),f315(f315(f73(a1),x92492),f71(a1))),x92491))+P1(f315(f315(f223(a1),f315(f315(f73(a1),x92494),x92493)),x92492))
% 168.60/168.40 [9277]~P1(f315(f315(f224(a1),f2(a1)),x92772))+~P1(f315(f315(f317(a1),x92773),x92774))+~P1(f315(f315(f224(a1),x92771),x92773))+P1(f315(f315(f317(a1),f455(x92774,x92773,x92772,x92771)),f291(a1,f71(a1),x92772)))+P1(f315(f315(f224(a1),f315(f315(f73(a1),x92771),x92772)),x92773))
% 168.60/168.40 [9368]~P1(f315(f315(f224(a1),f2(a1)),x93683))+~P1(f315(f315(f223(a1),x93684),x93682))+P1(f315(f315(f317(a1),f443(x93681,x93682,x93683,x93684)),x93681))+~P1(f315(f315(f317(a1),f315(f315(f73(a1),x93682),f71(a1))),x93681))+P1(f315(f315(f223(a1),f315(f315(f73(a1),x93684),x93683)),x93682))
% 168.60/168.40 [9415]~P1(f315(f315(f224(a1),f2(a1)),x94152))+~P1(f315(f315(f223(a1),x94151),x94153))+P1(f315(f315(f317(a1),f444(x94154,x94153,x94152,x94151)),f291(a1,f71(a1),x94152)))+~P1(f315(f315(f317(a1),f315(f315(f73(a1),x94153),f71(a1))),x94154))+P1(f315(f315(f223(a1),f315(f315(f73(a1),x94151),x94152)),x94153))
% 168.60/168.40 [9717]~P39(x97171,x97173)+~P27(x97171,x97174)+P39(x97171,f315(f315(f99(f909(f908(x97171,x97171),a899)),x97172),x97173))+~P1(f315(f315(f223(f909(f908(x97171,x97171),a899)),x97172),f315(f239(f909(f908(x97171,x97171),a899),f909(f908(x97171,x97171),a899)),x97174)))+~P1(f315(f315(f223(f909(f908(x97171,x97171),a899)),x97173),f315(f244(f909(f908(x97171,x97171),a899),f909(f908(x97171,x97171),a899)),x97174)))
% 168.60/168.40 [10104]~P19(x101042,x101044,x101043)+E(x101041,f177(f909(x101042,a899)))+~P1(f315(f54(x101042),x101041))+P1(f315(f315(f317(x101042),f315(x101043,x101041)),x101041))+~P1(f315(f315(f317(x101042),f315(f315(x101044,f431(x101041,x101043,x101044,x101042)),f448(x101041,x101043,x101044,x101042))),f315(f315(f297(x101042),f431(x101041,x101043,x101044,x101042)),f315(f315(f297(x101042),f448(x101041,x101043,x101044,x101042)),f177(f909(x101042,a899))))))
% 168.60/168.40 [10029]~P111(x100292)+~P64(x100291)+~P1(f315(f315(f223(f909(x100291,x100292)),x100293),x100294))+P1(f315(f315(f224(f909(x100291,x100292)),x100293),x100294))+~P1(f315(f49(x100291),f315(f315(f10(a899,a899,x100291),a310),f315(f315(f20(x100291,x100292,a899),f315(f315(f10(x100292,f909(x100292,a899),x100291),a312),x100293)),x100294))))
% 168.60/168.40 [9632]~P56(x96321,x96321,x96324)+P1(f315(f315(f317(f908(x96321,x96321)),f315(f315(f240(x96321,x96321),x96322),x96323)),f295(x96321,x96324)))+P1(f315(f315(f317(f908(x96321,x96321)),f315(f315(f240(x96321,x96321),x96323),x96322)),f295(x96321,x96324)))+~P1(f315(f315(f317(f908(x96321,x96321)),f315(f315(f240(x96321,x96321),x96325),x96322)),f295(x96321,x96324)))+~P1(f315(f315(f317(f908(x96321,x96321)),f315(f315(f240(x96321,x96321),x96325),x96323)),f295(x96321,x96324)))
% 168.60/168.40 [5707]E(x57071,f2(a901))+~E(f315(f28(x57072),x57075),x57071)+E(f315(f28(x57072),x57073),f315(a101,x57071))+~E(x57073,f315(f315(f297(x57072),x57074),x57075))+P1(f315(f315(f317(x57072),x57074),x57075))
% 168.60/168.40 [5829]~P66(x58292)+E(x58291,f2(x58292))+E(x58293,f2(x58292))+~E(f315(f315(f279(x58292),x58294),x58293),f315(f315(f279(x58292),x58295),x58291))+E(f315(f315(f74(x58292),x58294),x58291),f315(f315(f74(x58292),x58295),x58293))
% 168.60/168.40 [5830]~P66(x58302)+E(x58301,f2(x58302))+E(x58303,f2(x58302))+~E(f315(f315(f74(x58302),x58304),x58303),f315(f315(f74(x58302),x58305),x58301))+E(f315(f315(f279(x58302),x58304),x58301),f315(f315(f279(x58302),x58305),x58303))
% 168.60/168.40 [5908]~E(f315(f28(x59081),x59085),x59083)+~E(x59085,f177(f909(x59081,a899)))+E(f315(f28(x59081),x59082),f315(a101,x59083))+~E(x59082,f315(f315(f297(x59081),x59084),x59085))+P1(f315(f315(f317(x59081),x59084),x59085))
% 168.60/168.40 [6149]~P121(x61492)+~E(f315(x61493,x61495),f2(x61492))+E(f315(f315(f11(x61491,x61492),x61493),x61494),f2(x61492))+~P1(f315(f54(x61491),x61494))+~P1(f315(f315(f317(x61491),x61495),x61494))
% 168.60/168.40 [6533]~P110(x65333)+E(x65331,x65332)+~E(f315(f290(x65333,x65334),x65331),f315(f290(x65333,x65335),x65332))+~P1(f315(f315(f224(x65333),x65335),x65332))+~P1(f315(f315(f224(x65333),x65334),x65331))
% 168.60/168.40 [6534]~P110(x65343)+E(x65341,x65342)+~E(f315(f290(x65343,x65341),x65344),f315(f290(x65343,x65342),x65345))+~P1(f315(f315(f224(x65343),x65342),x65345))+~P1(f315(f315(f224(x65343),x65341),x65344))
% 168.60/168.40 [7619]~P110(x76191)+~P13(x76191,f315(f315(f123(x76191),x76194),x76195))+~P1(f315(f315(f317(x76191),x76193),f315(f161(x76191),x76195)))+~P1(f315(f315(f317(x76191),x76192),f315(f161(x76191),x76194)))+P1(f315(f315(f223(x76191),x76192),x76193))
% 168.60/168.40 [8717]~P111(x87171)+~P1(f315(f315(f224(f909(x87171,a899)),f291(x87171,x87175,x87172)),f291(x87171,x87174,x87173)))+~P1(f315(f315(f223(x87171),x87175),x87172))+P1(f315(f315(f224(x87171),x87172),x87173))+P1(f315(f315(f224(x87171),x87174),x87175))
% 168.60/168.40 [10147]~P18(x101472,x101475,x101473)+E(x101471,f177(f909(x101472,a899)))+~E(f315(f315(x101475,f315(x101474,f521(x101471,x101474,x101473,x101475,x101472))),f315(x101474,f522(x101471,x101474,x101473,x101475,x101472))),f315(x101474,f315(f315(x101475,f521(x101471,x101474,x101473,x101475,x101472)),f522(x101471,x101474,x101473,x101475,x101472))))+E(f315(x101473,f315(f298(x101472,x101472,x101474),x101471)),f315(x101474,f315(x101473,x101471)))+~P1(f315(f54(x101472),x101471))
% 168.60/168.40 [6530]~P19(x65302,x65305,x65303)+E(x65301,f177(f909(x65302,a899)))+~P1(f315(f54(x65302),x65301))+E(f315(x65303,f315(f315(f297(x65302),x65304),x65301)),f315(f315(x65305,x65304),f315(x65303,x65301)))+P1(f315(f315(f317(x65302),x65304),x65301))
% 168.60/168.40 [7379]~P18(x73792,x73793,x73794)+E(f315(f315(x73793,f315(x73794,x73791)),f315(x73794,x73795)),f315(x73794,x73795))+E(x73791,f177(f909(x73792,a899)))+~P1(f315(f54(x73792),x73795))+~P1(f315(f315(f223(f909(x73792,a899)),x73791),x73795))
% 168.60/168.40 [7756]~P19(x77564,x77565,x77561)+E(f315(x77561,x77562),x77563)+~P1(f315(f54(x77564),x77562))+~E(f315(f315(f3(f909(x77564,a899)),x77562),f315(f315(f297(x77564),x77563),f177(f909(x77564,a899)))),f177(f909(x77564,a899)))+~P1(f315(f315(f317(x77564),x77563),x77562))
% 168.60/168.40 [8638]~P77(x86381)+~P124(x86381)+~P1(f315(f54(x86382),x86385))+P1(f315(f315(f275(x86381),f315(f315(f11(x86382,x86381),x86383),x86384)),f315(f315(f11(x86382,x86381),x86383),x86385)))+~P1(f315(f315(f223(f909(x86382,a899)),x86384),x86385))
% 168.60/168.40 [8687]E(x86871,x86872)+~P8(x86873,x86874,x86875)+E(f315(f315(f90(f909(x86873,a899)),x86871),x86872),f177(f909(x86873,a899)))+~P1(f315(f315(f317(f909(x86873,a899)),x86872),f315(f315(f53(x86873),x86874),x86875)))+~P1(f315(f315(f317(f909(x86873,a899)),x86871),f315(f315(f53(x86873),x86874),x86875)))
% 168.60/168.40 [9498]~P72(x94982)+~E(f315(x94983,f866(x94983,x94984,x94985,x94981,x94982)),f2(x94982))+E(f315(f315(f8(x94981,x94982),x94983),x94984),f315(f315(f8(x94981,x94982),x94983),x94985))+~P1(f315(f54(x94981),x94985))+~P1(f315(f315(f223(f909(x94981,a899)),x94984),x94985))
% 168.60/168.40 [9499]~P72(x94992)+~E(f315(x94993,f869(x94993,x94994,x94995,x94991,x94992)),f2(x94992))+E(f315(f315(f8(x94991,x94992),x94993),x94994),f315(f315(f8(x94991,x94992),x94993),x94995))+~P1(f315(f54(x94991),x94995))+~P1(f315(f315(f223(f909(x94991,a899)),x94994),x94995))
% 168.60/168.40 [9500]~P77(x95002)+~E(f315(x95003,f867(x95003,x95004,x95005,x95001,x95002)),f71(x95002))+E(f315(f315(f11(x95001,x95002),x95003),x95004),f315(f315(f11(x95001,x95002),x95003),x95005))+~P1(f315(f54(x95001),x95005))+~P1(f315(f315(f223(f909(x95001,a899)),x95004),x95005))
% 168.60/168.40 [9501]~P77(x95012)+~E(f315(x95013,f868(x95013,x95014,x95015,x95011,x95012)),f71(x95012))+E(f315(f315(f11(x95011,x95012),x95013),x95014),f315(f315(f11(x95011,x95012),x95013),x95015))+~P1(f315(f54(x95011),x95015))+~P1(f315(f315(f223(f909(x95011,a899)),x95014),x95015))
% 168.60/168.40 [9982]~P91(x99821)+~P1(f315(f54(x99822),x99825))+~P1(f315(f315(f223(x99821),f2(x99821)),f315(x99823,f795(x99823,x99824,x99825,x99822,x99821))))+P1(f315(f315(f223(x99821),f315(f315(f8(x99822,x99821),x99823),x99824)),f315(f315(f8(x99822,x99821),x99823),x99825)))+~P1(f315(f315(f223(f909(x99822,a899)),x99824),x99825))
% 168.60/168.40 [7616]E(x76161,f2(a901))+P1(f315(x76162,x76163))+~E(x76164,f315(f315(f73(a901),f315(f315(f74(a901),x76161),x76163)),x76165))+~P1(f315(f315(f224(a901),x76165),x76161))+~P1(f315(x76162,f315(f315(f29(a901),x76164),x76161)))
% 168.60/168.40 [7694]E(x76941,f2(a901))+P1(f315(x76942,x76943))+~P1(f315(x76942,f38(a901,x76944,x76941)))+~E(x76944,f315(f315(f73(a901),f315(f315(f74(a901),x76941),x76945)),x76943))+~P1(f315(f315(f224(a901),x76943),x76941))
% 168.60/168.40 [7987]~P66(x79873)+E(f315(x79871,x79872),f2(x79873))+~P1(f315(f54(x79874),x79875))+E(f315(f315(f11(x79874,x79873),x79871),f315(f315(f3(f909(x79874,a899)),x79875),f315(f315(f297(x79874),x79872),f177(f909(x79874,a899))))),f315(f315(f11(x79874,x79873),x79871),x79875))+P1(f315(f315(f317(x79874),x79872),x79875))
% 168.60/168.40 [8386]~P72(x83861)+~P1(f315(f54(x83862),x83865))+~P1(f315(f54(x83862),x83864))+~E(f315(f315(f90(f909(x83862,a899)),x83864),x83865),f177(f909(x83862,a899)))+E(f315(f315(f73(x83861),f315(f315(f8(x83862,x83861),x83863),x83864)),f315(f315(f8(x83862,x83861),x83863),x83865)),f315(f315(f8(x83862,x83861),x83863),f315(f315(f99(f909(x83862,a899)),x83864),x83865)))
% 168.60/168.40 [8388]~P77(x83881)+~P1(f315(f54(x83882),x83885))+~P1(f315(f54(x83882),x83884))+~E(f315(f315(f90(f909(x83882,a899)),x83884),x83885),f177(f909(x83882,a899)))+E(f315(f315(f74(x83881),f315(f315(f11(x83882,x83881),x83883),x83884)),f315(f315(f11(x83882,x83881),x83883),x83885)),f315(f315(f11(x83882,x83881),x83883),f315(f315(f99(f909(x83882,a899)),x83884),x83885)))
% 168.60/168.40 [8487]~P66(x84873)+E(f315(x84871,x84872),f2(x84873))+~P1(f315(f54(x84874),x84875))+E(f315(f315(f11(x84874,x84873),x84871),f315(f315(f3(f909(x84874,a899)),x84875),f315(f315(f297(x84874),x84872),f177(f909(x84874,a899))))),f315(f315(f279(x84873),f315(f315(f11(x84874,x84873),x84871),x84875)),f315(x84871,x84872)))+~P1(f315(f315(f317(x84874),x84872),x84875))
% 168.60/168.40 [9207]~P8(x92071,x92075,x92074)+~E(f315(f315(f53(x92071),f315(f315(f297(x92071),x92072),f177(f909(x92071,a899)))),x92074),f315(f315(f53(x92071),f315(f315(f297(x92071),x92073),f177(f909(x92071,a899)))),x92074))+~P1(f315(f315(f317(x92071),x92073),x92075))+~P1(f315(f315(f317(x92071),x92072),x92075))+P1(f315(f315(f317(f908(x92071,x92071)),f315(f315(f240(x92071,x92071),x92072),x92073)),x92074))
% 168.60/168.40 [9229]~P8(x92291,x92295,x92293)+E(f315(f315(f53(x92291),f315(f315(f297(x92291),x92292),f177(f909(x92291,a899)))),x92293),f315(f315(f53(x92291),f315(f315(f297(x92291),x92294),f177(f909(x92291,a899)))),x92293))+~P1(f315(f315(f317(x92291),x92294),x92295))+~P1(f315(f315(f317(x92291),x92292),x92295))+~P1(f315(f315(f317(f908(x92291,x92291)),f315(f315(f240(x92291,x92291),x92292),x92294)),x92293))
% 168.60/168.40 [9527]~P77(x95271)+~P1(f315(f54(x95272),x95275))+~P1(f315(f54(x95272),x95274))+~E(f315(f315(f90(f909(x95272,a899)),x95274),x95275),f177(f909(x95272,a899)))+E(f315(f315(f74(x95271),f315(f315(f315(f58(x95271,x95272,f74(x95271)),x95273),f71(x95271)),x95274)),f315(f315(f315(f58(x95271,x95272,f74(x95271)),x95273),f71(x95271)),x95275)),f315(f315(f315(f58(x95271,x95272,f74(x95271)),x95273),f71(x95271)),f315(f315(f99(f909(x95272,a899)),x95274),x95275)))
% 168.60/168.40 [9538]~P72(x95381)+~E(f315(x95383,f856(x95383,x95385,x95384,x95382,x95381)),f2(x95381))+~P1(f315(f54(x95382),x95384))+~P1(f315(f54(x95382),x95385))+E(f315(f315(f73(x95381),f315(f315(f8(x95382,x95381),x95383),x95384)),f315(f315(f8(x95382,x95381),x95383),x95385)),f315(f315(f8(x95382,x95381),x95383),f315(f315(f99(f909(x95382,a899)),x95384),x95385)))
% 168.60/168.40 [9539]~P72(x95391)+~E(f315(x95393,f857(x95393,x95395,x95394,x95392,x95391)),f2(x95391))+~P1(f315(f54(x95392),x95394))+~P1(f315(f54(x95392),x95395))+E(f315(f315(f73(x95391),f315(f315(f8(x95392,x95391),x95393),x95394)),f315(f315(f8(x95392,x95391),x95393),x95395)),f315(f315(f8(x95392,x95391),x95393),f315(f315(f99(f909(x95392,a899)),x95394),x95395)))
% 168.60/168.40 [9540]~P77(x95401)+~E(f315(x95403,f854(x95403,x95405,x95404,x95402,x95401)),f71(x95401))+~P1(f315(f54(x95402),x95404))+~P1(f315(f54(x95402),x95405))+E(f315(f315(f74(x95401),f315(f315(f11(x95402,x95401),x95403),x95404)),f315(f315(f11(x95402,x95401),x95403),x95405)),f315(f315(f11(x95402,x95401),x95403),f315(f315(f99(f909(x95402,a899)),x95404),x95405)))
% 168.60/168.40 [9541]~P77(x95411)+~E(f315(x95413,f855(x95413,x95415,x95414,x95412,x95411)),f71(x95411))+~P1(f315(f54(x95412),x95414))+~P1(f315(f54(x95412),x95415))+E(f315(f315(f74(x95411),f315(f315(f11(x95412,x95411),x95413),x95414)),f315(f315(f11(x95412,x95411),x95413),x95415)),f315(f315(f11(x95412,x95411),x95413),f315(f315(f99(f909(x95412,a899)),x95414),x95415)))
% 168.60/168.40 [9760]~P77(x97601)+~E(f315(x97603,f817(x97603,x97605,x97604,x97602,x97601)),f71(x97601))+~P1(f315(f54(x97602),x97604))+~P1(f315(f54(x97602),x97605))+E(f315(f315(f74(x97601),f315(f315(f315(f58(x97601,x97602,f74(x97601)),x97603),f71(x97601)),x97604)),f315(f315(f315(f58(x97601,x97602,f74(x97601)),x97603),f71(x97601)),x97605)),f315(f315(f315(f58(x97601,x97602,f74(x97601)),x97603),f71(x97601)),f315(f315(f99(f909(x97602,a899)),x97604),x97605)))
% 168.60/168.40 [9870]~P72(x98702)+E(f315(f315(f8(x98701,x98702),x98703),x98704),f315(f315(f8(x98701,x98702),x98703),x98705))+~P1(f315(f54(x98701),x98705))+~P1(f315(f315(f223(f909(x98701,a899)),x98704),x98705))+P1(f315(f315(f317(x98701),f866(x98703,x98704,x98705,x98701,x98702)),f315(f315(f3(f909(x98701,a899)),x98705),x98704)))
% 168.60/168.40 [9871]~P72(x98712)+E(f315(f315(f8(x98711,x98712),x98713),x98714),f315(f315(f8(x98711,x98712),x98713),x98715))+~P1(f315(f54(x98711),x98715))+~P1(f315(f315(f223(f909(x98711,a899)),x98714),x98715))+P1(f315(f315(f317(x98711),f869(x98713,x98714,x98715,x98711,x98712)),f315(f315(f3(f909(x98711,a899)),x98715),x98714)))
% 168.60/168.40 [9872]~P77(x98722)+E(f315(f315(f11(x98721,x98722),x98723),x98724),f315(f315(f11(x98721,x98722),x98723),x98725))+~P1(f315(f54(x98721),x98725))+~P1(f315(f315(f223(f909(x98721,a899)),x98724),x98725))+P1(f315(f315(f317(x98721),f867(x98723,x98724,x98725,x98721,x98722)),f315(f315(f3(f909(x98721,a899)),x98725),x98724)))
% 168.60/168.40 [9873]~P77(x98732)+E(f315(f315(f11(x98731,x98732),x98733),x98734),f315(f315(f11(x98731,x98732),x98733),x98735))+~P1(f315(f54(x98731),x98735))+~P1(f315(f315(f223(f909(x98731,a899)),x98734),x98735))+P1(f315(f315(f317(x98731),f868(x98733,x98734,x98735,x98731,x98732)),f315(f315(f3(f909(x98731,a899)),x98735),x98734)))
% 168.60/168.40 [9891]~P72(x98911)+~P1(f315(f54(x98912),x98914))+~P1(f315(f54(x98912),x98915))+E(f315(f315(f73(x98911),f315(f315(f8(x98912,x98911),x98913),x98914)),f315(f315(f8(x98912,x98911),x98913),x98915)),f315(f315(f8(x98912,x98911),x98913),f315(f315(f99(f909(x98912,a899)),x98914),x98915)))+P1(f315(f315(f317(x98912),f856(x98913,x98915,x98914,x98912,x98911)),f315(f315(f90(f909(x98912,a899)),x98914),x98915)))
% 168.60/168.40 [9892]~P72(x98921)+~P1(f315(f54(x98922),x98924))+~P1(f315(f54(x98922),x98925))+E(f315(f315(f73(x98921),f315(f315(f8(x98922,x98921),x98923),x98924)),f315(f315(f8(x98922,x98921),x98923),x98925)),f315(f315(f8(x98922,x98921),x98923),f315(f315(f99(f909(x98922,a899)),x98924),x98925)))+P1(f315(f315(f317(x98922),f857(x98923,x98925,x98924,x98922,x98921)),f315(f315(f90(f909(x98922,a899)),x98924),x98925)))
% 168.60/168.40 [9893]~P77(x98931)+~P1(f315(f54(x98932),x98934))+~P1(f315(f54(x98932),x98935))+E(f315(f315(f74(x98931),f315(f315(f11(x98932,x98931),x98933),x98934)),f315(f315(f11(x98932,x98931),x98933),x98935)),f315(f315(f11(x98932,x98931),x98933),f315(f315(f99(f909(x98932,a899)),x98934),x98935)))+P1(f315(f315(f317(x98932),f854(x98933,x98935,x98934,x98932,x98931)),f315(f315(f90(f909(x98932,a899)),x98934),x98935)))
% 168.60/168.40 [9894]~P77(x98941)+~P1(f315(f54(x98942),x98944))+~P1(f315(f54(x98942),x98945))+E(f315(f315(f74(x98941),f315(f315(f11(x98942,x98941),x98943),x98944)),f315(f315(f11(x98942,x98941),x98943),x98945)),f315(f315(f11(x98942,x98941),x98943),f315(f315(f99(f909(x98942,a899)),x98944),x98945)))+P1(f315(f315(f317(x98942),f855(x98943,x98945,x98944,x98942,x98941)),f315(f315(f90(f909(x98942,a899)),x98944),x98945)))
% 168.60/168.40 [9900]~P91(x99005)+~P1(f315(f54(x99001),x99004))+P1(f315(f315(f223(x99005),f315(f315(f8(x99001,x99005),x99002),x99003)),f315(f315(f8(x99001,x99005),x99002),x99004)))+~P1(f315(f315(f223(f909(x99001,a899)),x99003),x99004))+P1(f315(f315(f317(x99001),f795(x99002,x99003,x99004,x99001,x99005)),f315(f315(f3(f909(x99001,a899)),x99004),x99003)))
% 168.60/168.40 [9944]~P77(x99441)+~P1(f315(f54(x99442),x99444))+~P1(f315(f54(x99442),x99445))+E(f315(f315(f74(x99441),f315(f315(f315(f58(x99441,x99442,f74(x99441)),x99443),f71(x99441)),x99444)),f315(f315(f315(f58(x99441,x99442,f74(x99441)),x99443),f71(x99441)),x99445)),f315(f315(f315(f58(x99441,x99442,f74(x99441)),x99443),f71(x99441)),f315(f315(f99(f909(x99442,a899)),x99444),x99445)))+P1(f315(f315(f317(x99442),f817(x99443,x99445,x99444,x99442,x99441)),f315(f315(f90(f909(x99442,a899)),x99444),x99445)))
% 168.60/168.40 [8896]~P19(x88961,x88964,x88965)+~P1(f315(f54(x88961),x88962))+E(f315(f315(f3(f909(x88961,a899)),x88962),f315(f315(f297(x88961),x88963),f177(f909(x88961,a899)))),f177(f909(x88961,a899)))+~P1(f315(f315(f317(x88961),x88963),x88962))+E(f315(f315(x88964,x88963),f315(x88965,f315(f315(f3(f909(x88961,a899)),x88962),f315(f315(f297(x88961),x88963),f177(f909(x88961,a899)))))),f315(x88965,x88962))
% 168.60/168.40 [8974]~P19(x89741,x89744,x89745)+~P1(f315(f54(x89741),x89743))+~P1(f315(f54(x89741),x89742))+E(f315(f315(f90(f909(x89741,a899)),x89742),x89743),f177(f909(x89741,a899)))+E(f315(f315(x89744,f315(x89745,f315(f315(f99(f909(x89741,a899)),x89742),x89743))),f315(x89745,f315(f315(f90(f909(x89741,a899)),x89742),x89743))),f315(f315(x89744,f315(x89745,x89742)),f315(x89745,x89743)))
% 168.60/168.40 [9543]~P1(f315(f315(f223(a1),x95434),f2(a1)))+~P1(f315(f315(f224(a1),x95433),x95435))+P1(f315(f315(f223(a1),x95431),x95432))+~P1(f315(f315(f224(a1),x95433),x95434))+~P1(f315(f315(f223(a1),f315(f315(f73(a1),f315(f315(f74(a1),x95433),x95432)),x95435)),f315(f315(f73(a1),f315(f315(f74(a1),x95433),x95431)),x95434)))
% 168.60/168.40 [9545]~P1(f315(f315(f223(a1),f2(a1)),x95455))+P1(f315(f315(f223(a1),x95451),x95452))+~P1(f315(f315(f224(a1),x95453),x95454))+~P1(f315(f315(f224(a1),x95455),x95454))+~P1(f315(f315(f223(a1),f315(f315(f73(a1),f315(f315(f74(a1),x95454),x95451)),x95455)),f315(f315(f73(a1),f315(f315(f74(a1),x95454),x95452)),x95453)))
% 168.60/168.40 [9669]~P66(x96695)+E(f315(x96691,f871(x96691,x96692,x96693,x96694,x96695)),f2(x96695))+~P1(f315(f54(x96694),x96693))+~P1(f315(f54(x96694),x96692))+E(f315(f315(f279(x96695),f315(f315(f74(x96695),f315(f315(f11(x96694,x96695),x96691),x96693)),f315(f315(f11(x96694,x96695),x96691),x96692))),f315(f315(f11(x96694,x96695),x96691),f315(f315(f90(f909(x96694,a899)),x96693),x96692))),f315(f315(f11(x96694,x96695),x96691),f315(f315(f99(f909(x96694,a899)),x96693),x96692)))
% 168.60/168.40 [9936]~P66(x99361)+~P1(f315(f54(x99362),x99364))+~P1(f315(f54(x99362),x99365))+E(f315(f315(f279(x99361),f315(f315(f74(x99361),f315(f315(f11(x99362,x99361),x99363),x99364)),f315(f315(f11(x99362,x99361),x99363),x99365))),f315(f315(f11(x99362,x99361),x99363),f315(f315(f90(f909(x99362,a899)),x99364),x99365))),f315(f315(f11(x99362,x99361),x99363),f315(f315(f99(f909(x99362,a899)),x99364),x99365)))+P1(f315(f315(f317(x99362),f871(x99363,x99365,x99364,x99362,x99361)),f315(f315(f90(f909(x99362,a899)),x99364),x99365)))
% 168.60/168.40 [9248]E(f315(f315(f123(x92481),x92482),x92483),f315(f315(f123(x92481),x92484),x92485))+~E(f315(f315(f164(x92481),f315(f178(f902(x92481)),x92484)),x92482),x92484)+~E(f315(f315(f164(x92481),f315(f178(f902(x92481)),x92482)),x92484),x92482)+~E(x92485,f315(f315(f123(x92481),f315(f315(f127(x92481),f315(f178(f902(x92481)),x92484)),x92482)),x92483))+~E(f315(f315(f123(x92481),f315(f315(f127(x92481),f315(f178(f902(x92481)),x92482)),x92484)),x92485),x92483)
% 168.60/168.40 [9667]~P110(x96672)+E(f315(f315(f137(x96671,x96672,x96673),x96674),f159(x96671,x96674,x96675)),x96675)+~P13(x96672,f315(f315(f143(x96671,x96672),x96673),x96675))+~P1(f315(f315(f317(x96671),x96674),f315(f161(x96671),x96675)))+~E(f315(f130(x96671),f315(f125(x96671,f315(f315(f10(x96672,a899,x96671),f315(a312,f315(x96673,x96674))),x96673)),x96675)),x96674)
% 168.60/168.40 [10000]~P70(x100001)+~P1(f315(f59(x100001,x100001,f74(x100001),x100002,x100003),x100005))+~P1(f315(f315(f317(x100001),x100004),x100003))+P1(f315(f315(f317(x100001),x100002),x100003))+P1(f315(f59(x100001,x100001,f74(x100001),x100004,f315(f315(f297(x100001),x100002),f315(f315(f3(f909(x100001,a899)),x100003),f315(f315(f297(x100001),x100004),f177(f909(x100001,a899)))))),x100005))
% 168.60/168.40 [7387]E(x73871,x73872)+~P25(x73874,x73875,x73873,x73876)+~E(f315(x73873,x73871),f315(x73873,x73872))+~P1(f315(f315(f317(x73874),x73872),x73876))+~P1(f315(f315(f317(x73874),x73871),x73876))
% 168.60/168.40 [6626]~P145(x66264)+E(x66261,x66262)+~E(x66265,x66266)+E(x66263,f2(x66264))+~E(f315(f315(f73(x66264),x66265),f315(f315(f74(x66264),x66263),x66261)),f315(f315(f73(x66264),x66266),f315(f315(f74(x66264),x66263),x66262)))
% 168.60/168.40 [7674]~P110(x76741)+~P5(x76741)+~P1(f315(f315(f224(x76741),x76742),f315(x76745,x76746)))+~P1(f315(f315(f317(x76743),x76746),x76744))+P1(f315(f315(f224(x76741),x76742),f315(f315(f33(x76743,x76741),x76744),x76745)))
% 168.60/168.40 [9996]~P25(x99962,x99961,x99963,x99964)+~P25(x99961,x99962,x99966,x99965)+P26(x99961,x99962,f808(x99963,x99964,x99965,x99966,x99962,x99961),x99965,x99964)+~P1(f315(f315(f223(f909(x99962,a899)),f315(f298(x99961,x99962,x99966),x99965)),x99964))+~P1(f315(f315(f223(f909(x99961,a899)),f315(f298(x99962,x99961,x99963),x99964)),x99965))
% 168.60/168.40 [8357]~P110(x83571)+~P5(x83571)+~P1(f315(f315(f224(x83571),f315(x83574,x83576)),x83575))+~P1(f315(f315(f317(x83572),x83576),x83573))+P1(f315(f315(f224(x83571),f315(f315(f32(x83572,x83571),x83573),x83574)),x83575))
% 168.60/168.40 [8610]~P20(x86102,x86105,x86106,x86101)+~P1(f315(f54(x86102),x86104))+~P1(f315(f54(x86102),x86103))+~E(f315(f315(f90(f909(x86102,a899)),x86103),x86104),f177(f909(x86102,a899)))+E(f315(x86101,f315(f315(f99(f909(x86102,a899)),x86103),x86104)),f315(f66(x86105,x86105,x86105,f315(x86101,x86103)),f315(x86101,x86104)))
% 168.60/168.40 [10206]~P77(x102061)+~E(f798(x102064,x102065,x102063,x102066,x102062,x102061),f797(x102064,x102065,x102063,x102066,x102062,x102061))+~P1(f315(f54(x102062),x102066))+E(f315(f315(f315(f58(x102061,x102062,f74(x102061)),f315(f315(f10(f909(x102063,a899),x102061,x102062),f315(f315(f58(x102061,x102063,f74(x102061)),x102064),f71(x102061))),x102065)),f71(x102061)),x102066),f315(f315(f315(f58(x102061,x102063,f74(x102061)),x102064),f71(x102061)),f315(f315(f33(x102062,f909(x102063,a899)),x102066),x102065)))+P1(f315(f315(f317(x102062),f796(x102064,x102065,x102063,x102066,x102062,x102061)),x102066))
% 168.60/168.40 [10236]~P77(x102361)+~E(f798(x102364,x102365,x102363,x102366,x102362,x102361),f797(x102364,x102365,x102363,x102366,x102362,x102361))+~P1(f315(f54(x102362),x102366))+E(f315(f315(f315(f58(x102361,x102362,f74(x102361)),f315(f315(f10(f909(x102363,a899),x102361,x102362),f315(f315(f58(x102361,x102363,f74(x102361)),x102364),f71(x102361))),x102365)),f71(x102361)),x102366),f315(f315(f315(f58(x102361,x102363,f74(x102361)),x102364),f71(x102361)),f315(f315(f33(x102362,f909(x102363,a899)),x102366),x102365)))+~P1(f315(f54(x102363),f315(x102365,f796(x102364,x102365,x102363,x102366,x102362,x102361))))
% 168.60/168.40 [10239]~P77(x102391)+~P1(f315(f54(x102392),x102396))+E(f315(f315(f315(f58(x102391,x102392,f74(x102391)),f315(f315(f10(f909(x102393,a899),x102391,x102392),f315(f315(f58(x102391,x102393,f74(x102391)),x102394),f71(x102391))),x102395)),f71(x102391)),x102396),f315(f315(f315(f58(x102391,x102393,f74(x102391)),x102394),f71(x102391)),f315(f315(f33(x102392,f909(x102393,a899)),x102396),x102395)))+P1(f315(f315(f317(x102392),f796(x102394,x102395,x102393,x102396,x102392,x102391)),x102396))+P1(f315(f315(f317(x102392),f797(x102394,x102395,x102393,x102396,x102392,x102391)),x102396))
% 168.60/168.40 [10240]~P77(x102401)+~P1(f315(f54(x102402),x102406))+E(f315(f315(f315(f58(x102401,x102402,f74(x102401)),f315(f315(f10(f909(x102403,a899),x102401,x102402),f315(f315(f58(x102401,x102403,f74(x102401)),x102404),f71(x102401))),x102405)),f71(x102401)),x102406),f315(f315(f315(f58(x102401,x102403,f74(x102401)),x102404),f71(x102401)),f315(f315(f33(x102402,f909(x102403,a899)),x102406),x102405)))+P1(f315(f315(f317(x102402),f796(x102404,x102405,x102403,x102406,x102402,x102401)),x102406))+P1(f315(f315(f317(x102402),f798(x102404,x102405,x102403,x102406,x102402,x102401)),x102406))
% 168.60/168.40 [10259]~P77(x102591)+~P1(f315(f54(x102592),x102596))+E(f315(f315(f315(f58(x102591,x102592,f74(x102591)),f315(f315(f10(f909(x102593,a899),x102591,x102592),f315(f315(f58(x102591,x102593,f74(x102591)),x102594),f71(x102591))),x102595)),f71(x102591)),x102596),f315(f315(f315(f58(x102591,x102593,f74(x102591)),x102594),f71(x102591)),f315(f315(f33(x102592,f909(x102593,a899)),x102596),x102595)))+P1(f315(f315(f317(x102592),f797(x102594,x102595,x102593,x102596,x102592,x102591)),x102596))+~P1(f315(f54(x102593),f315(x102595,f796(x102594,x102595,x102593,x102596,x102592,x102591))))
% 168.60/168.40 [10260]~P77(x102601)+~P1(f315(f54(x102602),x102606))+E(f315(f315(f315(f58(x102601,x102602,f74(x102601)),f315(f315(f10(f909(x102603,a899),x102601,x102602),f315(f315(f58(x102601,x102603,f74(x102601)),x102604),f71(x102601))),x102605)),f71(x102601)),x102606),f315(f315(f315(f58(x102601,x102603,f74(x102601)),x102604),f71(x102601)),f315(f315(f33(x102602,f909(x102603,a899)),x102606),x102605)))+P1(f315(f315(f317(x102602),f798(x102604,x102605,x102603,x102606,x102602,x102601)),x102606))+~P1(f315(f54(x102603),f315(x102605,f796(x102604,x102605,x102603,x102606,x102602,x102601))))
% 168.60/168.40 [10271]~P77(x102711)+~E(f315(f315(f90(f909(x102713,a899)),f315(x102715,f797(x102714,x102715,x102713,x102716,x102712,x102711))),f315(x102715,f798(x102714,x102715,x102713,x102716,x102712,x102711))),f177(f909(x102713,a899)))+~P1(f315(f54(x102712),x102716))+E(f315(f315(f315(f58(x102711,x102712,f74(x102711)),f315(f315(f10(f909(x102713,a899),x102711,x102712),f315(f315(f58(x102711,x102713,f74(x102711)),x102714),f71(x102711))),x102715)),f71(x102711)),x102716),f315(f315(f315(f58(x102711,x102713,f74(x102711)),x102714),f71(x102711)),f315(f315(f33(x102712,f909(x102713,a899)),x102716),x102715)))+P1(f315(f315(f317(x102712),f796(x102714,x102715,x102713,x102716,x102712,x102711)),x102716))
% 168.60/168.40 [10282]~P77(x102821)+~E(f315(f315(f90(f909(x102823,a899)),f315(x102825,f797(x102824,x102825,x102823,x102826,x102822,x102821))),f315(x102825,f798(x102824,x102825,x102823,x102826,x102822,x102821))),f177(f909(x102823,a899)))+~P1(f315(f54(x102822),x102826))+E(f315(f315(f315(f58(x102821,x102822,f74(x102821)),f315(f315(f10(f909(x102823,a899),x102821,x102822),f315(f315(f58(x102821,x102823,f74(x102821)),x102824),f71(x102821))),x102825)),f71(x102821)),x102826),f315(f315(f315(f58(x102821,x102823,f74(x102821)),x102824),f71(x102821)),f315(f315(f33(x102822,f909(x102823,a899)),x102826),x102825)))+~P1(f315(f54(x102823),f315(x102825,f796(x102824,x102825,x102823,x102826,x102822,x102821))))
% 168.60/168.40 [9338]~P124(x93381)+~P120(x93381)+~P1(f315(f315(f275(x93381),x93382),x93385))+~P1(f315(f315(f275(x93381),x93382),f315(f315(f73(x93381),x93383),x93386)))+P1(f315(f315(f275(x93381),x93382),f315(f315(f73(x93381),f315(f315(f3(x93381),x93383),f315(f315(f74(x93381),x93384),x93385))),x93386)))
% 168.60/168.40 [9532]~P124(x95321)+~P120(x95321)+~P1(f315(f315(f275(x95321),x95322),x95325))+P1(f315(f315(f275(x95321),x95322),f315(f315(f73(x95321),x95323),x95324)))+~P1(f315(f315(f275(x95321),x95322),f315(f315(f73(x95321),f315(f315(f3(x95321),x95323),f315(f315(f74(x95321),x95326),x95325))),x95324)))
% 168.60/168.40 [8944]E(x89441,x89442)+~P58(x89444,x89445,x89446,x89443,x89447)+~E(f315(x89443,x89441),f315(x89443,x89442))+~P1(f315(f315(f317(x89445),x89442),x89447))+~P1(f315(f315(f317(x89445),x89441),x89447))
% 168.60/168.40 [10247]~P1(f315(x102472,x102474))+~E(x102475,f315(f125(x102471,x102472),x102477))+E(f315(f125(x102471,x102472),x102473),f315(f315(f140(x102471),x102474),x102475))+~E(x102473,f315(f315(f123(x102471),x102476),f315(f315(f140(x102471),x102474),x102477)))+P1(f315(x102472,f730(x102475,x102474,x102473,x102472,x102471,x102476,x102477)))
% 168.60/168.40 [10248]~P1(f315(x102484,x102482))+~E(x102483,f315(f125(x102481,x102484),x102487))+E(f315(f315(f140(x102481),x102482),x102483),f315(f125(x102481,x102484),x102485))+~E(x102485,f315(f315(f123(x102481),x102486),f315(f315(f140(x102481),x102482),x102487)))+P1(f315(x102484,f729(x102485,x102484,x102483,x102482,x102481,x102486,x102487)))
% 168.60/168.40 [10298]~P1(f315(x102982,x102984))+~E(x102985,f315(f125(x102981,x102982),x102987))+E(f315(f125(x102981,x102982),x102983),f315(f315(f140(x102981),x102984),x102985))+~E(x102983,f315(f315(f123(x102981),x102986),f315(f315(f140(x102981),x102984),x102987)))+P1(f315(f315(f317(x102981),f730(x102985,x102984,x102983,x102982,x102981,x102986,x102987)),f315(f161(x102981),x102986)))
% 168.60/168.40 [10299]~P1(f315(x102994,x102992))+~E(x102993,f315(f125(x102991,x102994),x102997))+E(f315(f315(f140(x102991),x102992),x102993),f315(f125(x102991,x102994),x102995))+~E(x102995,f315(f315(f123(x102991),x102996),f315(f315(f140(x102991),x102992),x102997)))+P1(f315(f315(f317(x102991),f729(x102995,x102994,x102993,x102992,x102991,x102996,x102997)),f315(f161(x102991),x102996)))
% 168.60/168.40 [10303]~P8(x103031,x103037,x103036)+~P11(x103031,f909(x103035,a899),x103036,x103034)+P1(f315(f315(f317(x103031),f477(x103032,x103033,x103034,x103035,x103036,x103037,x103031)),x103037))+~P1(f315(f315(f317(f909(x103031,a899)),x103033),f315(f315(f53(x103031),x103037),x103036)))+P1(f315(f315(f317(f909(x103035,a899)),f315(f315(f33(x103031,f909(x103035,a899)),x103033),x103034)),x103032))
% 168.60/168.40 [10358]~P8(x103582,x103586,x103587)+~P11(x103582,f909(x103581,a899),x103587,x103584)+~P1(f315(f315(f317(f909(x103582,a899)),x103583),f315(f315(f53(x103582),x103586),x103587)))+~P1(f315(f315(f317(f909(x103581,a899)),f315(x103584,f477(x103585,x103583,x103584,x103581,x103587,x103586,x103582))),x103585))+P1(f315(f315(f317(f909(x103581,a899)),f315(f315(f33(x103582,f909(x103581,a899)),x103583),x103584)),x103585))
% 168.60/168.40 [8529]~P77(x85292)+~P25(x85291,x85295,x85298,x85294)+~E(x85293,f315(f66(x85295,x85292,x85291,x85296),x85298))+~E(x85297,f315(f298(x85291,x85295,x85298),x85294))+E(f315(f315(f11(x85291,x85292),x85293),x85294),f315(f315(f11(x85295,x85292),x85296),x85297))
% 168.60/168.40 [10362]~P77(x103622)+~P25(x103625,x103621,x103628,x103627)+~E(f315(x103626,f578(x103623,x103626,x103624,x103627,x103628,x103621,x103625,x103622)),f315(f315(f66(x103621,x103622,x103625,x103623),x103628),f578(x103623,x103626,x103624,x103627,x103628,x103621,x103625,x103622)))+~E(x103624,f315(f298(x103625,x103621,x103628),x103627))+E(f315(f315(f11(x103621,x103622),x103623),x103624),f315(f315(f11(x103625,x103622),x103626),x103627))
% 168.60/168.40 [10365]~P72(x103652)+~P25(x103651,x103655,x103658,x103654)+~E(x103657,f315(f298(x103651,x103655,x103658),x103654))+E(f315(f315(f8(x103651,x103652),x103653),x103654),f315(f315(f8(x103655,x103652),x103656),x103657))+P1(f315(f315(f317(x103651),f593(x103656,x103653,x103657,x103654,x103658,x103655,x103651,x103652)),x103654))
% 168.60/168.40 [10366]~P77(x103662)+~P25(x103661,x103665,x103668,x103664)+~E(x103667,f315(f298(x103661,x103665,x103668),x103664))+E(f315(f315(f11(x103661,x103662),x103663),x103664),f315(f315(f11(x103665,x103662),x103666),x103667))+P1(f315(f315(f317(x103661),f578(x103666,x103663,x103667,x103664,x103668,x103665,x103661,x103662)),x103664))
% 168.60/168.40 [10371]~P72(x103712)+~P25(x103715,x103711,x103718,x103717)+~E(x103714,f315(f298(x103715,x103711,x103718),x103717))+~E(f315(x103716,f593(x103713,x103716,x103714,x103717,x103718,x103711,x103715,x103712)),f315(x103713,f315(x103718,f593(x103713,x103716,x103714,x103717,x103718,x103711,x103715,x103712))))+E(f315(f315(f8(x103711,x103712),x103713),x103714),f315(f315(f8(x103715,x103712),x103716),x103717))
% 168.60/168.40 [9833]~P24(x98336,x98332,x98335,x98337,x98338,x98331)+~P1(f315(f54(x98332),x98334))+~P1(f315(f54(x98332),x98333))+~E(f315(f315(f90(f909(x98332,a899)),x98333),x98334),f177(f909(x98332,a899)))+E(f315(x98331,f315(f315(f99(f909(x98332,a899)),x98333),x98334)),f315(f315(x98335,f315(x98331,x98333)),f315(x98331,x98334)))
% 168.60/168.40 [10233]~P24(x102338,x102332,x102335,x102337,x102336,x102331)+~E(f315(x102336,f643(x102334,x102333,x102331,x102336,x102337,x102335,x102332)),x102337)+~P1(f315(f54(x102332),x102333))+~P1(f315(f54(x102332),x102334))+E(f315(x102331,f315(f315(f99(f909(x102332,a899)),x102333),x102334)),f315(f315(x102335,f315(x102331,x102333)),f315(x102331,x102334)))
% 168.60/168.40 [10310]~P24(x103108,x103102,x103105,x103107,x103106,x103101)+~P1(f315(f54(x103102),x103103))+~P1(f315(f54(x103102),x103104))+E(f315(x103101,f315(f315(f99(f909(x103102,a899)),x103103),x103104)),f315(f315(x103105,f315(x103101,x103103)),f315(x103101,x103104)))+P1(f315(f315(f317(x103102),f643(x103104,x103103,x103101,x103106,x103107,x103105,x103102)),f315(f315(f90(f909(x103102,a899)),x103103),x103104)))
% 168.60/168.40 [9987]~P8(x99874,x99878,x99875)+~P8(x99871,x99879,x99873)+~P12(x99871,x99874,f909(x99872,a899),x99873,x99875,x99877)+P11(x99871,f909(x99872,a899),x99873,f315(f315(f10(f909(x99874,f909(x99872,a899)),f909(x99872,a899),x99871),f315(f33(x99874,f909(x99872,a899)),f315(f273(x99874,x99874,x99875),f315(f315(f297(x99874),x99876),f177(f909(x99874,a899)))))),x99877))+~P1(f315(f315(f317(x99874),x99876),x99878))
% 168.60/168.40 [5501]~P110(x55013)+~P13(x55013,x55011)+E(x55011,f707(x55012,x55013))+~E(f315(f161(x55013),x55011),x55012)+~P1(f315(f54(x55013),x55012))+~P1(f315(f126(x55013),x55011))
% 168.60/168.40 [7378]P16(x73781,x73782)+~E(f315(x73782,f788(x73782)),f315(x73782,f789(x73782)))+~P1(f315(f315(x73782,f788(x73782)),f788(x73782)))+~P1(f315(f315(x73782,f788(x73782)),f789(x73782)))+~P1(f315(f315(x73782,f789(x73782)),f789(x73782)))+~P1(f315(f315(x73782,x73783),x73783))
% 168.60/168.40 [5126]~P134(x51262)+~P135(x51262)+~P146(x51262)+~P117(x51262)+E(x51261,f2(x51262))+~E(f315(f315(f232(x51262),x51261),x51263),f2(x51262))
% 168.60/168.40 [5127]~P134(x51272)+~P135(x51272)+~P146(x51272)+~P117(x51272)+~E(x51271,f2(a901))+~E(f315(f315(f232(x51272),x51273),x51271),f2(x51272))
% 168.60/168.40 [6608]~P91(x66081)+~E(x66083,f2(x66081))+~E(x66082,f2(x66081))+E(f315(f315(f73(x66081),x66082),x66083),f2(x66081))+~P1(f315(f315(f223(x66081),f2(x66081)),x66083))+~P1(f315(f315(f223(x66081),f2(x66081)),x66082))
% 168.60/168.40 [9012]~E(f315(f239(a901,a901),x90123),f2(a901))+~E(x90121,f315(f315(f73(a901),f315(f315(f74(a901),f315(f239(a901,a901),x90123)),x90122)),f315(f244(a901,a901),x90123)))+P1(f315(f41(x90121,x90122),x90123))+~P1(f315(f315(f223(a901),f315(f244(a901,a901),x90123)),f2(a901)))+P1(f315(f315(f224(a901),f2(a901)),x90122))+~P1(f315(f315(f224(a901),x90122),f315(f244(a901,a901),x90123)))
% 168.60/168.40 [9020]E(x90201,f2(a901))+~E(x90202,f315(f315(f73(a901),f315(f315(f74(a901),f315(f239(a901,a901),x90203)),x90201)),f315(f244(a901,a901),x90203)))+P1(f315(f41(x90202,x90201),x90203))+~P1(f315(f315(f224(a901),f2(a901)),x90201))+~P1(f315(f315(f223(a901),f2(a901)),f315(f244(a901,a901),x90203)))+~P1(f315(f315(f224(a901),f315(f244(a901,a901),x90203)),x90201))
% 168.60/168.40 [9039]~E(f315(f239(a901,a901),x90393),f2(a901))+~E(x90391,f315(f315(f73(a901),f315(f315(f74(a901),f315(f239(a901,a901),x90393)),x90392)),f315(f244(a901,a901),x90393)))+P1(f315(f41(x90391,x90392),x90393))+~P1(f315(f315(f224(a901),f2(a901)),x90392))+~P1(f315(f315(f223(a901),f2(a901)),f315(f244(a901,a901),x90393)))+~P1(f315(f315(f224(a901),f315(f244(a901,a901),x90393)),x90392))
% 168.60/168.40 [6999]~P80(x69992)+E(x69991,f177(f909(x69992,a899)))+E(x69993,f177(f909(x69992,a899)))+~P1(f315(f54(x69992),x69991))+~P1(f315(f54(x69992),x69993))+E(f12(x69992,f315(f315(f99(f909(x69992,a899)),x69993),x69991)),f315(f315(f99(x69992),f12(x69992,x69993)),f12(x69992,x69991)))
% 168.60/168.40 [7000]~P80(x70002)+E(x70001,f177(f909(x70002,a899)))+E(x70003,f177(f909(x70002,a899)))+~P1(f315(f54(x70002),x70001))+~P1(f315(f54(x70002),x70003))+E(f13(x70002,f315(f315(f99(f909(x70002,a899)),x70003),x70001)),f315(f315(f90(x70002),f13(x70002,x70003)),f13(x70002,x70001)))
% 168.60/168.40 [7001]~P110(x70012)+E(x70011,f177(f909(x70012,a899)))+E(x70013,f177(f909(x70012,a899)))+~P1(f315(f54(x70012),x70011))+~P1(f315(f54(x70012),x70013))+E(f16(x70012,f315(f315(f99(f909(x70012,a899)),x70013),x70011)),f315(f315(f221(x70012),f16(x70012,x70013)),f16(x70012,x70011)))
% 168.60/168.40 [7002]~P110(x70022)+E(x70021,f177(f909(x70022,a899)))+E(x70023,f177(f909(x70022,a899)))+~P1(f315(f54(x70022),x70021))+~P1(f315(f54(x70022),x70023))+E(f17(x70022,f315(f315(f99(f909(x70022,a899)),x70023),x70021)),f315(f315(f222(x70022),f17(x70022,x70023)),f17(x70022,x70021)))
% 168.60/168.40 [7648]~P99(x76482)+E(x76481,f177(f909(x76482,a899)))+E(x76483,f177(f909(x76482,a899)))+~P1(f315(f54(x76482),x76481))+~P1(f315(f54(x76482),x76483))+E(f315(f315(f74(x76482),f315(f56(x76482,f74(x76482)),x76483)),f315(f56(x76482,f74(x76482)),x76481)),f315(f56(x76482,f74(x76482)),f315(f315(f99(f909(x76482,a899)),x76483),x76481)))
% 168.60/168.40 [7810]~P110(x78102)+E(x78101,f177(f909(x78102,a899)))+E(x78103,f177(f909(x78102,a899)))+~P1(f315(f54(x78102),x78101))+~P1(f315(f54(x78102),x78103))+E(f315(f315(f221(x78102),f14(x78102,f221(x78102),x78103)),f14(x78102,f221(x78102),x78101)),f14(x78102,f221(x78102),f315(f315(f99(f909(x78102,a899)),x78103),x78101)))
% 168.60/168.40 [7811]~P110(x78112)+E(x78111,f177(f909(x78112,a899)))+E(x78113,f177(f909(x78112,a899)))+~P1(f315(f54(x78112),x78111))+~P1(f315(f54(x78112),x78113))+E(f315(f315(f222(x78112),f15(x78112,f222(x78112),x78113)),f15(x78112,f222(x78112),x78111)),f15(x78112,f222(x78112),f315(f315(f99(f909(x78112,a899)),x78113),x78111)))
% 168.60/168.40 [8845]~P1(f315(x88451,x88453))+P1(f315(x88451,f460(x88451,x88452)))+P1(f315(x88451,f456(x88451,x88452)))+~P1(f315(f315(f224(a1),f2(a1)),x88452))+~P1(f315(f315(f317(a1),x88453),f291(a1,f71(a1),x88452)))+P1(f315(x88451,f315(f315(f3(a1),f456(x88451,x88452)),f315(f315(f74(a1),f459(x88451,x88452)),x88452))))
% 168.60/168.40 [9147]~P1(f315(x91471,x91473))+~P1(f315(x91471,f456(x91471,x91472)))+P1(f315(x91471,f460(x91471,x91472)))+~P1(f315(f315(f224(a1),f2(a1)),x91472))+~P1(f315(f315(f317(a1),x91473),f291(a1,f71(a1),x91472)))+~P1(f315(x91471,f315(f315(f3(a1),f456(x91471,x91472)),f315(f315(f74(a1),f459(x91471,x91472)),x91472))))
% 168.60/168.40 [10398]~P101(x103982)+E(x103981,f177(f909(x103982,a899)))+E(x103983,f177(f909(x103982,a899)))+~P1(f315(f54(x103982),x103981))+~P1(f315(f54(x103982),x103983))+E(f13(x103982,f315(f250(x103982),f315(f315(f10(f909(x103982,a899),a899,x103982),f80(x103982)),f315(f315(f10(f909(x103982,f909(x103982,a899)),f909(x103982,a899),x103982),f315(f10(f909(x103982,a899),a899,x103982),f80(x103982))),f315(f315(f9(x103982,f909(x103982,f909(x103982,a899)),f909(x103982,f909(x103982,a899))),f315(f315(f10(f909(x103982,f909(f909(x103982,a899),f909(x103982,a899))),f909(f909(x103982,f909(x103982,a899)),f909(x103982,f909(x103982,a899))),x103982),f20(x103982,f909(x103982,a899),f909(x103982,a899))),f315(f315(f10(f909(x103982,f909(x103982,f909(a899,a899))),f909(x103982,f909(f909(x103982,a899),f909(x103982,a899))),x103982),f315(f10(f909(x103982,f909(a899,a899)),f909(f909(x103982,a899),f909(x103982,a899)),x103982),f20(x103982,a899,a899))),f315(f315(f10(f909(x103982,f909(x103982,a899)),f909(x103982,f909(x103982,f909(a899,a899))),x103982),f315(f10(f909(x103982,a899),f909(x103982,f909(a899,a899)),x103982),f315(f10(a899,f909(a899,a899),x103982),a313))),f315(f315(f9(x103982,f909(x103982,f909(x103982,x103982)),f909(x103982,f909(x103982,a899))),f315(f315(f10(f909(f909(x103982,x103982),f909(x103982,a899)),f909(f909(x103982,f909(x103982,x103982)),f909(x103982,f909(x103982,a899))),x103982),f10(f909(x103982,x103982),f909(x103982,a899),x103982)),f315(f315(f10(f909(x103982,a899),f909(f909(x103982,x103982),f909(x103982,a899)),x103982),f10(x103982,a899,x103982)),a312))),f99(x103982)))))),f315(f315(f9(x103982,f909(x103982,a899),f909(x103982,a899)),f315(f315(f10(f909(a899,a899),f909(f909(x103982,a899),f909(x103982,a899)),x103982),f10(a899,a899,x103982)),f315(f315(f10(a899,f909(a899,a899),x103982),a313),f315(f315(f9(x103982,f909(x103982,a899),a899),f317(x103982)),x103983)))),f315(f315(f9(x103982,f909(x103982,a899),a899),f317(x103982)),x103981))))))),f315(f315(f99(x103982),f13(x103982,x103983)),f13(x103982,x103981)))
% 168.60/168.40 [10399]~P101(x103992)+E(x103991,f177(f909(x103992,a899)))+E(x103993,f177(f909(x103992,a899)))+~P1(f315(f54(x103992),x103991))+~P1(f315(f54(x103992),x103993))+E(f12(x103992,f315(f250(x103992),f315(f315(f10(f909(x103992,a899),a899,x103992),f80(x103992)),f315(f315(f10(f909(x103992,f909(x103992,a899)),f909(x103992,a899),x103992),f315(f10(f909(x103992,a899),a899,x103992),f80(x103992))),f315(f315(f9(x103992,f909(x103992,f909(x103992,a899)),f909(x103992,f909(x103992,a899))),f315(f315(f10(f909(x103992,f909(f909(x103992,a899),f909(x103992,a899))),f909(f909(x103992,f909(x103992,a899)),f909(x103992,f909(x103992,a899))),x103992),f20(x103992,f909(x103992,a899),f909(x103992,a899))),f315(f315(f10(f909(x103992,f909(x103992,f909(a899,a899))),f909(x103992,f909(f909(x103992,a899),f909(x103992,a899))),x103992),f315(f10(f909(x103992,f909(a899,a899)),f909(f909(x103992,a899),f909(x103992,a899)),x103992),f20(x103992,a899,a899))),f315(f315(f10(f909(x103992,f909(x103992,a899)),f909(x103992,f909(x103992,f909(a899,a899))),x103992),f315(f10(f909(x103992,a899),f909(x103992,f909(a899,a899)),x103992),f315(f10(a899,f909(a899,a899),x103992),a313))),f315(f315(f9(x103992,f909(x103992,f909(x103992,x103992)),f909(x103992,f909(x103992,a899))),f315(f315(f10(f909(f909(x103992,x103992),f909(x103992,a899)),f909(f909(x103992,f909(x103992,x103992)),f909(x103992,f909(x103992,a899))),x103992),f10(f909(x103992,x103992),f909(x103992,a899),x103992)),f315(f315(f10(f909(x103992,a899),f909(f909(x103992,x103992),f909(x103992,a899)),x103992),f10(x103992,a899,x103992)),a312))),f90(x103992)))))),f315(f315(f9(x103992,f909(x103992,a899),f909(x103992,a899)),f315(f315(f10(f909(a899,a899),f909(f909(x103992,a899),f909(x103992,a899)),x103992),f10(a899,a899,x103992)),f315(f315(f10(a899,f909(a899,a899),x103992),a313),f315(f315(f9(x103992,f909(x103992,a899),a899),f317(x103992)),x103993)))),f315(f315(f9(x103992,f909(x103992,a899),a899),f317(x103992)),x103991))))))),f315(f315(f90(x103992),f12(x103992,x103993)),f12(x103992,x103991)))
% 168.60/168.40 [10400]~P110(x104002)+E(x104001,f177(f909(x104002,a899)))+E(x104003,f177(f909(x104002,a899)))+~P1(f315(f54(x104002),x104001))+~P1(f315(f54(x104002),x104003))+E(f15(x104002,f222(x104002),f315(f250(x104002),f315(f315(f10(f909(x104002,a899),a899,x104002),f80(x104002)),f315(f315(f10(f909(x104002,f909(x104002,a899)),f909(x104002,a899),x104002),f315(f10(f909(x104002,a899),a899,x104002),f80(x104002))),f315(f315(f9(x104002,f909(x104002,f909(x104002,a899)),f909(x104002,f909(x104002,a899))),f315(f315(f10(f909(x104002,f909(f909(x104002,a899),f909(x104002,a899))),f909(f909(x104002,f909(x104002,a899)),f909(x104002,f909(x104002,a899))),x104002),f20(x104002,f909(x104002,a899),f909(x104002,a899))),f315(f315(f10(f909(x104002,f909(x104002,f909(a899,a899))),f909(x104002,f909(f909(x104002,a899),f909(x104002,a899))),x104002),f315(f10(f909(x104002,f909(a899,a899)),f909(f909(x104002,a899),f909(x104002,a899)),x104002),f20(x104002,a899,a899))),f315(f315(f10(f909(x104002,f909(x104002,a899)),f909(x104002,f909(x104002,f909(a899,a899))),x104002),f315(f10(f909(x104002,a899),f909(x104002,f909(a899,a899)),x104002),f315(f10(a899,f909(a899,a899),x104002),a313))),f315(f315(f9(x104002,f909(x104002,f909(x104002,x104002)),f909(x104002,f909(x104002,a899))),f315(f315(f10(f909(f909(x104002,x104002),f909(x104002,a899)),f909(f909(x104002,f909(x104002,x104002)),f909(x104002,f909(x104002,a899))),x104002),f10(f909(x104002,x104002),f909(x104002,a899),x104002)),f315(f315(f10(f909(x104002,a899),f909(f909(x104002,x104002),f909(x104002,a899)),x104002),f10(x104002,a899,x104002)),a312))),f221(x104002)))))),f315(f315(f9(x104002,f909(x104002,a899),f909(x104002,a899)),f315(f315(f10(f909(a899,a899),f909(f909(x104002,a899),f909(x104002,a899)),x104002),f10(a899,a899,x104002)),f315(f315(f10(a899,f909(a899,a899),x104002),a313),f315(f315(f9(x104002,f909(x104002,a899),a899),f317(x104002)),x104003)))),f315(f315(f9(x104002,f909(x104002,a899),a899),f317(x104002)),x104001))))))),f315(f315(f221(x104002),f15(x104002,f222(x104002),x104003)),f15(x104002,f222(x104002),x104001)))
% 168.60/168.40 [10401]~P110(x104012)+E(x104011,f177(f909(x104012,a899)))+E(x104013,f177(f909(x104012,a899)))+~P1(f315(f54(x104012),x104011))+~P1(f315(f54(x104012),x104013))+E(f14(x104012,f221(x104012),f315(f250(x104012),f315(f315(f10(f909(x104012,a899),a899,x104012),f80(x104012)),f315(f315(f10(f909(x104012,f909(x104012,a899)),f909(x104012,a899),x104012),f315(f10(f909(x104012,a899),a899,x104012),f80(x104012))),f315(f315(f9(x104012,f909(x104012,f909(x104012,a899)),f909(x104012,f909(x104012,a899))),f315(f315(f10(f909(x104012,f909(f909(x104012,a899),f909(x104012,a899))),f909(f909(x104012,f909(x104012,a899)),f909(x104012,f909(x104012,a899))),x104012),f20(x104012,f909(x104012,a899),f909(x104012,a899))),f315(f315(f10(f909(x104012,f909(x104012,f909(a899,a899))),f909(x104012,f909(f909(x104012,a899),f909(x104012,a899))),x104012),f315(f10(f909(x104012,f909(a899,a899)),f909(f909(x104012,a899),f909(x104012,a899)),x104012),f20(x104012,a899,a899))),f315(f315(f10(f909(x104012,f909(x104012,a899)),f909(x104012,f909(x104012,f909(a899,a899))),x104012),f315(f10(f909(x104012,a899),f909(x104012,f909(a899,a899)),x104012),f315(f10(a899,f909(a899,a899),x104012),a313))),f315(f315(f9(x104012,f909(x104012,f909(x104012,x104012)),f909(x104012,f909(x104012,a899))),f315(f315(f10(f909(f909(x104012,x104012),f909(x104012,a899)),f909(f909(x104012,f909(x104012,x104012)),f909(x104012,f909(x104012,a899))),x104012),f10(f909(x104012,x104012),f909(x104012,a899),x104012)),f315(f315(f10(f909(x104012,a899),f909(f909(x104012,x104012),f909(x104012,a899)),x104012),f10(x104012,a899,x104012)),a312))),f222(x104012)))))),f315(f315(f9(x104012,f909(x104012,a899),f909(x104012,a899)),f315(f315(f10(f909(a899,a899),f909(f909(x104012,a899),f909(x104012,a899)),x104012),f10(a899,a899,x104012)),f315(f315(f10(a899,f909(a899,a899),x104012),a313),f315(f315(f9(x104012,f909(x104012,a899),a899),f317(x104012)),x104013)))),f315(f315(f9(x104012,f909(x104012,a899),a899),f317(x104012)),x104011))))))),f315(f315(f222(x104012),f14(x104012,f221(x104012),x104013)),f14(x104012,f221(x104012),x104011)))
% 168.60/168.40 [7334]~P128(x73343)+E(x73341,x73342)+~E(f315(f315(f232(x73343),x73341),x73344),f315(f315(f232(x73343),x73342),x73344))+~P1(f315(f315(f223(x73343),f2(x73343)),x73342))+~P1(f315(f315(f223(x73343),f2(x73343)),x73341))+~P1(f315(f315(f224(a901),f2(a901)),x73344))
% 168.60/168.40 [7608]~P110(x76082)+E(x76081,f177(f909(x76082,a899)))+~P1(f315(f54(x76082),x76081))+~P1(f315(f315(f317(x76082),x76084),x76081))+P1(f315(f315(f223(x76082),x76083),x76084))+~P1(f315(f315(f223(x76082),x76083),f315(f56(x76082,f221(x76082)),x76081)))
% 168.60/168.40 [7609]~P104(x76092)+E(x76091,f177(f909(x76092,a899)))+~P1(f315(f54(x76092),x76091))+~P1(f315(f315(f317(x76092),x76094),x76091))+P1(f315(f315(f223(x76092),x76093),x76094))+~P1(f315(f315(f223(x76092),x76093),f315(f56(x76092,f90(x76092)),x76091)))
% 168.60/168.40 [7610]~P110(x76102)+E(x76101,f177(f909(x76102,a899)))+~P1(f315(f54(x76102),x76101))+~P1(f315(f315(f317(x76102),x76104),x76101))+P1(f315(f315(f224(x76102),x76103),x76104))+~P1(f315(f315(f224(x76102),x76103),f315(f56(x76102,f221(x76102)),x76101)))
% 168.60/168.40 [7514]E(x75141,f2(a1))+E(f315(f315(f29(a1),x75142),x75141),x75143)+~P1(f315(f315(f223(a1),x75144),f2(a1)))+~E(x75142,f315(f315(f73(a1),f315(f315(f74(a1),x75141),x75143)),x75144))+P1(f315(f315(f224(a1),f2(a1)),x75141))+~P1(f315(f315(f224(a1),x75141),x75144))
% 168.60/168.40 [7531]E(f38(a1,x75312,x75311),x75313)+E(x75311,f2(a1))+~P1(f315(f315(f223(a1),x75313),f2(a1)))+~E(x75312,f315(f315(f73(a1),f315(f315(f74(a1),x75311),x75314)),x75313))+P1(f315(f315(f224(a1),f2(a1)),x75311))+~P1(f315(f315(f224(a1),x75311),x75313))
% 168.60/168.40 [7647]E(x76471,f2(a1))+E(f315(f315(f29(a1),x76472),x76471),x76473)+~E(x76472,f315(f315(f73(a1),f315(f315(f74(a1),x76471),x76473)),x76474))+~P1(f315(f315(f223(a1),f2(a1)),x76474))+~P1(f315(f315(f224(a1),f2(a1)),x76471))+~P1(f315(f315(f224(a1),x76474),x76471))
% 168.60/168.40 [7670]E(f38(a1,x76702,x76701),x76703)+E(x76701,f2(a1))+~E(x76702,f315(f315(f73(a1),f315(f315(f74(a1),x76701),x76704)),x76703))+~P1(f315(f315(f223(a1),f2(a1)),x76703))+~P1(f315(f315(f224(a1),f2(a1)),x76701))+~P1(f315(f315(f224(a1),x76703),x76701))
% 168.60/168.40 [7814]~P110(x78142)+E(x78141,f177(f909(x78142,a899)))+~P1(f315(f54(x78142),x78141))+~P1(f315(f315(f223(x78142),x78144),x78143))+~P1(f315(f315(f317(x78142),x78144),x78141))+P1(f315(f315(f223(x78142),f315(f56(x78142,f221(x78142)),x78141)),x78143))
% 168.60/168.40 [7815]~P110(x78152)+E(x78151,f177(f909(x78152,a899)))+~P1(f315(f54(x78152),x78151))+~P1(f315(f315(f224(x78152),x78154),x78153))+~P1(f315(f315(f317(x78152),x78154),x78151))+P1(f315(f315(f224(x78152),f315(f56(x78152,f221(x78152)),x78151)),x78153))
% 168.60/168.40 [8381]~P1(f315(f315(f223(a1),x83814),f2(a1)))+~E(x83811,f315(f315(f73(a1),f315(f315(f74(a1),x83812),x83813)),x83814))+~P1(f315(f315(f223(a1),f2(a1)),x83814))+~P1(f315(f315(f224(a1),x83814),x83812))+~P1(f315(f315(f224(a1),x83812),x83814))+P1(f315(f42(x83811,x83812),f315(f315(f240(a1,a1),x83813),x83814)))
% 168.60/168.40 [8549]~P111(x85491)+P1(f315(f315(f224(f909(x85491,a899)),f291(x85491,x85492,x85493)),f291(x85491,x85494,x85495)))+~P1(f315(f315(f223(x85491),x85494),x85492))+~P1(f315(f315(f223(x85491),x85494),x85495))+~P1(f315(f315(f223(x85491),x85493),x85495))+~P1(f315(f315(f224(x85491),x85493),x85495))
% 168.60/168.40 [8550]~P111(x85501)+P1(f315(f315(f224(f909(x85501,a899)),f291(x85501,x85502,x85503)),f291(x85501,x85504,x85505)))+~P1(f315(f315(f223(x85501),x85503),x85505))+~P1(f315(f315(f223(x85501),x85504),x85505))+~P1(f315(f315(f223(x85501),x85504),x85502))+~P1(f315(f315(f224(x85501),x85504),x85502))
% 168.60/168.40 [9411]P60(x94112,x94113,x94114,x94111)+E(x94111,f177(f909(x94112,a899)))+~P1(f315(f54(x94112),x94114))+~P1(f315(f54(x94112),x94111))+~P1(f315(f315(x94113,f503(x94111,x94114,x94113,x94112)),x94115))+~P1(f315(f315(f317(x94112),x94115),x94111))
% 168.60/168.40 [9412]P60(x94122,x94123,x94124,x94121)+E(x94121,f177(f909(x94122,a899)))+~P1(f315(f54(x94122),x94124))+~P1(f315(f54(x94122),x94121))+~P1(f315(f315(x94123,f779(x94123,x94121,x94124,x94122)),x94125))+~P1(f315(f315(f317(x94122),x94125),x94121))
% 168.60/168.40 [9413]P60(x94132,x94133,x94134,x94131)+E(x94131,f177(f909(x94132,a899)))+~P1(f315(f54(x94132),x94134))+~P1(f315(f54(x94132),x94131))+~P1(f315(f315(x94133,f780(x94131,x94134,x94133,x94132)),x94135))+~P1(f315(f315(f317(x94132),x94135),x94131))
% 168.60/168.40 [9561]~E(x95613,x95615)+~P72(x95611)+~P77(x95611)+~P42(x95613)+E(f315(f315(f8(a1,x95611),x95612),x95613),f315(f315(f8(a1,x95611),x95614),x95615))+P1(f315(f315(f223(a1),f2(a1)),f517(x95612,x95614,x95613,x95615,x95611)))
% 168.60/168.40 [9562]~E(x95623,x95625)+~P72(x95621)+~P77(x95621)+~P42(x95623)+E(f315(f315(f11(a1,x95621),x95622),x95623),f315(f315(f11(a1,x95621),x95624),x95625))+P1(f315(f315(f223(a1),f2(a1)),f518(x95622,x95624,x95623,x95625,x95621)))
% 168.60/168.40 [9743]~E(x97435,x97433)+~P72(x97431)+~P77(x97431)+~P42(x97435)+~E(f315(x97432,f517(x97434,x97432,x97435,x97433,x97431)),f315(x97434,f517(x97434,x97432,x97435,x97433,x97431)))+E(f315(f315(f8(a1,x97431),x97432),x97433),f315(f315(f8(a1,x97431),x97434),x97435))
% 168.60/168.40 [9744]~E(x97445,x97443)+~P72(x97441)+~P77(x97441)+~P42(x97445)+~E(f315(x97442,f518(x97444,x97442,x97445,x97443,x97441)),f315(x97444,f518(x97444,x97442,x97445,x97443,x97441)))+E(f315(f315(f11(a1,x97441),x97442),x97443),f315(f315(f11(a1,x97441),x97444),x97445))
% 168.60/168.40 [9831]~P82(x98313)+E(f315(x98311,x98312),f2(x98313))+~E(f315(f315(f8(x98314,x98313),x98311),x98315),f2(x98313))+~P1(f315(f54(x98314),x98315))+P1(f315(f315(f317(x98314),f406(x98312,x98311,x98315,x98314,x98313)),x98315))+~P1(f315(f315(f317(x98314),x98312),x98315))
% 168.60/168.40 [9958]~P82(x99583)+E(f315(x99581,x99582),f2(x99583))+~E(f315(f315(f8(x99584,x99583),x99581),x99585),f2(x99583))+~P1(f315(f54(x99584),x99585))+~P1(f315(f315(f317(x99584),x99582),x99585))+~P1(f315(f315(f223(x99583),f2(x99583)),f315(x99581,f406(x99582,x99581,x99585,x99584,x99583))))
% 168.60/168.40 [8466]~P139(x84661)+~P1(f315(f315(f223(x84661),x84663),x84665))+~P1(f315(f315(f223(x84661),x84662),x84664))+~P1(f315(f315(f223(x84661),f2(x84661)),x84663))+~P1(f315(f315(f223(x84661),f2(x84661)),x84664))+P1(f315(f315(f223(x84661),f315(f315(f74(x84661),x84662),x84663)),f315(f315(f74(x84661),x84664),x84665)))
% 168.60/168.40 [8467]~P139(x84671)+~P1(f315(f315(f223(x84671),x84673),x84675))+~P1(f315(f315(f223(x84671),x84672),x84674))+~P1(f315(f315(f223(x84671),f2(x84671)),x84673))+~P1(f315(f315(f223(x84671),f2(x84671)),x84672))+P1(f315(f315(f223(x84671),f315(f315(f74(x84671),x84672),x84673)),f315(f315(f74(x84671),x84674),x84675)))
% 168.60/168.40 [8468]~P68(x84681)+~P1(f315(f315(f224(x84681),f2(x84681)),x84685))+~P1(f315(f315(f223(x84681),x84685),x84683))+~P1(f315(f315(f223(x84681),x84682),x84684))+~P1(f315(f315(f223(x84681),f2(x84681)),x84682))+P1(f315(f315(f223(x84681),f315(f315(f279(x84681),x84682),x84683)),f315(f315(f279(x84681),x84684),x84685)))
% 168.60/168.40 [8469]~P136(x84691)+~P1(f315(f315(f223(x84691),x84693),x84695))+~P1(f315(f315(f223(x84691),f2(x84691)),x84692))+~P1(f315(f315(f224(x84691),x84692),x84694))+~P1(f315(f315(f224(x84691),f2(x84691)),x84693))+P1(f315(f315(f224(x84691),f315(f315(f74(x84691),x84692),x84693)),f315(f315(f74(x84691),x84694),x84695)))
% 168.60/168.40 [8470]~P136(x84701)+~P1(f315(f315(f223(x84701),x84702),x84704))+~P1(f315(f315(f223(x84701),f2(x84701)),x84703))+~P1(f315(f315(f224(x84701),x84703),x84705))+~P1(f315(f315(f224(x84701),f2(x84701)),x84702))+P1(f315(f315(f224(x84701),f315(f315(f74(x84701),x84702),x84703)),f315(f315(f74(x84701),x84704),x84705)))
% 168.60/168.40 [8471]~P136(x84711)+~P1(f315(f315(f223(x84711),f2(x84711)),x84713))+~P1(f315(f315(f223(x84711),f2(x84711)),x84712))+~P1(f315(f315(f224(x84711),x84713),x84715))+~P1(f315(f315(f224(x84711),x84712),x84714))+P1(f315(f315(f224(x84711),f315(f315(f74(x84711),x84712),x84713)),f315(f315(f74(x84711),x84714),x84715)))
% 168.60/168.40 [8472]~P136(x84721)+~P1(f315(f315(f223(x84721),f2(x84721)),x84723))+~P1(f315(f315(f224(x84721),x84723),x84725))+~P1(f315(f315(f224(x84721),x84722),x84724))+~P1(f315(f315(f224(x84721),f2(x84721)),x84724))+P1(f315(f315(f224(x84721),f315(f315(f74(x84721),x84722),x84723)),f315(f315(f74(x84721),x84724),x84725)))
% 168.60/168.40 [8473]~P68(x84731)+~P1(f315(f315(f223(x84731),x84735),x84733))+~P1(f315(f315(f223(x84731),f2(x84731)),x84732))+~P1(f315(f315(f224(x84731),x84732),x84734))+~P1(f315(f315(f224(x84731),f2(x84731)),x84735))+P1(f315(f315(f224(x84731),f315(f315(f279(x84731),x84732),x84733)),f315(f315(f279(x84731),x84734),x84735)))
% 168.60/168.40 [8474]~P68(x84741)+~P1(f315(f315(f223(x84741),x84742),x84744))+~P1(f315(f315(f224(x84741),x84745),x84743))+~P1(f315(f315(f224(x84741),f2(x84741)),x84745))+~P1(f315(f315(f224(x84741),f2(x84741)),x84742))+P1(f315(f315(f224(x84741),f315(f315(f279(x84741),x84742),x84743)),f315(f315(f279(x84741),x84744),x84745)))
% 168.60/168.40 [9874]~P72(x98745)+~P86(x98745)+E(x98741,f177(f909(x98742,a899)))+~P1(f315(f54(x98742),x98741))+P1(f315(f315(f317(x98742),f590(x98743,x98744,x98741,x98742,x98745)),x98741))+P1(f315(f315(f224(x98745),f315(f315(f8(x98742,x98745),x98744),x98741)),f315(f315(f8(x98742,x98745),x98743),x98741)))
% 168.60/168.40 [9983]~P72(x99831)+~P88(x99831)+~P1(f315(f54(x99832),x99835))+~P1(f315(f315(f223(x99831),f2(x99831)),f315(x99833,f859(x99833,x99834,x99835,x99832,x99831))))+P1(f315(f315(f223(x99831),f315(f315(f8(x99832,x99831),x99833),x99834)),f315(f315(f8(x99832,x99831),x99833),x99835)))+~P1(f315(f315(f223(f909(x99832,a899)),x99834),x99835))
% 168.60/168.40 [10152]~P72(x101523)+~P86(x101523)+E(x101521,f177(f909(x101522,a899)))+~P1(f315(f54(x101522),x101521))+~P1(f315(f315(f224(x101523),f315(x101524,f590(x101525,x101524,x101521,x101522,x101523))),f315(x101525,f590(x101525,x101524,x101521,x101522,x101523))))+P1(f315(f315(f224(x101523),f315(f315(f8(x101522,x101523),x101524),x101521)),f315(f315(f8(x101522,x101523),x101525),x101521)))
% 168.60/168.40 [7188]~P18(x71882,x71885,x71884)+E(x71881,f177(f909(x71882,a899)))+E(x71883,f177(f909(x71882,a899)))+~P1(f315(f54(x71882),x71881))+~P1(f315(f54(x71882),x71883))+E(f315(x71884,f315(f315(f99(f909(x71882,a899)),x71883),x71881)),f315(f315(x71885,f315(x71884,x71883)),f315(x71884,x71881)))
% 168.60/168.40 [7780]~P150(x77801,x77803,x77804)+P1(f315(x77801,x77802))+~P1(f315(f315(f224(a1),x77804),f2(a1)))+~P1(f315(f315(f223(a1),x77805),f2(a1)))+~E(x77803,f315(f315(f73(a1),f315(f315(f74(a1),x77804),x77802)),x77805))+~P1(f315(f315(f224(a1),x77804),x77805))
% 168.60/168.40 [7781]~P149(x77811,x77813,x77814)+P1(f315(x77811,x77812))+~P1(f315(f315(f224(a1),x77814),f2(a1)))+~P1(f315(f315(f223(a1),x77812),f2(a1)))+~E(x77813,f315(f315(f73(a1),f315(f315(f74(a1),x77814),x77815)),x77812))+~P1(f315(f315(f224(a1),x77814),x77812))
% 168.60/168.40 [7823]~P150(x78231,x78233,x78234)+P1(f315(x78231,x78232))+~E(x78233,f315(f315(f73(a1),f315(f315(f74(a1),x78234),x78232)),x78235))+~P1(f315(f315(f223(a1),f2(a1)),x78235))+~P1(f315(f315(f224(a1),f2(a1)),x78234))+~P1(f315(f315(f224(a1),x78235),x78234))
% 168.60/168.40 [7824]~P149(x78241,x78243,x78244)+P1(f315(x78241,x78242))+~E(x78243,f315(f315(f73(a1),f315(f315(f74(a1),x78244),x78245)),x78242))+~P1(f315(f315(f223(a1),f2(a1)),x78242))+~P1(f315(f315(f224(a1),f2(a1)),x78244))+~P1(f315(f315(f224(a1),x78242),x78244))
% 168.60/168.40 [8758]P1(f315(f315(x87581,x87582),x87583))+~P1(f315(f315(x87581,f315(f315(f29(a1),x87584),x87585)),f38(a1,x87584,x87585)))+~P1(f315(f315(f224(a1),x87585),f2(a1)))+~P1(f315(f315(f223(a1),x87583),f2(a1)))+~E(x87584,f315(f315(f73(a1),f315(f315(f74(a1),x87585),x87582)),x87583))+~P1(f315(f315(f224(a1),x87585),x87583))
% 168.60/168.40 [8767]P1(f315(f315(x87671,x87672),x87673))+~P1(f315(f315(x87671,f315(f315(f29(a1),x87674),x87675)),f38(a1,x87674,x87675)))+~E(x87674,f315(f315(f73(a1),f315(f315(f74(a1),x87675),x87672)),x87673))+~P1(f315(f315(f223(a1),f2(a1)),x87673))+~P1(f315(f315(f224(a1),f2(a1)),x87675))+~P1(f315(f315(f224(a1),x87673),x87675))
% 168.60/168.40 [9028]E(x90281,x90282)+~P57(x90283,x90285,x90284)+~P1(f315(f315(f317(x90283),x90282),x90285))+~P1(f315(f315(f317(x90283),x90281),x90285))+P1(f315(f315(f317(f908(x90283,x90283)),f315(f315(f240(x90283,x90283),x90281),x90282)),x90284))+P1(f315(f315(f317(f908(x90283,x90283)),f315(f315(f240(x90283,x90283),x90282),x90281)),x90284))
% 168.60/168.40 [9901]~P72(x99015)+~P88(x99015)+~P1(f315(f54(x99011),x99014))+P1(f315(f315(f223(x99015),f315(f315(f8(x99011,x99015),x99012),x99013)),f315(f315(f8(x99011,x99015),x99012),x99014)))+~P1(f315(f315(f223(f909(x99011,a899)),x99013),x99014))+P1(f315(f315(f317(x99011),f859(x99012,x99013,x99014,x99011,x99015)),f315(f315(f3(f909(x99011,a899)),x99014),x99013)))
% 168.60/168.40 [9991]E(x99911,f177(f909(x99912,a899)))+~P1(f315(f54(x99912),x99913))+~P1(f315(f54(x99912),x99911))+P1(f315(f315(f317(f908(f909(x99912,a899),f909(x99912,a899))),f315(f315(f240(f909(x99912,a899),f909(x99912,a899)),x99913),x99911)),f306(x99912,x99914)))+~P1(f315(f315(f317(x99912),x99915),x99911))+~P1(f315(f315(f317(f908(x99912,x99912)),f315(f315(f240(x99912,x99912),f384(x99914,x99911,x99913,x99912)),x99915)),x99914))
% 168.60/168.40 [9992]E(x99921,f177(f909(x99922,a899)))+~P1(f315(f54(x99922),x99923))+~P1(f315(f54(x99922),x99921))+P1(f315(f315(f317(f908(f909(x99922,a899),f909(x99922,a899))),f315(f315(f240(f909(x99922,a899),f909(x99922,a899)),x99923),x99921)),f306(x99922,x99924)))+~P1(f315(f315(f317(x99922),x99925),x99921))+~P1(f315(f315(f317(f908(x99922,x99922)),f315(f315(f240(x99922,x99922),f588(x99924,x99921,x99923,x99922)),x99925)),x99924))
% 168.60/168.40 [10156]~P82(x101561)+~E(f315(f315(f8(x101565,x101561),x101562),x101566),x101564)+~P1(f315(f54(x101565),x101566))+P1(f315(f315(f317(x101565),f407(x101563,x101564,x101562,x101566,x101565,x101561)),x101566))+P1(f315(f315(f223(x101561),f315(x101562,x101563)),x101564))+~P1(f315(f315(f317(x101565),x101563),x101566))
% 168.60/168.40 [10203]~P82(x102031)+~E(f315(f315(f8(x102035,x102031),x102032),x102036),x102034)+~P1(f315(f54(x102035),x102036))+~P1(f315(f315(f317(x102035),x102033),x102036))+~P1(f315(f315(f223(x102031),f2(x102031)),f315(x102032,f407(x102033,x102034,x102032,x102036,x102035,x102031))))+P1(f315(f315(f223(x102031),f315(x102032,x102033)),x102034))
% 168.60/168.40 [10345]~E(x103455,x103458)+~E(x103454,x103457)+~P109(x103451)+~P72(x103452)+E(f315(f315(f8(x103451,x103452),x103453),f315(f290(x103451,x103454),x103455)),f315(f315(f8(x103451,x103452),x103456),f315(f290(x103451,x103457),x103458)))+P1(f315(f315(f223(x103451),x103454),f592(x103453,x103456,x103455,x103458,x103454,x103457,x103451,x103452)))
% 168.60/168.40 [10361]~E(x103617,x103614)+~E(x103618,x103615)+~P109(x103611)+~P72(x103612)+~E(f315(x103613,f592(x103616,x103613,x103618,x103615,x103617,x103614,x103611,x103612)),f315(x103616,f592(x103616,x103613,x103618,x103615,x103617,x103614,x103611,x103612)))+E(f315(f315(f8(x103611,x103612),x103613),f315(f290(x103611,x103614),x103615)),f315(f315(f8(x103611,x103612),x103616),f315(f290(x103611,x103617),x103618)))
% 168.60/168.40 [10364]~E(x103644,x103647)+~E(x103645,x103648)+~P109(x103641)+~P72(x103642)+E(f315(f315(f8(x103641,x103642),x103643),f315(f290(x103641,x103644),x103645)),f315(f315(f8(x103641,x103642),x103646),f315(f290(x103641,x103647),x103648)))+P1(f315(f315(f224(x103641),f592(x103643,x103646,x103645,x103648,x103644,x103647,x103641,x103642)),x103645))
% 168.60/168.40 [9998]~P8(x99985,x99989,x99986)+~P8(x99981,x999810,x99983)+~P12(x99981,x99985,f909(x99982,a899),x99983,x99986,x99988)+~P1(f315(f315(f317(x99985),x99987),x99989))+~P1(f315(f315(f317(x99981),x99984),x999810))+E(f315(f315(f33(x99981,f909(x99982,a899)),f315(f273(x99981,x99981,x99983),f315(f315(f297(x99981),x99984),f177(f909(x99981,a899))))),f315(f315(f10(f909(x99985,f909(x99982,a899)),f909(x99982,a899),x99981),f315(f33(x99985,f909(x99982,a899)),f315(f273(x99985,x99985,x99986),f315(f315(f297(x99985),x99987),f177(f909(x99985,a899)))))),x99988)),f315(f315(x99988,x99984),x99987))
% 168.60/168.40 [5676]~P110(x56763)+~P13(x56763,x56762)+~P13(x56763,x56761)+E(x56761,x56762)+~E(f315(f161(x56763),x56761),f315(f161(x56763),x56762))+~P1(f315(f126(x56763),x56762))+~P1(f315(f126(x56763),x56761))
% 168.60/168.40 [5000]~P134(x50002)+~P135(x50002)+~P146(x50002)+~P117(x50002)+~E(x50003,f2(x50002))+E(x50001,f2(a901))+E(f315(f315(f232(x50002),x50003),x50001),f2(x50002))
% 168.60/168.40 [9284]E(x92841,f2(a901))+~E(x92842,f315(f315(f73(a901),f315(f315(f74(a901),f315(f239(a901,a901),x92843)),x92841)),f315(f244(a901,a901),x92843)))+P1(f315(f41(x92842,x92841),x92843))+~P1(f315(f315(f223(a901),f315(f244(a901,a901),x92843)),f2(a901)))+~P1(f315(f315(f223(a901),f2(a901)),f315(f244(a901,a901),x92843)))+~P1(f315(f315(f224(a901),x92841),f315(f244(a901,a901),x92843)))+~P1(f315(f315(f224(a901),f315(f244(a901,a901),x92843)),x92841))
% 168.60/168.40 [9292]~E(f315(f239(a901,a901),x92923),f2(a901))+~E(x92921,f315(f315(f73(a901),f315(f315(f74(a901),f315(f239(a901,a901),x92923)),x92922)),f315(f244(a901,a901),x92923)))+P1(f315(f41(x92921,x92922),x92923))+~P1(f315(f315(f223(a901),f315(f244(a901,a901),x92923)),f2(a901)))+~P1(f315(f315(f223(a901),f2(a901)),f315(f244(a901,a901),x92923)))+~P1(f315(f315(f224(a901),x92922),f315(f244(a901,a901),x92923)))+~P1(f315(f315(f224(a901),f315(f244(a901,a901),x92923)),x92922))
% 168.60/168.40 [8134]~P70(x81342)+E(x81341,f177(f909(x81342,a899)))+E(x81343,f177(f909(x81342,a899)))+~P1(f315(f54(x81342),x81341))+~P1(f315(f54(x81342),x81343))+~E(f315(f315(f90(f909(x81342,a899)),x81343),x81341),f177(f909(x81342,a899)))+E(f315(f315(f74(x81342),f315(f56(x81342,f74(x81342)),x81343)),f315(f56(x81342,f74(x81342)),x81341)),f315(f56(x81342,f74(x81342)),f315(f315(f99(f909(x81342,a899)),x81343),x81341)))
% 168.60/168.40 [7918]E(x79181,f2(a1))+E(f315(f315(f29(a1),x79182),x79181),x79183)+~P1(f315(f315(f223(a1),x79184),f2(a1)))+~E(x79182,f315(f315(f73(a1),f315(f315(f74(a1),x79181),x79183)),x79184))+~P1(f315(f315(f223(a1),f2(a1)),x79184))+~P1(f315(f315(f224(a1),x79184),x79181))+~P1(f315(f315(f224(a1),x79181),x79184))
% 168.60/168.40 [7926]E(f38(a1,x79262,x79261),x79263)+E(x79261,f2(a1))+~P1(f315(f315(f223(a1),x79263),f2(a1)))+~E(x79262,f315(f315(f73(a1),f315(f315(f74(a1),x79261),x79264)),x79263))+~P1(f315(f315(f223(a1),f2(a1)),x79263))+~P1(f315(f315(f224(a1),x79263),x79261))+~P1(f315(f315(f224(a1),x79261),x79263))
% 168.60/168.40 [6966]~P62(x69662)+E(x69661,f2(x69662))+E(x69663,f2(x69662))+~E(f315(f315(f29(x69662),x69664),x69663),f315(f315(f29(x69662),x69665),x69661))+E(f315(f315(f74(x69662),x69664),x69661),f315(f315(f74(x69662),x69663),x69665))+~P1(f315(f315(f275(x69662),x69661),x69665))+~P1(f315(f315(f275(x69662),x69663),x69664))
% 168.60/168.40 [6967]~P62(x69672)+E(x69671,f2(x69672))+E(x69673,f2(x69672))+~E(f315(f315(f74(x69672),x69674),x69673),f315(f315(f74(x69672),x69671),x69675))+E(f315(f315(f29(x69672),x69674),x69671),f315(f315(f29(x69672),x69675),x69673))+~P1(f315(f315(f275(x69672),x69671),x69674))+~P1(f315(f315(f275(x69672),x69673),x69675))
% 168.60/168.40 [7833]~P19(x78332,x78335,x78334)+E(x78331,f177(f909(x78332,a899)))+E(x78333,f177(f909(x78332,a899)))+~P1(f315(f54(x78332),x78331))+~P1(f315(f54(x78332),x78333))+~E(f315(f315(f90(f909(x78332,a899)),x78333),x78331),f177(f909(x78332,a899)))+E(f315(x78334,f315(f315(f99(f909(x78332,a899)),x78333),x78331)),f315(f315(x78335,f315(x78334,x78333)),f315(x78334,x78331)))
% 168.60/168.40 [9534]~P25(x95343,x95341,x95345,x95344)+~P25(x95341,x95343,x95346,x95342)+E(f315(f28(x95341),x95342),f315(f28(x95343),x95344))+~P1(f315(f54(x95343),x95344))+~P1(f315(f54(x95341),x95342))+~P1(f315(f315(f223(f909(x95343,a899)),f315(f298(x95341,x95343,x95346),x95342)),x95344))+~P1(f315(f315(f223(f909(x95341,a899)),f315(f298(x95343,x95341,x95345),x95344)),x95342))
% 168.60/168.40 [9476]~P1(f315(f315(f224(a1),f315(f315(f73(a1),f315(f315(f74(a1),x94765),x94761)),x94766)),f2(a1)))+~E(f315(f315(f73(a1),f315(f315(f74(a1),x94763),x94762)),x94764),f315(f315(f73(a1),f315(f315(f74(a1),x94765),x94761)),x94766))+~P1(f315(f315(f223(a1),f2(a1)),x94766))+~P1(f315(f315(f224(a1),f2(a1)),x94765))+~P1(f315(f315(f223(a1),x94765),x94763))+~P1(f315(f315(f224(a1),x94764),x94763))+P1(f315(f315(f223(a1),x94761),x94762))
% 168.60/168.40 [9235]~E(f315(f315(f73(a1),f315(f315(f74(a1),x92353),x92351)),x92354),f315(f315(f73(a1),f315(f315(f74(a1),x92355),x92352)),x92356))+~P1(f315(f315(f223(a1),f2(a1)),x92354))+~P1(f315(f315(f224(a1),f2(a1)),x92355))+~P1(f315(f315(f223(a1),x92355),x92353))+~P1(f315(f315(f224(a1),x92356),x92355))+P1(f315(f315(f223(a1),x92351),x92352))+~P1(f315(f315(f223(a1),f2(a1)),f315(f315(f73(a1),f315(f315(f74(a1),x92355),x92352)),x92356)))
% 168.60/168.40 [9416]~P133(x94161)+~E(f315(f315(f73(x94161),x94162),x94164),f71(x94161))+~P1(f315(f315(f223(x94161),x94165),x94166))+~P1(f315(f315(f223(x94161),x94163),x94166))+~P1(f315(f315(f223(x94161),f2(x94161)),x94164))+~P1(f315(f315(f223(x94161),f2(x94161)),x94162))+P1(f315(f315(f223(x94161),f315(f315(f73(x94161),f315(f315(f74(x94161),x94162),x94163)),f315(f315(f74(x94161),x94164),x94165))),x94166))
% 168.60/168.40 [9417]~P131(x94171)+~E(f315(f315(f73(x94171),x94172),x94174),f71(x94171))+~P1(f315(f315(f223(x94171),f2(x94171)),x94174))+~P1(f315(f315(f223(x94171),f2(x94171)),x94172))+~P1(f315(f315(f224(x94171),x94175),x94176))+~P1(f315(f315(f224(x94171),x94173),x94176))+P1(f315(f315(f224(x94171),f315(f315(f73(x94171),f315(f315(f74(x94171),x94172),x94173)),f315(f315(f74(x94171),x94174),x94175))),x94176))
% 168.60/168.40 [10250]~P8(x102507,x102506,x102505)+E(x102501,x102502)+~P11(x102507,f909(x102504,a899),x102505,x102503)+E(f315(x102503,f475(x102501,x102502,x102503,x102504,x102505,x102506,x102507)),f315(x102503,f476(x102501,x102502,x102503,x102504,x102505,x102506,x102507)))+~E(f315(f315(f33(x102507,f909(x102504,a899)),x102501),x102503),f315(f315(f33(x102507,f909(x102504,a899)),x102502),x102503))+~P1(f315(f315(f317(f909(x102507,a899)),x102502),f315(f315(f53(x102507),x102506),x102505)))+~P1(f315(f315(f317(f909(x102507,a899)),x102501),f315(f315(f53(x102507),x102506),x102505)))
% 168.60/168.40 [10301]~P8(x103013,x103017,x103016)+E(x103011,x103012)+~P11(x103013,f909(x103015,a899),x103016,x103014)+~E(f315(f315(f33(x103013,f909(x103015,a899)),x103011),x103014),f315(f315(f33(x103013,f909(x103015,a899)),x103012),x103014))+P1(f315(f315(f317(x103013),f476(x103011,x103012,x103014,x103015,x103016,x103017,x103013)),x103017))+~P1(f315(f315(f317(f909(x103013,a899)),x103012),f315(f315(f53(x103013),x103017),x103016)))+~P1(f315(f315(f317(f909(x103013,a899)),x103011),f315(f315(f53(x103013),x103017),x103016)))
% 168.60/168.40 [10302]~P8(x103023,x103027,x103026)+E(x103021,x103022)+~P11(x103023,f909(x103025,a899),x103026,x103024)+~E(f315(f315(f33(x103023,f909(x103025,a899)),x103021),x103024),f315(f315(f33(x103023,f909(x103025,a899)),x103022),x103024))+P1(f315(f315(f317(x103023),f475(x103021,x103022,x103024,x103025,x103026,x103027,x103023)),x103027))+~P1(f315(f315(f317(f909(x103023,a899)),x103022),f315(f315(f53(x103023),x103027),x103026)))+~P1(f315(f315(f317(f909(x103023,a899)),x103021),f315(f315(f53(x103023),x103027),x103026)))
% 168.60/168.40 [10380]E(x103801,x103802)+~P8(x103803,x103806,x103807)+~P11(x103803,f909(x103804,a899),x103807,x103805)+~E(f315(f315(f33(x103803,f909(x103804,a899)),x103801),x103805),f315(f315(f33(x103803,f909(x103804,a899)),x103802),x103805))+~P1(f315(f315(f317(f908(x103803,x103803)),f315(f315(f240(x103803,x103803),f476(x103801,x103802,x103805,x103804,x103807,x103806,x103803)),f475(x103801,x103802,x103805,x103804,x103807,x103806,x103803))),x103807))+~P1(f315(f315(f317(f909(x103803,a899)),x103802),f315(f315(f53(x103803),x103806),x103807)))+~P1(f315(f315(f317(f909(x103803,a899)),x103801),f315(f315(f53(x103803),x103806),x103807)))
% 168.60/168.40 [9234]~P8(x92341,x92347,x92344)+~E(x92345,x92346)+~P1(f315(f315(f317(x92341),x92343),x92346))+~P1(f315(f315(f317(x92341),x92342),x92345))+~P1(f315(f315(f317(f909(x92341,a899)),x92346),f315(f315(f53(x92341),x92347),x92344)))+~P1(f315(f315(f317(f909(x92341,a899)),x92345),f315(f315(f53(x92341),x92347),x92344)))+P1(f315(f315(f317(f908(x92341,x92341)),f315(f315(f240(x92341,x92341),x92342),x92343)),x92344))
% 168.60/168.40 [9373]E(x93731,x93732)+~P8(x93733,x93734,x93735)+~P1(f315(f315(f317(x93733),x93736),x93732))+~P1(f315(f315(f317(x93733),x93737),x93731))+~P1(f315(f315(f317(f909(x93733,a899)),x93732),f315(f315(f53(x93733),x93734),x93735)))+~P1(f315(f315(f317(f909(x93733,a899)),x93731),f315(f315(f53(x93733),x93734),x93735)))+~P1(f315(f315(f317(f908(x93733,x93733)),f315(f315(f240(x93733,x93733),x93737),x93736)),x93735))
% 168.60/168.40 [10407]~P8(x104079,x104078,x104077)+~P8(x104071,x1040711,x1040710)+~P12(x104071,x104079,f909(x104076,a899),x1040710,x104077,x104075)+P1(f315(f315(f317(x104071),f478(x104072,x104073,x104074,x104075,x104076,x104077,x104078,x104079,x1040710,x1040711,x104071)),x1040711))+~P1(f315(f315(f317(f909(x104079,a899)),x104073),f315(f315(f53(x104079),x104078),x104077)))+~P1(f315(f315(f317(f909(x104071,a899)),x104074),f315(f315(f53(x104071),x1040711),x1040710)))+P1(f315(f315(f317(f909(x104076,a899)),f315(f315(f33(x104071,f909(x104076,a899)),x104074),f315(f315(f10(f909(x104079,f909(x104076,a899)),f909(x104076,a899),x104071),f315(f33(x104079,f909(x104076,a899)),x104073)),x104075))),x104072))
% 168.60/168.40 [10408]~P8(x1040811,x1040810,x104089)+~P8(x104081,x104088,x104087)+~P12(x1040811,x104081,f909(x104086,a899),x104089,x104087,x104085)+P1(f315(f315(f317(x104081),f479(x104082,x104083,x104084,x104085,x104086,x104087,x104088,x104081,x104089,x1040810,x1040811)),x104088))+~P1(f315(f315(f317(f909(x1040811,a899)),x104084),f315(f315(f53(x1040811),x1040810),x104089)))+~P1(f315(f315(f317(f909(x104081,a899)),x104083),f315(f315(f53(x104081),x104088),x104087)))+P1(f315(f315(f317(f909(x104086,a899)),f315(f315(f33(x1040811,f909(x104086,a899)),x104084),f315(f315(f10(f909(x104081,f909(x104086,a899)),f909(x104086,a899),x1040811),f315(f33(x104081,f909(x104086,a899)),x104083)),x104085))),x104082))
% 168.60/168.40 [10409]~P8(x104092,x104098,x104099)+~P8(x104094,x1040910,x1040911)+~P12(x104092,x104094,f909(x104091,a899),x104099,x1040911,x104096)+~P1(f315(f315(f317(f909(x104092,a899)),x104093),f315(f315(f53(x104092),x104098),x104099)))+~P1(f315(f315(f317(f909(x104094,a899)),x104095),f315(f315(f53(x104094),x1040910),x1040911)))+~P1(f315(f315(f317(f909(x104091,a899)),f315(f315(x104096,f478(x104097,x104095,x104093,x104096,x104091,x1040911,x1040910,x104094,x104099,x104098,x104092)),f479(x104097,x104095,x104093,x104096,x104091,x1040911,x1040910,x104094,x104099,x104098,x104092))),x104097))+P1(f315(f315(f317(f909(x104091,a899)),f315(f315(f33(x104092,f909(x104091,a899)),x104093),f315(f315(f10(f909(x104094,f909(x104091,a899)),f909(x104091,a899),x104092),f315(f33(x104094,f909(x104091,a899)),x104095)),x104096))),x104097))
% 168.60/168.40 [9270]E(x92701,x92702)+~P110(x92704)+~P25(x92703,x92704,x92705,f315(f315(f99(f909(x92703,a899)),f315(f161(x92703),x92701)),f315(f161(x92703),x92702)))+~E(f315(f161(x92703),x92701),f315(f161(x92703),x92702))+~P13(x92704,f315(f315(f143(x92703,x92704),x92705),x92702))+~P13(x92704,f315(f315(f143(x92703,x92704),x92705),x92701))+~P1(f315(f126(x92704),f315(f315(f143(x92703,x92704),x92705),x92702)))+~P1(f315(f126(x92704),f315(f315(f143(x92703,x92704),x92705),x92701)))
% 168.60/168.40 %EqnAxiom
% 168.60/168.40 [1]E(x11,x11)
% 168.60/168.40 [2]E(x22,x21)+~E(x21,x22)
% 168.60/168.40 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 168.60/168.40 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 168.60/168.40 [5]~E(x51,x52)+E(f3(x51),f3(x52))
% 168.60/168.40 [6]~E(x61,x62)+E(f89(x61),f89(x62))
% 168.60/168.40 [7]~E(x71,x72)+E(f177(x71),f177(x72))
% 168.60/168.40 [8]~E(x81,x82)+E(f315(x81,x83),f315(x82,x83))
% 168.60/168.40 [9]~E(x91,x92)+E(f315(x93,x91),f315(x93,x92))
% 168.60/168.40 [10]~E(x101,x102)+E(f90(x101),f90(x102))
% 168.60/168.40 [11]~E(x111,x112)+E(f221(x111),f221(x112))
% 168.60/168.40 [12]~E(x121,x122)+E(f99(x121),f99(x122))
% 168.60/168.40 [13]~E(x131,x132)+E(f222(x131),f222(x132))
% 168.60/168.40 [14]~E(x141,x142)+E(f91(x141),f91(x142))
% 168.60/168.40 [15]~E(x151,x152)+E(f25(x151),f25(x152))
% 168.60/168.40 [16]~E(x161,x162)+E(f77(x161),f77(x162))
% 168.60/168.40 [17]~E(x171,x172)+E(f10(x171,x173,x174),f10(x172,x173,x174))
% 168.60/168.40 [18]~E(x181,x182)+E(f10(x183,x181,x184),f10(x183,x182,x184))
% 168.60/168.40 [19]~E(x191,x192)+E(f10(x193,x194,x191),f10(x193,x194,x192))
% 168.60/168.40 [20]~E(x201,x202)+E(f909(x201,x203),f909(x202,x203))
% 168.60/168.40 [21]~E(x211,x212)+E(f909(x213,x211),f909(x213,x212))
% 168.60/168.40 [22]~E(x221,x222)+E(f902(x221),f902(x222))
% 168.60/168.40 [23]~E(x231,x232)+E(f71(x231),f71(x232))
% 168.60/168.40 [24]~E(x241,x242)+E(f479(x241,x243,x244,x245,x246,x247,x248,x249,x2410,x2411,x2412),f479(x242,x243,x244,x245,x246,x247,x248,x249,x2410,x2411,x2412))
% 168.60/168.40 [25]~E(x251,x252)+E(f479(x253,x251,x254,x255,x256,x257,x258,x259,x2510,x2511,x2512),f479(x253,x252,x254,x255,x256,x257,x258,x259,x2510,x2511,x2512))
% 168.60/168.40 [26]~E(x261,x262)+E(f479(x263,x264,x261,x265,x266,x267,x268,x269,x2610,x2611,x2612),f479(x263,x264,x262,x265,x266,x267,x268,x269,x2610,x2611,x2612))
% 168.60/168.40 [27]~E(x271,x272)+E(f479(x273,x274,x275,x271,x276,x277,x278,x279,x2710,x2711,x2712),f479(x273,x274,x275,x272,x276,x277,x278,x279,x2710,x2711,x2712))
% 168.60/168.40 [28]~E(x281,x282)+E(f479(x283,x284,x285,x286,x281,x287,x288,x289,x2810,x2811,x2812),f479(x283,x284,x285,x286,x282,x287,x288,x289,x2810,x2811,x2812))
% 168.60/168.40 [29]~E(x291,x292)+E(f479(x293,x294,x295,x296,x297,x291,x298,x299,x2910,x2911,x2912),f479(x293,x294,x295,x296,x297,x292,x298,x299,x2910,x2911,x2912))
% 168.60/168.40 [30]~E(x301,x302)+E(f479(x303,x304,x305,x306,x307,x308,x301,x309,x3010,x3011,x3012),f479(x303,x304,x305,x306,x307,x308,x302,x309,x3010,x3011,x3012))
% 168.60/168.40 [31]~E(x311,x312)+E(f479(x313,x314,x315,x316,x317,x318,x319,x311,x3110,x3111,x3112),f479(x313,x314,x315,x316,x317,x318,x319,x312,x3110,x3111,x3112))
% 168.60/168.40 [32]~E(x321,x322)+E(f479(x323,x324,x325,x326,x327,x328,x329,x3210,x321,x3211,x3212),f479(x323,x324,x325,x326,x327,x328,x329,x3210,x322,x3211,x3212))
% 168.60/168.40 [33]~E(x331,x332)+E(f479(x333,x334,x335,x336,x337,x338,x339,x3310,x3311,x331,x3312),f479(x333,x334,x335,x336,x337,x338,x339,x3310,x3311,x332,x3312))
% 168.60/168.40 [34]~E(x341,x342)+E(f479(x343,x344,x345,x346,x347,x348,x349,x3410,x3411,x3412,x341),f479(x343,x344,x345,x346,x347,x348,x349,x3410,x3411,x3412,x342))
% 168.60/168.40 [35]~E(x351,x352)+E(f224(x351),f224(x352))
% 168.60/168.40 [36]~E(x361,x362)+E(f6(x361),f6(x362))
% 168.60/168.40 [37]~E(x371,x372)+E(f478(x371,x373,x374,x375,x376,x377,x378,x379,x3710,x3711,x3712),f478(x372,x373,x374,x375,x376,x377,x378,x379,x3710,x3711,x3712))
% 168.60/168.40 [38]~E(x381,x382)+E(f478(x383,x381,x384,x385,x386,x387,x388,x389,x3810,x3811,x3812),f478(x383,x382,x384,x385,x386,x387,x388,x389,x3810,x3811,x3812))
% 168.60/168.40 [39]~E(x391,x392)+E(f478(x393,x394,x391,x395,x396,x397,x398,x399,x3910,x3911,x3912),f478(x393,x394,x392,x395,x396,x397,x398,x399,x3910,x3911,x3912))
% 168.60/168.40 [40]~E(x401,x402)+E(f478(x403,x404,x405,x401,x406,x407,x408,x409,x4010,x4011,x4012),f478(x403,x404,x405,x402,x406,x407,x408,x409,x4010,x4011,x4012))
% 168.60/168.40 [41]~E(x411,x412)+E(f478(x413,x414,x415,x416,x411,x417,x418,x419,x4110,x4111,x4112),f478(x413,x414,x415,x416,x412,x417,x418,x419,x4110,x4111,x4112))
% 168.60/168.40 [42]~E(x421,x422)+E(f478(x423,x424,x425,x426,x427,x421,x428,x429,x4210,x4211,x4212),f478(x423,x424,x425,x426,x427,x422,x428,x429,x4210,x4211,x4212))
% 168.60/168.40 [43]~E(x431,x432)+E(f478(x433,x434,x435,x436,x437,x438,x431,x439,x4310,x4311,x4312),f478(x433,x434,x435,x436,x437,x438,x432,x439,x4310,x4311,x4312))
% 168.60/168.40 [44]~E(x441,x442)+E(f478(x443,x444,x445,x446,x447,x448,x449,x441,x4410,x4411,x4412),f478(x443,x444,x445,x446,x447,x448,x449,x442,x4410,x4411,x4412))
% 168.60/168.40 [45]~E(x451,x452)+E(f478(x453,x454,x455,x456,x457,x458,x459,x4510,x451,x4511,x4512),f478(x453,x454,x455,x456,x457,x458,x459,x4510,x452,x4511,x4512))
% 168.60/168.40 [46]~E(x461,x462)+E(f478(x463,x464,x465,x466,x467,x468,x469,x4610,x4611,x461,x4612),f478(x463,x464,x465,x466,x467,x468,x469,x4610,x4611,x462,x4612))
% 168.60/168.40 [47]~E(x471,x472)+E(f478(x473,x474,x475,x476,x477,x478,x479,x4710,x4711,x4712,x471),f478(x473,x474,x475,x476,x477,x478,x479,x4710,x4711,x4712,x472))
% 168.60/168.40 [48]~E(x481,x482)+E(f317(x481),f317(x482))
% 168.60/168.40 [49]~E(x491,x492)+E(f100(x491),f100(x492))
% 168.60/168.40 [50]~E(x501,x502)+E(f143(x501,x503),f143(x502,x503))
% 168.60/168.40 [51]~E(x511,x512)+E(f143(x513,x511),f143(x513,x512))
% 168.60/168.40 [52]~E(x521,x522)+E(f900(x521),f900(x522))
% 168.60/168.40 [53]~E(x531,x532)+E(f905(x531),f905(x532))
% 168.60/168.40 [54]~E(x541,x542)+E(f223(x541),f223(x542))
% 168.60/168.40 [55]~E(x551,x552)+E(f903(x551),f903(x552))
% 168.60/168.40 [56]~E(x561,x562)+E(f72(x561),f72(x562))
% 168.60/168.40 [57]~E(x571,x572)+E(f20(x571,x573,x574),f20(x572,x573,x574))
% 168.60/168.40 [58]~E(x581,x582)+E(f20(x583,x581,x584),f20(x583,x582,x584))
% 168.60/168.40 [59]~E(x591,x592)+E(f20(x593,x594,x591),f20(x593,x594,x592))
% 168.60/168.40 [60]~E(x601,x602)+E(f92(x601),f92(x602))
% 168.60/168.40 [61]~E(x611,x612)+E(f28(x611),f28(x612))
% 168.60/168.40 [62]~E(x621,x622)+E(f178(x621),f178(x622))
% 168.60/168.40 [63]~E(x631,x632)+E(f250(x631),f250(x632))
% 168.60/168.40 [64]~E(x641,x642)+E(f30(x641,x643),f30(x642,x643))
% 168.60/168.40 [65]~E(x651,x652)+E(f30(x653,x651),f30(x653,x652))
% 168.60/168.40 [66]~E(x661,x662)+E(f54(x661),f54(x662))
% 168.60/168.40 [67]~E(x671,x672)+E(f845(x671,x673,x674),f845(x672,x673,x674))
% 168.60/168.40 [68]~E(x681,x682)+E(f845(x683,x681,x684),f845(x683,x682,x684))
% 168.60/168.40 [69]~E(x691,x692)+E(f845(x693,x694,x691),f845(x693,x694,x692))
% 168.60/168.40 [70]~E(x701,x702)+E(f73(x701),f73(x702))
% 168.60/168.40 [71]~E(x711,x712)+E(f908(x711,x713),f908(x712,x713))
% 168.60/168.40 [72]~E(x721,x722)+E(f908(x723,x721),f908(x723,x722))
% 168.60/168.40 [73]~E(x731,x732)+E(f140(x731),f140(x732))
% 168.60/168.40 [74]~E(x741,x742)+E(f245(x741,x743,x744),f245(x742,x743,x744))
% 168.60/168.40 [75]~E(x751,x752)+E(f245(x753,x751,x754),f245(x753,x752,x754))
% 168.60/168.40 [76]~E(x761,x762)+E(f245(x763,x764,x761),f245(x763,x764,x762))
% 168.60/168.40 [77]~E(x771,x772)+E(f102(x771),f102(x772))
% 168.60/168.40 [78]~E(x781,x782)+E(f123(x781),f123(x782))
% 168.60/168.40 [79]~E(x791,x792)+E(f126(x791),f126(x792))
% 168.60/168.40 [80]~E(x801,x802)+E(f74(x801),f74(x802))
% 168.60/168.40 [81]~E(x811,x812)+E(f295(x811,x813),f295(x812,x813))
% 168.60/168.40 [82]~E(x821,x822)+E(f295(x823,x821),f295(x823,x822))
% 168.60/168.40 [83]~E(x831,x832)+E(f53(x831),f53(x832))
% 168.60/168.40 [84]~E(x841,x842)+E(f878(x841,x843,x844),f878(x842,x843,x844))
% 168.60/168.40 [85]~E(x851,x852)+E(f878(x853,x851,x854),f878(x853,x852,x854))
% 168.60/168.40 [86]~E(x861,x862)+E(f878(x863,x864,x861),f878(x863,x864,x862))
% 168.60/168.40 [87]~E(x871,x872)+E(f153(x871),f153(x872))
% 168.60/168.40 [88]~E(x881,x882)+E(f298(x881,x883,x884),f298(x882,x883,x884))
% 168.60/168.40 [89]~E(x891,x892)+E(f298(x893,x891,x894),f298(x893,x892,x894))
% 168.60/168.40 [90]~E(x901,x902)+E(f298(x903,x904,x901),f298(x903,x904,x902))
% 168.60/168.40 [91]~E(x911,x912)+E(f9(x911,x913,x914),f9(x912,x913,x914))
% 168.60/168.40 [92]~E(x921,x922)+E(f9(x923,x921,x924),f9(x923,x922,x924))
% 168.60/168.40 [93]~E(x931,x932)+E(f9(x933,x934,x931),f9(x933,x934,x932))
% 168.60/168.40 [94]~E(x941,x942)+E(f127(x941),f127(x942))
% 168.60/168.40 [95]~E(x951,x952)+E(f29(x951),f29(x952))
% 168.60/168.40 [96]~E(x961,x962)+E(f16(x961,x963),f16(x962,x963))
% 168.60/168.40 [97]~E(x971,x972)+E(f16(x973,x971),f16(x973,x972))
% 168.60/168.40 [98]~E(x981,x982)+E(f161(x981),f161(x982))
% 168.60/168.40 [99]~E(x991,x992)+E(f740(x991,x993,x994),f740(x992,x993,x994))
% 168.60/168.40 [100]~E(x1001,x1002)+E(f740(x1003,x1001,x1004),f740(x1003,x1002,x1004))
% 168.60/168.40 [101]~E(x1011,x1012)+E(f740(x1013,x1014,x1011),f740(x1013,x1014,x1012))
% 168.60/168.40 [102]~E(x1021,x1022)+E(f297(x1021),f297(x1022))
% 168.60/168.40 [103]~E(x1031,x1032)+E(f325(x1031),f325(x1032))
% 168.60/168.40 [104]~E(x1041,x1042)+E(f137(x1041,x1043,x1044),f137(x1042,x1043,x1044))
% 168.60/168.40 [105]~E(x1051,x1052)+E(f137(x1053,x1051,x1054),f137(x1053,x1052,x1054))
% 168.60/168.40 [106]~E(x1061,x1062)+E(f137(x1063,x1064,x1061),f137(x1063,x1064,x1062))
% 168.60/168.40 [107]~E(x1071,x1072)+E(f240(x1071,x1073),f240(x1072,x1073))
% 168.60/168.40 [108]~E(x1081,x1082)+E(f240(x1083,x1081),f240(x1083,x1082))
% 168.60/168.40 [109]~E(x1091,x1092)+E(f471(x1091,x1093,x1094,x1095),f471(x1092,x1093,x1094,x1095))
% 168.60/168.40 [110]~E(x1101,x1102)+E(f471(x1103,x1101,x1104,x1105),f471(x1103,x1102,x1104,x1105))
% 168.60/168.40 [111]~E(x1111,x1112)+E(f471(x1113,x1114,x1111,x1115),f471(x1113,x1114,x1112,x1115))
% 168.60/168.40 [112]~E(x1121,x1122)+E(f471(x1123,x1124,x1125,x1121),f471(x1123,x1124,x1125,x1122))
% 168.60/168.40 [113]~E(x1131,x1132)+E(f279(x1131),f279(x1132))
% 168.60/168.40 [114]~E(x1141,x1142)+E(f69(x1141),f69(x1142))
% 168.60/168.40 [115]~E(x1151,x1152)+E(f415(x1151,x1153,x1154,x1155,x1156),f415(x1152,x1153,x1154,x1155,x1156))
% 168.60/168.40 [116]~E(x1161,x1162)+E(f415(x1163,x1161,x1164,x1165,x1166),f415(x1163,x1162,x1164,x1165,x1166))
% 168.60/168.40 [117]~E(x1171,x1172)+E(f415(x1173,x1174,x1171,x1175,x1176),f415(x1173,x1174,x1172,x1175,x1176))
% 168.60/168.40 [118]~E(x1181,x1182)+E(f415(x1183,x1184,x1185,x1181,x1186),f415(x1183,x1184,x1185,x1182,x1186))
% 168.60/168.40 [119]~E(x1191,x1192)+E(f415(x1193,x1194,x1195,x1196,x1191),f415(x1193,x1194,x1195,x1196,x1192))
% 168.60/168.40 [120]~E(x1201,x1202)+E(f134(x1201,x1203),f134(x1202,x1203))
% 168.60/168.40 [121]~E(x1211,x1212)+E(f134(x1213,x1211),f134(x1213,x1212))
% 168.60/168.40 [122]~E(x1221,x1222)+E(f230(x1221),f230(x1222))
% 168.60/168.40 [123]~E(x1231,x1232)+E(f55(x1231,x1233,x1234),f55(x1232,x1233,x1234))
% 168.60/168.40 [124]~E(x1241,x1242)+E(f55(x1243,x1241,x1244),f55(x1243,x1242,x1244))
% 168.60/168.40 [125]~E(x1251,x1252)+E(f55(x1253,x1254,x1251),f55(x1253,x1254,x1252))
% 168.60/168.40 [126]~E(x1261,x1262)+E(f355(x1261,x1263,x1264),f355(x1262,x1263,x1264))
% 168.60/168.40 [127]~E(x1271,x1272)+E(f355(x1273,x1271,x1274),f355(x1273,x1272,x1274))
% 168.60/168.40 [128]~E(x1281,x1282)+E(f355(x1283,x1284,x1281),f355(x1283,x1284,x1282))
% 168.60/168.40 [129]~E(x1291,x1292)+E(f115(x1291,x1293,x1294),f115(x1292,x1293,x1294))
% 168.60/168.40 [130]~E(x1301,x1302)+E(f115(x1303,x1301,x1304),f115(x1303,x1302,x1304))
% 168.60/168.40 [131]~E(x1311,x1312)+E(f115(x1313,x1314,x1311),f115(x1313,x1314,x1312))
% 168.60/168.40 [132]~E(x1321,x1322)+E(f271(x1321),f271(x1322))
% 168.60/168.40 [133]~E(x1331,x1332)+E(f94(x1331),f94(x1332))
% 168.60/168.40 [134]~E(x1341,x1342)+E(f96(x1341),f96(x1342))
% 168.60/168.40 [135]~E(x1351,x1352)+E(f316(x1351),f316(x1352))
% 168.60/168.40 [136]~E(x1361,x1362)+E(f156(x1361),f156(x1362))
% 168.60/168.40 [137]~E(x1371,x1372)+E(f561(x1371),f561(x1372))
% 168.60/168.40 [138]~E(x1381,x1382)+E(f824(x1381,x1383,x1384,x1385,x1386,x1387,x1388,x1389),f824(x1382,x1383,x1384,x1385,x1386,x1387,x1388,x1389))
% 168.60/168.40 [139]~E(x1391,x1392)+E(f824(x1393,x1391,x1394,x1395,x1396,x1397,x1398,x1399),f824(x1393,x1392,x1394,x1395,x1396,x1397,x1398,x1399))
% 168.60/168.40 [140]~E(x1401,x1402)+E(f824(x1403,x1404,x1401,x1405,x1406,x1407,x1408,x1409),f824(x1403,x1404,x1402,x1405,x1406,x1407,x1408,x1409))
% 168.60/168.40 [141]~E(x1411,x1412)+E(f824(x1413,x1414,x1415,x1411,x1416,x1417,x1418,x1419),f824(x1413,x1414,x1415,x1412,x1416,x1417,x1418,x1419))
% 168.60/168.40 [142]~E(x1421,x1422)+E(f824(x1423,x1424,x1425,x1426,x1421,x1427,x1428,x1429),f824(x1423,x1424,x1425,x1426,x1422,x1427,x1428,x1429))
% 168.60/168.40 [143]~E(x1431,x1432)+E(f824(x1433,x1434,x1435,x1436,x1437,x1431,x1438,x1439),f824(x1433,x1434,x1435,x1436,x1437,x1432,x1438,x1439))
% 168.60/168.40 [144]~E(x1441,x1442)+E(f824(x1443,x1444,x1445,x1446,x1447,x1448,x1441,x1449),f824(x1443,x1444,x1445,x1446,x1447,x1448,x1442,x1449))
% 168.60/168.40 [145]~E(x1451,x1452)+E(f824(x1453,x1454,x1455,x1456,x1457,x1458,x1459,x1451),f824(x1453,x1454,x1455,x1456,x1457,x1458,x1459,x1452))
% 168.60/168.40 [146]~E(x1461,x1462)+E(f38(x1461,x1463,x1464),f38(x1462,x1463,x1464))
% 168.60/168.40 [147]~E(x1471,x1472)+E(f38(x1473,x1471,x1474),f38(x1473,x1472,x1474))
% 168.60/168.40 [148]~E(x1481,x1482)+E(f38(x1483,x1484,x1481),f38(x1483,x1484,x1482))
% 168.60/168.40 [149]~E(x1491,x1492)+E(f229(x1491,x1493),f229(x1492,x1493))
% 168.60/168.40 [150]~E(x1501,x1502)+E(f229(x1503,x1501),f229(x1503,x1502))
% 168.60/168.40 [151]~E(x1511,x1512)+E(f387(x1511,x1513),f387(x1512,x1513))
% 168.60/168.40 [152]~E(x1521,x1522)+E(f387(x1523,x1521),f387(x1523,x1522))
% 168.60/168.40 [153]~E(x1531,x1532)+E(f542(x1531,x1533,x1534,x1535,x1536),f542(x1532,x1533,x1534,x1535,x1536))
% 168.60/168.40 [154]~E(x1541,x1542)+E(f542(x1543,x1541,x1544,x1545,x1546),f542(x1543,x1542,x1544,x1545,x1546))
% 168.60/168.40 [155]~E(x1551,x1552)+E(f542(x1553,x1554,x1551,x1555,x1556),f542(x1553,x1554,x1552,x1555,x1556))
% 168.60/168.40 [156]~E(x1561,x1562)+E(f542(x1563,x1564,x1565,x1561,x1566),f542(x1563,x1564,x1565,x1562,x1566))
% 168.60/168.40 [157]~E(x1571,x1572)+E(f542(x1573,x1574,x1575,x1576,x1571),f542(x1573,x1574,x1575,x1576,x1572))
% 168.60/168.40 [158]~E(x1581,x1582)+E(f18(x1581,x1583),f18(x1582,x1583))
% 168.60/168.40 [159]~E(x1591,x1592)+E(f18(x1593,x1591),f18(x1593,x1592))
% 168.60/168.40 [160]~E(x1601,x1602)+E(f31(x1601,x1603),f31(x1602,x1603))
% 168.60/168.40 [161]~E(x1611,x1612)+E(f31(x1613,x1611),f31(x1613,x1612))
% 168.60/168.40 [162]~E(x1621,x1622)+E(f7(x1621),f7(x1622))
% 168.60/168.40 [163]~E(x1631,x1632)+E(f784(x1631,x1633,x1634),f784(x1632,x1633,x1634))
% 168.60/168.40 [164]~E(x1641,x1642)+E(f784(x1643,x1641,x1644),f784(x1643,x1642,x1644))
% 168.60/168.40 [165]~E(x1651,x1652)+E(f784(x1653,x1654,x1651),f784(x1653,x1654,x1652))
% 168.60/168.40 [166]~E(x1661,x1662)+E(f690(x1661,x1663),f690(x1662,x1663))
% 168.60/168.40 [167]~E(x1671,x1672)+E(f690(x1673,x1671),f690(x1673,x1672))
% 168.60/168.40 [168]~E(x1681,x1682)+E(f456(x1681,x1683),f456(x1682,x1683))
% 168.60/168.40 [169]~E(x1691,x1692)+E(f456(x1693,x1691),f456(x1693,x1692))
% 168.60/168.40 [170]~E(x1701,x1702)+E(f201(x1701),f201(x1702))
% 168.60/168.40 [171]~E(x1711,x1712)+E(f239(x1711,x1713),f239(x1712,x1713))
% 168.60/168.40 [172]~E(x1721,x1722)+E(f239(x1723,x1721),f239(x1723,x1722))
% 168.60/168.40 [173]~E(x1731,x1732)+E(f66(x1731,x1733,x1734,x1735),f66(x1732,x1733,x1734,x1735))
% 168.60/168.40 [174]~E(x1741,x1742)+E(f66(x1743,x1741,x1744,x1745),f66(x1743,x1742,x1744,x1745))
% 168.60/168.40 [175]~E(x1751,x1752)+E(f66(x1753,x1754,x1751,x1755),f66(x1753,x1754,x1752,x1755))
% 168.60/168.40 [176]~E(x1761,x1762)+E(f66(x1763,x1764,x1765,x1761),f66(x1763,x1764,x1765,x1762))
% 168.60/168.40 [177]~E(x1771,x1772)+E(f166(x1771,x1773,x1774),f166(x1772,x1773,x1774))
% 168.60/168.40 [178]~E(x1781,x1782)+E(f166(x1783,x1781,x1784),f166(x1783,x1782,x1784))
% 168.60/168.40 [179]~E(x1791,x1792)+E(f166(x1793,x1794,x1791),f166(x1793,x1794,x1792))
% 168.60/168.40 [180]~E(x1801,x1802)+E(f847(x1801,x1803,x1804),f847(x1802,x1803,x1804))
% 168.60/168.40 [181]~E(x1811,x1812)+E(f847(x1813,x1811,x1814),f847(x1813,x1812,x1814))
% 168.60/168.40 [182]~E(x1821,x1822)+E(f847(x1823,x1824,x1821),f847(x1823,x1824,x1822))
% 168.60/168.40 [183]~E(x1831,x1832)+E(f158(x1831,x1833,x1834),f158(x1832,x1833,x1834))
% 168.60/168.40 [184]~E(x1841,x1842)+E(f158(x1843,x1841,x1844),f158(x1843,x1842,x1844))
% 168.60/168.40 [185]~E(x1851,x1852)+E(f158(x1853,x1854,x1851),f158(x1853,x1854,x1852))
% 168.60/168.40 [186]~E(x1861,x1862)+E(f877(x1861,x1863,x1864),f877(x1862,x1863,x1864))
% 168.60/168.40 [187]~E(x1871,x1872)+E(f877(x1873,x1871,x1874),f877(x1873,x1872,x1874))
% 168.60/168.40 [188]~E(x1881,x1882)+E(f877(x1883,x1884,x1881),f877(x1883,x1884,x1882))
% 168.60/168.40 [189]~E(x1891,x1892)+E(f32(x1891,x1893),f32(x1892,x1893))
% 168.60/168.40 [190]~E(x1901,x1902)+E(f32(x1903,x1901),f32(x1903,x1902))
% 168.60/168.40 [191]~E(x1911,x1912)+E(f662(x1911,x1913,x1914,x1915,x1916),f662(x1912,x1913,x1914,x1915,x1916))
% 168.60/168.40 [192]~E(x1921,x1922)+E(f662(x1923,x1921,x1924,x1925,x1926),f662(x1923,x1922,x1924,x1925,x1926))
% 168.60/168.40 [193]~E(x1931,x1932)+E(f662(x1933,x1934,x1931,x1935,x1936),f662(x1933,x1934,x1932,x1935,x1936))
% 168.60/168.40 [194]~E(x1941,x1942)+E(f662(x1943,x1944,x1945,x1941,x1946),f662(x1943,x1944,x1945,x1942,x1946))
% 168.60/168.40 [195]~E(x1951,x1952)+E(f662(x1953,x1954,x1955,x1956,x1951),f662(x1953,x1954,x1955,x1956,x1952))
% 168.60/168.40 [196]~E(x1961,x1962)+E(f876(x1961,x1963,x1964),f876(x1962,x1963,x1964))
% 168.60/168.40 [197]~E(x1971,x1972)+E(f876(x1973,x1971,x1974),f876(x1973,x1972,x1974))
% 168.60/168.40 [198]~E(x1981,x1982)+E(f876(x1983,x1984,x1981),f876(x1983,x1984,x1982))
% 168.60/168.40 [199]~E(x1991,x1992)+E(f33(x1991,x1993),f33(x1992,x1993))
% 168.60/168.40 [200]~E(x2001,x2002)+E(f33(x2003,x2001),f33(x2003,x2002))
% 168.60/168.40 [201]~E(x2011,x2012)+E(f815(x2011,x2013,x2014,x2015),f815(x2012,x2013,x2014,x2015))
% 168.60/168.40 [202]~E(x2021,x2022)+E(f815(x2023,x2021,x2024,x2025),f815(x2023,x2022,x2024,x2025))
% 168.60/168.40 [203]~E(x2031,x2032)+E(f815(x2033,x2034,x2031,x2035),f815(x2033,x2034,x2032,x2035))
% 168.60/168.40 [204]~E(x2041,x2042)+E(f815(x2043,x2044,x2045,x2041),f815(x2043,x2044,x2045,x2042))
% 168.60/168.40 [205]~E(x2051,x2052)+E(f275(x2051),f275(x2052))
% 168.60/168.40 [206]~E(x2061,x2062)+E(f848(x2061,x2063,x2064),f848(x2062,x2063,x2064))
% 168.60/168.40 [207]~E(x2071,x2072)+E(f848(x2073,x2071,x2074),f848(x2073,x2072,x2074))
% 168.60/168.40 [208]~E(x2081,x2082)+E(f848(x2083,x2084,x2081),f848(x2083,x2084,x2082))
% 168.60/168.40 [209]~E(x2091,x2092)+E(f291(x2091,x2093,x2094),f291(x2092,x2093,x2094))
% 168.60/168.40 [210]~E(x2101,x2102)+E(f291(x2103,x2101,x2104),f291(x2103,x2102,x2104))
% 168.60/168.40 [211]~E(x2111,x2112)+E(f291(x2113,x2114,x2111),f291(x2113,x2114,x2112))
% 168.60/168.40 [212]~E(x2121,x2122)+E(f11(x2121,x2123),f11(x2122,x2123))
% 168.60/168.40 [213]~E(x2131,x2132)+E(f11(x2133,x2131),f11(x2133,x2132))
% 168.60/168.40 [214]~E(x2141,x2142)+E(f290(x2141,x2143),f290(x2142,x2143))
% 168.60/168.40 [215]~E(x2151,x2152)+E(f290(x2153,x2151),f290(x2153,x2152))
% 168.60/168.40 [216]~E(x2161,x2162)+E(f844(x2161,x2163,x2164),f844(x2162,x2163,x2164))
% 168.60/168.40 [217]~E(x2171,x2172)+E(f844(x2173,x2171,x2174),f844(x2173,x2172,x2174))
% 168.60/168.40 [218]~E(x2181,x2182)+E(f844(x2183,x2184,x2181),f844(x2183,x2184,x2182))
% 168.60/168.40 [219]~E(x2191,x2192)+E(f232(x2191),f232(x2192))
% 168.60/168.40 [220]~E(x2201,x2202)+E(f78(x2201,x2203),f78(x2202,x2203))
% 168.60/168.40 [221]~E(x2211,x2212)+E(f78(x2213,x2211),f78(x2213,x2212))
% 168.60/168.40 [222]~E(x2221,x2222)+E(f652(x2221,x2223,x2224,x2225),f652(x2222,x2223,x2224,x2225))
% 168.60/168.40 [223]~E(x2231,x2232)+E(f652(x2233,x2231,x2234,x2235),f652(x2233,x2232,x2234,x2235))
% 168.60/168.40 [224]~E(x2241,x2242)+E(f652(x2243,x2244,x2241,x2245),f652(x2243,x2244,x2242,x2245))
% 168.60/168.40 [225]~E(x2251,x2252)+E(f652(x2253,x2254,x2255,x2251),f652(x2253,x2254,x2255,x2252))
% 168.60/168.40 [226]~E(x2261,x2262)+E(f244(x2261,x2263),f244(x2262,x2263))
% 168.60/168.40 [227]~E(x2271,x2272)+E(f244(x2273,x2271),f244(x2273,x2272))
% 168.60/168.40 [228]~E(x2281,x2282)+E(f278(x2281,x2283,x2284,x2285),f278(x2282,x2283,x2284,x2285))
% 168.60/168.40 [229]~E(x2291,x2292)+E(f278(x2293,x2291,x2294,x2295),f278(x2293,x2292,x2294,x2295))
% 168.60/168.40 [230]~E(x2301,x2302)+E(f278(x2303,x2304,x2301,x2305),f278(x2303,x2304,x2302,x2305))
% 168.60/168.40 [231]~E(x2311,x2312)+E(f278(x2313,x2314,x2315,x2311),f278(x2313,x2314,x2315,x2312))
% 168.60/168.40 [232]~E(x2321,x2322)+E(f535(x2321,x2323,x2324,x2325,x2326,x2327,x2328,x2329),f535(x2322,x2323,x2324,x2325,x2326,x2327,x2328,x2329))
% 168.60/168.40 [233]~E(x2331,x2332)+E(f535(x2333,x2331,x2334,x2335,x2336,x2337,x2338,x2339),f535(x2333,x2332,x2334,x2335,x2336,x2337,x2338,x2339))
% 168.60/168.40 [234]~E(x2341,x2342)+E(f535(x2343,x2344,x2341,x2345,x2346,x2347,x2348,x2349),f535(x2343,x2344,x2342,x2345,x2346,x2347,x2348,x2349))
% 168.60/168.40 [235]~E(x2351,x2352)+E(f535(x2353,x2354,x2355,x2351,x2356,x2357,x2358,x2359),f535(x2353,x2354,x2355,x2352,x2356,x2357,x2358,x2359))
% 168.60/168.40 [236]~E(x2361,x2362)+E(f535(x2363,x2364,x2365,x2366,x2361,x2367,x2368,x2369),f535(x2363,x2364,x2365,x2366,x2362,x2367,x2368,x2369))
% 168.60/168.40 [237]~E(x2371,x2372)+E(f535(x2373,x2374,x2375,x2376,x2377,x2371,x2378,x2379),f535(x2373,x2374,x2375,x2376,x2377,x2372,x2378,x2379))
% 168.60/168.40 [238]~E(x2381,x2382)+E(f535(x2383,x2384,x2385,x2386,x2387,x2388,x2381,x2389),f535(x2383,x2384,x2385,x2386,x2387,x2388,x2382,x2389))
% 168.60/168.40 [239]~E(x2391,x2392)+E(f535(x2393,x2394,x2395,x2396,x2397,x2398,x2399,x2391),f535(x2393,x2394,x2395,x2396,x2397,x2398,x2399,x2392))
% 168.60/168.40 [240]~E(x2401,x2402)+E(f276(x2401,x2403),f276(x2402,x2403))
% 168.60/168.40 [241]~E(x2411,x2412)+E(f276(x2413,x2411),f276(x2413,x2412))
% 168.60/168.40 [242]~E(x2421,x2422)+E(f157(x2421),f157(x2422))
% 168.60/168.40 [243]~E(x2431,x2432)+E(f299(x2431,x2433,x2434),f299(x2432,x2433,x2434))
% 168.60/168.40 [244]~E(x2441,x2442)+E(f299(x2443,x2441,x2444),f299(x2443,x2442,x2444))
% 168.60/168.40 [245]~E(x2451,x2452)+E(f299(x2453,x2454,x2451),f299(x2453,x2454,x2452))
% 168.60/168.40 [246]~E(x2461,x2462)+E(f476(x2461,x2463,x2464,x2465,x2466,x2467,x2468),f476(x2462,x2463,x2464,x2465,x2466,x2467,x2468))
% 168.60/168.40 [247]~E(x2471,x2472)+E(f476(x2473,x2471,x2474,x2475,x2476,x2477,x2478),f476(x2473,x2472,x2474,x2475,x2476,x2477,x2478))
% 168.60/168.40 [248]~E(x2481,x2482)+E(f476(x2483,x2484,x2481,x2485,x2486,x2487,x2488),f476(x2483,x2484,x2482,x2485,x2486,x2487,x2488))
% 168.60/168.40 [249]~E(x2491,x2492)+E(f476(x2493,x2494,x2495,x2491,x2496,x2497,x2498),f476(x2493,x2494,x2495,x2492,x2496,x2497,x2498))
% 168.60/168.40 [250]~E(x2501,x2502)+E(f476(x2503,x2504,x2505,x2506,x2501,x2507,x2508),f476(x2503,x2504,x2505,x2506,x2502,x2507,x2508))
% 168.60/168.40 [251]~E(x2511,x2512)+E(f476(x2513,x2514,x2515,x2516,x2517,x2511,x2518),f476(x2513,x2514,x2515,x2516,x2517,x2512,x2518))
% 168.60/168.40 [252]~E(x2521,x2522)+E(f476(x2523,x2524,x2525,x2526,x2527,x2528,x2521),f476(x2523,x2524,x2525,x2526,x2527,x2528,x2522))
% 168.60/168.40 [253]~E(x2531,x2532)+E(f40(x2531,x2533),f40(x2532,x2533))
% 168.60/168.40 [254]~E(x2541,x2542)+E(f40(x2543,x2541),f40(x2543,x2542))
% 168.60/168.40 [255]~E(x2551,x2552)+E(f170(x2551,x2553),f170(x2552,x2553))
% 168.60/168.40 [256]~E(x2561,x2562)+E(f170(x2563,x2561),f170(x2563,x2562))
% 168.60/168.40 [257]~E(x2571,x2572)+E(f8(x2571,x2573),f8(x2572,x2573))
% 168.60/168.40 [258]~E(x2581,x2582)+E(f8(x2583,x2581),f8(x2583,x2582))
% 168.60/168.40 [259]~E(x2591,x2592)+E(f816(x2591,x2593,x2594,x2595),f816(x2592,x2593,x2594,x2595))
% 168.60/168.40 [260]~E(x2601,x2602)+E(f816(x2603,x2601,x2604,x2605),f816(x2603,x2602,x2604,x2605))
% 168.60/168.40 [261]~E(x2611,x2612)+E(f816(x2613,x2614,x2611,x2615),f816(x2613,x2614,x2612,x2615))
% 168.60/168.40 [262]~E(x2621,x2622)+E(f816(x2623,x2624,x2625,x2621),f816(x2623,x2624,x2625,x2622))
% 168.60/168.40 [263]~E(x2631,x2632)+E(f553(x2631,x2633,x2634,x2635,x2636),f553(x2632,x2633,x2634,x2635,x2636))
% 168.60/168.40 [264]~E(x2641,x2642)+E(f553(x2643,x2641,x2644,x2645,x2646),f553(x2643,x2642,x2644,x2645,x2646))
% 168.60/168.40 [265]~E(x2651,x2652)+E(f553(x2653,x2654,x2651,x2655,x2656),f553(x2653,x2654,x2652,x2655,x2656))
% 168.60/168.40 [266]~E(x2661,x2662)+E(f553(x2663,x2664,x2665,x2661,x2666),f553(x2663,x2664,x2665,x2662,x2666))
% 168.60/168.40 [267]~E(x2671,x2672)+E(f553(x2673,x2674,x2675,x2676,x2671),f553(x2673,x2674,x2675,x2676,x2672))
% 168.60/168.40 [268]~E(x2681,x2682)+E(f103(x2681,x2683),f103(x2682,x2683))
% 168.60/168.40 [269]~E(x2691,x2692)+E(f103(x2693,x2691),f103(x2693,x2692))
% 168.60/168.40 [270]~E(x2701,x2702)+E(f812(x2701,x2703,x2704),f812(x2702,x2703,x2704))
% 168.60/168.40 [271]~E(x2711,x2712)+E(f812(x2713,x2711,x2714),f812(x2713,x2712,x2714))
% 168.60/168.40 [272]~E(x2721,x2722)+E(f812(x2723,x2724,x2721),f812(x2723,x2724,x2722))
% 168.60/168.40 [273]~E(x2731,x2732)+E(f98(x2731),f98(x2732))
% 168.60/168.40 [274]~E(x2741,x2742)+E(f141(x2741,x2743),f141(x2742,x2743))
% 168.60/168.40 [275]~E(x2751,x2752)+E(f141(x2753,x2751),f141(x2753,x2752))
% 168.60/168.40 [276]~E(x2761,x2762)+E(f356(x2761,x2763,x2764,x2765),f356(x2762,x2763,x2764,x2765))
% 168.60/168.40 [277]~E(x2771,x2772)+E(f356(x2773,x2771,x2774,x2775),f356(x2773,x2772,x2774,x2775))
% 168.60/168.40 [278]~E(x2781,x2782)+E(f356(x2783,x2784,x2781,x2785),f356(x2783,x2784,x2782,x2785))
% 168.60/168.40 [279]~E(x2791,x2792)+E(f356(x2793,x2794,x2795,x2791),f356(x2793,x2794,x2795,x2792))
% 168.60/168.40 [280]~E(x2801,x2802)+E(f180(x2801),f180(x2802))
% 168.60/168.40 [281]~E(x2811,x2812)+E(f242(x2811,x2813),f242(x2812,x2813))
% 168.60/168.40 [282]~E(x2821,x2822)+E(f242(x2823,x2821),f242(x2823,x2822))
% 168.60/168.40 [283]~E(x2831,x2832)+E(f104(x2831),f104(x2832))
% 168.60/168.40 [284]~E(x2841,x2842)+E(f907(x2841,x2843),f907(x2842,x2843))
% 168.60/168.40 [285]~E(x2851,x2852)+E(f907(x2853,x2851),f907(x2853,x2852))
% 168.60/168.40 [286]~E(x2861,x2862)+E(f142(x2861,x2863),f142(x2862,x2863))
% 168.60/168.40 [287]~E(x2871,x2872)+E(f142(x2873,x2871),f142(x2873,x2872))
% 168.60/168.40 [288]~E(x2881,x2882)+E(f906(x2881,x2883),f906(x2882,x2883))
% 168.60/168.40 [289]~E(x2891,x2892)+E(f906(x2893,x2891),f906(x2893,x2892))
% 168.60/168.40 [290]~E(x2901,x2902)+E(f128(x2901,x2903),f128(x2902,x2903))
% 168.60/168.40 [291]~E(x2911,x2912)+E(f128(x2913,x2911),f128(x2913,x2912))
% 168.60/168.40 [292]~E(x2921,x2922)+E(f43(x2921,x2923),f43(x2922,x2923))
% 168.60/168.40 [293]~E(x2931,x2932)+E(f43(x2933,x2931),f43(x2933,x2932))
% 168.60/168.40 [294]~E(x2941,x2942)+E(f131(x2941,x2943,x2944,x2945),f131(x2942,x2943,x2944,x2945))
% 168.60/168.40 [295]~E(x2951,x2952)+E(f131(x2953,x2951,x2954,x2955),f131(x2953,x2952,x2954,x2955))
% 168.60/168.40 [296]~E(x2961,x2962)+E(f131(x2963,x2964,x2961,x2965),f131(x2963,x2964,x2962,x2965))
% 168.60/168.40 [297]~E(x2971,x2972)+E(f131(x2973,x2974,x2975,x2971),f131(x2973,x2974,x2975,x2972))
% 168.60/168.40 [298]~E(x2981,x2982)+E(f14(x2981,x2983,x2984),f14(x2982,x2983,x2984))
% 168.60/168.40 [299]~E(x2991,x2992)+E(f14(x2993,x2991,x2994),f14(x2993,x2992,x2994))
% 168.60/168.40 [300]~E(x3001,x3002)+E(f14(x3003,x3004,x3001),f14(x3003,x3004,x3002))
% 168.60/168.40 [301]~E(x3011,x3012)+E(f160(x3011),f160(x3012))
% 168.60/168.40 [302]~E(x3021,x3022)+E(f698(x3021,x3023,x3024),f698(x3022,x3023,x3024))
% 168.60/168.40 [303]~E(x3031,x3032)+E(f698(x3033,x3031,x3034),f698(x3033,x3032,x3034))
% 168.60/168.40 [304]~E(x3041,x3042)+E(f698(x3043,x3044,x3041),f698(x3043,x3044,x3042))
% 168.60/168.40 [305]~E(x3051,x3052)+E(f236(x3051,x3053),f236(x3052,x3053))
% 168.60/168.40 [306]~E(x3061,x3062)+E(f236(x3063,x3061),f236(x3063,x3062))
% 168.60/168.40 [307]~E(x3071,x3072)+E(f444(x3071,x3073,x3074,x3075),f444(x3072,x3073,x3074,x3075))
% 168.60/168.40 [308]~E(x3081,x3082)+E(f444(x3083,x3081,x3084,x3085),f444(x3083,x3082,x3084,x3085))
% 168.60/168.40 [309]~E(x3091,x3092)+E(f444(x3093,x3094,x3091,x3095),f444(x3093,x3094,x3092,x3095))
% 168.60/168.40 [310]~E(x3101,x3102)+E(f444(x3103,x3104,x3105,x3101),f444(x3103,x3104,x3105,x3102))
% 168.60/168.40 [311]~E(x3111,x3112)+E(f246(x3111,x3113,x3114,x3115,x3116,x3117),f246(x3112,x3113,x3114,x3115,x3116,x3117))
% 168.60/168.40 [312]~E(x3121,x3122)+E(f246(x3123,x3121,x3124,x3125,x3126,x3127),f246(x3123,x3122,x3124,x3125,x3126,x3127))
% 168.60/168.40 [313]~E(x3131,x3132)+E(f246(x3133,x3134,x3131,x3135,x3136,x3137),f246(x3133,x3134,x3132,x3135,x3136,x3137))
% 168.60/168.40 [314]~E(x3141,x3142)+E(f246(x3143,x3144,x3145,x3141,x3146,x3147),f246(x3143,x3144,x3145,x3142,x3146,x3147))
% 168.60/168.40 [315]~E(x3151,x3152)+E(f246(x3153,x3154,x3155,x3156,x3151,x3157),f246(x3153,x3154,x3155,x3156,x3152,x3157))
% 168.60/168.40 [316]~E(x3161,x3162)+E(f246(x3163,x3164,x3165,x3166,x3167,x3161),f246(x3163,x3164,x3165,x3166,x3167,x3162))
% 168.60/168.40 [317]~E(x3171,x3172)+E(f273(x3171,x3173,x3174),f273(x3172,x3173,x3174))
% 168.60/168.40 [318]~E(x3181,x3182)+E(f273(x3183,x3181,x3184),f273(x3183,x3182,x3184))
% 168.60/168.40 [319]~E(x3191,x3192)+E(f273(x3193,x3194,x3191),f273(x3193,x3194,x3192))
% 168.60/168.40 [320]~E(x3201,x3202)+E(f168(x3201,x3203),f168(x3202,x3203))
% 168.60/168.40 [321]~E(x3211,x3212)+E(f168(x3213,x3211),f168(x3213,x3212))
% 168.60/168.40 [322]~E(x3221,x3222)+E(f736(x3221,x3223,x3224),f736(x3222,x3223,x3224))
% 168.60/168.40 [323]~E(x3231,x3232)+E(f736(x3233,x3231,x3234),f736(x3233,x3232,x3234))
% 168.60/168.40 [324]~E(x3241,x3242)+E(f736(x3243,x3244,x3241),f736(x3243,x3244,x3242))
% 168.60/168.40 [325]~E(x3251,x3252)+E(f259(x3251,x3253,x3254,x3255),f259(x3252,x3253,x3254,x3255))
% 168.60/168.40 [326]~E(x3261,x3262)+E(f259(x3263,x3261,x3264,x3265),f259(x3263,x3262,x3264,x3265))
% 168.60/168.40 [327]~E(x3271,x3272)+E(f259(x3273,x3274,x3271,x3275),f259(x3273,x3274,x3272,x3275))
% 168.60/168.40 [328]~E(x3281,x3282)+E(f259(x3283,x3284,x3285,x3281),f259(x3283,x3284,x3285,x3282))
% 168.60/168.40 [329]~E(x3291,x3292)+E(f172(x3291,x3293),f172(x3292,x3293))
% 168.60/168.40 [330]~E(x3301,x3302)+E(f172(x3303,x3301),f172(x3303,x3302))
% 168.60/168.40 [331]~E(x3311,x3312)+E(f401(x3311,x3313,x3314,x3315),f401(x3312,x3313,x3314,x3315))
% 168.60/168.40 [332]~E(x3321,x3322)+E(f401(x3323,x3321,x3324,x3325),f401(x3323,x3322,x3324,x3325))
% 168.60/168.40 [333]~E(x3331,x3332)+E(f401(x3333,x3334,x3331,x3335),f401(x3333,x3334,x3332,x3335))
% 168.60/168.40 [334]~E(x3341,x3342)+E(f401(x3343,x3344,x3345,x3341),f401(x3343,x3344,x3345,x3342))
% 168.60/168.40 [335]~E(x3351,x3352)+E(f643(x3351,x3353,x3354,x3355,x3356,x3357,x3358),f643(x3352,x3353,x3354,x3355,x3356,x3357,x3358))
% 168.60/168.40 [336]~E(x3361,x3362)+E(f643(x3363,x3361,x3364,x3365,x3366,x3367,x3368),f643(x3363,x3362,x3364,x3365,x3366,x3367,x3368))
% 168.60/168.40 [337]~E(x3371,x3372)+E(f643(x3373,x3374,x3371,x3375,x3376,x3377,x3378),f643(x3373,x3374,x3372,x3375,x3376,x3377,x3378))
% 168.60/168.40 [338]~E(x3381,x3382)+E(f643(x3383,x3384,x3385,x3381,x3386,x3387,x3388),f643(x3383,x3384,x3385,x3382,x3386,x3387,x3388))
% 168.60/168.40 [339]~E(x3391,x3392)+E(f643(x3393,x3394,x3395,x3396,x3391,x3397,x3398),f643(x3393,x3394,x3395,x3396,x3392,x3397,x3398))
% 168.60/168.40 [340]~E(x3401,x3402)+E(f643(x3403,x3404,x3405,x3406,x3407,x3401,x3408),f643(x3403,x3404,x3405,x3406,x3407,x3402,x3408))
% 168.60/168.40 [341]~E(x3411,x3412)+E(f643(x3413,x3414,x3415,x3416,x3417,x3418,x3411),f643(x3413,x3414,x3415,x3416,x3417,x3418,x3412))
% 168.60/168.40 [342]~E(x3421,x3422)+E(f277(x3421,x3423,x3424),f277(x3422,x3423,x3424))
% 168.60/168.40 [343]~E(x3431,x3432)+E(f277(x3433,x3431,x3434),f277(x3433,x3432,x3434))
% 168.60/168.40 [344]~E(x3441,x3442)+E(f277(x3443,x3444,x3441),f277(x3443,x3444,x3442))
% 168.60/168.40 [345]~E(x3451,x3452)+E(f306(x3451,x3453),f306(x3452,x3453))
% 168.60/168.40 [346]~E(x3461,x3462)+E(f306(x3463,x3461),f306(x3463,x3462))
% 168.60/168.40 [347]~E(x3471,x3472)+E(f670(x3471,x3473,x3474,x3475,x3476),f670(x3472,x3473,x3474,x3475,x3476))
% 168.60/168.40 [348]~E(x3481,x3482)+E(f670(x3483,x3481,x3484,x3485,x3486),f670(x3483,x3482,x3484,x3485,x3486))
% 168.60/168.40 [349]~E(x3491,x3492)+E(f670(x3493,x3494,x3491,x3495,x3496),f670(x3493,x3494,x3492,x3495,x3496))
% 168.60/168.40 [350]~E(x3501,x3502)+E(f670(x3503,x3504,x3505,x3501,x3506),f670(x3503,x3504,x3505,x3502,x3506))
% 168.60/168.40 [351]~E(x3511,x3512)+E(f670(x3513,x3514,x3515,x3516,x3511),f670(x3513,x3514,x3515,x3516,x3512))
% 168.60/168.40 [352]~E(x3521,x3522)+E(f308(x3521,x3523),f308(x3522,x3523))
% 168.60/168.40 [353]~E(x3531,x3532)+E(f308(x3533,x3531),f308(x3533,x3532))
% 168.60/168.40 [354]~E(x3541,x3542)+E(f615(x3541,x3543,x3544,x3545,x3546),f615(x3542,x3543,x3544,x3545,x3546))
% 168.60/168.40 [355]~E(x3551,x3552)+E(f615(x3553,x3551,x3554,x3555,x3556),f615(x3553,x3552,x3554,x3555,x3556))
% 168.60/168.40 [356]~E(x3561,x3562)+E(f615(x3563,x3564,x3561,x3565,x3566),f615(x3563,x3564,x3562,x3565,x3566))
% 168.60/168.40 [357]~E(x3571,x3572)+E(f615(x3573,x3574,x3575,x3571,x3576),f615(x3573,x3574,x3575,x3572,x3576))
% 168.60/168.40 [358]~E(x3581,x3582)+E(f615(x3583,x3584,x3585,x3586,x3581),f615(x3583,x3584,x3585,x3586,x3582))
% 168.60/168.40 [359]~E(x3591,x3592)+E(f449(x3591,x3593,x3594,x3595),f449(x3592,x3593,x3594,x3595))
% 168.60/168.40 [360]~E(x3601,x3602)+E(f449(x3603,x3601,x3604,x3605),f449(x3603,x3602,x3604,x3605))
% 168.60/168.40 [361]~E(x3611,x3612)+E(f449(x3613,x3614,x3611,x3615),f449(x3613,x3614,x3612,x3615))
% 168.60/168.40 [362]~E(x3621,x3622)+E(f449(x3623,x3624,x3625,x3621),f449(x3623,x3624,x3625,x3622))
% 168.60/168.40 [363]~E(x3631,x3632)+E(f644(x3631,x3633,x3634),f644(x3632,x3633,x3634))
% 168.60/168.40 [364]~E(x3641,x3642)+E(f644(x3643,x3641,x3644),f644(x3643,x3642,x3644))
% 168.60/168.40 [365]~E(x3651,x3652)+E(f644(x3653,x3654,x3651),f644(x3653,x3654,x3652))
% 168.60/168.40 [366]~E(x3661,x3662)+E(f164(x3661),f164(x3662))
% 168.60/168.40 [367]~E(x3671,x3672)+E(f771(x3671,x3673,x3674,x3675,x3676,x3677,x3678),f771(x3672,x3673,x3674,x3675,x3676,x3677,x3678))
% 168.60/168.40 [368]~E(x3681,x3682)+E(f771(x3683,x3681,x3684,x3685,x3686,x3687,x3688),f771(x3683,x3682,x3684,x3685,x3686,x3687,x3688))
% 168.60/168.40 [369]~E(x3691,x3692)+E(f771(x3693,x3694,x3691,x3695,x3696,x3697,x3698),f771(x3693,x3694,x3692,x3695,x3696,x3697,x3698))
% 168.60/168.40 [370]~E(x3701,x3702)+E(f771(x3703,x3704,x3705,x3701,x3706,x3707,x3708),f771(x3703,x3704,x3705,x3702,x3706,x3707,x3708))
% 168.60/168.40 [371]~E(x3711,x3712)+E(f771(x3713,x3714,x3715,x3716,x3711,x3717,x3718),f771(x3713,x3714,x3715,x3716,x3712,x3717,x3718))
% 168.60/168.40 [372]~E(x3721,x3722)+E(f771(x3723,x3724,x3725,x3726,x3727,x3721,x3728),f771(x3723,x3724,x3725,x3726,x3727,x3722,x3728))
% 168.60/168.40 [373]~E(x3731,x3732)+E(f771(x3733,x3734,x3735,x3736,x3737,x3738,x3731),f771(x3733,x3734,x3735,x3736,x3737,x3738,x3732))
% 168.60/168.40 [374]~E(x3741,x3742)+E(f849(x3741,x3743,x3744),f849(x3742,x3743,x3744))
% 168.60/168.40 [375]~E(x3751,x3752)+E(f849(x3753,x3751,x3754),f849(x3753,x3752,x3754))
% 168.60/168.40 [376]~E(x3761,x3762)+E(f849(x3763,x3764,x3761),f849(x3763,x3764,x3762))
% 168.60/168.40 [377]~E(x3771,x3772)+E(f413(x3771,x3773,x3774,x3775,x3776,x3777,x3778),f413(x3772,x3773,x3774,x3775,x3776,x3777,x3778))
% 168.60/168.40 [378]~E(x3781,x3782)+E(f413(x3783,x3781,x3784,x3785,x3786,x3787,x3788),f413(x3783,x3782,x3784,x3785,x3786,x3787,x3788))
% 168.60/168.40 [379]~E(x3791,x3792)+E(f413(x3793,x3794,x3791,x3795,x3796,x3797,x3798),f413(x3793,x3794,x3792,x3795,x3796,x3797,x3798))
% 168.60/168.40 [380]~E(x3801,x3802)+E(f413(x3803,x3804,x3805,x3801,x3806,x3807,x3808),f413(x3803,x3804,x3805,x3802,x3806,x3807,x3808))
% 168.60/168.40 [381]~E(x3811,x3812)+E(f413(x3813,x3814,x3815,x3816,x3811,x3817,x3818),f413(x3813,x3814,x3815,x3816,x3812,x3817,x3818))
% 168.60/168.40 [382]~E(x3821,x3822)+E(f413(x3823,x3824,x3825,x3826,x3827,x3821,x3828),f413(x3823,x3824,x3825,x3826,x3827,x3822,x3828))
% 168.60/168.40 [383]~E(x3831,x3832)+E(f413(x3833,x3834,x3835,x3836,x3837,x3838,x3831),f413(x3833,x3834,x3835,x3836,x3837,x3838,x3832))
% 168.60/168.40 [384]~E(x3841,x3842)+E(f154(x3841),f154(x3842))
% 168.60/168.40 [385]~E(x3851,x3852)+E(f653(x3851,x3853,x3854,x3855),f653(x3852,x3853,x3854,x3855))
% 168.60/168.40 [386]~E(x3861,x3862)+E(f653(x3863,x3861,x3864,x3865),f653(x3863,x3862,x3864,x3865))
% 168.60/168.40 [387]~E(x3871,x3872)+E(f653(x3873,x3874,x3871,x3875),f653(x3873,x3874,x3872,x3875))
% 168.60/168.40 [388]~E(x3881,x3882)+E(f653(x3883,x3884,x3885,x3881),f653(x3883,x3884,x3885,x3882))
% 168.60/168.40 [389]~E(x3891,x3892)+E(f148(x3891,x3893),f148(x3892,x3893))
% 168.60/168.40 [390]~E(x3901,x3902)+E(f148(x3903,x3901),f148(x3903,x3902))
% 168.60/168.40 [391]~E(x3911,x3912)+E(f293(x3911,x3913,x3914),f293(x3912,x3913,x3914))
% 168.60/168.40 [392]~E(x3921,x3922)+E(f293(x3923,x3921,x3924),f293(x3923,x3922,x3924))
% 168.60/168.40 [393]~E(x3931,x3932)+E(f293(x3933,x3934,x3931),f293(x3933,x3934,x3932))
% 168.60/168.40 [394]~E(x3941,x3942)+E(f289(x3941),f289(x3942))
% 168.60/168.40 [395]~E(x3951,x3952)+E(f150(x3951,x3953),f150(x3952,x3953))
% 168.60/168.40 [396]~E(x3961,x3962)+E(f150(x3963,x3961),f150(x3963,x3962))
% 168.60/168.40 [397]~E(x3971,x3972)+E(f41(x3971,x3973),f41(x3972,x3973))
% 168.60/168.40 [398]~E(x3981,x3982)+E(f41(x3983,x3981),f41(x3983,x3982))
% 168.60/168.40 [399]~E(x3991,x3992)+E(f108(x3991),f108(x3992))
% 168.60/168.40 [400]~E(x4001,x4002)+E(f109(x4001,x4003),f109(x4002,x4003))
% 168.60/168.40 [401]~E(x4011,x4012)+E(f109(x4013,x4011),f109(x4013,x4012))
% 168.60/168.40 [402]~E(x4021,x4022)+E(f455(x4021,x4023,x4024,x4025),f455(x4022,x4023,x4024,x4025))
% 168.60/168.40 [403]~E(x4031,x4032)+E(f455(x4033,x4031,x4034,x4035),f455(x4033,x4032,x4034,x4035))
% 168.60/168.40 [404]~E(x4041,x4042)+E(f455(x4043,x4044,x4041,x4045),f455(x4043,x4044,x4042,x4045))
% 168.60/168.40 [405]~E(x4051,x4052)+E(f455(x4053,x4054,x4055,x4051),f455(x4053,x4054,x4055,x4052))
% 168.60/168.40 [406]~E(x4061,x4062)+E(f410(x4061,x4063,x4064,x4065),f410(x4062,x4063,x4064,x4065))
% 168.60/168.40 [407]~E(x4071,x4072)+E(f410(x4073,x4071,x4074,x4075),f410(x4073,x4072,x4074,x4075))
% 168.60/168.40 [408]~E(x4081,x4082)+E(f410(x4083,x4084,x4081,x4085),f410(x4083,x4084,x4082,x4085))
% 168.60/168.40 [409]~E(x4091,x4092)+E(f410(x4093,x4094,x4095,x4091),f410(x4093,x4094,x4095,x4092))
% 168.60/168.40 [410]~E(x4101,x4102)+E(f764(x4101,x4103,x4104,x4105,x4106,x4107,x4108),f764(x4102,x4103,x4104,x4105,x4106,x4107,x4108))
% 168.60/168.40 [411]~E(x4111,x4112)+E(f764(x4113,x4111,x4114,x4115,x4116,x4117,x4118),f764(x4113,x4112,x4114,x4115,x4116,x4117,x4118))
% 168.60/168.40 [412]~E(x4121,x4122)+E(f764(x4123,x4124,x4121,x4125,x4126,x4127,x4128),f764(x4123,x4124,x4122,x4125,x4126,x4127,x4128))
% 168.60/168.40 [413]~E(x4131,x4132)+E(f764(x4133,x4134,x4135,x4131,x4136,x4137,x4138),f764(x4133,x4134,x4135,x4132,x4136,x4137,x4138))
% 168.60/168.40 [414]~E(x4141,x4142)+E(f764(x4143,x4144,x4145,x4146,x4141,x4147,x4148),f764(x4143,x4144,x4145,x4146,x4142,x4147,x4148))
% 168.60/168.40 [415]~E(x4151,x4152)+E(f764(x4153,x4154,x4155,x4156,x4157,x4151,x4158),f764(x4153,x4154,x4155,x4156,x4157,x4152,x4158))
% 168.60/168.40 [416]~E(x4161,x4162)+E(f764(x4163,x4164,x4165,x4166,x4167,x4168,x4161),f764(x4163,x4164,x4165,x4166,x4167,x4168,x4162))
% 168.60/168.40 [417]~E(x4171,x4172)+E(f459(x4171,x4173),f459(x4172,x4173))
% 168.60/168.40 [418]~E(x4181,x4182)+E(f459(x4183,x4181),f459(x4183,x4182))
% 168.60/168.40 [419]~E(x4191,x4192)+E(f292(x4191),f292(x4192))
% 168.60/168.40 [420]~E(x4201,x4202)+E(f13(x4201,x4203),f13(x4202,x4203))
% 168.60/168.40 [421]~E(x4211,x4212)+E(f13(x4213,x4211),f13(x4213,x4212))
% 168.60/168.40 [422]~E(x4221,x4222)+E(f83(x4221,x4223),f83(x4222,x4223))
% 168.60/168.40 [423]~E(x4231,x4232)+E(f83(x4233,x4231),f83(x4233,x4232))
% 168.60/168.40 [424]~E(x4241,x4242)+E(f167(x4241,x4243),f167(x4242,x4243))
% 168.60/168.40 [425]~E(x4251,x4252)+E(f167(x4253,x4251),f167(x4253,x4252))
% 168.60/168.40 [426]~E(x4261,x4262)+E(f162(x4261,x4263,x4264),f162(x4262,x4263,x4264))
% 168.60/168.40 [427]~E(x4271,x4272)+E(f162(x4273,x4271,x4274),f162(x4273,x4272,x4274))
% 168.60/168.40 [428]~E(x4281,x4282)+E(f162(x4283,x4284,x4281),f162(x4283,x4284,x4282))
% 168.60/168.40 [429]~E(x4291,x4292)+E(f251(x4291,x4293),f251(x4292,x4293))
% 168.60/168.40 [430]~E(x4301,x4302)+E(f251(x4303,x4301),f251(x4303,x4302))
% 168.60/168.40 [431]~E(x4311,x4312)+E(f59(x4311,x4313,x4314,x4315,x4316),f59(x4312,x4313,x4314,x4315,x4316))
% 168.60/168.40 [432]~E(x4321,x4322)+E(f59(x4323,x4321,x4324,x4325,x4326),f59(x4323,x4322,x4324,x4325,x4326))
% 168.60/168.40 [433]~E(x4331,x4332)+E(f59(x4333,x4334,x4331,x4335,x4336),f59(x4333,x4334,x4332,x4335,x4336))
% 168.60/168.40 [434]~E(x4341,x4342)+E(f59(x4343,x4344,x4345,x4341,x4346),f59(x4343,x4344,x4345,x4342,x4346))
% 168.60/168.40 [435]~E(x4351,x4352)+E(f59(x4353,x4354,x4355,x4356,x4351),f59(x4353,x4354,x4355,x4356,x4352))
% 168.60/168.40 [436]~E(x4361,x4362)+E(f861(x4361,x4363,x4364),f861(x4362,x4363,x4364))
% 168.60/168.40 [437]~E(x4371,x4372)+E(f861(x4373,x4371,x4374),f861(x4373,x4372,x4374))
% 168.60/168.40 [438]~E(x4381,x4382)+E(f861(x4383,x4384,x4381),f861(x4383,x4384,x4382))
% 168.60/168.40 [439]~E(x4391,x4392)+E(f598(x4391,x4393,x4394),f598(x4392,x4393,x4394))
% 168.60/168.40 [440]~E(x4401,x4402)+E(f598(x4403,x4401,x4404),f598(x4403,x4402,x4404))
% 168.60/168.40 [441]~E(x4411,x4412)+E(f598(x4413,x4414,x4411),f598(x4413,x4414,x4412))
% 168.60/168.40 [442]~E(x4421,x4422)+E(f274(x4421,x4423),f274(x4422,x4423))
% 168.60/168.40 [443]~E(x4431,x4432)+E(f274(x4433,x4431),f274(x4433,x4432))
% 168.60/168.40 [444]~E(x4441,x4442)+E(f889(x4441,x4443,x4444,x4445),f889(x4442,x4443,x4444,x4445))
% 168.60/168.40 [445]~E(x4451,x4452)+E(f889(x4453,x4451,x4454,x4455),f889(x4453,x4452,x4454,x4455))
% 168.60/168.40 [446]~E(x4461,x4462)+E(f889(x4463,x4464,x4461,x4465),f889(x4463,x4464,x4462,x4465))
% 168.60/168.40 [447]~E(x4471,x4472)+E(f889(x4473,x4474,x4475,x4471),f889(x4473,x4474,x4475,x4472))
% 168.60/168.40 [448]~E(x4481,x4482)+E(f125(x4481,x4483),f125(x4482,x4483))
% 168.60/168.40 [449]~E(x4491,x4492)+E(f125(x4493,x4491),f125(x4493,x4492))
% 168.60/168.40 [450]~E(x4501,x4502)+E(f349(x4501,x4503,x4504),f349(x4502,x4503,x4504))
% 168.60/168.40 [451]~E(x4511,x4512)+E(f349(x4513,x4511,x4514),f349(x4513,x4512,x4514))
% 168.60/168.40 [452]~E(x4521,x4522)+E(f349(x4523,x4524,x4521),f349(x4523,x4524,x4522))
% 168.60/168.40 [453]~E(x4531,x4532)+E(f851(x4531,x4533,x4534),f851(x4532,x4533,x4534))
% 168.60/168.40 [454]~E(x4541,x4542)+E(f851(x4543,x4541,x4544),f851(x4543,x4542,x4544))
% 168.60/168.40 [455]~E(x4551,x4552)+E(f851(x4553,x4554,x4551),f851(x4553,x4554,x4552))
% 168.60/168.40 [456]~E(x4561,x4562)+E(f453(x4561,x4563,x4564),f453(x4562,x4563,x4564))
% 168.60/168.40 [457]~E(x4571,x4572)+E(f453(x4573,x4571,x4574),f453(x4573,x4572,x4574))
% 168.60/168.40 [458]~E(x4581,x4582)+E(f453(x4583,x4584,x4581),f453(x4583,x4584,x4582))
% 168.60/168.40 [459]~E(x4591,x4592)+E(f174(x4591,x4593,x4594,x4595),f174(x4592,x4593,x4594,x4595))
% 168.60/168.40 [460]~E(x4601,x4602)+E(f174(x4603,x4601,x4604,x4605),f174(x4603,x4602,x4604,x4605))
% 168.60/168.40 [461]~E(x4611,x4612)+E(f174(x4613,x4614,x4611,x4615),f174(x4613,x4614,x4612,x4615))
% 168.60/168.40 [462]~E(x4621,x4622)+E(f174(x4623,x4624,x4625,x4621),f174(x4623,x4624,x4625,x4622))
% 168.60/168.40 [463]~E(x4631,x4632)+E(f50(x4631),f50(x4632))
% 168.60/168.40 [464]~E(x4641,x4642)+E(f303(x4641,x4643),f303(x4642,x4643))
% 168.60/168.40 [465]~E(x4651,x4652)+E(f303(x4653,x4651),f303(x4653,x4652))
% 168.60/168.40 [466]~E(x4661,x4662)+E(f429(x4661,x4663,x4664,x4665,x4666,x4667,x4668),f429(x4662,x4663,x4664,x4665,x4666,x4667,x4668))
% 168.60/168.40 [467]~E(x4671,x4672)+E(f429(x4673,x4671,x4674,x4675,x4676,x4677,x4678),f429(x4673,x4672,x4674,x4675,x4676,x4677,x4678))
% 168.60/168.40 [468]~E(x4681,x4682)+E(f429(x4683,x4684,x4681,x4685,x4686,x4687,x4688),f429(x4683,x4684,x4682,x4685,x4686,x4687,x4688))
% 168.60/168.40 [469]~E(x4691,x4692)+E(f429(x4693,x4694,x4695,x4691,x4696,x4697,x4698),f429(x4693,x4694,x4695,x4692,x4696,x4697,x4698))
% 168.60/168.40 [470]~E(x4701,x4702)+E(f429(x4703,x4704,x4705,x4706,x4701,x4707,x4708),f429(x4703,x4704,x4705,x4706,x4702,x4707,x4708))
% 168.60/168.40 [471]~E(x4711,x4712)+E(f429(x4713,x4714,x4715,x4716,x4717,x4711,x4718),f429(x4713,x4714,x4715,x4716,x4717,x4712,x4718))
% 168.60/168.40 [472]~E(x4721,x4722)+E(f429(x4723,x4724,x4725,x4726,x4727,x4728,x4721),f429(x4723,x4724,x4725,x4726,x4727,x4728,x4722))
% 168.60/168.40 [473]~E(x4731,x4732)+E(f376(x4731,x4733,x4734),f376(x4732,x4733,x4734))
% 168.60/168.40 [474]~E(x4741,x4742)+E(f376(x4743,x4741,x4744),f376(x4743,x4742,x4744))
% 168.60/168.40 [475]~E(x4751,x4752)+E(f376(x4753,x4754,x4751),f376(x4753,x4754,x4752))
% 168.60/168.40 [476]~E(x4761,x4762)+E(f17(x4761,x4763),f17(x4762,x4763))
% 168.60/168.40 [477]~E(x4771,x4772)+E(f17(x4773,x4771),f17(x4773,x4772))
% 168.60/168.40 [478]~E(x4781,x4782)+E(f136(x4781,x4783),f136(x4782,x4783))
% 168.60/168.40 [479]~E(x4791,x4792)+E(f136(x4793,x4791),f136(x4793,x4792))
% 168.60/168.40 [480]~E(x4801,x4802)+E(f12(x4801,x4803),f12(x4802,x4803))
% 168.60/168.40 [481]~E(x4811,x4812)+E(f12(x4813,x4811),f12(x4813,x4812))
% 168.60/168.40 [482]~E(x4821,x4822)+E(f260(x4821,x4823),f260(x4822,x4823))
% 168.60/168.40 [483]~E(x4831,x4832)+E(f260(x4833,x4831),f260(x4833,x4832))
% 168.60/168.40 [484]~E(x4841,x4842)+E(f307(x4841,x4843,x4844,x4845),f307(x4842,x4843,x4844,x4845))
% 168.60/168.40 [485]~E(x4851,x4852)+E(f307(x4853,x4851,x4854,x4855),f307(x4853,x4852,x4854,x4855))
% 168.60/168.40 [486]~E(x4861,x4862)+E(f307(x4863,x4864,x4861,x4865),f307(x4863,x4864,x4862,x4865))
% 168.60/168.40 [487]~E(x4871,x4872)+E(f307(x4873,x4874,x4875,x4871),f307(x4873,x4874,x4875,x4872))
% 168.60/168.40 [488]~E(x4881,x4882)+E(f231(x4881,x4883,x4884),f231(x4882,x4883,x4884))
% 168.60/168.40 [489]~E(x4891,x4892)+E(f231(x4893,x4891,x4894),f231(x4893,x4892,x4894))
% 168.60/168.40 [490]~E(x4901,x4902)+E(f231(x4903,x4904,x4901),f231(x4903,x4904,x4902))
% 168.60/168.40 [491]~E(x4911,x4912)+E(f769(x4911,x4913,x4914,x4915,x4916,x4917,x4918),f769(x4912,x4913,x4914,x4915,x4916,x4917,x4918))
% 168.60/168.40 [492]~E(x4921,x4922)+E(f769(x4923,x4921,x4924,x4925,x4926,x4927,x4928),f769(x4923,x4922,x4924,x4925,x4926,x4927,x4928))
% 168.60/168.40 [493]~E(x4931,x4932)+E(f769(x4933,x4934,x4931,x4935,x4936,x4937,x4938),f769(x4933,x4934,x4932,x4935,x4936,x4937,x4938))
% 168.60/168.40 [494]~E(x4941,x4942)+E(f769(x4943,x4944,x4945,x4941,x4946,x4947,x4948),f769(x4943,x4944,x4945,x4942,x4946,x4947,x4948))
% 168.60/168.40 [495]~E(x4951,x4952)+E(f769(x4953,x4954,x4955,x4956,x4951,x4957,x4958),f769(x4953,x4954,x4955,x4956,x4952,x4957,x4958))
% 168.60/168.40 [496]~E(x4961,x4962)+E(f769(x4963,x4964,x4965,x4966,x4967,x4961,x4968),f769(x4963,x4964,x4965,x4966,x4967,x4962,x4968))
% 168.60/168.40 [497]~E(x4971,x4972)+E(f769(x4973,x4974,x4975,x4976,x4977,x4978,x4971),f769(x4973,x4974,x4975,x4976,x4977,x4978,x4972))
% 168.60/168.40 [498]~E(x4981,x4982)+E(f296(x4981),f296(x4982))
% 168.60/168.40 [499]~E(x4991,x4992)+E(f70(x4991,x4993,x4994,x4995),f70(x4992,x4993,x4994,x4995))
% 168.60/168.40 [500]~E(x5001,x5002)+E(f70(x5003,x5001,x5004,x5005),f70(x5003,x5002,x5004,x5005))
% 168.60/168.40 [501]~E(x5011,x5012)+E(f70(x5013,x5014,x5011,x5015),f70(x5013,x5014,x5012,x5015))
% 168.60/168.40 [502]~E(x5021,x5022)+E(f70(x5023,x5024,x5025,x5021),f70(x5023,x5024,x5025,x5022))
% 168.60/168.40 [503]~E(x5031,x5032)+E(f302(x5031),f302(x5032))
% 168.60/168.40 [504]~E(x5041,x5042)+E(f699(x5041,x5043),f699(x5042,x5043))
% 168.60/168.40 [505]~E(x5051,x5052)+E(f699(x5053,x5051),f699(x5053,x5052))
% 168.60/168.40 [506]~E(x5061,x5062)+E(f803(x5061,x5063,x5064),f803(x5062,x5063,x5064))
% 168.60/168.40 [507]~E(x5071,x5072)+E(f803(x5073,x5071,x5074),f803(x5073,x5072,x5074))
% 168.60/168.40 [508]~E(x5081,x5082)+E(f803(x5083,x5084,x5081),f803(x5083,x5084,x5082))
% 168.60/168.40 [509]~E(x5091,x5092)+E(f581(x5091,x5093),f581(x5092,x5093))
% 168.60/168.40 [510]~E(x5101,x5102)+E(f581(x5103,x5101),f581(x5103,x5102))
% 168.60/168.40 [511]~E(x5111,x5112)+E(f810(x5111,x5113,x5114,x5115,x5116),f810(x5112,x5113,x5114,x5115,x5116))
% 168.60/168.40 [512]~E(x5121,x5122)+E(f810(x5123,x5121,x5124,x5125,x5126),f810(x5123,x5122,x5124,x5125,x5126))
% 168.60/168.40 [513]~E(x5131,x5132)+E(f810(x5133,x5134,x5131,x5135,x5136),f810(x5133,x5134,x5132,x5135,x5136))
% 168.60/168.40 [514]~E(x5141,x5142)+E(f810(x5143,x5144,x5145,x5141,x5146),f810(x5143,x5144,x5145,x5142,x5146))
% 168.60/168.40 [515]~E(x5151,x5152)+E(f810(x5153,x5154,x5155,x5156,x5151),f810(x5153,x5154,x5155,x5156,x5152))
% 168.60/168.40 [516]~E(x5161,x5162)+E(f146(x5161,x5163),f146(x5162,x5163))
% 168.60/168.40 [517]~E(x5171,x5172)+E(f146(x5173,x5171),f146(x5173,x5172))
% 168.60/168.40 [518]~E(x5181,x5182)+E(f57(x5181,x5183,x5184),f57(x5182,x5183,x5184))
% 168.60/168.40 [519]~E(x5191,x5192)+E(f57(x5193,x5191,x5194),f57(x5193,x5192,x5194))
% 168.60/168.40 [520]~E(x5201,x5202)+E(f57(x5203,x5204,x5201),f57(x5203,x5204,x5202))
% 168.60/168.40 [521]~E(x5211,x5212)+E(f829(x5211,x5213,x5214,x5215,x5216,x5217,x5218),f829(x5212,x5213,x5214,x5215,x5216,x5217,x5218))
% 168.60/168.40 [522]~E(x5221,x5222)+E(f829(x5223,x5221,x5224,x5225,x5226,x5227,x5228),f829(x5223,x5222,x5224,x5225,x5226,x5227,x5228))
% 168.60/168.40 [523]~E(x5231,x5232)+E(f829(x5233,x5234,x5231,x5235,x5236,x5237,x5238),f829(x5233,x5234,x5232,x5235,x5236,x5237,x5238))
% 168.60/168.40 [524]~E(x5241,x5242)+E(f829(x5243,x5244,x5245,x5241,x5246,x5247,x5248),f829(x5243,x5244,x5245,x5242,x5246,x5247,x5248))
% 168.60/168.40 [525]~E(x5251,x5252)+E(f829(x5253,x5254,x5255,x5256,x5251,x5257,x5258),f829(x5253,x5254,x5255,x5256,x5252,x5257,x5258))
% 168.60/168.40 [526]~E(x5261,x5262)+E(f829(x5263,x5264,x5265,x5266,x5267,x5261,x5268),f829(x5263,x5264,x5265,x5266,x5267,x5262,x5268))
% 168.60/168.40 [527]~E(x5271,x5272)+E(f829(x5273,x5274,x5275,x5276,x5277,x5278,x5271),f829(x5273,x5274,x5275,x5276,x5277,x5278,x5272))
% 168.60/168.40 [528]~E(x5281,x5282)+E(f648(x5281,x5283),f648(x5282,x5283))
% 168.60/168.40 [529]~E(x5291,x5292)+E(f648(x5293,x5291),f648(x5293,x5292))
% 168.60/168.40 [530]~E(x5301,x5302)+E(f186(x5301,x5303,x5304,x5305),f186(x5302,x5303,x5304,x5305))
% 168.60/168.40 [531]~E(x5311,x5312)+E(f186(x5313,x5311,x5314,x5315),f186(x5313,x5312,x5314,x5315))
% 168.60/168.40 [532]~E(x5321,x5322)+E(f186(x5323,x5324,x5321,x5325),f186(x5323,x5324,x5322,x5325))
% 168.60/168.40 [533]~E(x5331,x5332)+E(f186(x5333,x5334,x5335,x5331),f186(x5333,x5334,x5335,x5332))
% 168.60/168.40 [534]~E(x5341,x5342)+E(f132(x5341,x5343),f132(x5342,x5343))
% 168.60/168.40 [535]~E(x5351,x5352)+E(f132(x5353,x5351),f132(x5353,x5352))
% 168.60/168.40 [536]~E(x5361,x5362)+E(f622(x5361,x5363,x5364,x5365),f622(x5362,x5363,x5364,x5365))
% 168.60/168.40 [537]~E(x5371,x5372)+E(f622(x5373,x5371,x5374,x5375),f622(x5373,x5372,x5374,x5375))
% 168.60/168.40 [538]~E(x5381,x5382)+E(f622(x5383,x5384,x5381,x5385),f622(x5383,x5384,x5382,x5385))
% 168.60/168.40 [539]~E(x5391,x5392)+E(f622(x5393,x5394,x5395,x5391),f622(x5393,x5394,x5395,x5392))
% 168.60/168.40 [540]~E(x5401,x5402)+E(f105(x5401,x5403,x5404),f105(x5402,x5403,x5404))
% 168.60/168.40 [541]~E(x5411,x5412)+E(f105(x5413,x5411,x5414),f105(x5413,x5412,x5414))
% 168.60/168.40 [542]~E(x5421,x5422)+E(f105(x5423,x5424,x5421),f105(x5423,x5424,x5422))
% 168.60/168.40 [543]~E(x5431,x5432)+E(f428(x5431,x5433,x5434,x5435,x5436,x5437,x5438),f428(x5432,x5433,x5434,x5435,x5436,x5437,x5438))
% 168.60/168.40 [544]~E(x5441,x5442)+E(f428(x5443,x5441,x5444,x5445,x5446,x5447,x5448),f428(x5443,x5442,x5444,x5445,x5446,x5447,x5448))
% 168.60/168.40 [545]~E(x5451,x5452)+E(f428(x5453,x5454,x5451,x5455,x5456,x5457,x5458),f428(x5453,x5454,x5452,x5455,x5456,x5457,x5458))
% 168.60/168.40 [546]~E(x5461,x5462)+E(f428(x5463,x5464,x5465,x5461,x5466,x5467,x5468),f428(x5463,x5464,x5465,x5462,x5466,x5467,x5468))
% 168.60/168.40 [547]~E(x5471,x5472)+E(f428(x5473,x5474,x5475,x5476,x5471,x5477,x5478),f428(x5473,x5474,x5475,x5476,x5472,x5477,x5478))
% 168.60/168.40 [548]~E(x5481,x5482)+E(f428(x5483,x5484,x5485,x5486,x5487,x5481,x5488),f428(x5483,x5484,x5485,x5486,x5487,x5482,x5488))
% 168.60/168.40 [549]~E(x5491,x5492)+E(f428(x5493,x5494,x5495,x5496,x5497,x5498,x5491),f428(x5493,x5494,x5495,x5496,x5497,x5498,x5492))
% 168.60/168.40 [550]~E(x5501,x5502)+E(f270(x5501),f270(x5502))
% 168.60/168.40 [551]~E(x5511,x5512)+E(f269(x5511),f269(x5512))
% 168.60/168.40 [552]~E(x5521,x5522)+E(f84(x5521,x5523,x5524,x5525),f84(x5522,x5523,x5524,x5525))
% 168.60/168.40 [553]~E(x5531,x5532)+E(f84(x5533,x5531,x5534,x5535),f84(x5533,x5532,x5534,x5535))
% 168.60/168.40 [554]~E(x5541,x5542)+E(f84(x5543,x5544,x5541,x5545),f84(x5543,x5544,x5542,x5545))
% 168.60/168.40 [555]~E(x5551,x5552)+E(f84(x5553,x5554,x5555,x5551),f84(x5553,x5554,x5555,x5552))
% 168.60/168.40 [556]~E(x5561,x5562)+E(f433(x5561,x5563,x5564),f433(x5562,x5563,x5564))
% 168.60/168.40 [557]~E(x5571,x5572)+E(f433(x5573,x5571,x5574),f433(x5573,x5572,x5574))
% 168.60/168.40 [558]~E(x5581,x5582)+E(f433(x5583,x5584,x5581),f433(x5583,x5584,x5582))
% 168.60/168.40 [559]~E(x5591,x5592)+E(f75(x5591,x5593),f75(x5592,x5593))
% 168.60/168.40 [560]~E(x5601,x5602)+E(f75(x5603,x5601),f75(x5603,x5602))
% 168.60/168.40 [561]~E(x5611,x5612)+E(f473(x5611,x5613,x5614),f473(x5612,x5613,x5614))
% 168.60/168.40 [562]~E(x5621,x5622)+E(f473(x5623,x5621,x5624),f473(x5623,x5622,x5624))
% 168.60/168.40 [563]~E(x5631,x5632)+E(f473(x5633,x5634,x5631),f473(x5633,x5634,x5632))
% 168.60/168.40 [564]~E(x5641,x5642)+E(f58(x5641,x5643,x5644),f58(x5642,x5643,x5644))
% 168.60/168.40 [565]~E(x5651,x5652)+E(f58(x5653,x5651,x5654),f58(x5653,x5652,x5654))
% 168.60/168.40 [566]~E(x5661,x5662)+E(f58(x5663,x5664,x5661),f58(x5663,x5664,x5662))
% 168.60/168.40 [567]~E(x5671,x5672)+E(f281(x5671,x5673),f281(x5672,x5673))
% 168.60/168.40 [568]~E(x5681,x5682)+E(f281(x5683,x5681),f281(x5683,x5682))
% 168.60/168.40 [569]~E(x5691,x5692)+E(f763(x5691,x5693,x5694),f763(x5692,x5693,x5694))
% 168.60/168.40 [570]~E(x5701,x5702)+E(f763(x5703,x5701,x5704),f763(x5703,x5702,x5704))
% 168.60/168.40 [571]~E(x5711,x5712)+E(f763(x5713,x5714,x5711),f763(x5713,x5714,x5712))
% 168.60/168.40 [572]~E(x5721,x5722)+E(f159(x5721,x5723,x5724),f159(x5722,x5723,x5724))
% 168.60/168.40 [573]~E(x5731,x5732)+E(f159(x5733,x5731,x5734),f159(x5733,x5732,x5734))
% 168.60/168.40 [574]~E(x5741,x5742)+E(f159(x5743,x5744,x5741),f159(x5743,x5744,x5742))
% 168.60/168.40 [575]~E(x5751,x5752)+E(f887(x5751,x5753,x5754),f887(x5752,x5753,x5754))
% 168.60/168.40 [576]~E(x5761,x5762)+E(f887(x5763,x5761,x5764),f887(x5763,x5762,x5764))
% 168.60/168.40 [577]~E(x5771,x5772)+E(f887(x5773,x5774,x5771),f887(x5773,x5774,x5772))
% 168.60/168.40 [578]~E(x5781,x5782)+E(f48(x5781,x5783,x5784),f48(x5782,x5783,x5784))
% 168.60/168.40 [579]~E(x5791,x5792)+E(f48(x5793,x5791,x5794),f48(x5793,x5792,x5794))
% 168.60/168.40 [580]~E(x5801,x5802)+E(f48(x5803,x5804,x5801),f48(x5803,x5804,x5802))
% 168.60/168.40 [581]~E(x5811,x5812)+E(f605(x5811,x5813,x5814),f605(x5812,x5813,x5814))
% 168.60/168.40 [582]~E(x5821,x5822)+E(f605(x5823,x5821,x5824),f605(x5823,x5822,x5824))
% 168.60/168.40 [583]~E(x5831,x5832)+E(f605(x5833,x5834,x5831),f605(x5833,x5834,x5832))
% 168.60/168.40 [584]~E(x5841,x5842)+E(f350(x5841,x5843,x5844),f350(x5842,x5843,x5844))
% 168.60/168.40 [585]~E(x5851,x5852)+E(f350(x5853,x5851,x5854),f350(x5853,x5852,x5854))
% 168.60/168.40 [586]~E(x5861,x5862)+E(f350(x5863,x5864,x5861),f350(x5863,x5864,x5862))
% 168.60/168.40 [587]~E(x5871,x5872)+E(f467(x5871,x5873),f467(x5872,x5873))
% 168.60/168.40 [588]~E(x5881,x5882)+E(f467(x5883,x5881),f467(x5883,x5882))
% 168.60/168.40 [589]~E(x5891,x5892)+E(f233(x5891,x5893,x5894),f233(x5892,x5893,x5894))
% 168.60/168.40 [590]~E(x5901,x5902)+E(f233(x5903,x5901,x5904),f233(x5903,x5902,x5904))
% 168.60/168.40 [591]~E(x5911,x5912)+E(f233(x5913,x5914,x5911),f233(x5913,x5914,x5912))
% 168.60/168.40 [592]~E(x5921,x5922)+E(f285(x5921,x5923,x5924,x5925,x5926),f285(x5922,x5923,x5924,x5925,x5926))
% 168.60/168.40 [593]~E(x5931,x5932)+E(f285(x5933,x5931,x5934,x5935,x5936),f285(x5933,x5932,x5934,x5935,x5936))
% 168.60/168.40 [594]~E(x5941,x5942)+E(f285(x5943,x5944,x5941,x5945,x5946),f285(x5943,x5944,x5942,x5945,x5946))
% 168.60/168.40 [595]~E(x5951,x5952)+E(f285(x5953,x5954,x5955,x5951,x5956),f285(x5953,x5954,x5955,x5952,x5956))
% 168.60/168.40 [596]~E(x5961,x5962)+E(f285(x5963,x5964,x5965,x5966,x5961),f285(x5963,x5964,x5965,x5966,x5962))
% 168.60/168.40 [597]~E(x5971,x5972)+E(f483(x5971,x5973),f483(x5972,x5973))
% 168.60/168.40 [598]~E(x5981,x5982)+E(f483(x5983,x5981),f483(x5983,x5982))
% 168.60/168.40 [599]~E(x5991,x5992)+E(f147(x5991,x5993),f147(x5992,x5993))
% 168.60/168.40 [600]~E(x6001,x6002)+E(f147(x6003,x6001),f147(x6003,x6002))
% 168.60/168.40 [601]~E(x6011,x6012)+E(f114(x6011,x6013),f114(x6012,x6013))
% 168.60/168.40 [602]~E(x6021,x6022)+E(f114(x6023,x6021),f114(x6023,x6022))
% 168.60/168.40 [603]~E(x6031,x6032)+E(f627(x6031,x6033,x6034,x6035,x6036,x6037),f627(x6032,x6033,x6034,x6035,x6036,x6037))
% 168.60/168.40 [604]~E(x6041,x6042)+E(f627(x6043,x6041,x6044,x6045,x6046,x6047),f627(x6043,x6042,x6044,x6045,x6046,x6047))
% 168.60/168.40 [605]~E(x6051,x6052)+E(f627(x6053,x6054,x6051,x6055,x6056,x6057),f627(x6053,x6054,x6052,x6055,x6056,x6057))
% 168.60/168.40 [606]~E(x6061,x6062)+E(f627(x6063,x6064,x6065,x6061,x6066,x6067),f627(x6063,x6064,x6065,x6062,x6066,x6067))
% 168.60/168.40 [607]~E(x6071,x6072)+E(f627(x6073,x6074,x6075,x6076,x6071,x6077),f627(x6073,x6074,x6075,x6076,x6072,x6077))
% 168.60/168.40 [608]~E(x6081,x6082)+E(f627(x6083,x6084,x6085,x6086,x6087,x6081),f627(x6083,x6084,x6085,x6086,x6087,x6082))
% 168.60/168.40 [609]~E(x6091,x6092)+E(f135(x6091,x6093),f135(x6092,x6093))
% 168.60/168.40 [610]~E(x6101,x6102)+E(f135(x6103,x6101),f135(x6103,x6102))
% 168.60/168.40 [611]~E(x6111,x6112)+E(f252(x6111,x6113),f252(x6112,x6113))
% 168.60/168.40 [612]~E(x6121,x6122)+E(f252(x6123,x6121),f252(x6123,x6122))
% 168.60/168.40 [613]~E(x6131,x6132)+E(f477(x6131,x6133,x6134,x6135,x6136,x6137,x6138),f477(x6132,x6133,x6134,x6135,x6136,x6137,x6138))
% 168.60/168.40 [614]~E(x6141,x6142)+E(f477(x6143,x6141,x6144,x6145,x6146,x6147,x6148),f477(x6143,x6142,x6144,x6145,x6146,x6147,x6148))
% 168.60/168.40 [615]~E(x6151,x6152)+E(f477(x6153,x6154,x6151,x6155,x6156,x6157,x6158),f477(x6153,x6154,x6152,x6155,x6156,x6157,x6158))
% 168.60/168.40 [616]~E(x6161,x6162)+E(f477(x6163,x6164,x6165,x6161,x6166,x6167,x6168),f477(x6163,x6164,x6165,x6162,x6166,x6167,x6168))
% 168.60/168.40 [617]~E(x6171,x6172)+E(f477(x6173,x6174,x6175,x6176,x6171,x6177,x6178),f477(x6173,x6174,x6175,x6176,x6172,x6177,x6178))
% 168.60/168.40 [618]~E(x6181,x6182)+E(f477(x6183,x6184,x6185,x6186,x6187,x6181,x6188),f477(x6183,x6184,x6185,x6186,x6187,x6182,x6188))
% 168.60/168.40 [619]~E(x6191,x6192)+E(f477(x6193,x6194,x6195,x6196,x6197,x6198,x6191),f477(x6193,x6194,x6195,x6196,x6197,x6198,x6192))
% 168.60/168.40 [620]~E(x6201,x6202)+E(f420(x6201,x6203,x6204,x6205,x6206),f420(x6202,x6203,x6204,x6205,x6206))
% 168.60/168.40 [621]~E(x6211,x6212)+E(f420(x6213,x6211,x6214,x6215,x6216),f420(x6213,x6212,x6214,x6215,x6216))
% 168.60/168.40 [622]~E(x6221,x6222)+E(f420(x6223,x6224,x6221,x6225,x6226),f420(x6223,x6224,x6222,x6225,x6226))
% 168.60/168.40 [623]~E(x6231,x6232)+E(f420(x6233,x6234,x6235,x6231,x6236),f420(x6233,x6234,x6235,x6232,x6236))
% 168.60/168.40 [624]~E(x6241,x6242)+E(f420(x6243,x6244,x6245,x6246,x6241),f420(x6243,x6244,x6245,x6246,x6242))
% 168.60/168.40 [625]~E(x6251,x6252)+E(f879(x6251,x6253,x6254,x6255),f879(x6252,x6253,x6254,x6255))
% 168.60/168.40 [626]~E(x6261,x6262)+E(f879(x6263,x6261,x6264,x6265),f879(x6263,x6262,x6264,x6265))
% 168.60/168.40 [627]~E(x6271,x6272)+E(f879(x6273,x6274,x6271,x6275),f879(x6273,x6274,x6272,x6275))
% 168.60/168.40 [628]~E(x6281,x6282)+E(f879(x6283,x6284,x6285,x6281),f879(x6283,x6284,x6285,x6282))
% 168.60/168.40 [629]~E(x6291,x6292)+E(f388(x6291,x6293,x6294),f388(x6292,x6293,x6294))
% 168.60/168.40 [630]~E(x6301,x6302)+E(f388(x6303,x6301,x6304),f388(x6303,x6302,x6304))
% 168.60/168.40 [631]~E(x6311,x6312)+E(f388(x6313,x6314,x6311),f388(x6313,x6314,x6312))
% 168.60/168.40 [632]~E(x6321,x6322)+E(f49(x6321),f49(x6322))
% 168.60/168.40 [633]~E(x6331,x6332)+E(f547(x6331,x6333,x6334,x6335,x6336,x6337),f547(x6332,x6333,x6334,x6335,x6336,x6337))
% 168.60/168.40 [634]~E(x6341,x6342)+E(f547(x6343,x6341,x6344,x6345,x6346,x6347),f547(x6343,x6342,x6344,x6345,x6346,x6347))
% 168.60/168.40 [635]~E(x6351,x6352)+E(f547(x6353,x6354,x6351,x6355,x6356,x6357),f547(x6353,x6354,x6352,x6355,x6356,x6357))
% 168.60/168.40 [636]~E(x6361,x6362)+E(f547(x6363,x6364,x6365,x6361,x6366,x6367),f547(x6363,x6364,x6365,x6362,x6366,x6367))
% 168.60/168.40 [637]~E(x6371,x6372)+E(f547(x6373,x6374,x6375,x6376,x6371,x6377),f547(x6373,x6374,x6375,x6376,x6372,x6377))
% 168.60/168.40 [638]~E(x6381,x6382)+E(f547(x6383,x6384,x6385,x6386,x6387,x6381),f547(x6383,x6384,x6385,x6386,x6387,x6382))
% 168.60/168.40 [639]~E(x6391,x6392)+E(f218(x6391,x6393,x6394,x6395),f218(x6392,x6393,x6394,x6395))
% 168.60/168.40 [640]~E(x6401,x6402)+E(f218(x6403,x6401,x6404,x6405),f218(x6403,x6402,x6404,x6405))
% 168.60/168.40 [641]~E(x6411,x6412)+E(f218(x6413,x6414,x6411,x6415),f218(x6413,x6414,x6412,x6415))
% 168.60/168.40 [642]~E(x6421,x6422)+E(f218(x6423,x6424,x6425,x6421),f218(x6423,x6424,x6425,x6422))
% 168.60/168.40 [643]~E(x6431,x6432)+E(f773(x6431,x6433),f773(x6432,x6433))
% 168.60/168.40 [644]~E(x6441,x6442)+E(f773(x6443,x6441),f773(x6443,x6442))
% 168.60/168.40 [645]~E(x6451,x6452)+E(f760(x6451,x6453,x6454,x6455),f760(x6452,x6453,x6454,x6455))
% 168.60/168.40 [646]~E(x6461,x6462)+E(f760(x6463,x6461,x6464,x6465),f760(x6463,x6462,x6464,x6465))
% 168.60/168.40 [647]~E(x6471,x6472)+E(f760(x6473,x6474,x6471,x6475),f760(x6473,x6474,x6472,x6475))
% 168.60/168.40 [648]~E(x6481,x6482)+E(f760(x6483,x6484,x6485,x6481),f760(x6483,x6484,x6485,x6482))
% 168.60/168.40 [649]~E(x6491,x6492)+E(f846(x6491,x6493,x6494),f846(x6492,x6493,x6494))
% 168.60/168.40 [650]~E(x6501,x6502)+E(f846(x6503,x6501,x6504),f846(x6503,x6502,x6504))
% 168.60/168.40 [651]~E(x6511,x6512)+E(f846(x6513,x6514,x6511),f846(x6513,x6514,x6512))
% 168.60/168.40 [652]~E(x6521,x6522)+E(f15(x6521,x6523,x6524),f15(x6522,x6523,x6524))
% 168.60/168.40 [653]~E(x6531,x6532)+E(f15(x6533,x6531,x6534),f15(x6533,x6532,x6534))
% 168.60/168.40 [654]~E(x6541,x6542)+E(f15(x6543,x6544,x6541),f15(x6543,x6544,x6542))
% 168.60/168.40 [655]~E(x6551,x6552)+E(f799(x6551,x6553),f799(x6552,x6553))
% 168.60/168.40 [656]~E(x6561,x6562)+E(f799(x6563,x6561),f799(x6563,x6562))
% 168.60/168.40 [657]~E(x6571,x6572)+E(f204(x6571,x6573),f204(x6572,x6573))
% 168.60/168.40 [658]~E(x6581,x6582)+E(f204(x6583,x6581),f204(x6583,x6582))
% 168.60/168.40 [659]~E(x6591,x6592)+E(f333(x6591,x6593,x6594,x6595),f333(x6592,x6593,x6594,x6595))
% 168.60/168.40 [660]~E(x6601,x6602)+E(f333(x6603,x6601,x6604,x6605),f333(x6603,x6602,x6604,x6605))
% 168.60/168.40 [661]~E(x6611,x6612)+E(f333(x6613,x6614,x6611,x6615),f333(x6613,x6614,x6612,x6615))
% 168.60/168.40 [662]~E(x6621,x6622)+E(f333(x6623,x6624,x6625,x6621),f333(x6623,x6624,x6625,x6622))
% 168.60/168.40 [663]~E(x6631,x6632)+E(f212(x6631,x6633,x6634,x6635,x6636),f212(x6632,x6633,x6634,x6635,x6636))
% 168.60/168.40 [664]~E(x6641,x6642)+E(f212(x6643,x6641,x6644,x6645,x6646),f212(x6643,x6642,x6644,x6645,x6646))
% 168.60/168.40 [665]~E(x6651,x6652)+E(f212(x6653,x6654,x6651,x6655,x6656),f212(x6653,x6654,x6652,x6655,x6656))
% 168.60/168.40 [666]~E(x6661,x6662)+E(f212(x6663,x6664,x6665,x6661,x6666),f212(x6663,x6664,x6665,x6662,x6666))
% 168.60/168.40 [667]~E(x6671,x6672)+E(f212(x6673,x6674,x6675,x6676,x6671),f212(x6673,x6674,x6675,x6676,x6672))
% 168.60/168.40 [668]~E(x6681,x6682)+E(f853(x6681,x6683,x6684),f853(x6682,x6683,x6684))
% 168.60/168.40 [669]~E(x6691,x6692)+E(f853(x6693,x6691,x6694),f853(x6693,x6692,x6694))
% 168.60/168.40 [670]~E(x6701,x6702)+E(f853(x6703,x6704,x6701),f853(x6703,x6704,x6702))
% 168.60/168.40 [671]~E(x6711,x6712)+E(f117(x6711,x6713),f117(x6712,x6713))
% 168.60/168.40 [672]~E(x6721,x6722)+E(f117(x6723,x6721),f117(x6723,x6722))
% 168.60/168.40 [673]~E(x6731,x6732)+E(f209(x6731,x6733,x6734,x6735),f209(x6732,x6733,x6734,x6735))
% 168.60/168.40 [674]~E(x6741,x6742)+E(f209(x6743,x6741,x6744,x6745),f209(x6743,x6742,x6744,x6745))
% 168.60/168.40 [675]~E(x6751,x6752)+E(f209(x6753,x6754,x6751,x6755),f209(x6753,x6754,x6752,x6755))
% 168.60/168.40 [676]~E(x6761,x6762)+E(f209(x6763,x6764,x6765,x6761),f209(x6763,x6764,x6765,x6762))
% 168.60/168.40 [677]~E(x6771,x6772)+E(f359(x6771,x6773,x6774),f359(x6772,x6773,x6774))
% 168.60/168.40 [678]~E(x6781,x6782)+E(f359(x6783,x6781,x6784),f359(x6783,x6782,x6784))
% 168.60/168.40 [679]~E(x6791,x6792)+E(f359(x6793,x6794,x6791),f359(x6793,x6794,x6792))
% 168.60/168.40 [680]~E(x6801,x6802)+E(f642(x6801,x6803,x6804,x6805),f642(x6802,x6803,x6804,x6805))
% 168.60/168.40 [681]~E(x6811,x6812)+E(f642(x6813,x6811,x6814,x6815),f642(x6813,x6812,x6814,x6815))
% 168.60/168.40 [682]~E(x6821,x6822)+E(f642(x6823,x6824,x6821,x6825),f642(x6823,x6824,x6822,x6825))
% 168.60/168.40 [683]~E(x6831,x6832)+E(f642(x6833,x6834,x6835,x6831),f642(x6833,x6834,x6835,x6832))
% 168.60/168.40 [684]~E(x6841,x6842)+E(f612(x6841,x6843,x6844,x6845,x6846),f612(x6842,x6843,x6844,x6845,x6846))
% 168.60/168.40 [685]~E(x6851,x6852)+E(f612(x6853,x6851,x6854,x6855,x6856),f612(x6853,x6852,x6854,x6855,x6856))
% 168.60/168.40 [686]~E(x6861,x6862)+E(f612(x6863,x6864,x6861,x6865,x6866),f612(x6863,x6864,x6862,x6865,x6866))
% 168.60/168.40 [687]~E(x6871,x6872)+E(f612(x6873,x6874,x6875,x6871,x6876),f612(x6873,x6874,x6875,x6872,x6876))
% 168.60/168.40 [688]~E(x6881,x6882)+E(f612(x6883,x6884,x6885,x6886,x6881),f612(x6883,x6884,x6885,x6886,x6882))
% 168.60/168.40 [689]~E(x6891,x6892)+E(f393(x6891,x6893),f393(x6892,x6893))
% 168.60/168.40 [690]~E(x6901,x6902)+E(f393(x6903,x6901),f393(x6903,x6902))
% 168.60/168.40 [691]~E(x6911,x6912)+E(f570(x6911,x6913,x6914),f570(x6912,x6913,x6914))
% 168.60/168.40 [692]~E(x6921,x6922)+E(f570(x6923,x6921,x6924),f570(x6923,x6922,x6924))
% 168.60/168.40 [693]~E(x6931,x6932)+E(f570(x6933,x6934,x6931),f570(x6933,x6934,x6932))
% 168.60/168.40 [694]~E(x6941,x6942)+E(f360(x6941,x6943,x6944),f360(x6942,x6943,x6944))
% 168.60/168.40 [695]~E(x6951,x6952)+E(f360(x6953,x6951,x6954),f360(x6953,x6952,x6954))
% 168.60/168.40 [696]~E(x6961,x6962)+E(f360(x6963,x6964,x6961),f360(x6963,x6964,x6962))
% 168.60/168.40 [697]~E(x6971,x6972)+E(f149(x6971,x6973),f149(x6972,x6973))
% 168.60/168.40 [698]~E(x6981,x6982)+E(f149(x6983,x6981),f149(x6983,x6982))
% 168.60/168.40 [699]~E(x6991,x6992)+E(f475(x6991,x6993,x6994,x6995,x6996,x6997,x6998),f475(x6992,x6993,x6994,x6995,x6996,x6997,x6998))
% 168.60/168.40 [700]~E(x7001,x7002)+E(f475(x7003,x7001,x7004,x7005,x7006,x7007,x7008),f475(x7003,x7002,x7004,x7005,x7006,x7007,x7008))
% 168.60/168.40 [701]~E(x7011,x7012)+E(f475(x7013,x7014,x7011,x7015,x7016,x7017,x7018),f475(x7013,x7014,x7012,x7015,x7016,x7017,x7018))
% 168.60/168.40 [702]~E(x7021,x7022)+E(f475(x7023,x7024,x7025,x7021,x7026,x7027,x7028),f475(x7023,x7024,x7025,x7022,x7026,x7027,x7028))
% 168.60/168.40 [703]~E(x7031,x7032)+E(f475(x7033,x7034,x7035,x7036,x7031,x7037,x7038),f475(x7033,x7034,x7035,x7036,x7032,x7037,x7038))
% 168.60/168.40 [704]~E(x7041,x7042)+E(f475(x7043,x7044,x7045,x7046,x7047,x7041,x7048),f475(x7043,x7044,x7045,x7046,x7047,x7042,x7048))
% 168.60/168.40 [705]~E(x7051,x7052)+E(f475(x7053,x7054,x7055,x7056,x7057,x7058,x7051),f475(x7053,x7054,x7055,x7056,x7057,x7058,x7052))
% 168.60/168.40 [706]~E(x7061,x7062)+E(f67(x7061,x7063),f67(x7062,x7063))
% 168.60/168.40 [707]~E(x7071,x7072)+E(f67(x7073,x7071),f67(x7073,x7072))
% 168.60/168.40 [708]~E(x7081,x7082)+E(f817(x7081,x7083,x7084,x7085,x7086),f817(x7082,x7083,x7084,x7085,x7086))
% 168.60/168.40 [709]~E(x7091,x7092)+E(f817(x7093,x7091,x7094,x7095,x7096),f817(x7093,x7092,x7094,x7095,x7096))
% 168.60/168.40 [710]~E(x7101,x7102)+E(f817(x7103,x7104,x7101,x7105,x7106),f817(x7103,x7104,x7102,x7105,x7106))
% 168.60/168.40 [711]~E(x7111,x7112)+E(f817(x7113,x7114,x7115,x7111,x7116),f817(x7113,x7114,x7115,x7112,x7116))
% 168.60/168.40 [712]~E(x7121,x7122)+E(f817(x7123,x7124,x7125,x7126,x7121),f817(x7123,x7124,x7125,x7126,x7122))
% 168.60/168.40 [713]~E(x7131,x7132)+E(f165(x7131,x7133,x7134),f165(x7132,x7133,x7134))
% 168.60/168.40 [714]~E(x7141,x7142)+E(f165(x7143,x7141,x7144),f165(x7143,x7142,x7144))
% 168.60/168.40 [715]~E(x7151,x7152)+E(f165(x7153,x7154,x7151),f165(x7153,x7154,x7152))
% 168.60/168.40 [716]~E(x7161,x7162)+E(f486(x7161,x7163,x7164,x7165),f486(x7162,x7163,x7164,x7165))
% 168.60/168.40 [717]~E(x7171,x7172)+E(f486(x7173,x7171,x7174,x7175),f486(x7173,x7172,x7174,x7175))
% 168.60/168.40 [718]~E(x7181,x7182)+E(f486(x7183,x7184,x7181,x7185),f486(x7183,x7184,x7182,x7185))
% 168.60/168.40 [719]~E(x7191,x7192)+E(f486(x7193,x7194,x7195,x7191),f486(x7193,x7194,x7195,x7192))
% 168.60/168.40 [720]~E(x7201,x7202)+E(f463(x7201,x7203,x7204,x7205),f463(x7202,x7203,x7204,x7205))
% 168.60/168.40 [721]~E(x7211,x7212)+E(f463(x7213,x7211,x7214,x7215),f463(x7213,x7212,x7214,x7215))
% 168.60/168.40 [722]~E(x7221,x7222)+E(f463(x7223,x7224,x7221,x7225),f463(x7223,x7224,x7222,x7225))
% 168.60/168.40 [723]~E(x7231,x7232)+E(f463(x7233,x7234,x7235,x7231),f463(x7233,x7234,x7235,x7232))
% 168.60/168.40 [724]~E(x7241,x7242)+E(f79(x7241,x7243),f79(x7242,x7243))
% 168.60/168.40 [725]~E(x7251,x7252)+E(f79(x7253,x7251),f79(x7253,x7252))
% 168.60/168.40 [726]~E(x7261,x7262)+E(f660(x7261,x7263,x7264,x7265),f660(x7262,x7263,x7264,x7265))
% 168.60/168.40 [727]~E(x7271,x7272)+E(f660(x7273,x7271,x7274,x7275),f660(x7273,x7272,x7274,x7275))
% 168.60/168.40 [728]~E(x7281,x7282)+E(f660(x7283,x7284,x7281,x7285),f660(x7283,x7284,x7282,x7285))
% 168.60/168.40 [729]~E(x7291,x7292)+E(f660(x7293,x7294,x7295,x7291),f660(x7293,x7294,x7295,x7292))
% 168.60/168.40 [730]~E(x7301,x7302)+E(f601(x7301,x7303,x7304),f601(x7302,x7303,x7304))
% 168.60/168.40 [731]~E(x7311,x7312)+E(f601(x7313,x7311,x7314),f601(x7313,x7312,x7314))
% 168.60/168.40 [732]~E(x7321,x7322)+E(f601(x7323,x7324,x7321),f601(x7323,x7324,x7322))
% 168.60/168.40 [733]~E(x7331,x7332)+E(f335(x7331,x7333,x7334,x7335,x7336),f335(x7332,x7333,x7334,x7335,x7336))
% 168.60/168.40 [734]~E(x7341,x7342)+E(f335(x7343,x7341,x7344,x7345,x7346),f335(x7343,x7342,x7344,x7345,x7346))
% 168.60/168.40 [735]~E(x7351,x7352)+E(f335(x7353,x7354,x7351,x7355,x7356),f335(x7353,x7354,x7352,x7355,x7356))
% 168.60/168.40 [736]~E(x7361,x7362)+E(f335(x7363,x7364,x7365,x7361,x7366),f335(x7363,x7364,x7365,x7362,x7366))
% 168.60/168.40 [737]~E(x7371,x7372)+E(f335(x7373,x7374,x7375,x7376,x7371),f335(x7373,x7374,x7375,x7376,x7372))
% 168.60/168.40 [738]~E(x7381,x7382)+E(f56(x7381,x7383),f56(x7382,x7383))
% 168.60/168.40 [739]~E(x7391,x7392)+E(f56(x7393,x7391),f56(x7393,x7392))
% 168.60/168.40 [740]~E(x7401,x7402)+E(f722(x7401,x7403,x7404),f722(x7402,x7403,x7404))
% 168.60/168.40 [741]~E(x7411,x7412)+E(f722(x7413,x7411,x7414),f722(x7413,x7412,x7414))
% 168.60/168.40 [742]~E(x7421,x7422)+E(f722(x7423,x7424,x7421),f722(x7423,x7424,x7422))
% 168.60/168.40 [743]~E(x7431,x7432)+E(f121(x7431,x7433),f121(x7432,x7433))
% 168.60/168.40 [744]~E(x7441,x7442)+E(f121(x7443,x7441),f121(x7443,x7442))
% 168.60/168.40 [745]~E(x7451,x7452)+E(f871(x7451,x7453,x7454,x7455,x7456),f871(x7452,x7453,x7454,x7455,x7456))
% 168.60/168.40 [746]~E(x7461,x7462)+E(f871(x7463,x7461,x7464,x7465,x7466),f871(x7463,x7462,x7464,x7465,x7466))
% 168.60/168.40 [747]~E(x7471,x7472)+E(f871(x7473,x7474,x7471,x7475,x7476),f871(x7473,x7474,x7472,x7475,x7476))
% 168.60/168.40 [748]~E(x7481,x7482)+E(f871(x7483,x7484,x7485,x7481,x7486),f871(x7483,x7484,x7485,x7482,x7486))
% 168.60/168.40 [749]~E(x7491,x7492)+E(f871(x7493,x7494,x7495,x7496,x7491),f871(x7493,x7494,x7495,x7496,x7492))
% 168.60/168.40 [750]~E(x7501,x7502)+E(f375(x7501,x7503,x7504),f375(x7502,x7503,x7504))
% 168.60/168.40 [751]~E(x7511,x7512)+E(f375(x7513,x7511,x7514),f375(x7513,x7512,x7514))
% 168.60/168.40 [752]~E(x7521,x7522)+E(f375(x7523,x7524,x7521),f375(x7523,x7524,x7522))
% 168.60/168.40 [753]~E(x7531,x7532)+E(f341(x7531,x7533,x7534),f341(x7532,x7533,x7534))
% 168.60/168.40 [754]~E(x7541,x7542)+E(f341(x7543,x7541,x7544),f341(x7543,x7542,x7544))
% 168.60/168.40 [755]~E(x7551,x7552)+E(f341(x7553,x7554,x7551),f341(x7553,x7554,x7552))
% 168.60/168.40 [756]~E(x7561,x7562)+E(f732(x7561,x7563,x7564),f732(x7562,x7563,x7564))
% 168.60/168.40 [757]~E(x7571,x7572)+E(f732(x7573,x7571,x7574),f732(x7573,x7572,x7574))
% 168.60/168.40 [758]~E(x7581,x7582)+E(f732(x7583,x7584,x7581),f732(x7583,x7584,x7582))
% 168.60/168.40 [759]~E(x7591,x7592)+E(f864(x7591,x7593,x7594),f864(x7592,x7593,x7594))
% 168.60/168.40 [760]~E(x7601,x7602)+E(f864(x7603,x7601,x7604),f864(x7603,x7602,x7604))
% 168.60/168.40 [761]~E(x7611,x7612)+E(f864(x7613,x7614,x7611),f864(x7613,x7614,x7612))
% 168.60/168.40 [762]~E(x7621,x7622)+E(f258(x7621,x7623),f258(x7622,x7623))
% 168.60/168.40 [763]~E(x7631,x7632)+E(f258(x7633,x7631),f258(x7633,x7632))
% 168.60/168.40 [764]~E(x7641,x7642)+E(f144(x7641,x7643,x7644),f144(x7642,x7643,x7644))
% 168.60/168.40 [765]~E(x7651,x7652)+E(f144(x7653,x7651,x7654),f144(x7653,x7652,x7654))
% 168.60/168.40 [766]~E(x7661,x7662)+E(f144(x7663,x7664,x7661),f144(x7663,x7664,x7662))
% 168.60/168.40 [767]~E(x7671,x7672)+E(f304(x7671,x7673),f304(x7672,x7673))
% 168.60/168.40 [768]~E(x7681,x7682)+E(f304(x7683,x7681),f304(x7683,x7682))
% 168.60/168.40 [769]~E(x7691,x7692)+E(f563(x7691,x7693),f563(x7692,x7693))
% 168.60/168.40 [770]~E(x7701,x7702)+E(f563(x7703,x7701),f563(x7703,x7702))
% 168.60/168.40 [771]~E(x7711,x7712)+E(f548(x7711,x7713,x7714,x7715),f548(x7712,x7713,x7714,x7715))
% 168.60/168.40 [772]~E(x7721,x7722)+E(f548(x7723,x7721,x7724,x7725),f548(x7723,x7722,x7724,x7725))
% 168.60/168.40 [773]~E(x7731,x7732)+E(f548(x7733,x7734,x7731,x7735),f548(x7733,x7734,x7732,x7735))
% 168.60/168.40 [774]~E(x7741,x7742)+E(f548(x7743,x7744,x7745,x7741),f548(x7743,x7744,x7745,x7742))
% 168.60/168.40 [775]~E(x7751,x7752)+E(f766(x7751,x7753,x7754),f766(x7752,x7753,x7754))
% 168.60/168.40 [776]~E(x7761,x7762)+E(f766(x7763,x7761,x7764),f766(x7763,x7762,x7764))
% 168.60/168.40 [777]~E(x7771,x7772)+E(f766(x7773,x7774,x7771),f766(x7773,x7774,x7772))
% 168.60/168.40 [778]~E(x7781,x7782)+E(f80(x7781),f80(x7782))
% 168.60/168.40 [779]~E(x7791,x7792)+E(f665(x7791,x7793,x7794,x7795,x7796),f665(x7792,x7793,x7794,x7795,x7796))
% 168.60/168.40 [780]~E(x7801,x7802)+E(f665(x7803,x7801,x7804,x7805,x7806),f665(x7803,x7802,x7804,x7805,x7806))
% 168.60/168.40 [781]~E(x7811,x7812)+E(f665(x7813,x7814,x7811,x7815,x7816),f665(x7813,x7814,x7812,x7815,x7816))
% 168.60/168.40 [782]~E(x7821,x7822)+E(f665(x7823,x7824,x7825,x7821,x7826),f665(x7823,x7824,x7825,x7822,x7826))
% 168.60/168.40 [783]~E(x7831,x7832)+E(f665(x7833,x7834,x7835,x7836,x7831),f665(x7833,x7834,x7835,x7836,x7832))
% 168.60/168.40 [784]~E(x7841,x7842)+E(f775(x7841,x7843,x7844,x7845),f775(x7842,x7843,x7844,x7845))
% 168.60/168.40 [785]~E(x7851,x7852)+E(f775(x7853,x7851,x7854,x7855),f775(x7853,x7852,x7854,x7855))
% 168.60/168.40 [786]~E(x7861,x7862)+E(f775(x7863,x7864,x7861,x7865),f775(x7863,x7864,x7862,x7865))
% 168.60/168.40 [787]~E(x7871,x7872)+E(f775(x7873,x7874,x7875,x7871),f775(x7873,x7874,x7875,x7872))
% 168.60/168.40 [788]~E(x7881,x7882)+E(f788(x7881),f788(x7882))
% 168.60/168.40 [789]~E(x7891,x7892)+E(f838(x7891,x7893,x7894,x7895,x7896,x7897,x7898),f838(x7892,x7893,x7894,x7895,x7896,x7897,x7898))
% 168.60/168.40 [790]~E(x7901,x7902)+E(f838(x7903,x7901,x7904,x7905,x7906,x7907,x7908),f838(x7903,x7902,x7904,x7905,x7906,x7907,x7908))
% 168.60/168.40 [791]~E(x7911,x7912)+E(f838(x7913,x7914,x7911,x7915,x7916,x7917,x7918),f838(x7913,x7914,x7912,x7915,x7916,x7917,x7918))
% 168.60/168.40 [792]~E(x7921,x7922)+E(f838(x7923,x7924,x7925,x7921,x7926,x7927,x7928),f838(x7923,x7924,x7925,x7922,x7926,x7927,x7928))
% 168.60/168.40 [793]~E(x7931,x7932)+E(f838(x7933,x7934,x7935,x7936,x7931,x7937,x7938),f838(x7933,x7934,x7935,x7936,x7932,x7937,x7938))
% 168.60/168.40 [794]~E(x7941,x7942)+E(f838(x7943,x7944,x7945,x7946,x7947,x7941,x7948),f838(x7943,x7944,x7945,x7946,x7947,x7942,x7948))
% 168.60/168.40 [795]~E(x7951,x7952)+E(f838(x7953,x7954,x7955,x7956,x7957,x7958,x7951),f838(x7953,x7954,x7955,x7956,x7957,x7958,x7952))
% 168.60/168.40 [796]~E(x7961,x7962)+E(f357(x7961,x7963,x7964),f357(x7962,x7963,x7964))
% 168.60/168.40 [797]~E(x7971,x7972)+E(f357(x7973,x7971,x7974),f357(x7973,x7972,x7974))
% 168.60/168.40 [798]~E(x7981,x7982)+E(f357(x7983,x7984,x7981),f357(x7983,x7984,x7982))
% 168.60/168.40 [799]~E(x7991,x7992)+E(f254(x7991,x7993),f254(x7992,x7993))
% 168.60/168.40 [800]~E(x8001,x8002)+E(f254(x8003,x8001),f254(x8003,x8002))
% 168.60/168.40 [801]~E(x8011,x8012)+E(f868(x8011,x8013,x8014,x8015,x8016),f868(x8012,x8013,x8014,x8015,x8016))
% 168.60/168.40 [802]~E(x8021,x8022)+E(f868(x8023,x8021,x8024,x8025,x8026),f868(x8023,x8022,x8024,x8025,x8026))
% 168.60/168.40 [803]~E(x8031,x8032)+E(f868(x8033,x8034,x8031,x8035,x8036),f868(x8033,x8034,x8032,x8035,x8036))
% 168.60/168.40 [804]~E(x8041,x8042)+E(f868(x8043,x8044,x8045,x8041,x8046),f868(x8043,x8044,x8045,x8042,x8046))
% 168.60/168.40 [805]~E(x8051,x8052)+E(f868(x8053,x8054,x8055,x8056,x8051),f868(x8053,x8054,x8055,x8056,x8052))
% 168.60/168.40 [806]~E(x8061,x8062)+E(f133(x8061,x8063),f133(x8062,x8063))
% 168.60/168.40 [807]~E(x8071,x8072)+E(f133(x8073,x8071),f133(x8073,x8072))
% 168.60/168.40 [808]~E(x8081,x8082)+E(f247(x8081,x8083,x8084,x8085),f247(x8082,x8083,x8084,x8085))
% 168.60/168.40 [809]~E(x8091,x8092)+E(f247(x8093,x8091,x8094,x8095),f247(x8093,x8092,x8094,x8095))
% 168.60/168.40 [810]~E(x8101,x8102)+E(f247(x8103,x8104,x8101,x8105),f247(x8103,x8104,x8102,x8105))
% 168.60/168.40 [811]~E(x8111,x8112)+E(f247(x8113,x8114,x8115,x8111),f247(x8113,x8114,x8115,x8112))
% 168.60/168.40 [812]~E(x8121,x8122)+E(f256(x8121,x8123),f256(x8122,x8123))
% 168.60/168.40 [813]~E(x8131,x8132)+E(f256(x8133,x8131),f256(x8133,x8132))
% 168.60/168.40 [814]~E(x8141,x8142)+E(f729(x8141,x8143,x8144,x8145,x8146,x8147,x8148),f729(x8142,x8143,x8144,x8145,x8146,x8147,x8148))
% 168.60/168.40 [815]~E(x8151,x8152)+E(f729(x8153,x8151,x8154,x8155,x8156,x8157,x8158),f729(x8153,x8152,x8154,x8155,x8156,x8157,x8158))
% 168.60/168.40 [816]~E(x8161,x8162)+E(f729(x8163,x8164,x8161,x8165,x8166,x8167,x8168),f729(x8163,x8164,x8162,x8165,x8166,x8167,x8168))
% 168.60/168.40 [817]~E(x8171,x8172)+E(f729(x8173,x8174,x8175,x8171,x8176,x8177,x8178),f729(x8173,x8174,x8175,x8172,x8176,x8177,x8178))
% 168.60/168.40 [818]~E(x8181,x8182)+E(f729(x8183,x8184,x8185,x8186,x8181,x8187,x8188),f729(x8183,x8184,x8185,x8186,x8182,x8187,x8188))
% 168.60/168.40 [819]~E(x8191,x8192)+E(f729(x8193,x8194,x8195,x8196,x8197,x8191,x8198),f729(x8193,x8194,x8195,x8196,x8197,x8192,x8198))
% 168.60/168.40 [820]~E(x8201,x8202)+E(f729(x8203,x8204,x8205,x8206,x8207,x8208,x8201),f729(x8203,x8204,x8205,x8206,x8207,x8208,x8202))
% 168.60/168.40 [821]~E(x8211,x8212)+E(f728(x8211,x8213,x8214,x8215,x8216),f728(x8212,x8213,x8214,x8215,x8216))
% 168.60/168.40 [822]~E(x8221,x8222)+E(f728(x8223,x8221,x8224,x8225,x8226),f728(x8223,x8222,x8224,x8225,x8226))
% 168.60/168.40 [823]~E(x8231,x8232)+E(f728(x8233,x8234,x8231,x8235,x8236),f728(x8233,x8234,x8232,x8235,x8236))
% 168.60/168.40 [824]~E(x8241,x8242)+E(f728(x8243,x8244,x8245,x8241,x8246),f728(x8243,x8244,x8245,x8242,x8246))
% 168.60/168.40 [825]~E(x8251,x8252)+E(f728(x8253,x8254,x8255,x8256,x8251),f728(x8253,x8254,x8255,x8256,x8252))
% 168.60/168.40 [826]~E(x8261,x8262)+E(f546(x8261,x8263,x8264,x8265),f546(x8262,x8263,x8264,x8265))
% 168.60/168.40 [827]~E(x8271,x8272)+E(f546(x8273,x8271,x8274,x8275),f546(x8273,x8272,x8274,x8275))
% 168.60/168.40 [828]~E(x8281,x8282)+E(f546(x8283,x8284,x8281,x8285),f546(x8283,x8284,x8282,x8285))
% 168.60/168.40 [829]~E(x8291,x8292)+E(f546(x8293,x8294,x8295,x8291),f546(x8293,x8294,x8295,x8292))
% 168.60/168.40 [830]~E(x8301,x8302)+E(f85(x8301),f85(x8302))
% 168.60/168.40 [831]~E(x8311,x8312)+E(f681(x8311,x8313,x8314,x8315,x8316),f681(x8312,x8313,x8314,x8315,x8316))
% 168.60/168.40 [832]~E(x8321,x8322)+E(f681(x8323,x8321,x8324,x8325,x8326),f681(x8323,x8322,x8324,x8325,x8326))
% 168.60/168.40 [833]~E(x8331,x8332)+E(f681(x8333,x8334,x8331,x8335,x8336),f681(x8333,x8334,x8332,x8335,x8336))
% 168.60/168.40 [834]~E(x8341,x8342)+E(f681(x8343,x8344,x8345,x8341,x8346),f681(x8343,x8344,x8345,x8342,x8346))
% 168.60/168.40 [835]~E(x8351,x8352)+E(f681(x8353,x8354,x8355,x8356,x8351),f681(x8353,x8354,x8355,x8356,x8352))
% 168.60/168.40 [836]~E(x8361,x8362)+E(f520(x8361,x8363,x8364,x8365,x8366),f520(x8362,x8363,x8364,x8365,x8366))
% 168.60/168.40 [837]~E(x8371,x8372)+E(f520(x8373,x8371,x8374,x8375,x8376),f520(x8373,x8372,x8374,x8375,x8376))
% 168.60/168.40 [838]~E(x8381,x8382)+E(f520(x8383,x8384,x8381,x8385,x8386),f520(x8383,x8384,x8382,x8385,x8386))
% 168.60/168.40 [839]~E(x8391,x8392)+E(f520(x8393,x8394,x8395,x8391,x8396),f520(x8393,x8394,x8395,x8392,x8396))
% 168.60/168.40 [840]~E(x8401,x8402)+E(f520(x8403,x8404,x8405,x8406,x8401),f520(x8403,x8404,x8405,x8406,x8402))
% 168.60/168.40 [841]~E(x8411,x8412)+E(f130(x8411),f130(x8412))
% 168.60/168.40 [842]~E(x8421,x8422)+E(f789(x8421),f789(x8422))
% 168.60/168.40 [843]~E(x8431,x8432)+E(f811(x8431),f811(x8432))
% 168.60/168.40 [844]~E(x8441,x8442)+E(f517(x8441,x8443,x8444,x8445,x8446),f517(x8442,x8443,x8444,x8445,x8446))
% 168.60/168.40 [845]~E(x8451,x8452)+E(f517(x8453,x8451,x8454,x8455,x8456),f517(x8453,x8452,x8454,x8455,x8456))
% 168.60/168.40 [846]~E(x8461,x8462)+E(f517(x8463,x8464,x8461,x8465,x8466),f517(x8463,x8464,x8462,x8465,x8466))
% 168.60/168.40 [847]~E(x8471,x8472)+E(f517(x8473,x8474,x8475,x8471,x8476),f517(x8473,x8474,x8475,x8472,x8476))
% 168.60/168.40 [848]~E(x8481,x8482)+E(f517(x8483,x8484,x8485,x8486,x8481),f517(x8483,x8484,x8485,x8486,x8482))
% 168.60/168.40 [849]~E(x8491,x8492)+E(f397(x8491,x8493),f397(x8492,x8493))
% 168.60/168.40 [850]~E(x8501,x8502)+E(f397(x8503,x8501),f397(x8503,x8502))
% 168.60/168.40 [851]~E(x8511,x8512)+E(f272(x8511,x8513),f272(x8512,x8513))
% 168.60/168.40 [852]~E(x8521,x8522)+E(f272(x8523,x8521),f272(x8523,x8522))
% 168.60/168.40 [853]~E(x8531,x8532)+E(f155(x8531,x8533,x8534),f155(x8532,x8533,x8534))
% 168.60/168.40 [854]~E(x8541,x8542)+E(f155(x8543,x8541,x8544),f155(x8543,x8542,x8544))
% 168.60/168.40 [855]~E(x8551,x8552)+E(f155(x8553,x8554,x8551),f155(x8553,x8554,x8552))
% 168.60/168.40 [856]~E(x8561,x8562)+E(f187(x8561,x8563,x8564,x8565),f187(x8562,x8563,x8564,x8565))
% 168.60/168.40 [857]~E(x8571,x8572)+E(f187(x8573,x8571,x8574,x8575),f187(x8573,x8572,x8574,x8575))
% 168.60/168.40 [858]~E(x8581,x8582)+E(f187(x8583,x8584,x8581,x8585),f187(x8583,x8584,x8582,x8585))
% 168.60/168.40 [859]~E(x8591,x8592)+E(f187(x8593,x8594,x8595,x8591),f187(x8593,x8594,x8595,x8592))
% 168.60/168.40 [860]~E(x8601,x8602)+E(f617(x8601,x8603,x8604,x8605,x8606),f617(x8602,x8603,x8604,x8605,x8606))
% 168.60/168.40 [861]~E(x8611,x8612)+E(f617(x8613,x8611,x8614,x8615,x8616),f617(x8613,x8612,x8614,x8615,x8616))
% 168.60/168.40 [862]~E(x8621,x8622)+E(f617(x8623,x8624,x8621,x8625,x8626),f617(x8623,x8624,x8622,x8625,x8626))
% 168.60/168.40 [863]~E(x8631,x8632)+E(f617(x8633,x8634,x8635,x8631,x8636),f617(x8633,x8634,x8635,x8632,x8636))
% 168.60/168.40 [864]~E(x8641,x8642)+E(f617(x8643,x8644,x8645,x8646,x8641),f617(x8643,x8644,x8645,x8646,x8642))
% 168.60/168.40 [865]~E(x8651,x8652)+E(f894(x8651,x8653,x8654,x8655),f894(x8652,x8653,x8654,x8655))
% 168.60/168.40 [866]~E(x8661,x8662)+E(f894(x8663,x8661,x8664,x8665),f894(x8663,x8662,x8664,x8665))
% 168.60/168.40 [867]~E(x8671,x8672)+E(f894(x8673,x8674,x8671,x8675),f894(x8673,x8674,x8672,x8675))
% 168.60/168.40 [868]~E(x8681,x8682)+E(f894(x8683,x8684,x8685,x8681),f894(x8683,x8684,x8685,x8682))
% 168.60/168.40 [869]~E(x8691,x8692)+E(f328(x8691),f328(x8692))
% 168.60/168.40 [870]~E(x8701,x8702)+E(f730(x8701,x8703,x8704,x8705,x8706,x8707,x8708),f730(x8702,x8703,x8704,x8705,x8706,x8707,x8708))
% 168.60/168.40 [871]~E(x8711,x8712)+E(f730(x8713,x8711,x8714,x8715,x8716,x8717,x8718),f730(x8713,x8712,x8714,x8715,x8716,x8717,x8718))
% 168.60/168.40 [872]~E(x8721,x8722)+E(f730(x8723,x8724,x8721,x8725,x8726,x8727,x8728),f730(x8723,x8724,x8722,x8725,x8726,x8727,x8728))
% 168.60/168.40 [873]~E(x8731,x8732)+E(f730(x8733,x8734,x8735,x8731,x8736,x8737,x8738),f730(x8733,x8734,x8735,x8732,x8736,x8737,x8738))
% 168.60/168.40 [874]~E(x8741,x8742)+E(f730(x8743,x8744,x8745,x8746,x8741,x8747,x8748),f730(x8743,x8744,x8745,x8746,x8742,x8747,x8748))
% 168.60/168.40 [875]~E(x8751,x8752)+E(f730(x8753,x8754,x8755,x8756,x8757,x8751,x8758),f730(x8753,x8754,x8755,x8756,x8757,x8752,x8758))
% 168.60/168.40 [876]~E(x8761,x8762)+E(f730(x8763,x8764,x8765,x8766,x8767,x8768,x8761),f730(x8763,x8764,x8765,x8766,x8767,x8768,x8762))
% 168.60/168.40 [877]~E(x8771,x8772)+E(f633(x8771,x8773,x8774),f633(x8772,x8773,x8774))
% 168.60/168.40 [878]~E(x8781,x8782)+E(f633(x8783,x8781,x8784),f633(x8783,x8782,x8784))
% 168.60/168.40 [879]~E(x8791,x8792)+E(f633(x8793,x8794,x8791),f633(x8793,x8794,x8792))
% 168.60/168.40 [880]~E(x8801,x8802)+E(f674(x8801,x8803,x8804),f674(x8802,x8803,x8804))
% 168.60/168.40 [881]~E(x8811,x8812)+E(f674(x8813,x8811,x8814),f674(x8813,x8812,x8814))
% 168.60/168.40 [882]~E(x8821,x8822)+E(f674(x8823,x8824,x8821),f674(x8823,x8824,x8822))
% 168.60/168.40 [883]~E(x8831,x8832)+E(f592(x8831,x8833,x8834,x8835,x8836,x8837,x8838,x8839),f592(x8832,x8833,x8834,x8835,x8836,x8837,x8838,x8839))
% 168.60/168.40 [884]~E(x8841,x8842)+E(f592(x8843,x8841,x8844,x8845,x8846,x8847,x8848,x8849),f592(x8843,x8842,x8844,x8845,x8846,x8847,x8848,x8849))
% 168.60/168.40 [885]~E(x8851,x8852)+E(f592(x8853,x8854,x8851,x8855,x8856,x8857,x8858,x8859),f592(x8853,x8854,x8852,x8855,x8856,x8857,x8858,x8859))
% 168.60/168.40 [886]~E(x8861,x8862)+E(f592(x8863,x8864,x8865,x8861,x8866,x8867,x8868,x8869),f592(x8863,x8864,x8865,x8862,x8866,x8867,x8868,x8869))
% 168.60/168.40 [887]~E(x8871,x8872)+E(f592(x8873,x8874,x8875,x8876,x8871,x8877,x8878,x8879),f592(x8873,x8874,x8875,x8876,x8872,x8877,x8878,x8879))
% 168.60/168.40 [888]~E(x8881,x8882)+E(f592(x8883,x8884,x8885,x8886,x8887,x8881,x8888,x8889),f592(x8883,x8884,x8885,x8886,x8887,x8882,x8888,x8889))
% 168.60/168.40 [889]~E(x8891,x8892)+E(f592(x8893,x8894,x8895,x8896,x8897,x8898,x8891,x8899),f592(x8893,x8894,x8895,x8896,x8897,x8898,x8892,x8899))
% 168.60/168.40 [890]~E(x8901,x8902)+E(f592(x8903,x8904,x8905,x8906,x8907,x8908,x8909,x8901),f592(x8903,x8904,x8905,x8906,x8907,x8908,x8909,x8902))
% 168.60/168.40 [891]~E(x8911,x8912)+E(f831(x8911,x8913,x8914,x8915,x8916,x8917,x8918,x8919),f831(x8912,x8913,x8914,x8915,x8916,x8917,x8918,x8919))
% 168.60/168.40 [892]~E(x8921,x8922)+E(f831(x8923,x8921,x8924,x8925,x8926,x8927,x8928,x8929),f831(x8923,x8922,x8924,x8925,x8926,x8927,x8928,x8929))
% 168.60/168.40 [893]~E(x8931,x8932)+E(f831(x8933,x8934,x8931,x8935,x8936,x8937,x8938,x8939),f831(x8933,x8934,x8932,x8935,x8936,x8937,x8938,x8939))
% 168.60/168.40 [894]~E(x8941,x8942)+E(f831(x8943,x8944,x8945,x8941,x8946,x8947,x8948,x8949),f831(x8943,x8944,x8945,x8942,x8946,x8947,x8948,x8949))
% 168.60/168.40 [895]~E(x8951,x8952)+E(f831(x8953,x8954,x8955,x8956,x8951,x8957,x8958,x8959),f831(x8953,x8954,x8955,x8956,x8952,x8957,x8958,x8959))
% 168.60/168.40 [896]~E(x8961,x8962)+E(f831(x8963,x8964,x8965,x8966,x8967,x8961,x8968,x8969),f831(x8963,x8964,x8965,x8966,x8967,x8962,x8968,x8969))
% 168.60/168.40 [897]~E(x8971,x8972)+E(f831(x8973,x8974,x8975,x8976,x8977,x8978,x8971,x8979),f831(x8973,x8974,x8975,x8976,x8977,x8978,x8972,x8979))
% 168.60/168.40 [898]~E(x8981,x8982)+E(f831(x8983,x8984,x8985,x8986,x8987,x8988,x8989,x8981),f831(x8983,x8984,x8985,x8986,x8987,x8988,x8989,x8982))
% 168.60/168.40 [899]~E(x8991,x8992)+E(f326(x8991,x8993),f326(x8992,x8993))
% 168.60/168.40 [900]~E(x9001,x9002)+E(f326(x9003,x9001),f326(x9003,x9002))
% 168.60/168.40 [901]~E(x9011,x9012)+E(f796(x9011,x9013,x9014,x9015,x9016,x9017),f796(x9012,x9013,x9014,x9015,x9016,x9017))
% 168.60/168.40 [902]~E(x9021,x9022)+E(f796(x9023,x9021,x9024,x9025,x9026,x9027),f796(x9023,x9022,x9024,x9025,x9026,x9027))
% 168.60/168.40 [903]~E(x9031,x9032)+E(f796(x9033,x9034,x9031,x9035,x9036,x9037),f796(x9033,x9034,x9032,x9035,x9036,x9037))
% 168.60/168.40 [904]~E(x9041,x9042)+E(f796(x9043,x9044,x9045,x9041,x9046,x9047),f796(x9043,x9044,x9045,x9042,x9046,x9047))
% 168.60/168.40 [905]~E(x9051,x9052)+E(f796(x9053,x9054,x9055,x9056,x9051,x9057),f796(x9053,x9054,x9055,x9056,x9052,x9057))
% 168.60/168.40 [906]~E(x9061,x9062)+E(f796(x9063,x9064,x9065,x9066,x9067,x9061),f796(x9063,x9064,x9065,x9066,x9067,x9062))
% 168.60/168.40 [907]~E(x9071,x9072)+E(f238(x9071,x9073,x9074),f238(x9072,x9073,x9074))
% 168.60/168.40 [908]~E(x9081,x9082)+E(f238(x9083,x9081,x9084),f238(x9083,x9082,x9084))
% 168.60/168.40 [909]~E(x9091,x9092)+E(f238(x9093,x9094,x9091),f238(x9093,x9094,x9092))
% 168.60/168.40 [910]~E(x9101,x9102)+E(f883(x9101,x9103,x9104),f883(x9102,x9103,x9104))
% 168.60/168.40 [911]~E(x9111,x9112)+E(f883(x9113,x9111,x9114),f883(x9113,x9112,x9114))
% 168.60/168.40 [912]~E(x9121,x9122)+E(f883(x9123,x9124,x9121),f883(x9123,x9124,x9122))
% 168.60/168.40 [913]~E(x9131,x9132)+E(f42(x9131,x9133),f42(x9132,x9133))
% 168.60/168.40 [914]~E(x9141,x9142)+E(f42(x9143,x9141),f42(x9143,x9142))
% 168.60/168.40 [915]~E(x9151,x9152)+E(f138(x9151,x9153,x9154,x9155,x9156),f138(x9152,x9153,x9154,x9155,x9156))
% 168.60/168.40 [916]~E(x9161,x9162)+E(f138(x9163,x9161,x9164,x9165,x9166),f138(x9163,x9162,x9164,x9165,x9166))
% 168.60/168.40 [917]~E(x9171,x9172)+E(f138(x9173,x9174,x9171,x9175,x9176),f138(x9173,x9174,x9172,x9175,x9176))
% 168.60/168.40 [918]~E(x9181,x9182)+E(f138(x9183,x9184,x9185,x9181,x9186),f138(x9183,x9184,x9185,x9182,x9186))
% 168.60/168.40 [919]~E(x9191,x9192)+E(f138(x9193,x9194,x9195,x9196,x9191),f138(x9193,x9194,x9195,x9196,x9192))
% 168.60/168.40 [920]~E(x9201,x9202)+E(f118(x9201),f118(x9202))
% 168.60/168.40 [921]~E(x9211,x9212)+E(f552(x9211,x9213),f552(x9212,x9213))
% 168.60/168.40 [922]~E(x9221,x9222)+E(f552(x9223,x9221),f552(x9223,x9222))
% 168.60/168.40 [923]~E(x9231,x9232)+E(f850(x9231,x9233,x9234),f850(x9232,x9233,x9234))
% 168.60/168.40 [924]~E(x9241,x9242)+E(f850(x9243,x9241,x9244),f850(x9243,x9242,x9244))
% 168.60/168.40 [925]~E(x9251,x9252)+E(f850(x9253,x9254,x9251),f850(x9253,x9254,x9252))
% 168.60/168.40 [926]~E(x9261,x9262)+E(f457(x9261,x9263,x9264,x9265),f457(x9262,x9263,x9264,x9265))
% 168.60/168.40 [927]~E(x9271,x9272)+E(f457(x9273,x9271,x9274,x9275),f457(x9273,x9272,x9274,x9275))
% 168.60/168.40 [928]~E(x9281,x9282)+E(f457(x9283,x9284,x9281,x9285),f457(x9283,x9284,x9282,x9285))
% 168.60/168.40 [929]~E(x9291,x9292)+E(f457(x9293,x9294,x9295,x9291),f457(x9293,x9294,x9295,x9292))
% 168.60/168.40 [930]~E(x9301,x9302)+E(f344(x9301),f344(x9302))
% 168.60/168.40 [931]~E(x9311,x9312)+E(f593(x9311,x9313,x9314,x9315,x9316,x9317,x9318,x9319),f593(x9312,x9313,x9314,x9315,x9316,x9317,x9318,x9319))
% 168.60/168.40 [932]~E(x9321,x9322)+E(f593(x9323,x9321,x9324,x9325,x9326,x9327,x9328,x9329),f593(x9323,x9322,x9324,x9325,x9326,x9327,x9328,x9329))
% 168.60/168.40 [933]~E(x9331,x9332)+E(f593(x9333,x9334,x9331,x9335,x9336,x9337,x9338,x9339),f593(x9333,x9334,x9332,x9335,x9336,x9337,x9338,x9339))
% 168.60/168.40 [934]~E(x9341,x9342)+E(f593(x9343,x9344,x9345,x9341,x9346,x9347,x9348,x9349),f593(x9343,x9344,x9345,x9342,x9346,x9347,x9348,x9349))
% 168.60/168.40 [935]~E(x9351,x9352)+E(f593(x9353,x9354,x9355,x9356,x9351,x9357,x9358,x9359),f593(x9353,x9354,x9355,x9356,x9352,x9357,x9358,x9359))
% 168.60/168.40 [936]~E(x9361,x9362)+E(f593(x9363,x9364,x9365,x9366,x9367,x9361,x9368,x9369),f593(x9363,x9364,x9365,x9366,x9367,x9362,x9368,x9369))
% 168.60/168.40 [937]~E(x9371,x9372)+E(f593(x9373,x9374,x9375,x9376,x9377,x9378,x9371,x9379),f593(x9373,x9374,x9375,x9376,x9377,x9378,x9372,x9379))
% 168.60/168.40 [938]~E(x9381,x9382)+E(f593(x9383,x9384,x9385,x9386,x9387,x9388,x9389,x9381),f593(x9383,x9384,x9385,x9386,x9387,x9388,x9389,x9382))
% 168.60/168.40 [939]~E(x9391,x9392)+E(f181(x9391,x9393),f181(x9392,x9393))
% 168.60/168.40 [940]~E(x9401,x9402)+E(f181(x9403,x9401),f181(x9403,x9402))
% 168.60/168.40 [941]~E(x9411,x9412)+E(f365(x9411,x9413,x9414,x9415),f365(x9412,x9413,x9414,x9415))
% 168.60/168.40 [942]~E(x9421,x9422)+E(f365(x9423,x9421,x9424,x9425),f365(x9423,x9422,x9424,x9425))
% 168.60/168.40 [943]~E(x9431,x9432)+E(f365(x9433,x9434,x9431,x9435),f365(x9433,x9434,x9432,x9435))
% 168.60/168.40 [944]~E(x9441,x9442)+E(f365(x9443,x9444,x9445,x9441),f365(x9443,x9444,x9445,x9442))
% 168.60/168.40 [945]~E(x9451,x9452)+E(f110(x9451,x9453),f110(x9452,x9453))
% 168.60/168.40 [946]~E(x9461,x9462)+E(f110(x9463,x9461),f110(x9463,x9462))
% 168.60/168.40 [947]~E(x9471,x9472)+E(f607(x9471,x9473,x9474,x9475,x9476),f607(x9472,x9473,x9474,x9475,x9476))
% 168.60/168.40 [948]~E(x9481,x9482)+E(f607(x9483,x9481,x9484,x9485,x9486),f607(x9483,x9482,x9484,x9485,x9486))
% 168.60/168.40 [949]~E(x9491,x9492)+E(f607(x9493,x9494,x9491,x9495,x9496),f607(x9493,x9494,x9492,x9495,x9496))
% 168.60/168.40 [950]~E(x9501,x9502)+E(f607(x9503,x9504,x9505,x9501,x9506),f607(x9503,x9504,x9505,x9502,x9506))
% 168.60/168.40 [951]~E(x9511,x9512)+E(f607(x9513,x9514,x9515,x9516,x9511),f607(x9513,x9514,x9515,x9516,x9512))
% 168.60/168.40 [952]~E(x9521,x9522)+E(f538(x9521,x9523),f538(x9522,x9523))
% 168.60/168.40 [953]~E(x9531,x9532)+E(f538(x9533,x9531),f538(x9533,x9532))
% 168.60/168.40 [954]~E(x9541,x9542)+E(f416(x9541,x9543,x9544,x9545),f416(x9542,x9543,x9544,x9545))
% 168.60/168.40 [955]~E(x9551,x9552)+E(f416(x9553,x9551,x9554,x9555),f416(x9553,x9552,x9554,x9555))
% 168.60/168.40 [956]~E(x9561,x9562)+E(f416(x9563,x9564,x9561,x9565),f416(x9563,x9564,x9562,x9565))
% 168.60/168.40 [957]~E(x9571,x9572)+E(f416(x9573,x9574,x9575,x9571),f416(x9573,x9574,x9575,x9572))
% 168.60/168.40 [958]~E(x9581,x9582)+E(f522(x9581,x9583,x9584,x9585,x9586),f522(x9582,x9583,x9584,x9585,x9586))
% 168.60/168.40 [959]~E(x9591,x9592)+E(f522(x9593,x9591,x9594,x9595,x9596),f522(x9593,x9592,x9594,x9595,x9596))
% 168.60/168.40 [960]~E(x9601,x9602)+E(f522(x9603,x9604,x9601,x9605,x9606),f522(x9603,x9604,x9602,x9605,x9606))
% 168.60/168.40 [961]~E(x9611,x9612)+E(f522(x9613,x9614,x9615,x9611,x9616),f522(x9613,x9614,x9615,x9612,x9616))
% 168.60/168.40 [962]~E(x9621,x9622)+E(f522(x9623,x9624,x9625,x9626,x9621),f522(x9623,x9624,x9625,x9626,x9622))
% 168.60/168.40 [963]~E(x9631,x9632)+E(f733(x9631,x9633,x9634),f733(x9632,x9633,x9634))
% 168.60/168.40 [964]~E(x9641,x9642)+E(f733(x9643,x9641,x9644),f733(x9643,x9642,x9644))
% 168.60/168.40 [965]~E(x9651,x9652)+E(f733(x9653,x9654,x9651),f733(x9653,x9654,x9652))
% 168.60/168.40 [966]~E(x9661,x9662)+E(f637(x9661,x9663,x9664,x9665,x9666),f637(x9662,x9663,x9664,x9665,x9666))
% 168.60/168.40 [967]~E(x9671,x9672)+E(f637(x9673,x9671,x9674,x9675,x9676),f637(x9673,x9672,x9674,x9675,x9676))
% 168.60/168.40 [968]~E(x9681,x9682)+E(f637(x9683,x9684,x9681,x9685,x9686),f637(x9683,x9684,x9682,x9685,x9686))
% 168.60/168.40 [969]~E(x9691,x9692)+E(f637(x9693,x9694,x9695,x9691,x9696),f637(x9693,x9694,x9695,x9692,x9696))
% 168.60/168.40 [970]~E(x9701,x9702)+E(f637(x9703,x9704,x9705,x9706,x9701),f637(x9703,x9704,x9705,x9706,x9702))
% 168.60/168.40 [971]~E(x9711,x9712)+E(f485(x9711,x9713,x9714,x9715),f485(x9712,x9713,x9714,x9715))
% 168.60/168.40 [972]~E(x9721,x9722)+E(f485(x9723,x9721,x9724,x9725),f485(x9723,x9722,x9724,x9725))
% 168.60/168.40 [973]~E(x9731,x9732)+E(f485(x9733,x9734,x9731,x9735),f485(x9733,x9734,x9732,x9735))
% 168.60/168.40 [974]~E(x9741,x9742)+E(f485(x9743,x9744,x9745,x9741),f485(x9743,x9744,x9745,x9742))
% 168.60/168.40 [975]~E(x9751,x9752)+E(f294(x9751,x9753,x9754),f294(x9752,x9753,x9754))
% 168.60/168.40 [976]~E(x9761,x9762)+E(f294(x9763,x9761,x9764),f294(x9763,x9762,x9764))
% 168.60/168.40 [977]~E(x9771,x9772)+E(f294(x9773,x9774,x9771),f294(x9773,x9774,x9772))
% 168.60/168.40 [978]~E(x9781,x9782)+E(f237(x9781,x9783,x9784),f237(x9782,x9783,x9784))
% 168.60/168.40 [979]~E(x9791,x9792)+E(f237(x9793,x9791,x9794),f237(x9793,x9792,x9794))
% 168.60/168.40 [980]~E(x9801,x9802)+E(f237(x9803,x9804,x9801),f237(x9803,x9804,x9802))
% 168.60/168.40 [981]~E(x9811,x9812)+E(f354(x9811,x9813,x9814),f354(x9812,x9813,x9814))
% 168.60/168.40 [982]~E(x9821,x9822)+E(f354(x9823,x9821,x9824),f354(x9823,x9822,x9824))
% 168.60/168.40 [983]~E(x9831,x9832)+E(f354(x9833,x9834,x9831),f354(x9833,x9834,x9832))
% 168.60/168.40 [984]~E(x9841,x9842)+E(f470(x9841,x9843,x9844),f470(x9842,x9843,x9844))
% 168.60/168.40 [985]~E(x9851,x9852)+E(f470(x9853,x9851,x9854),f470(x9853,x9852,x9854))
% 168.60/168.40 [986]~E(x9861,x9862)+E(f470(x9863,x9864,x9861),f470(x9863,x9864,x9862))
% 168.60/168.40 [987]~E(x9871,x9872)+E(f185(x9871,x9873,x9874,x9875),f185(x9872,x9873,x9874,x9875))
% 168.60/168.40 [988]~E(x9881,x9882)+E(f185(x9883,x9881,x9884,x9885),f185(x9883,x9882,x9884,x9885))
% 168.60/168.40 [989]~E(x9891,x9892)+E(f185(x9893,x9894,x9891,x9895),f185(x9893,x9894,x9892,x9895))
% 168.60/168.40 [990]~E(x9901,x9902)+E(f185(x9903,x9904,x9905,x9901),f185(x9903,x9904,x9905,x9902))
% 168.60/168.40 [991]~E(x9911,x9912)+E(f139(x9911,x9913,x9914,x9915),f139(x9912,x9913,x9914,x9915))
% 168.60/168.40 [992]~E(x9921,x9922)+E(f139(x9923,x9921,x9924,x9925),f139(x9923,x9922,x9924,x9925))
% 168.60/168.40 [993]~E(x9931,x9932)+E(f139(x9933,x9934,x9931,x9935),f139(x9933,x9934,x9932,x9935))
% 168.60/168.40 [994]~E(x9941,x9942)+E(f139(x9943,x9944,x9945,x9941),f139(x9943,x9944,x9945,x9942))
% 168.60/168.40 [995]~E(x9951,x9952)+E(f426(x9951,x9953,x9954,x9955,x9956),f426(x9952,x9953,x9954,x9955,x9956))
% 168.60/168.40 [996]~E(x9961,x9962)+E(f426(x9963,x9961,x9964,x9965,x9966),f426(x9963,x9962,x9964,x9965,x9966))
% 168.60/168.40 [997]~E(x9971,x9972)+E(f426(x9973,x9974,x9971,x9975,x9976),f426(x9973,x9974,x9972,x9975,x9976))
% 168.60/168.40 [998]~E(x9981,x9982)+E(f426(x9983,x9984,x9985,x9981,x9986),f426(x9983,x9984,x9985,x9982,x9986))
% 168.60/168.40 [999]~E(x9991,x9992)+E(f426(x9993,x9994,x9995,x9996,x9991),f426(x9993,x9994,x9995,x9996,x9992))
% 168.60/168.40 [1000]~E(x10001,x10002)+E(f368(x10001,x10003,x10004,x10005),f368(x10002,x10003,x10004,x10005))
% 168.60/168.40 [1001]~E(x10011,x10012)+E(f368(x10013,x10011,x10014,x10015),f368(x10013,x10012,x10014,x10015))
% 168.60/168.40 [1002]~E(x10021,x10022)+E(f368(x10023,x10024,x10021,x10025),f368(x10023,x10024,x10022,x10025))
% 168.60/168.40 [1003]~E(x10031,x10032)+E(f368(x10033,x10034,x10035,x10031),f368(x10033,x10034,x10035,x10032))
% 168.60/168.40 [1004]~E(x10041,x10042)+E(f384(x10041,x10043,x10044,x10045),f384(x10042,x10043,x10044,x10045))
% 168.60/168.40 [1005]~E(x10051,x10052)+E(f384(x10053,x10051,x10054,x10055),f384(x10053,x10052,x10054,x10055))
% 168.60/168.40 [1006]~E(x10061,x10062)+E(f384(x10063,x10064,x10061,x10065),f384(x10063,x10064,x10062,x10065))
% 168.60/168.40 [1007]~E(x10071,x10072)+E(f384(x10073,x10074,x10075,x10071),f384(x10073,x10074,x10075,x10072))
% 168.60/168.40 [1008]~E(x10081,x10082)+E(f494(x10081,x10083,x10084),f494(x10082,x10083,x10084))
% 168.60/168.40 [1009]~E(x10091,x10092)+E(f494(x10093,x10091,x10094),f494(x10093,x10092,x10094))
% 168.60/168.40 [1010]~E(x10101,x10102)+E(f494(x10103,x10104,x10101),f494(x10103,x10104,x10102))
% 168.60/168.40 [1011]~E(x10111,x10112)+E(f173(x10111,x10113,x10114),f173(x10112,x10113,x10114))
% 168.60/168.40 [1012]~E(x10121,x10122)+E(f173(x10123,x10121,x10124),f173(x10123,x10122,x10124))
% 168.60/168.40 [1013]~E(x10131,x10132)+E(f173(x10133,x10134,x10131),f173(x10133,x10134,x10132))
% 168.60/168.40 [1014]~E(x10141,x10142)+E(f632(x10141,x10143),f632(x10142,x10143))
% 168.60/168.40 [1015]~E(x10151,x10152)+E(f632(x10153,x10151),f632(x10153,x10152))
% 168.60/168.40 [1016]~E(x10161,x10162)+E(f241(x10161,x10163,x10164,x10165,x10166),f241(x10162,x10163,x10164,x10165,x10166))
% 168.60/168.40 [1017]~E(x10171,x10172)+E(f241(x10173,x10171,x10174,x10175,x10176),f241(x10173,x10172,x10174,x10175,x10176))
% 168.60/168.40 [1018]~E(x10181,x10182)+E(f241(x10183,x10184,x10181,x10185,x10186),f241(x10183,x10184,x10182,x10185,x10186))
% 168.60/168.40 [1019]~E(x10191,x10192)+E(f241(x10193,x10194,x10195,x10191,x10196),f241(x10193,x10194,x10195,x10192,x10196))
% 168.60/168.40 [1020]~E(x10201,x10202)+E(f241(x10203,x10204,x10205,x10206,x10201),f241(x10203,x10204,x10205,x10206,x10202))
% 168.60/168.40 [1021]~E(x10211,x10212)+E(f654(x10211,x10213),f654(x10212,x10213))
% 168.60/168.40 [1022]~E(x10221,x10222)+E(f654(x10223,x10221),f654(x10223,x10222))
% 168.60/168.40 [1023]~E(x10231,x10232)+E(f798(x10231,x10233,x10234,x10235,x10236,x10237),f798(x10232,x10233,x10234,x10235,x10236,x10237))
% 168.60/168.40 [1024]~E(x10241,x10242)+E(f798(x10243,x10241,x10244,x10245,x10246,x10247),f798(x10243,x10242,x10244,x10245,x10246,x10247))
% 168.60/168.40 [1025]~E(x10251,x10252)+E(f798(x10253,x10254,x10251,x10255,x10256,x10257),f798(x10253,x10254,x10252,x10255,x10256,x10257))
% 168.60/168.40 [1026]~E(x10261,x10262)+E(f798(x10263,x10264,x10265,x10261,x10266,x10267),f798(x10263,x10264,x10265,x10262,x10266,x10267))
% 168.60/168.40 [1027]~E(x10271,x10272)+E(f798(x10273,x10274,x10275,x10276,x10271,x10277),f798(x10273,x10274,x10275,x10276,x10272,x10277))
% 168.60/168.40 [1028]~E(x10281,x10282)+E(f798(x10283,x10284,x10285,x10286,x10287,x10281),f798(x10283,x10284,x10285,x10286,x10287,x10282))
% 168.60/168.40 [1029]~E(x10291,x10292)+E(f716(x10291,x10293),f716(x10292,x10293))
% 168.60/168.40 [1030]~E(x10301,x10302)+E(f716(x10303,x10301),f716(x10303,x10302))
% 168.60/168.40 [1031]~E(x10311,x10312)+E(f703(x10311,x10313),f703(x10312,x10313))
% 168.60/168.40 [1032]~E(x10321,x10322)+E(f703(x10323,x10321),f703(x10323,x10322))
% 168.60/168.40 [1033]~E(x10331,x10332)+E(f462(x10331,x10333,x10334,x10335),f462(x10332,x10333,x10334,x10335))
% 168.60/168.40 [1034]~E(x10341,x10342)+E(f462(x10343,x10341,x10344,x10345),f462(x10343,x10342,x10344,x10345))
% 168.60/168.40 [1035]~E(x10351,x10352)+E(f462(x10353,x10354,x10351,x10355),f462(x10353,x10354,x10352,x10355))
% 168.60/168.40 [1036]~E(x10361,x10362)+E(f462(x10363,x10364,x10365,x10361),f462(x10363,x10364,x10365,x10362))
% 168.60/168.40 [1037]~E(x10371,x10372)+E(f440(x10371,x10373,x10374,x10375),f440(x10372,x10373,x10374,x10375))
% 168.60/168.40 [1038]~E(x10381,x10382)+E(f440(x10383,x10381,x10384,x10385),f440(x10383,x10382,x10384,x10385))
% 168.60/168.40 [1039]~E(x10391,x10392)+E(f440(x10393,x10394,x10391,x10395),f440(x10393,x10394,x10392,x10395))
% 168.60/168.40 [1040]~E(x10401,x10402)+E(f440(x10403,x10404,x10405,x10401),f440(x10403,x10404,x10405,x10402))
% 168.60/168.40 [1041]~E(x10411,x10412)+E(f635(x10411,x10413,x10414,x10415,x10416),f635(x10412,x10413,x10414,x10415,x10416))
% 168.60/168.40 [1042]~E(x10421,x10422)+E(f635(x10423,x10421,x10424,x10425,x10426),f635(x10423,x10422,x10424,x10425,x10426))
% 168.60/168.40 [1043]~E(x10431,x10432)+E(f635(x10433,x10434,x10431,x10435,x10436),f635(x10433,x10434,x10432,x10435,x10436))
% 168.60/168.40 [1044]~E(x10441,x10442)+E(f635(x10443,x10444,x10445,x10441,x10446),f635(x10443,x10444,x10445,x10442,x10446))
% 168.60/168.40 [1045]~E(x10451,x10452)+E(f635(x10453,x10454,x10455,x10456,x10451),f635(x10453,x10454,x10455,x10456,x10452))
% 168.60/168.40 [1046]~E(x10461,x10462)+E(f347(x10461,x10463),f347(x10462,x10463))
% 168.60/168.40 [1047]~E(x10471,x10472)+E(f347(x10473,x10471),f347(x10473,x10472))
% 168.60/168.40 [1048]~E(x10481,x10482)+E(f81(x10481),f81(x10482))
% 168.60/168.40 [1049]~E(x10491,x10492)+E(f762(x10491,x10493,x10494,x10495),f762(x10492,x10493,x10494,x10495))
% 168.60/168.40 [1050]~E(x10501,x10502)+E(f762(x10503,x10501,x10504,x10505),f762(x10503,x10502,x10504,x10505))
% 168.60/168.40 [1051]~E(x10511,x10512)+E(f762(x10513,x10514,x10511,x10515),f762(x10513,x10514,x10512,x10515))
% 168.60/168.40 [1052]~E(x10521,x10522)+E(f762(x10523,x10524,x10525,x10521),f762(x10523,x10524,x10525,x10522))
% 168.60/168.40 [1053]~E(x10531,x10532)+E(f613(x10531,x10533,x10534,x10535,x10536),f613(x10532,x10533,x10534,x10535,x10536))
% 168.60/168.40 [1054]~E(x10541,x10542)+E(f613(x10543,x10541,x10544,x10545,x10546),f613(x10543,x10542,x10544,x10545,x10546))
% 168.60/168.40 [1055]~E(x10551,x10552)+E(f613(x10553,x10554,x10551,x10555,x10556),f613(x10553,x10554,x10552,x10555,x10556))
% 168.60/168.40 [1056]~E(x10561,x10562)+E(f613(x10563,x10564,x10565,x10561,x10566),f613(x10563,x10564,x10565,x10562,x10566))
% 168.60/168.40 [1057]~E(x10571,x10572)+E(f613(x10573,x10574,x10575,x10576,x10571),f613(x10573,x10574,x10575,x10576,x10572))
% 168.60/168.40 [1058]~E(x10581,x10582)+E(f575(x10581,x10583,x10584),f575(x10582,x10583,x10584))
% 168.60/168.40 [1059]~E(x10591,x10592)+E(f575(x10593,x10591,x10594),f575(x10593,x10592,x10594))
% 168.60/168.40 [1060]~E(x10601,x10602)+E(f575(x10603,x10604,x10601),f575(x10603,x10604,x10602))
% 168.60/168.40 [1061]~E(x10611,x10612)+E(f458(x10611,x10613),f458(x10612,x10613))
% 168.60/168.40 [1062]~E(x10621,x10622)+E(f458(x10623,x10621),f458(x10623,x10622))
% 168.60/168.40 [1063]~E(x10631,x10632)+E(f179(x10631,x10633,x10634,x10635),f179(x10632,x10633,x10634,x10635))
% 168.60/168.40 [1064]~E(x10641,x10642)+E(f179(x10643,x10641,x10644,x10645),f179(x10643,x10642,x10644,x10645))
% 168.60/168.40 [1065]~E(x10651,x10652)+E(f179(x10653,x10654,x10651,x10655),f179(x10653,x10654,x10652,x10655))
% 168.60/168.40 [1066]~E(x10661,x10662)+E(f179(x10663,x10664,x10665,x10661),f179(x10663,x10664,x10665,x10662))
% 168.60/168.40 [1067]~E(x10671,x10672)+E(f714(x10671,x10673),f714(x10672,x10673))
% 168.60/168.40 [1068]~E(x10681,x10682)+E(f714(x10683,x10681),f714(x10683,x10682))
% 168.60/168.40 [1069]~E(x10691,x10692)+E(f704(x10691,x10693,x10694),f704(x10692,x10693,x10694))
% 168.60/168.40 [1070]~E(x10701,x10702)+E(f704(x10703,x10701,x10704),f704(x10703,x10702,x10704))
% 168.60/168.40 [1071]~E(x10711,x10712)+E(f704(x10713,x10714,x10711),f704(x10713,x10714,x10712))
% 168.60/168.40 [1072]~E(x10721,x10722)+E(f720(x10721,x10723,x10724),f720(x10722,x10723,x10724))
% 168.60/168.40 [1073]~E(x10731,x10732)+E(f720(x10733,x10731,x10734),f720(x10733,x10732,x10734))
% 168.60/168.40 [1074]~E(x10741,x10742)+E(f720(x10743,x10744,x10741),f720(x10743,x10744,x10742))
% 168.60/168.40 [1075]~E(x10751,x10752)+E(f818(x10751,x10753,x10754,x10755,x10756),f818(x10752,x10753,x10754,x10755,x10756))
% 168.60/168.40 [1076]~E(x10761,x10762)+E(f818(x10763,x10761,x10764,x10765,x10766),f818(x10763,x10762,x10764,x10765,x10766))
% 168.60/168.40 [1077]~E(x10771,x10772)+E(f818(x10773,x10774,x10771,x10775,x10776),f818(x10773,x10774,x10772,x10775,x10776))
% 168.60/168.40 [1078]~E(x10781,x10782)+E(f818(x10783,x10784,x10785,x10781,x10786),f818(x10783,x10784,x10785,x10782,x10786))
% 168.60/168.40 [1079]~E(x10791,x10792)+E(f818(x10793,x10794,x10795,x10796,x10791),f818(x10793,x10794,x10795,x10796,x10792))
% 168.60/168.40 [1080]~E(x10801,x10802)+E(f377(x10801,x10803,x10804),f377(x10802,x10803,x10804))
% 168.60/168.40 [1081]~E(x10811,x10812)+E(f377(x10813,x10811,x10814),f377(x10813,x10812,x10814))
% 168.60/168.40 [1082]~E(x10821,x10822)+E(f377(x10823,x10824,x10821),f377(x10823,x10824,x10822))
% 168.60/168.40 [1083]~E(x10831,x10832)+E(f718(x10831,x10833,x10834,x10835,x10836),f718(x10832,x10833,x10834,x10835,x10836))
% 168.60/168.40 [1084]~E(x10841,x10842)+E(f718(x10843,x10841,x10844,x10845,x10846),f718(x10843,x10842,x10844,x10845,x10846))
% 168.60/168.40 [1085]~E(x10851,x10852)+E(f718(x10853,x10854,x10851,x10855,x10856),f718(x10853,x10854,x10852,x10855,x10856))
% 168.60/168.40 [1086]~E(x10861,x10862)+E(f718(x10863,x10864,x10865,x10861,x10866),f718(x10863,x10864,x10865,x10862,x10866))
% 168.60/168.40 [1087]~E(x10871,x10872)+E(f718(x10873,x10874,x10875,x10876,x10871),f718(x10873,x10874,x10875,x10876,x10872))
% 168.60/168.40 [1088]~E(x10881,x10882)+E(f671(x10881,x10883,x10884),f671(x10882,x10883,x10884))
% 168.60/168.40 [1089]~E(x10891,x10892)+E(f671(x10893,x10891,x10894),f671(x10893,x10892,x10894))
% 168.60/168.40 [1090]~E(x10901,x10902)+E(f671(x10903,x10904,x10901),f671(x10903,x10904,x10902))
% 168.60/168.40 [1091]~E(x10911,x10912)+E(f583(x10911,x10913,x10914),f583(x10912,x10913,x10914))
% 168.60/168.40 [1092]~E(x10921,x10922)+E(f583(x10923,x10921,x10924),f583(x10923,x10922,x10924))
% 168.60/168.40 [1093]~E(x10931,x10932)+E(f583(x10933,x10934,x10931),f583(x10933,x10934,x10932))
% 168.60/168.40 [1094]~E(x10941,x10942)+E(f855(x10941,x10943,x10944,x10945,x10946),f855(x10942,x10943,x10944,x10945,x10946))
% 168.60/168.40 [1095]~E(x10951,x10952)+E(f855(x10953,x10951,x10954,x10955,x10956),f855(x10953,x10952,x10954,x10955,x10956))
% 168.60/168.40 [1096]~E(x10961,x10962)+E(f855(x10963,x10964,x10961,x10965,x10966),f855(x10963,x10964,x10962,x10965,x10966))
% 168.60/168.40 [1097]~E(x10971,x10972)+E(f855(x10973,x10974,x10975,x10971,x10976),f855(x10973,x10974,x10975,x10972,x10976))
% 168.60/168.40 [1098]~E(x10981,x10982)+E(f855(x10983,x10984,x10985,x10986,x10981),f855(x10983,x10984,x10985,x10986,x10982))
% 168.60/168.40 [1099]~E(x10991,x10992)+E(f338(x10991,x10993,x10994),f338(x10992,x10993,x10994))
% 168.60/168.40 [1100]~E(x11001,x11002)+E(f338(x11003,x11001,x11004),f338(x11003,x11002,x11004))
% 168.60/168.40 [1101]~E(x11011,x11012)+E(f338(x11013,x11014,x11011),f338(x11013,x11014,x11012))
% 168.60/168.40 [1102]~E(x11021,x11022)+E(f692(x11021,x11023),f692(x11022,x11023))
% 168.60/168.40 [1103]~E(x11031,x11032)+E(f692(x11033,x11031),f692(x11033,x11032))
% 168.60/168.40 [1104]~E(x11041,x11042)+E(f787(x11041,x11043),f787(x11042,x11043))
% 168.60/168.40 [1105]~E(x11051,x11052)+E(f787(x11053,x11051),f787(x11053,x11052))
% 168.60/168.40 [1106]~E(x11061,x11062)+E(f875(x11061,x11063,x11064,x11065,x11066,x11067,x11068),f875(x11062,x11063,x11064,x11065,x11066,x11067,x11068))
% 168.60/168.40 [1107]~E(x11071,x11072)+E(f875(x11073,x11071,x11074,x11075,x11076,x11077,x11078),f875(x11073,x11072,x11074,x11075,x11076,x11077,x11078))
% 168.60/168.40 [1108]~E(x11081,x11082)+E(f875(x11083,x11084,x11081,x11085,x11086,x11087,x11088),f875(x11083,x11084,x11082,x11085,x11086,x11087,x11088))
% 168.60/168.40 [1109]~E(x11091,x11092)+E(f875(x11093,x11094,x11095,x11091,x11096,x11097,x11098),f875(x11093,x11094,x11095,x11092,x11096,x11097,x11098))
% 168.60/168.40 [1110]~E(x11101,x11102)+E(f875(x11103,x11104,x11105,x11106,x11101,x11107,x11108),f875(x11103,x11104,x11105,x11106,x11102,x11107,x11108))
% 168.60/168.40 [1111]~E(x11111,x11112)+E(f875(x11113,x11114,x11115,x11116,x11117,x11111,x11118),f875(x11113,x11114,x11115,x11116,x11117,x11112,x11118))
% 168.60/168.40 [1112]~E(x11121,x11122)+E(f875(x11123,x11124,x11125,x11126,x11127,x11128,x11121),f875(x11123,x11124,x11125,x11126,x11127,x11128,x11122))
% 168.60/168.40 [1113]~E(x11131,x11132)+E(f533(x11131,x11133,x11134,x11135,x11136),f533(x11132,x11133,x11134,x11135,x11136))
% 168.60/168.40 [1114]~E(x11141,x11142)+E(f533(x11143,x11141,x11144,x11145,x11146),f533(x11143,x11142,x11144,x11145,x11146))
% 168.60/168.40 [1115]~E(x11151,x11152)+E(f533(x11153,x11154,x11151,x11155,x11156),f533(x11153,x11154,x11152,x11155,x11156))
% 168.60/168.40 [1116]~E(x11161,x11162)+E(f533(x11163,x11164,x11165,x11161,x11166),f533(x11163,x11164,x11165,x11162,x11166))
% 168.60/168.40 [1117]~E(x11171,x11172)+E(f533(x11173,x11174,x11175,x11176,x11171),f533(x11173,x11174,x11175,x11176,x11172))
% 168.60/168.40 [1118]~E(x11181,x11182)+E(f884(x11181,x11183,x11184,x11185),f884(x11182,x11183,x11184,x11185))
% 168.60/168.40 [1119]~E(x11191,x11192)+E(f884(x11193,x11191,x11194,x11195),f884(x11193,x11192,x11194,x11195))
% 168.60/168.40 [1120]~E(x11201,x11202)+E(f884(x11203,x11204,x11201,x11205),f884(x11203,x11204,x11202,x11205))
% 168.60/168.40 [1121]~E(x11211,x11212)+E(f884(x11213,x11214,x11215,x11211),f884(x11213,x11214,x11215,x11212))
% 168.60/168.40 [1122]~E(x11221,x11222)+E(f301(x11221,x11223,x11224,x11225),f301(x11222,x11223,x11224,x11225))
% 168.60/168.40 [1123]~E(x11231,x11232)+E(f301(x11233,x11231,x11234,x11235),f301(x11233,x11232,x11234,x11235))
% 168.60/168.40 [1124]~E(x11241,x11242)+E(f301(x11243,x11244,x11241,x11245),f301(x11243,x11244,x11242,x11245))
% 168.60/168.40 [1125]~E(x11251,x11252)+E(f301(x11253,x11254,x11255,x11251),f301(x11253,x11254,x11255,x11252))
% 168.60/168.40 [1126]~E(x11261,x11262)+E(f198(x11261,x11263,x11264,x11265),f198(x11262,x11263,x11264,x11265))
% 168.60/168.40 [1127]~E(x11271,x11272)+E(f198(x11273,x11271,x11274,x11275),f198(x11273,x11272,x11274,x11275))
% 168.60/168.40 [1128]~E(x11281,x11282)+E(f198(x11283,x11284,x11281,x11285),f198(x11283,x11284,x11282,x11285))
% 168.60/168.40 [1129]~E(x11291,x11292)+E(f198(x11293,x11294,x11295,x11291),f198(x11293,x11294,x11295,x11292))
% 168.60/168.40 [1130]~E(x11301,x11302)+E(f309(x11301,x11303,x11304),f309(x11302,x11303,x11304))
% 168.60/168.40 [1131]~E(x11311,x11312)+E(f309(x11313,x11311,x11314),f309(x11313,x11312,x11314))
% 168.60/168.40 [1132]~E(x11321,x11322)+E(f309(x11323,x11324,x11321),f309(x11323,x11324,x11322))
% 168.60/168.40 [1133]~E(x11331,x11332)+E(f412(x11331,x11333,x11334,x11335,x11336),f412(x11332,x11333,x11334,x11335,x11336))
% 168.60/168.40 [1134]~E(x11341,x11342)+E(f412(x11343,x11341,x11344,x11345,x11346),f412(x11343,x11342,x11344,x11345,x11346))
% 168.60/168.40 [1135]~E(x11351,x11352)+E(f412(x11353,x11354,x11351,x11355,x11356),f412(x11353,x11354,x11352,x11355,x11356))
% 168.60/168.40 [1136]~E(x11361,x11362)+E(f412(x11363,x11364,x11365,x11361,x11366),f412(x11363,x11364,x11365,x11362,x11366))
% 168.60/168.40 [1137]~E(x11371,x11372)+E(f412(x11373,x11374,x11375,x11376,x11371),f412(x11373,x11374,x11375,x11376,x11372))
% 168.60/168.40 [1138]~E(x11381,x11382)+E(f835(x11381,x11383,x11384,x11385,x11386,x11387),f835(x11382,x11383,x11384,x11385,x11386,x11387))
% 168.60/168.40 [1139]~E(x11391,x11392)+E(f835(x11393,x11391,x11394,x11395,x11396,x11397),f835(x11393,x11392,x11394,x11395,x11396,x11397))
% 168.60/168.40 [1140]~E(x11401,x11402)+E(f835(x11403,x11404,x11401,x11405,x11406,x11407),f835(x11403,x11404,x11402,x11405,x11406,x11407))
% 168.60/168.40 [1141]~E(x11411,x11412)+E(f835(x11413,x11414,x11415,x11411,x11416,x11417),f835(x11413,x11414,x11415,x11412,x11416,x11417))
% 168.60/168.40 [1142]~E(x11421,x11422)+E(f835(x11423,x11424,x11425,x11426,x11421,x11427),f835(x11423,x11424,x11425,x11426,x11422,x11427))
% 168.60/168.40 [1143]~E(x11431,x11432)+E(f835(x11433,x11434,x11435,x11436,x11437,x11431),f835(x11433,x11434,x11435,x11436,x11437,x11432))
% 168.60/168.40 [1144]~E(x11441,x11442)+E(f466(x11441),f466(x11442))
% 168.60/168.40 [1145]~E(x11451,x11452)+E(f183(x11451,x11453),f183(x11452,x11453))
% 168.60/168.40 [1146]~E(x11461,x11462)+E(f183(x11463,x11461),f183(x11463,x11462))
% 168.60/168.40 [1147]~E(x11471,x11472)+E(f441(x11471,x11473,x11474,x11475),f441(x11472,x11473,x11474,x11475))
% 168.60/168.40 [1148]~E(x11481,x11482)+E(f441(x11483,x11481,x11484,x11485),f441(x11483,x11482,x11484,x11485))
% 168.60/168.40 [1149]~E(x11491,x11492)+E(f441(x11493,x11494,x11491,x11495),f441(x11493,x11494,x11492,x11495))
% 168.60/168.40 [1150]~E(x11501,x11502)+E(f441(x11503,x11504,x11505,x11501),f441(x11503,x11504,x11505,x11502))
% 168.60/168.40 [1151]~E(x11511,x11512)+E(f726(x11511,x11513,x11514,x11515,x11516),f726(x11512,x11513,x11514,x11515,x11516))
% 168.60/168.40 [1152]~E(x11521,x11522)+E(f726(x11523,x11521,x11524,x11525,x11526),f726(x11523,x11522,x11524,x11525,x11526))
% 168.60/168.40 [1153]~E(x11531,x11532)+E(f726(x11533,x11534,x11531,x11535,x11536),f726(x11533,x11534,x11532,x11535,x11536))
% 168.60/168.40 [1154]~E(x11541,x11542)+E(f726(x11543,x11544,x11545,x11541,x11546),f726(x11543,x11544,x11545,x11542,x11546))
% 168.60/168.40 [1155]~E(x11551,x11552)+E(f726(x11553,x11554,x11555,x11556,x11551),f726(x11553,x11554,x11555,x11556,x11552))
% 168.60/168.40 [1156]~E(x11561,x11562)+E(f595(x11561,x11563),f595(x11562,x11563))
% 168.60/168.40 [1157]~E(x11571,x11572)+E(f595(x11573,x11571),f595(x11573,x11572))
% 168.60/168.40 [1158]~E(x11581,x11582)+E(f719(x11581,x11583),f719(x11582,x11583))
% 168.60/168.40 [1159]~E(x11591,x11592)+E(f719(x11593,x11591),f719(x11593,x11592))
% 168.60/168.40 [1160]~E(x11601,x11602)+E(f339(x11601,x11603,x11604),f339(x11602,x11603,x11604))
% 168.60/168.40 [1161]~E(x11611,x11612)+E(f339(x11613,x11611,x11614),f339(x11613,x11612,x11614))
% 168.60/168.40 [1162]~E(x11621,x11622)+E(f339(x11623,x11624,x11621),f339(x11623,x11624,x11622))
% 168.60/168.40 [1163]~E(x11631,x11632)+E(f190(x11631),f190(x11632))
% 168.60/168.40 [1164]~E(x11641,x11642)+E(f36(x11641),f36(x11642))
% 168.60/168.40 [1165]~E(x11651,x11652)+E(f435(x11651,x11653,x11654),f435(x11652,x11653,x11654))
% 168.60/168.40 [1166]~E(x11661,x11662)+E(f435(x11663,x11661,x11664),f435(x11663,x11662,x11664))
% 168.60/168.40 [1167]~E(x11671,x11672)+E(f435(x11673,x11674,x11671),f435(x11673,x11674,x11672))
% 168.60/168.40 [1168]~E(x11681,x11682)+E(f865(x11681,x11683,x11684),f865(x11682,x11683,x11684))
% 168.60/168.40 [1169]~E(x11691,x11692)+E(f865(x11693,x11691,x11694),f865(x11693,x11692,x11694))
% 168.60/168.40 [1170]~E(x11701,x11702)+E(f865(x11703,x11704,x11701),f865(x11703,x11704,x11702))
% 168.60/168.40 [1171]~E(x11711,x11712)+E(f550(x11711,x11713,x11714,x11715),f550(x11712,x11713,x11714,x11715))
% 168.60/168.40 [1172]~E(x11721,x11722)+E(f550(x11723,x11721,x11724,x11725),f550(x11723,x11722,x11724,x11725))
% 168.60/168.40 [1173]~E(x11731,x11732)+E(f550(x11733,x11734,x11731,x11735),f550(x11733,x11734,x11732,x11735))
% 168.60/168.40 [1174]~E(x11741,x11742)+E(f550(x11743,x11744,x11745,x11741),f550(x11743,x11744,x11745,x11742))
% 168.60/168.40 [1175]~E(x11751,x11752)+E(f761(x11751,x11753,x11754,x11755),f761(x11752,x11753,x11754,x11755))
% 168.60/168.40 [1176]~E(x11761,x11762)+E(f761(x11763,x11761,x11764,x11765),f761(x11763,x11762,x11764,x11765))
% 168.60/168.40 [1177]~E(x11771,x11772)+E(f761(x11773,x11774,x11771,x11775),f761(x11773,x11774,x11772,x11775))
% 168.60/168.40 [1178]~E(x11781,x11782)+E(f761(x11783,x11784,x11785,x11781),f761(x11783,x11784,x11785,x11782))
% 168.60/168.40 [1179]~E(x11791,x11792)+E(f858(x11791,x11793),f858(x11792,x11793))
% 168.60/168.40 [1180]~E(x11801,x11802)+E(f858(x11803,x11801),f858(x11803,x11802))
% 168.60/168.40 [1181]~E(x11811,x11812)+E(f364(x11811,x11813,x11814),f364(x11812,x11813,x11814))
% 168.60/168.40 [1182]~E(x11821,x11822)+E(f364(x11823,x11821,x11824),f364(x11823,x11822,x11824))
% 168.60/168.40 [1183]~E(x11831,x11832)+E(f364(x11833,x11834,x11831),f364(x11833,x11834,x11832))
% 168.60/168.40 [1184]~E(x11841,x11842)+E(f650(x11841,x11843,x11844,x11845),f650(x11842,x11843,x11844,x11845))
% 168.60/168.40 [1185]~E(x11851,x11852)+E(f650(x11853,x11851,x11854,x11855),f650(x11853,x11852,x11854,x11855))
% 168.60/168.40 [1186]~E(x11861,x11862)+E(f650(x11863,x11864,x11861,x11865),f650(x11863,x11864,x11862,x11865))
% 168.60/168.40 [1187]~E(x11871,x11872)+E(f650(x11873,x11874,x11875,x11871),f650(x11873,x11874,x11875,x11872))
% 168.60/168.40 [1188]~E(x11881,x11882)+E(f216(x11881,x11883),f216(x11882,x11883))
% 168.60/168.40 [1189]~E(x11891,x11892)+E(f216(x11893,x11891),f216(x11893,x11892))
% 168.60/168.40 [1190]~E(x11901,x11902)+E(f673(x11901,x11903,x11904),f673(x11902,x11903,x11904))
% 168.60/168.40 [1191]~E(x11911,x11912)+E(f673(x11913,x11911,x11914),f673(x11913,x11912,x11914))
% 168.60/168.40 [1192]~E(x11921,x11922)+E(f673(x11923,x11924,x11921),f673(x11923,x11924,x11922))
% 168.60/168.40 [1193]~E(x11931,x11932)+E(f145(x11931,x11933,x11934,x11935),f145(x11932,x11933,x11934,x11935))
% 168.60/168.40 [1194]~E(x11941,x11942)+E(f145(x11943,x11941,x11944,x11945),f145(x11943,x11942,x11944,x11945))
% 168.60/168.40 [1195]~E(x11951,x11952)+E(f145(x11953,x11954,x11951,x11955),f145(x11953,x11954,x11952,x11955))
% 168.60/168.40 [1196]~E(x11961,x11962)+E(f145(x11963,x11964,x11965,x11961),f145(x11963,x11964,x11965,x11962))
% 168.60/168.40 [1197]~E(x11971,x11972)+E(f52(x11971,x11973,x11974,x11975),f52(x11972,x11973,x11974,x11975))
% 168.60/168.40 [1198]~E(x11981,x11982)+E(f52(x11983,x11981,x11984,x11985),f52(x11983,x11982,x11984,x11985))
% 168.60/168.40 [1199]~E(x11991,x11992)+E(f52(x11993,x11994,x11991,x11995),f52(x11993,x11994,x11992,x11995))
% 168.60/168.40 [1200]~E(x12001,x12002)+E(f52(x12003,x12004,x12005,x12001),f52(x12003,x12004,x12005,x12002))
% 168.60/168.40 [1201]~E(x12011,x12012)+E(f797(x12011,x12013,x12014,x12015,x12016,x12017),f797(x12012,x12013,x12014,x12015,x12016,x12017))
% 168.60/168.40 [1202]~E(x12021,x12022)+E(f797(x12023,x12021,x12024,x12025,x12026,x12027),f797(x12023,x12022,x12024,x12025,x12026,x12027))
% 168.60/168.40 [1203]~E(x12031,x12032)+E(f797(x12033,x12034,x12031,x12035,x12036,x12037),f797(x12033,x12034,x12032,x12035,x12036,x12037))
% 168.60/168.40 [1204]~E(x12041,x12042)+E(f797(x12043,x12044,x12045,x12041,x12046,x12047),f797(x12043,x12044,x12045,x12042,x12046,x12047))
% 168.60/168.40 [1205]~E(x12051,x12052)+E(f797(x12053,x12054,x12055,x12056,x12051,x12057),f797(x12053,x12054,x12055,x12056,x12052,x12057))
% 168.60/168.40 [1206]~E(x12061,x12062)+E(f797(x12063,x12064,x12065,x12066,x12067,x12061),f797(x12063,x12064,x12065,x12066,x12067,x12062))
% 168.60/168.40 [1207]~E(x12071,x12072)+E(f489(x12071,x12073,x12074),f489(x12072,x12073,x12074))
% 168.60/168.40 [1208]~E(x12081,x12082)+E(f489(x12083,x12081,x12084),f489(x12083,x12082,x12084))
% 168.60/168.40 [1209]~E(x12091,x12092)+E(f489(x12093,x12094,x12091),f489(x12093,x12094,x12092))
% 168.60/168.40 [1210]~E(x12101,x12102)+E(f549(x12101,x12103,x12104,x12105),f549(x12102,x12103,x12104,x12105))
% 168.60/168.40 [1211]~E(x12111,x12112)+E(f549(x12113,x12111,x12114,x12115),f549(x12113,x12112,x12114,x12115))
% 168.60/168.40 [1212]~E(x12121,x12122)+E(f549(x12123,x12124,x12121,x12125),f549(x12123,x12124,x12122,x12125))
% 168.60/168.40 [1213]~E(x12131,x12132)+E(f549(x12133,x12134,x12135,x12131),f549(x12133,x12134,x12135,x12132))
% 168.60/168.40 [1214]~E(x12141,x12142)+E(f188(x12141,x12143),f188(x12142,x12143))
% 168.60/168.40 [1215]~E(x12151,x12152)+E(f188(x12153,x12151),f188(x12153,x12152))
% 168.60/168.40 [1216]~E(x12161,x12162)+E(f498(x12161,x12163,x12164,x12165,x12166,x12167,x12168,x12169),f498(x12162,x12163,x12164,x12165,x12166,x12167,x12168,x12169))
% 168.60/168.40 [1217]~E(x12171,x12172)+E(f498(x12173,x12171,x12174,x12175,x12176,x12177,x12178,x12179),f498(x12173,x12172,x12174,x12175,x12176,x12177,x12178,x12179))
% 168.60/168.40 [1218]~E(x12181,x12182)+E(f498(x12183,x12184,x12181,x12185,x12186,x12187,x12188,x12189),f498(x12183,x12184,x12182,x12185,x12186,x12187,x12188,x12189))
% 168.60/168.40 [1219]~E(x12191,x12192)+E(f498(x12193,x12194,x12195,x12191,x12196,x12197,x12198,x12199),f498(x12193,x12194,x12195,x12192,x12196,x12197,x12198,x12199))
% 168.60/168.40 [1220]~E(x12201,x12202)+E(f498(x12203,x12204,x12205,x12206,x12201,x12207,x12208,x12209),f498(x12203,x12204,x12205,x12206,x12202,x12207,x12208,x12209))
% 168.60/168.40 [1221]~E(x12211,x12212)+E(f498(x12213,x12214,x12215,x12216,x12217,x12211,x12218,x12219),f498(x12213,x12214,x12215,x12216,x12217,x12212,x12218,x12219))
% 168.60/168.40 [1222]~E(x12221,x12222)+E(f498(x12223,x12224,x12225,x12226,x12227,x12228,x12221,x12229),f498(x12223,x12224,x12225,x12226,x12227,x12228,x12222,x12229))
% 168.60/168.40 [1223]~E(x12231,x12232)+E(f498(x12233,x12234,x12235,x12236,x12237,x12238,x12239,x12231),f498(x12233,x12234,x12235,x12236,x12237,x12238,x12239,x12232))
% 168.60/168.40 [1224]~E(x12241,x12242)+E(f286(x12241,x12243,x12244),f286(x12242,x12243,x12244))
% 168.60/168.40 [1225]~E(x12251,x12252)+E(f286(x12253,x12251,x12254),f286(x12253,x12252,x12254))
% 168.60/168.40 [1226]~E(x12261,x12262)+E(f286(x12263,x12264,x12261),f286(x12263,x12264,x12262))
% 168.60/168.40 [1227]~E(x12271,x12272)+E(f827(x12271,x12273,x12274,x12275,x12276,x12277,x12278,x12279),f827(x12272,x12273,x12274,x12275,x12276,x12277,x12278,x12279))
% 168.60/168.40 [1228]~E(x12281,x12282)+E(f827(x12283,x12281,x12284,x12285,x12286,x12287,x12288,x12289),f827(x12283,x12282,x12284,x12285,x12286,x12287,x12288,x12289))
% 168.60/168.40 [1229]~E(x12291,x12292)+E(f827(x12293,x12294,x12291,x12295,x12296,x12297,x12298,x12299),f827(x12293,x12294,x12292,x12295,x12296,x12297,x12298,x12299))
% 168.60/168.40 [1230]~E(x12301,x12302)+E(f827(x12303,x12304,x12305,x12301,x12306,x12307,x12308,x12309),f827(x12303,x12304,x12305,x12302,x12306,x12307,x12308,x12309))
% 168.60/168.40 [1231]~E(x12311,x12312)+E(f827(x12313,x12314,x12315,x12316,x12311,x12317,x12318,x12319),f827(x12313,x12314,x12315,x12316,x12312,x12317,x12318,x12319))
% 168.60/168.40 [1232]~E(x12321,x12322)+E(f827(x12323,x12324,x12325,x12326,x12327,x12321,x12328,x12329),f827(x12323,x12324,x12325,x12326,x12327,x12322,x12328,x12329))
% 168.60/168.40 [1233]~E(x12331,x12332)+E(f827(x12333,x12334,x12335,x12336,x12337,x12338,x12331,x12339),f827(x12333,x12334,x12335,x12336,x12337,x12338,x12332,x12339))
% 168.60/168.40 [1234]~E(x12341,x12342)+E(f827(x12343,x12344,x12345,x12346,x12347,x12348,x12349,x12341),f827(x12343,x12344,x12345,x12346,x12347,x12348,x12349,x12342))
% 168.60/168.40 [1235]~E(x12351,x12352)+E(f578(x12351,x12353,x12354,x12355,x12356,x12357,x12358,x12359),f578(x12352,x12353,x12354,x12355,x12356,x12357,x12358,x12359))
% 168.60/168.40 [1236]~E(x12361,x12362)+E(f578(x12363,x12361,x12364,x12365,x12366,x12367,x12368,x12369),f578(x12363,x12362,x12364,x12365,x12366,x12367,x12368,x12369))
% 168.60/168.40 [1237]~E(x12371,x12372)+E(f578(x12373,x12374,x12371,x12375,x12376,x12377,x12378,x12379),f578(x12373,x12374,x12372,x12375,x12376,x12377,x12378,x12379))
% 168.60/168.40 [1238]~E(x12381,x12382)+E(f578(x12383,x12384,x12385,x12381,x12386,x12387,x12388,x12389),f578(x12383,x12384,x12385,x12382,x12386,x12387,x12388,x12389))
% 168.60/168.40 [1239]~E(x12391,x12392)+E(f578(x12393,x12394,x12395,x12396,x12391,x12397,x12398,x12399),f578(x12393,x12394,x12395,x12396,x12392,x12397,x12398,x12399))
% 168.60/168.40 [1240]~E(x12401,x12402)+E(f578(x12403,x12404,x12405,x12406,x12407,x12401,x12408,x12409),f578(x12403,x12404,x12405,x12406,x12407,x12402,x12408,x12409))
% 168.60/168.40 [1241]~E(x12411,x12412)+E(f578(x12413,x12414,x12415,x12416,x12417,x12418,x12411,x12419),f578(x12413,x12414,x12415,x12416,x12417,x12418,x12412,x12419))
% 168.60/168.40 [1242]~E(x12421,x12422)+E(f578(x12423,x12424,x12425,x12426,x12427,x12428,x12429,x12421),f578(x12423,x12424,x12425,x12426,x12427,x12428,x12429,x12422))
% 168.60/168.40 [1243]~E(x12431,x12432)+E(f374(x12431,x12433,x12434),f374(x12432,x12433,x12434))
% 168.60/168.40 [1244]~E(x12441,x12442)+E(f374(x12443,x12441,x12444),f374(x12443,x12442,x12444))
% 168.60/168.40 [1245]~E(x12451,x12452)+E(f374(x12453,x12454,x12451),f374(x12453,x12454,x12452))
% 168.60/168.40 [1246]~E(x12461,x12462)+E(f779(x12461,x12463,x12464,x12465),f779(x12462,x12463,x12464,x12465))
% 168.60/168.40 [1247]~E(x12471,x12472)+E(f779(x12473,x12471,x12474,x12475),f779(x12473,x12472,x12474,x12475))
% 168.60/168.40 [1248]~E(x12481,x12482)+E(f779(x12483,x12484,x12481,x12485),f779(x12483,x12484,x12482,x12485))
% 168.60/168.40 [1249]~E(x12491,x12492)+E(f779(x12493,x12494,x12495,x12491),f779(x12493,x12494,x12495,x12492))
% 168.60/168.40 [1250]~E(x12501,x12502)+E(f367(x12501,x12503,x12504),f367(x12502,x12503,x12504))
% 168.60/168.40 [1251]~E(x12511,x12512)+E(f367(x12513,x12511,x12514),f367(x12513,x12512,x12514))
% 168.60/168.40 [1252]~E(x12521,x12522)+E(f367(x12523,x12524,x12521),f367(x12523,x12524,x12522))
% 168.60/168.40 [1253]~E(x12531,x12532)+E(f400(x12531,x12533,x12534,x12535),f400(x12532,x12533,x12534,x12535))
% 168.60/168.40 [1254]~E(x12541,x12542)+E(f400(x12543,x12541,x12544,x12545),f400(x12543,x12542,x12544,x12545))
% 168.60/168.40 [1255]~E(x12551,x12552)+E(f400(x12553,x12554,x12551,x12555),f400(x12553,x12554,x12552,x12555))
% 168.60/168.40 [1256]~E(x12561,x12562)+E(f400(x12563,x12564,x12565,x12561),f400(x12563,x12564,x12565,x12562))
% 168.60/168.40 [1257]~E(x12571,x12572)+E(f288(x12571,x12573,x12574,x12575,x12576),f288(x12572,x12573,x12574,x12575,x12576))
% 168.60/168.40 [1258]~E(x12581,x12582)+E(f288(x12583,x12581,x12584,x12585,x12586),f288(x12583,x12582,x12584,x12585,x12586))
% 168.60/168.40 [1259]~E(x12591,x12592)+E(f288(x12593,x12594,x12591,x12595,x12596),f288(x12593,x12594,x12592,x12595,x12596))
% 168.60/168.40 [1260]~E(x12601,x12602)+E(f288(x12603,x12604,x12605,x12601,x12606),f288(x12603,x12604,x12605,x12602,x12606))
% 168.60/168.40 [1261]~E(x12611,x12612)+E(f288(x12613,x12614,x12615,x12616,x12611),f288(x12613,x12614,x12615,x12616,x12612))
% 168.60/168.40 [1262]~E(x12621,x12622)+E(f175(x12621),f175(x12622))
% 168.60/168.40 [1263]~E(x12631,x12632)+E(f425(x12631,x12633,x12634,x12635,x12636),f425(x12632,x12633,x12634,x12635,x12636))
% 168.60/168.40 [1264]~E(x12641,x12642)+E(f425(x12643,x12641,x12644,x12645,x12646),f425(x12643,x12642,x12644,x12645,x12646))
% 168.60/168.40 [1265]~E(x12651,x12652)+E(f425(x12653,x12654,x12651,x12655,x12656),f425(x12653,x12654,x12652,x12655,x12656))
% 168.60/168.40 [1266]~E(x12661,x12662)+E(f425(x12663,x12664,x12665,x12661,x12666),f425(x12663,x12664,x12665,x12662,x12666))
% 168.60/168.40 [1267]~E(x12671,x12672)+E(f425(x12673,x12674,x12675,x12676,x12671),f425(x12673,x12674,x12675,x12676,x12672))
% 168.60/168.40 [1268]~E(x12681,x12682)+E(f490(x12681,x12683,x12684,x12685),f490(x12682,x12683,x12684,x12685))
% 168.60/168.40 [1269]~E(x12691,x12692)+E(f490(x12693,x12691,x12694,x12695),f490(x12693,x12692,x12694,x12695))
% 168.60/168.40 [1270]~E(x12701,x12702)+E(f490(x12703,x12704,x12701,x12705),f490(x12703,x12704,x12702,x12705))
% 168.60/168.40 [1271]~E(x12711,x12712)+E(f490(x12713,x12714,x12715,x12711),f490(x12713,x12714,x12715,x12712))
% 168.60/168.40 [1272]~E(x12721,x12722)+E(f469(x12721,x12723),f469(x12722,x12723))
% 168.60/168.40 [1273]~E(x12731,x12732)+E(f469(x12733,x12731),f469(x12733,x12732))
% 168.60/168.40 [1274]~E(x12741,x12742)+E(f874(x12741,x12743,x12744),f874(x12742,x12743,x12744))
% 168.60/168.40 [1275]~E(x12751,x12752)+E(f874(x12753,x12751,x12754),f874(x12753,x12752,x12754))
% 168.60/168.40 [1276]~E(x12761,x12762)+E(f874(x12763,x12764,x12761),f874(x12763,x12764,x12762))
% 168.60/168.40 [1277]~E(x12771,x12772)+E(f672(x12771,x12773,x12774),f672(x12772,x12773,x12774))
% 168.60/168.40 [1278]~E(x12781,x12782)+E(f672(x12783,x12781,x12784),f672(x12783,x12782,x12784))
% 168.60/168.40 [1279]~E(x12791,x12792)+E(f672(x12793,x12794,x12791),f672(x12793,x12794,x12792))
% 168.60/168.40 [1280]~E(x12801,x12802)+E(f659(x12801,x12803,x12804),f659(x12802,x12803,x12804))
% 168.60/168.40 [1281]~E(x12811,x12812)+E(f659(x12813,x12811,x12814),f659(x12813,x12812,x12814))
% 168.60/168.40 [1282]~E(x12821,x12822)+E(f659(x12823,x12824,x12821),f659(x12823,x12824,x12822))
% 168.60/168.40 [1283]~E(x12831,x12832)+E(f505(x12831,x12833,x12834),f505(x12832,x12833,x12834))
% 168.60/168.40 [1284]~E(x12841,x12842)+E(f505(x12843,x12841,x12844),f505(x12843,x12842,x12844))
% 168.60/168.40 [1285]~E(x12851,x12852)+E(f505(x12853,x12854,x12851),f505(x12853,x12854,x12852))
% 168.60/168.40 [1286]~E(x12861,x12862)+E(f813(x12861,x12863,x12864,x12865),f813(x12862,x12863,x12864,x12865))
% 168.60/168.40 [1287]~E(x12871,x12872)+E(f813(x12873,x12871,x12874,x12875),f813(x12873,x12872,x12874,x12875))
% 168.60/168.40 [1288]~E(x12881,x12882)+E(f813(x12883,x12884,x12881,x12885),f813(x12883,x12884,x12882,x12885))
% 168.60/168.40 [1289]~E(x12891,x12892)+E(f813(x12893,x12894,x12895,x12891),f813(x12893,x12894,x12895,x12892))
% 168.60/168.40 [1290]~E(x12901,x12902)+E(f734(x12901,x12903,x12904),f734(x12902,x12903,x12904))
% 168.60/168.40 [1291]~E(x12911,x12912)+E(f734(x12913,x12911,x12914),f734(x12913,x12912,x12914))
% 168.60/168.40 [1292]~E(x12921,x12922)+E(f734(x12923,x12924,x12921),f734(x12923,x12924,x12922))
% 168.60/168.40 [1293]~E(x12931,x12932)+E(f794(x12931,x12933,x12934,x12935,x12936),f794(x12932,x12933,x12934,x12935,x12936))
% 168.60/168.40 [1294]~E(x12941,x12942)+E(f794(x12943,x12941,x12944,x12945,x12946),f794(x12943,x12942,x12944,x12945,x12946))
% 168.60/168.40 [1295]~E(x12951,x12952)+E(f794(x12953,x12954,x12951,x12955,x12956),f794(x12953,x12954,x12952,x12955,x12956))
% 168.60/168.40 [1296]~E(x12961,x12962)+E(f794(x12963,x12964,x12965,x12961,x12966),f794(x12963,x12964,x12965,x12962,x12966))
% 168.60/168.40 [1297]~E(x12971,x12972)+E(f794(x12973,x12974,x12975,x12976,x12971),f794(x12973,x12974,x12975,x12976,x12972))
% 168.60/168.40 [1298]~E(x12981,x12982)+E(f591(x12981,x12983,x12984),f591(x12982,x12983,x12984))
% 168.60/168.40 [1299]~E(x12991,x12992)+E(f591(x12993,x12991,x12994),f591(x12993,x12992,x12994))
% 168.60/168.40 [1300]~E(x13001,x13002)+E(f591(x13003,x13004,x13001),f591(x13003,x13004,x13002))
% 168.60/168.40 [1301]~E(x13011,x13012)+E(f638(x13011,x13013,x13014,x13015),f638(x13012,x13013,x13014,x13015))
% 168.60/168.40 [1302]~E(x13021,x13022)+E(f638(x13023,x13021,x13024,x13025),f638(x13023,x13022,x13024,x13025))
% 168.60/168.40 [1303]~E(x13031,x13032)+E(f638(x13033,x13034,x13031,x13035),f638(x13033,x13034,x13032,x13035))
% 168.60/168.40 [1304]~E(x13041,x13042)+E(f638(x13043,x13044,x13045,x13041),f638(x13043,x13044,x13045,x13042))
% 168.60/168.40 [1305]~E(x13051,x13052)+E(f737(x13051,x13053,x13054),f737(x13052,x13053,x13054))
% 168.60/168.40 [1306]~E(x13061,x13062)+E(f737(x13063,x13061,x13064),f737(x13063,x13062,x13064))
% 168.60/168.40 [1307]~E(x13071,x13072)+E(f737(x13073,x13074,x13071),f737(x13073,x13074,x13072))
% 168.60/168.40 [1308]~E(x13081,x13082)+E(f776(x13081,x13083,x13084,x13085),f776(x13082,x13083,x13084,x13085))
% 168.60/168.40 [1309]~E(x13091,x13092)+E(f776(x13093,x13091,x13094,x13095),f776(x13093,x13092,x13094,x13095))
% 168.60/168.40 [1310]~E(x13101,x13102)+E(f776(x13103,x13104,x13101,x13105),f776(x13103,x13104,x13102,x13105))
% 168.60/168.40 [1311]~E(x13111,x13112)+E(f776(x13113,x13114,x13115,x13111),f776(x13113,x13114,x13115,x13112))
% 168.60/168.40 [1312]~E(x13121,x13122)+E(f383(x13121,x13123,x13124),f383(x13122,x13123,x13124))
% 168.60/168.40 [1313]~E(x13131,x13132)+E(f383(x13133,x13131,x13134),f383(x13133,x13132,x13134))
% 168.60/168.40 [1314]~E(x13141,x13142)+E(f383(x13143,x13144,x13141),f383(x13143,x13144,x13142))
% 168.60/168.40 [1315]~E(x13151,x13152)+E(f675(x13151,x13153,x13154,x13155,x13156),f675(x13152,x13153,x13154,x13155,x13156))
% 168.60/168.40 [1316]~E(x13161,x13162)+E(f675(x13163,x13161,x13164,x13165,x13166),f675(x13163,x13162,x13164,x13165,x13166))
% 168.60/168.40 [1317]~E(x13171,x13172)+E(f675(x13173,x13174,x13171,x13175,x13176),f675(x13173,x13174,x13172,x13175,x13176))
% 168.60/168.40 [1318]~E(x13181,x13182)+E(f675(x13183,x13184,x13185,x13181,x13186),f675(x13183,x13184,x13185,x13182,x13186))
% 168.60/168.40 [1319]~E(x13191,x13192)+E(f675(x13193,x13194,x13195,x13196,x13191),f675(x13193,x13194,x13195,x13196,x13192))
% 168.60/168.40 [1320]~E(x13201,x13202)+E(f609(x13201,x13203,x13204),f609(x13202,x13203,x13204))
% 168.60/168.40 [1321]~E(x13211,x13212)+E(f609(x13213,x13211,x13214),f609(x13213,x13212,x13214))
% 168.60/168.40 [1322]~E(x13221,x13222)+E(f609(x13223,x13224,x13221),f609(x13223,x13224,x13222))
% 168.60/168.40 [1323]~E(x13231,x13232)+E(f709(x13231,x13233),f709(x13232,x13233))
% 168.60/168.40 [1324]~E(x13241,x13242)+E(f709(x13243,x13241),f709(x13243,x13242))
% 168.60/168.40 [1325]~E(x13251,x13252)+E(f46(x13251,x13253),f46(x13252,x13253))
% 168.60/168.40 [1326]~E(x13261,x13262)+E(f46(x13263,x13261),f46(x13263,x13262))
% 168.60/168.40 [1327]~E(x13271,x13272)+E(f705(x13271,x13273,x13274,x13275),f705(x13272,x13273,x13274,x13275))
% 168.60/168.40 [1328]~E(x13281,x13282)+E(f705(x13283,x13281,x13284,x13285),f705(x13283,x13282,x13284,x13285))
% 168.60/168.40 [1329]~E(x13291,x13292)+E(f705(x13293,x13294,x13291,x13295),f705(x13293,x13294,x13292,x13295))
% 168.60/168.40 [1330]~E(x13301,x13302)+E(f705(x13303,x13304,x13305,x13301),f705(x13303,x13304,x13305,x13302))
% 168.60/168.40 [1331]~E(x13311,x13312)+E(f867(x13311,x13313,x13314,x13315,x13316),f867(x13312,x13313,x13314,x13315,x13316))
% 168.60/168.40 [1332]~E(x13321,x13322)+E(f867(x13323,x13321,x13324,x13325,x13326),f867(x13323,x13322,x13324,x13325,x13326))
% 168.60/168.40 [1333]~E(x13331,x13332)+E(f867(x13333,x13334,x13331,x13335,x13336),f867(x13333,x13334,x13332,x13335,x13336))
% 168.60/168.40 [1334]~E(x13341,x13342)+E(f867(x13343,x13344,x13345,x13341,x13346),f867(x13343,x13344,x13345,x13342,x13346))
% 168.60/168.40 [1335]~E(x13351,x13352)+E(f867(x13353,x13354,x13355,x13356,x13351),f867(x13353,x13354,x13355,x13356,x13352))
% 168.60/168.40 [1336]~E(x13361,x13362)+E(f461(x13361,x13363,x13364,x13365),f461(x13362,x13363,x13364,x13365))
% 168.60/168.40 [1337]~E(x13371,x13372)+E(f461(x13373,x13371,x13374,x13375),f461(x13373,x13372,x13374,x13375))
% 168.60/168.40 [1338]~E(x13381,x13382)+E(f461(x13383,x13384,x13381,x13385),f461(x13383,x13384,x13382,x13385))
% 168.60/168.40 [1339]~E(x13391,x13392)+E(f461(x13393,x13394,x13395,x13391),f461(x13393,x13394,x13395,x13392))
% 168.60/168.40 [1340]~E(x13401,x13402)+E(f833(x13401,x13403,x13404,x13405,x13406,x13407),f833(x13402,x13403,x13404,x13405,x13406,x13407))
% 168.60/168.40 [1341]~E(x13411,x13412)+E(f833(x13413,x13411,x13414,x13415,x13416,x13417),f833(x13413,x13412,x13414,x13415,x13416,x13417))
% 168.60/168.40 [1342]~E(x13421,x13422)+E(f833(x13423,x13424,x13421,x13425,x13426,x13427),f833(x13423,x13424,x13422,x13425,x13426,x13427))
% 168.60/168.40 [1343]~E(x13431,x13432)+E(f833(x13433,x13434,x13435,x13431,x13436,x13437),f833(x13433,x13434,x13435,x13432,x13436,x13437))
% 168.60/168.40 [1344]~E(x13441,x13442)+E(f833(x13443,x13444,x13445,x13446,x13441,x13447),f833(x13443,x13444,x13445,x13446,x13442,x13447))
% 168.60/168.40 [1345]~E(x13451,x13452)+E(f833(x13453,x13454,x13455,x13456,x13457,x13451),f833(x13453,x13454,x13455,x13456,x13457,x13452))
% 168.60/168.40 [1346]~E(x13461,x13462)+E(f460(x13461,x13463),f460(x13462,x13463))
% 168.60/168.40 [1347]~E(x13471,x13472)+E(f460(x13473,x13471),f460(x13473,x13472))
% 168.60/168.40 [1348]~E(x13481,x13482)+E(f523(x13481,x13483,x13484),f523(x13482,x13483,x13484))
% 168.60/168.40 [1349]~E(x13491,x13492)+E(f523(x13493,x13491,x13494),f523(x13493,x13492,x13494))
% 168.60/168.40 [1350]~E(x13501,x13502)+E(f523(x13503,x13504,x13501),f523(x13503,x13504,x13502))
% 168.60/168.40 [1351]~E(x13511,x13512)+E(f534(x13511,x13513,x13514,x13515,x13516),f534(x13512,x13513,x13514,x13515,x13516))
% 168.60/168.40 [1352]~E(x13521,x13522)+E(f534(x13523,x13521,x13524,x13525,x13526),f534(x13523,x13522,x13524,x13525,x13526))
% 168.60/168.40 [1353]~E(x13531,x13532)+E(f534(x13533,x13534,x13531,x13535,x13536),f534(x13533,x13534,x13532,x13535,x13536))
% 168.60/168.40 [1354]~E(x13541,x13542)+E(f534(x13543,x13544,x13545,x13541,x13546),f534(x13543,x13544,x13545,x13542,x13546))
% 168.60/168.40 [1355]~E(x13551,x13552)+E(f534(x13553,x13554,x13555,x13556,x13551),f534(x13553,x13554,x13555,x13556,x13552))
% 168.60/168.40 [1356]~E(x13561,x13562)+E(f752(x13561,x13563,x13564,x13565),f752(x13562,x13563,x13564,x13565))
% 168.60/168.40 [1357]~E(x13571,x13572)+E(f752(x13573,x13571,x13574,x13575),f752(x13573,x13572,x13574,x13575))
% 168.60/168.40 [1358]~E(x13581,x13582)+E(f752(x13583,x13584,x13581,x13585),f752(x13583,x13584,x13582,x13585))
% 168.60/168.40 [1359]~E(x13591,x13592)+E(f752(x13593,x13594,x13595,x13591),f752(x13593,x13594,x13595,x13592))
% 168.60/168.40 [1360]~E(x13601,x13602)+E(f284(x13601,x13603,x13604),f284(x13602,x13603,x13604))
% 168.60/168.40 [1361]~E(x13611,x13612)+E(f284(x13613,x13611,x13614),f284(x13613,x13612,x13614))
% 168.60/168.40 [1362]~E(x13621,x13622)+E(f284(x13623,x13624,x13621),f284(x13623,x13624,x13622))
% 168.60/168.40 [1363]~E(x13631,x13632)+E(f802(x13631,x13633,x13634),f802(x13632,x13633,x13634))
% 168.60/168.40 [1364]~E(x13641,x13642)+E(f802(x13643,x13641,x13644),f802(x13643,x13642,x13644))
% 168.60/168.40 [1365]~E(x13651,x13652)+E(f802(x13653,x13654,x13651),f802(x13653,x13654,x13652))
% 168.60/168.40 [1366]~E(x13661,x13662)+E(f614(x13661,x13663,x13664,x13665),f614(x13662,x13663,x13664,x13665))
% 168.60/168.40 [1367]~E(x13671,x13672)+E(f614(x13673,x13671,x13674,x13675),f614(x13673,x13672,x13674,x13675))
% 168.60/168.40 [1368]~E(x13681,x13682)+E(f614(x13683,x13684,x13681,x13685),f614(x13683,x13684,x13682,x13685))
% 168.60/168.40 [1369]~E(x13691,x13692)+E(f614(x13693,x13694,x13695,x13691),f614(x13693,x13694,x13695,x13692))
% 168.60/168.40 [1370]~E(x13701,x13702)+E(f531(x13701,x13703,x13704,x13705,x13706,x13707),f531(x13702,x13703,x13704,x13705,x13706,x13707))
% 168.60/168.40 [1371]~E(x13711,x13712)+E(f531(x13713,x13711,x13714,x13715,x13716,x13717),f531(x13713,x13712,x13714,x13715,x13716,x13717))
% 168.60/168.40 [1372]~E(x13721,x13722)+E(f531(x13723,x13724,x13721,x13725,x13726,x13727),f531(x13723,x13724,x13722,x13725,x13726,x13727))
% 168.60/168.40 [1373]~E(x13731,x13732)+E(f531(x13733,x13734,x13735,x13731,x13736,x13737),f531(x13733,x13734,x13735,x13732,x13736,x13737))
% 168.60/168.40 [1374]~E(x13741,x13742)+E(f531(x13743,x13744,x13745,x13746,x13741,x13747),f531(x13743,x13744,x13745,x13746,x13742,x13747))
% 168.60/168.40 [1375]~E(x13751,x13752)+E(f531(x13753,x13754,x13755,x13756,x13757,x13751),f531(x13753,x13754,x13755,x13756,x13757,x13752))
% 168.60/168.40 [1376]~E(x13761,x13762)+E(f619(x13761,x13763,x13764,x13765,x13766),f619(x13762,x13763,x13764,x13765,x13766))
% 168.60/168.40 [1377]~E(x13771,x13772)+E(f619(x13773,x13771,x13774,x13775,x13776),f619(x13773,x13772,x13774,x13775,x13776))
% 168.60/168.40 [1378]~E(x13781,x13782)+E(f619(x13783,x13784,x13781,x13785,x13786),f619(x13783,x13784,x13782,x13785,x13786))
% 168.60/168.40 [1379]~E(x13791,x13792)+E(f619(x13793,x13794,x13795,x13791,x13796),f619(x13793,x13794,x13795,x13792,x13796))
% 168.60/168.40 [1380]~E(x13801,x13802)+E(f619(x13803,x13804,x13805,x13806,x13801),f619(x13803,x13804,x13805,x13806,x13802))
% 168.60/168.40 [1381]~E(x13811,x13812)+E(f526(x13811,x13813,x13814,x13815),f526(x13812,x13813,x13814,x13815))
% 168.60/168.40 [1382]~E(x13821,x13822)+E(f526(x13823,x13821,x13824,x13825),f526(x13823,x13822,x13824,x13825))
% 168.60/168.40 [1383]~E(x13831,x13832)+E(f526(x13833,x13834,x13831,x13835),f526(x13833,x13834,x13832,x13835))
% 168.60/168.40 [1384]~E(x13841,x13842)+E(f526(x13843,x13844,x13845,x13841),f526(x13843,x13844,x13845,x13842))
% 168.60/168.40 [1385]~E(x13851,x13852)+E(f112(x13851),f112(x13852))
% 168.60/168.40 [1386]~E(x13861,x13862)+E(f119(x13861,x13863,x13864,x13865),f119(x13862,x13863,x13864,x13865))
% 168.60/168.40 [1387]~E(x13871,x13872)+E(f119(x13873,x13871,x13874,x13875),f119(x13873,x13872,x13874,x13875))
% 168.60/168.40 [1388]~E(x13881,x13882)+E(f119(x13883,x13884,x13881,x13885),f119(x13883,x13884,x13882,x13885))
% 168.60/168.40 [1389]~E(x13891,x13892)+E(f119(x13893,x13894,x13895,x13891),f119(x13893,x13894,x13895,x13892))
% 168.60/168.40 [1390]~E(x13901,x13902)+E(f68(x13901,x13903,x13904,x13905,x13906),f68(x13902,x13903,x13904,x13905,x13906))
% 168.60/168.40 [1391]~E(x13911,x13912)+E(f68(x13913,x13911,x13914,x13915,x13916),f68(x13913,x13912,x13914,x13915,x13916))
% 168.60/168.40 [1392]~E(x13921,x13922)+E(f68(x13923,x13924,x13921,x13925,x13926),f68(x13923,x13924,x13922,x13925,x13926))
% 168.60/168.40 [1393]~E(x13931,x13932)+E(f68(x13933,x13934,x13935,x13931,x13936),f68(x13933,x13934,x13935,x13932,x13936))
% 168.60/168.40 [1394]~E(x13941,x13942)+E(f68(x13943,x13944,x13945,x13946,x13941),f68(x13943,x13944,x13945,x13946,x13942))
% 168.60/168.40 [1395]~E(x13951,x13952)+E(f321(x13951),f321(x13952))
% 168.60/168.40 [1396]~E(x13961,x13962)+E(f711(x13961,x13963,x13964,x13965),f711(x13962,x13963,x13964,x13965))
% 168.60/168.40 [1397]~E(x13971,x13972)+E(f711(x13973,x13971,x13974,x13975),f711(x13973,x13972,x13974,x13975))
% 168.60/168.40 [1398]~E(x13981,x13982)+E(f711(x13983,x13984,x13981,x13985),f711(x13983,x13984,x13982,x13985))
% 168.60/168.40 [1399]~E(x13991,x13992)+E(f711(x13993,x13994,x13995,x13991),f711(x13993,x13994,x13995,x13992))
% 168.60/168.40 [1400]~E(x14001,x14002)+E(f361(x14001,x14003,x14004),f361(x14002,x14003,x14004))
% 168.60/168.40 [1401]~E(x14011,x14012)+E(f361(x14013,x14011,x14014),f361(x14013,x14012,x14014))
% 168.60/168.40 [1402]~E(x14021,x14022)+E(f361(x14023,x14024,x14021),f361(x14023,x14024,x14022))
% 168.60/168.40 [1403]~E(x14031,x14032)+E(f205(x14031,x14033),f205(x14032,x14033))
% 168.60/168.40 [1404]~E(x14041,x14042)+E(f205(x14043,x14041),f205(x14043,x14042))
% 168.60/168.40 [1405]~E(x14051,x14052)+E(f629(x14051,x14053,x14054,x14055,x14056,x14057),f629(x14052,x14053,x14054,x14055,x14056,x14057))
% 168.60/168.40 [1406]~E(x14061,x14062)+E(f629(x14063,x14061,x14064,x14065,x14066,x14067),f629(x14063,x14062,x14064,x14065,x14066,x14067))
% 168.60/168.40 [1407]~E(x14071,x14072)+E(f629(x14073,x14074,x14071,x14075,x14076,x14077),f629(x14073,x14074,x14072,x14075,x14076,x14077))
% 168.60/168.40 [1408]~E(x14081,x14082)+E(f629(x14083,x14084,x14085,x14081,x14086,x14087),f629(x14083,x14084,x14085,x14082,x14086,x14087))
% 168.60/168.40 [1409]~E(x14091,x14092)+E(f629(x14093,x14094,x14095,x14096,x14091,x14097),f629(x14093,x14094,x14095,x14096,x14092,x14097))
% 168.60/168.40 [1410]~E(x14101,x14102)+E(f629(x14103,x14104,x14105,x14106,x14107,x14101),f629(x14103,x14104,x14105,x14106,x14107,x14102))
% 168.60/168.40 [1411]~E(x14111,x14112)+E(f727(x14111,x14113,x14114,x14115,x14116),f727(x14112,x14113,x14114,x14115,x14116))
% 168.60/168.40 [1412]~E(x14121,x14122)+E(f727(x14123,x14121,x14124,x14125,x14126),f727(x14123,x14122,x14124,x14125,x14126))
% 168.60/168.40 [1413]~E(x14131,x14132)+E(f727(x14133,x14134,x14131,x14135,x14136),f727(x14133,x14134,x14132,x14135,x14136))
% 168.60/168.40 [1414]~E(x14141,x14142)+E(f727(x14143,x14144,x14145,x14141,x14146),f727(x14143,x14144,x14145,x14142,x14146))
% 168.60/168.40 [1415]~E(x14151,x14152)+E(f727(x14153,x14154,x14155,x14156,x14151),f727(x14153,x14154,x14155,x14156,x14152))
% 168.60/168.40 [1416]~E(x14161,x14162)+E(f484(x14161,x14163,x14164,x14165),f484(x14162,x14163,x14164,x14165))
% 168.60/168.40 [1417]~E(x14171,x14172)+E(f484(x14173,x14171,x14174,x14175),f484(x14173,x14172,x14174,x14175))
% 168.60/168.40 [1418]~E(x14181,x14182)+E(f484(x14183,x14184,x14181,x14185),f484(x14183,x14184,x14182,x14185))
% 168.60/168.40 [1419]~E(x14191,x14192)+E(f484(x14193,x14194,x14195,x14191),f484(x14193,x14194,x14195,x14192))
% 168.60/168.40 [1420]~E(x14201,x14202)+E(f398(x14201),f398(x14202))
% 168.60/168.40 [1421]~E(x14211,x14212)+E(f700(x14211,x14213,x14214),f700(x14212,x14213,x14214))
% 168.60/168.40 [1422]~E(x14221,x14222)+E(f700(x14223,x14221,x14224),f700(x14223,x14222,x14224))
% 168.60/168.40 [1423]~E(x14231,x14232)+E(f700(x14233,x14234,x14231),f700(x14233,x14234,x14232))
% 168.60/168.40 [1424]~E(x14241,x14242)+E(f521(x14241,x14243,x14244,x14245,x14246),f521(x14242,x14243,x14244,x14245,x14246))
% 168.60/168.40 [1425]~E(x14251,x14252)+E(f521(x14253,x14251,x14254,x14255,x14256),f521(x14253,x14252,x14254,x14255,x14256))
% 168.60/168.40 [1426]~E(x14261,x14262)+E(f521(x14263,x14264,x14261,x14265,x14266),f521(x14263,x14264,x14262,x14265,x14266))
% 168.60/168.40 [1427]~E(x14271,x14272)+E(f521(x14273,x14274,x14275,x14271,x14276),f521(x14273,x14274,x14275,x14272,x14276))
% 168.60/168.40 [1428]~E(x14281,x14282)+E(f521(x14283,x14284,x14285,x14286,x14281),f521(x14283,x14284,x14285,x14286,x14282))
% 168.60/168.40 [1429]~E(x14291,x14292)+E(f724(x14291,x14293,x14294,x14295,x14296),f724(x14292,x14293,x14294,x14295,x14296))
% 168.60/168.40 [1430]~E(x14301,x14302)+E(f724(x14303,x14301,x14304,x14305,x14306),f724(x14303,x14302,x14304,x14305,x14306))
% 168.60/168.40 [1431]~E(x14311,x14312)+E(f724(x14313,x14314,x14311,x14315,x14316),f724(x14313,x14314,x14312,x14315,x14316))
% 168.60/168.40 [1432]~E(x14321,x14322)+E(f724(x14323,x14324,x14325,x14321,x14326),f724(x14323,x14324,x14325,x14322,x14326))
% 168.60/168.40 [1433]~E(x14331,x14332)+E(f724(x14333,x14334,x14335,x14336,x14331),f724(x14333,x14334,x14335,x14336,x14332))
% 168.60/168.40 [1434]~E(x14341,x14342)+E(f480(x14341,x14343,x14344,x14345),f480(x14342,x14343,x14344,x14345))
% 168.60/168.40 [1435]~E(x14351,x14352)+E(f480(x14353,x14351,x14354,x14355),f480(x14353,x14352,x14354,x14355))
% 168.60/168.40 [1436]~E(x14361,x14362)+E(f480(x14363,x14364,x14361,x14365),f480(x14363,x14364,x14362,x14365))
% 168.60/168.40 [1437]~E(x14371,x14372)+E(f480(x14373,x14374,x14375,x14371),f480(x14373,x14374,x14375,x14372))
% 168.60/168.40 [1438]~E(x14381,x14382)+E(f207(x14381,x14383),f207(x14382,x14383))
% 168.60/168.40 [1439]~E(x14391,x14392)+E(f207(x14393,x14391),f207(x14393,x14392))
% 168.60/168.40 [1440]~E(x14401,x14402)+E(f625(x14401,x14403),f625(x14402,x14403))
% 168.60/168.40 [1441]~E(x14411,x14412)+E(f625(x14413,x14411),f625(x14413,x14412))
% 168.60/168.40 [1442]~E(x14421,x14422)+E(f755(x14421,x14423,x14424),f755(x14422,x14423,x14424))
% 168.60/168.40 [1443]~E(x14431,x14432)+E(f755(x14433,x14431,x14434),f755(x14433,x14432,x14434))
% 168.60/168.40 [1444]~E(x14441,x14442)+E(f755(x14443,x14444,x14441),f755(x14443,x14444,x14442))
% 168.60/168.40 [1445]~E(x14451,x14452)+E(f506(x14451,x14453,x14454),f506(x14452,x14453,x14454))
% 168.60/168.40 [1446]~E(x14461,x14462)+E(f506(x14463,x14461,x14464),f506(x14463,x14462,x14464))
% 168.60/168.40 [1447]~E(x14471,x14472)+E(f506(x14473,x14474,x14471),f506(x14473,x14474,x14472))
% 168.60/168.40 [1448]~E(x14481,x14482)+E(f530(x14481,x14483,x14484,x14485,x14486,x14487),f530(x14482,x14483,x14484,x14485,x14486,x14487))
% 168.60/168.40 [1449]~E(x14491,x14492)+E(f530(x14493,x14491,x14494,x14495,x14496,x14497),f530(x14493,x14492,x14494,x14495,x14496,x14497))
% 168.60/168.40 [1450]~E(x14501,x14502)+E(f530(x14503,x14504,x14501,x14505,x14506,x14507),f530(x14503,x14504,x14502,x14505,x14506,x14507))
% 168.60/168.40 [1451]~E(x14511,x14512)+E(f530(x14513,x14514,x14515,x14511,x14516,x14517),f530(x14513,x14514,x14515,x14512,x14516,x14517))
% 168.60/168.40 [1452]~E(x14521,x14522)+E(f530(x14523,x14524,x14525,x14526,x14521,x14527),f530(x14523,x14524,x14525,x14526,x14522,x14527))
% 168.60/168.40 [1453]~E(x14531,x14532)+E(f530(x14533,x14534,x14535,x14536,x14537,x14531),f530(x14533,x14534,x14535,x14536,x14537,x14532))
% 168.60/168.40 [1454]~E(x14541,x14542)+E(f823(x14541,x14543,x14544,x14545,x14546,x14547,x14548,x14549),f823(x14542,x14543,x14544,x14545,x14546,x14547,x14548,x14549))
% 168.60/168.40 [1455]~E(x14551,x14552)+E(f823(x14553,x14551,x14554,x14555,x14556,x14557,x14558,x14559),f823(x14553,x14552,x14554,x14555,x14556,x14557,x14558,x14559))
% 168.60/168.40 [1456]~E(x14561,x14562)+E(f823(x14563,x14564,x14561,x14565,x14566,x14567,x14568,x14569),f823(x14563,x14564,x14562,x14565,x14566,x14567,x14568,x14569))
% 168.60/168.40 [1457]~E(x14571,x14572)+E(f823(x14573,x14574,x14575,x14571,x14576,x14577,x14578,x14579),f823(x14573,x14574,x14575,x14572,x14576,x14577,x14578,x14579))
% 168.60/168.40 [1458]~E(x14581,x14582)+E(f823(x14583,x14584,x14585,x14586,x14581,x14587,x14588,x14589),f823(x14583,x14584,x14585,x14586,x14582,x14587,x14588,x14589))
% 168.60/168.40 [1459]~E(x14591,x14592)+E(f823(x14593,x14594,x14595,x14596,x14597,x14591,x14598,x14599),f823(x14593,x14594,x14595,x14596,x14597,x14592,x14598,x14599))
% 168.60/168.40 [1460]~E(x14601,x14602)+E(f823(x14603,x14604,x14605,x14606,x14607,x14608,x14601,x14609),f823(x14603,x14604,x14605,x14606,x14607,x14608,x14602,x14609))
% 168.60/168.40 [1461]~E(x14611,x14612)+E(f823(x14613,x14614,x14615,x14616,x14617,x14618,x14619,x14611),f823(x14613,x14614,x14615,x14616,x14617,x14618,x14619,x14612))
% 168.60/168.40 [1462]~E(x14621,x14622)+E(f590(x14621,x14623,x14624,x14625,x14626),f590(x14622,x14623,x14624,x14625,x14626))
% 168.60/168.40 [1463]~E(x14631,x14632)+E(f590(x14633,x14631,x14634,x14635,x14636),f590(x14633,x14632,x14634,x14635,x14636))
% 168.60/168.40 [1464]~E(x14641,x14642)+E(f590(x14643,x14644,x14641,x14645,x14646),f590(x14643,x14644,x14642,x14645,x14646))
% 168.60/168.40 [1465]~E(x14651,x14652)+E(f590(x14653,x14654,x14655,x14651,x14656),f590(x14653,x14654,x14655,x14652,x14656))
% 168.60/168.40 [1466]~E(x14661,x14662)+E(f590(x14663,x14664,x14665,x14666,x14661),f590(x14663,x14664,x14665,x14666,x14662))
% 168.60/168.40 [1467]~E(x14671,x14672)+E(f472(x14671,x14673,x14674),f472(x14672,x14673,x14674))
% 168.60/168.40 [1468]~E(x14681,x14682)+E(f472(x14683,x14681,x14684),f472(x14683,x14682,x14684))
% 168.60/168.40 [1469]~E(x14691,x14692)+E(f472(x14693,x14694,x14691),f472(x14693,x14694,x14692))
% 168.60/168.40 [1470]~E(x14701,x14702)+E(f885(x14701,x14703,x14704,x14705,x14706,x14707),f885(x14702,x14703,x14704,x14705,x14706,x14707))
% 168.60/168.40 [1471]~E(x14711,x14712)+E(f885(x14713,x14711,x14714,x14715,x14716,x14717),f885(x14713,x14712,x14714,x14715,x14716,x14717))
% 168.60/168.40 [1472]~E(x14721,x14722)+E(f885(x14723,x14724,x14721,x14725,x14726,x14727),f885(x14723,x14724,x14722,x14725,x14726,x14727))
% 168.60/168.40 [1473]~E(x14731,x14732)+E(f885(x14733,x14734,x14735,x14731,x14736,x14737),f885(x14733,x14734,x14735,x14732,x14736,x14737))
% 168.60/168.40 [1474]~E(x14741,x14742)+E(f885(x14743,x14744,x14745,x14746,x14741,x14747),f885(x14743,x14744,x14745,x14746,x14742,x14747))
% 168.60/168.40 [1475]~E(x14751,x14752)+E(f885(x14753,x14754,x14755,x14756,x14757,x14751),f885(x14753,x14754,x14755,x14756,x14757,x14752))
% 168.60/168.40 [1476]~E(x14761,x14762)+E(f663(x14761,x14763,x14764,x14765,x14766),f663(x14762,x14763,x14764,x14765,x14766))
% 168.60/168.40 [1477]~E(x14771,x14772)+E(f663(x14773,x14771,x14774,x14775,x14776),f663(x14773,x14772,x14774,x14775,x14776))
% 168.60/168.40 [1478]~E(x14781,x14782)+E(f663(x14783,x14784,x14781,x14785,x14786),f663(x14783,x14784,x14782,x14785,x14786))
% 168.60/168.40 [1479]~E(x14791,x14792)+E(f663(x14793,x14794,x14795,x14791,x14796),f663(x14793,x14794,x14795,x14792,x14796))
% 168.60/168.40 [1480]~E(x14801,x14802)+E(f663(x14803,x14804,x14805,x14806,x14801),f663(x14803,x14804,x14805,x14806,x14802))
% 168.60/168.40 [1481]~E(x14811,x14812)+E(f795(x14811,x14813,x14814,x14815,x14816),f795(x14812,x14813,x14814,x14815,x14816))
% 168.60/168.40 [1482]~E(x14821,x14822)+E(f795(x14823,x14821,x14824,x14825,x14826),f795(x14823,x14822,x14824,x14825,x14826))
% 168.60/168.40 [1483]~E(x14831,x14832)+E(f795(x14833,x14834,x14831,x14835,x14836),f795(x14833,x14834,x14832,x14835,x14836))
% 168.60/168.40 [1484]~E(x14841,x14842)+E(f795(x14843,x14844,x14845,x14841,x14846),f795(x14843,x14844,x14845,x14842,x14846))
% 168.60/168.40 [1485]~E(x14851,x14852)+E(f795(x14853,x14854,x14855,x14856,x14851),f795(x14853,x14854,x14855,x14856,x14852))
% 168.60/168.40 [1486]~E(x14861,x14862)+E(f554(x14861,x14863,x14864),f554(x14862,x14863,x14864))
% 168.60/168.40 [1487]~E(x14871,x14872)+E(f554(x14873,x14871,x14874),f554(x14873,x14872,x14874))
% 168.60/168.40 [1488]~E(x14881,x14882)+E(f554(x14883,x14884,x14881),f554(x14883,x14884,x14882))
% 168.60/168.40 [1489]~E(x14891,x14892)+E(f785(x14891,x14893),f785(x14892,x14893))
% 168.60/168.40 [1490]~E(x14901,x14902)+E(f785(x14903,x14901),f785(x14903,x14902))
% 168.60/168.40 [1491]~E(x14911,x14912)+E(f452(x14911,x14913,x14914,x14915),f452(x14912,x14913,x14914,x14915))
% 168.60/168.40 [1492]~E(x14921,x14922)+E(f452(x14923,x14921,x14924,x14925),f452(x14923,x14922,x14924,x14925))
% 168.60/168.40 [1493]~E(x14931,x14932)+E(f452(x14933,x14934,x14931,x14935),f452(x14933,x14934,x14932,x14935))
% 168.60/168.40 [1494]~E(x14941,x14942)+E(f452(x14943,x14944,x14945,x14941),f452(x14943,x14944,x14945,x14942))
% 168.60/168.40 [1495]~E(x14951,x14952)+E(f564(x14951,x14953),f564(x14952,x14953))
% 168.60/168.40 [1496]~E(x14961,x14962)+E(f564(x14963,x14961),f564(x14963,x14962))
% 168.60/168.40 [1497]~E(x14971,x14972)+E(f234(x14971,x14973,x14974,x14975,x14976,x14977),f234(x14972,x14973,x14974,x14975,x14976,x14977))
% 168.60/168.40 [1498]~E(x14981,x14982)+E(f234(x14983,x14981,x14984,x14985,x14986,x14987),f234(x14983,x14982,x14984,x14985,x14986,x14987))
% 168.60/168.40 [1499]~E(x14991,x14992)+E(f234(x14993,x14994,x14991,x14995,x14996,x14997),f234(x14993,x14994,x14992,x14995,x14996,x14997))
% 168.60/168.40 [1500]~E(x15001,x15002)+E(f234(x15003,x15004,x15005,x15001,x15006,x15007),f234(x15003,x15004,x15005,x15002,x15006,x15007))
% 168.60/168.40 [1501]~E(x15011,x15012)+E(f234(x15013,x15014,x15015,x15016,x15011,x15017),f234(x15013,x15014,x15015,x15016,x15012,x15017))
% 168.60/168.40 [1502]~E(x15021,x15022)+E(f234(x15023,x15024,x15025,x15026,x15027,x15021),f234(x15023,x15024,x15025,x15026,x15027,x15022))
% 168.60/168.40 [1503]~E(x15031,x15032)+E(f541(x15031,x15033,x15034,x15035),f541(x15032,x15033,x15034,x15035))
% 168.60/168.40 [1504]~E(x15041,x15042)+E(f541(x15043,x15041,x15044,x15045),f541(x15043,x15042,x15044,x15045))
% 168.60/168.40 [1505]~E(x15051,x15052)+E(f541(x15053,x15054,x15051,x15055),f541(x15053,x15054,x15052,x15055))
% 168.60/168.40 [1506]~E(x15061,x15062)+E(f541(x15063,x15064,x15065,x15061),f541(x15063,x15064,x15065,x15062))
% 168.60/168.40 [1507]~E(x15071,x15072)+E(f432(x15071),f432(x15072))
% 168.60/168.40 [1508]~E(x15081,x15082)+E(f621(x15081,x15083,x15084,x15085,x15086),f621(x15082,x15083,x15084,x15085,x15086))
% 168.60/168.40 [1509]~E(x15091,x15092)+E(f621(x15093,x15091,x15094,x15095,x15096),f621(x15093,x15092,x15094,x15095,x15096))
% 168.60/168.40 [1510]~E(x15101,x15102)+E(f621(x15103,x15104,x15101,x15105,x15106),f621(x15103,x15104,x15102,x15105,x15106))
% 168.60/168.40 [1511]~E(x15111,x15112)+E(f621(x15113,x15114,x15115,x15111,x15116),f621(x15113,x15114,x15115,x15112,x15116))
% 168.60/168.40 [1512]~E(x15121,x15122)+E(f621(x15123,x15124,x15125,x15126,x15121),f621(x15123,x15124,x15125,x15126,x15122))
% 168.60/168.40 [1513]~E(x15131,x15132)+E(f219(x15131,x15133,x15134),f219(x15132,x15133,x15134))
% 168.60/168.40 [1514]~E(x15141,x15142)+E(f219(x15143,x15141,x15144),f219(x15143,x15142,x15144))
% 168.60/168.40 [1515]~E(x15151,x15152)+E(f219(x15153,x15154,x15151),f219(x15153,x15154,x15152))
% 168.60/168.40 [1516]~E(x15161,x15162)+E(f518(x15161,x15163,x15164,x15165,x15166),f518(x15162,x15163,x15164,x15165,x15166))
% 168.60/168.40 [1517]~E(x15171,x15172)+E(f518(x15173,x15171,x15174,x15175,x15176),f518(x15173,x15172,x15174,x15175,x15176))
% 168.60/168.40 [1518]~E(x15181,x15182)+E(f518(x15183,x15184,x15181,x15185,x15186),f518(x15183,x15184,x15182,x15185,x15186))
% 168.60/168.40 [1519]~E(x15191,x15192)+E(f518(x15193,x15194,x15195,x15191,x15196),f518(x15193,x15194,x15195,x15192,x15196))
% 168.60/168.40 [1520]~E(x15201,x15202)+E(f518(x15203,x15204,x15205,x15206,x15201),f518(x15203,x15204,x15205,x15206,x15202))
% 168.60/168.40 [1521]~E(x15211,x15212)+E(f640(x15211,x15213,x15214),f640(x15212,x15213,x15214))
% 168.60/168.40 [1522]~E(x15221,x15222)+E(f640(x15223,x15221,x15224),f640(x15223,x15222,x15224))
% 168.60/168.40 [1523]~E(x15231,x15232)+E(f640(x15233,x15234,x15231),f640(x15233,x15234,x15232))
% 168.60/168.40 [1524]~E(x15241,x15242)+E(f60(x15241,x15243,x15244),f60(x15242,x15243,x15244))
% 168.60/168.40 [1525]~E(x15251,x15252)+E(f60(x15253,x15251,x15254),f60(x15253,x15252,x15254))
% 168.60/168.40 [1526]~E(x15261,x15262)+E(f60(x15263,x15264,x15261),f60(x15263,x15264,x15262))
% 168.60/168.40 [1527]~E(x15271,x15272)+E(f695(x15271,x15273,x15274),f695(x15272,x15273,x15274))
% 168.60/168.40 [1528]~E(x15281,x15282)+E(f695(x15283,x15281,x15284),f695(x15283,x15282,x15284))
% 168.60/168.40 [1529]~E(x15291,x15292)+E(f695(x15293,x15294,x15291),f695(x15293,x15294,x15292))
% 168.60/168.40 [1530]~E(x15301,x15302)+E(f107(x15301,x15303,x15304),f107(x15302,x15303,x15304))
% 168.60/168.40 [1531]~E(x15311,x15312)+E(f107(x15313,x15311,x15314),f107(x15313,x15312,x15314))
% 168.60/168.40 [1532]~E(x15321,x15322)+E(f107(x15323,x15324,x15321),f107(x15323,x15324,x15322))
% 168.60/168.40 [1533]~E(x15331,x15332)+E(f649(x15331,x15333,x15334),f649(x15332,x15333,x15334))
% 168.60/168.40 [1534]~E(x15341,x15342)+E(f649(x15343,x15341,x15344),f649(x15343,x15342,x15344))
% 168.60/168.40 [1535]~E(x15351,x15352)+E(f649(x15353,x15354,x15351),f649(x15353,x15354,x15352))
% 168.60/168.40 [1536]~E(x15361,x15362)+E(f129(x15361,x15363,x15364),f129(x15362,x15363,x15364))
% 168.60/168.40 [1537]~E(x15371,x15372)+E(f129(x15373,x15371,x15374),f129(x15373,x15372,x15374))
% 168.60/168.40 [1538]~E(x15381,x15382)+E(f129(x15383,x15384,x15381),f129(x15383,x15384,x15382))
% 168.60/168.40 [1539]~E(x15391,x15392)+E(f688(x15391,x15393),f688(x15392,x15393))
% 168.60/168.40 [1540]~E(x15401,x15402)+E(f688(x15403,x15401),f688(x15403,x15402))
% 168.60/168.40 [1541]~E(x15411,x15412)+E(f442(x15411,x15413,x15414,x15415),f442(x15412,x15413,x15414,x15415))
% 168.60/168.40 [1542]~E(x15421,x15422)+E(f442(x15423,x15421,x15424,x15425),f442(x15423,x15422,x15424,x15425))
% 168.60/168.40 [1543]~E(x15431,x15432)+E(f442(x15433,x15434,x15431,x15435),f442(x15433,x15434,x15432,x15435))
% 168.60/168.40 [1544]~E(x15441,x15442)+E(f442(x15443,x15444,x15445,x15441),f442(x15443,x15444,x15445,x15442))
% 168.60/168.40 [1545]~E(x15451,x15452)+E(f603(x15451,x15453,x15454),f603(x15452,x15453,x15454))
% 168.60/168.40 [1546]~E(x15461,x15462)+E(f603(x15463,x15461,x15464),f603(x15463,x15462,x15464))
% 168.60/168.40 [1547]~E(x15471,x15472)+E(f603(x15473,x15474,x15471),f603(x15473,x15474,x15472))
% 168.60/168.40 [1548]~E(x15481,x15482)+E(f427(x15481,x15483,x15484,x15485,x15486),f427(x15482,x15483,x15484,x15485,x15486))
% 168.60/168.40 [1549]~E(x15491,x15492)+E(f427(x15493,x15491,x15494,x15495,x15496),f427(x15493,x15492,x15494,x15495,x15496))
% 168.60/168.40 [1550]~E(x15501,x15502)+E(f427(x15503,x15504,x15501,x15505,x15506),f427(x15503,x15504,x15502,x15505,x15506))
% 168.60/168.40 [1551]~E(x15511,x15512)+E(f427(x15513,x15514,x15515,x15511,x15516),f427(x15513,x15514,x15515,x15512,x15516))
% 168.60/168.40 [1552]~E(x15521,x15522)+E(f427(x15523,x15524,x15525,x15526,x15521),f427(x15523,x15524,x15525,x15526,x15522))
% 168.60/168.40 [1553]~E(x15531,x15532)+E(f646(x15531,x15533,x15534,x15535),f646(x15532,x15533,x15534,x15535))
% 168.60/168.40 [1554]~E(x15541,x15542)+E(f646(x15543,x15541,x15544,x15545),f646(x15543,x15542,x15544,x15545))
% 168.60/168.40 [1555]~E(x15551,x15552)+E(f646(x15553,x15554,x15551,x15555),f646(x15553,x15554,x15552,x15555))
% 168.60/168.40 [1556]~E(x15561,x15562)+E(f646(x15563,x15564,x15565,x15561),f646(x15563,x15564,x15565,x15562))
% 168.60/168.40 [1557]~E(x15571,x15572)+E(f882(x15571,x15573,x15574),f882(x15572,x15573,x15574))
% 168.60/168.40 [1558]~E(x15581,x15582)+E(f882(x15583,x15581,x15584),f882(x15583,x15582,x15584))
% 168.60/168.40 [1559]~E(x15591,x15592)+E(f882(x15593,x15594,x15591),f882(x15593,x15594,x15592))
% 168.60/168.40 [1560]~E(x15601,x15602)+E(f836(x15601,x15603,x15604,x15605,x15606,x15607),f836(x15602,x15603,x15604,x15605,x15606,x15607))
% 168.60/168.40 [1561]~E(x15611,x15612)+E(f836(x15613,x15611,x15614,x15615,x15616,x15617),f836(x15613,x15612,x15614,x15615,x15616,x15617))
% 168.60/168.40 [1562]~E(x15621,x15622)+E(f836(x15623,x15624,x15621,x15625,x15626,x15627),f836(x15623,x15624,x15622,x15625,x15626,x15627))
% 168.60/168.40 [1563]~E(x15631,x15632)+E(f836(x15633,x15634,x15635,x15631,x15636,x15637),f836(x15633,x15634,x15635,x15632,x15636,x15637))
% 168.60/168.40 [1564]~E(x15641,x15642)+E(f836(x15643,x15644,x15645,x15646,x15641,x15647),f836(x15643,x15644,x15645,x15646,x15642,x15647))
% 168.60/168.40 [1565]~E(x15651,x15652)+E(f836(x15653,x15654,x15655,x15656,x15657,x15651),f836(x15653,x15654,x15655,x15656,x15657,x15652))
% 168.60/168.40 [1566]~E(x15661,x15662)+E(f565(x15661,x15663,x15664),f565(x15662,x15663,x15664))
% 168.60/168.40 [1567]~E(x15671,x15672)+E(f565(x15673,x15671,x15674),f565(x15673,x15672,x15674))
% 168.60/168.40 [1568]~E(x15681,x15682)+E(f565(x15683,x15684,x15681),f565(x15683,x15684,x15682))
% 168.60/168.40 [1569]~E(x15691,x15692)+E(f468(x15691,x15693),f468(x15692,x15693))
% 168.60/168.40 [1570]~E(x15701,x15702)+E(f468(x15703,x15701),f468(x15703,x15702))
% 168.60/168.40 [1571]~E(x15711,x15712)+E(f390(x15711,x15713,x15714),f390(x15712,x15713,x15714))
% 168.60/168.40 [1572]~E(x15721,x15722)+E(f390(x15723,x15721,x15724),f390(x15723,x15722,x15724))
% 168.60/168.40 [1573]~E(x15731,x15732)+E(f390(x15733,x15734,x15731),f390(x15733,x15734,x15732))
% 168.60/168.40 [1574]~E(x15741,x15742)+E(f39(x15741,x15743),f39(x15742,x15743))
% 168.60/168.40 [1575]~E(x15751,x15752)+E(f39(x15753,x15751),f39(x15753,x15752))
% 168.60/168.40 [1576]~E(x15761,x15762)+E(f497(x15761,x15763),f497(x15762,x15763))
% 168.60/168.40 [1577]~E(x15771,x15772)+E(f497(x15773,x15771),f497(x15773,x15772))
% 168.60/168.40 [1578]~E(x15781,x15782)+E(f636(x15781,x15783,x15784,x15785,x15786),f636(x15782,x15783,x15784,x15785,x15786))
% 168.60/168.40 [1579]~E(x15791,x15792)+E(f636(x15793,x15791,x15794,x15795,x15796),f636(x15793,x15792,x15794,x15795,x15796))
% 168.60/168.40 [1580]~E(x15801,x15802)+E(f636(x15803,x15804,x15801,x15805,x15806),f636(x15803,x15804,x15802,x15805,x15806))
% 168.60/168.40 [1581]~E(x15811,x15812)+E(f636(x15813,x15814,x15815,x15811,x15816),f636(x15813,x15814,x15815,x15812,x15816))
% 168.60/168.40 [1582]~E(x15821,x15822)+E(f636(x15823,x15824,x15825,x15826,x15821),f636(x15823,x15824,x15825,x15826,x15822))
% 168.60/168.40 [1583]~E(x15831,x15832)+E(f880(x15831,x15833,x15834,x15835),f880(x15832,x15833,x15834,x15835))
% 168.60/168.40 [1584]~E(x15841,x15842)+E(f880(x15843,x15841,x15844,x15845),f880(x15843,x15842,x15844,x15845))
% 168.60/168.40 [1585]~E(x15851,x15852)+E(f880(x15853,x15854,x15851,x15855),f880(x15853,x15854,x15852,x15855))
% 168.60/168.40 [1586]~E(x15861,x15862)+E(f880(x15863,x15864,x15865,x15861),f880(x15863,x15864,x15865,x15862))
% 168.60/168.40 [1587]~E(x15871,x15872)+E(f380(x15871,x15873,x15874),f380(x15872,x15873,x15874))
% 168.60/168.40 [1588]~E(x15881,x15882)+E(f380(x15883,x15881,x15884),f380(x15883,x15882,x15884))
% 168.60/168.40 [1589]~E(x15891,x15892)+E(f380(x15893,x15894,x15891),f380(x15893,x15894,x15892))
% 168.60/168.40 [1590]~E(x15901,x15902)+E(f679(x15901,x15903),f679(x15902,x15903))
% 168.60/168.40 [1591]~E(x15911,x15912)+E(f679(x15913,x15911),f679(x15913,x15912))
% 168.60/168.40 [1592]~E(x15921,x15922)+E(f501(x15921,x15923),f501(x15922,x15923))
% 168.60/168.40 [1593]~E(x15931,x15932)+E(f501(x15933,x15931),f501(x15933,x15932))
% 168.60/168.40 [1594]~E(x15941,x15942)+E(f821(x15941,x15943,x15944,x15945,x15946,x15947),f821(x15942,x15943,x15944,x15945,x15946,x15947))
% 168.60/168.40 [1595]~E(x15951,x15952)+E(f821(x15953,x15951,x15954,x15955,x15956,x15957),f821(x15953,x15952,x15954,x15955,x15956,x15957))
% 168.60/168.40 [1596]~E(x15961,x15962)+E(f821(x15963,x15964,x15961,x15965,x15966,x15967),f821(x15963,x15964,x15962,x15965,x15966,x15967))
% 168.60/168.40 [1597]~E(x15971,x15972)+E(f821(x15973,x15974,x15975,x15971,x15976,x15977),f821(x15973,x15974,x15975,x15972,x15976,x15977))
% 168.60/168.40 [1598]~E(x15981,x15982)+E(f821(x15983,x15984,x15985,x15986,x15981,x15987),f821(x15983,x15984,x15985,x15986,x15982,x15987))
% 168.60/168.40 [1599]~E(x15991,x15992)+E(f821(x15993,x15994,x15995,x15996,x15997,x15991),f821(x15993,x15994,x15995,x15996,x15997,x15992))
% 168.60/168.40 [1600]~E(x16001,x16002)+E(f620(x16001,x16003,x16004,x16005,x16006),f620(x16002,x16003,x16004,x16005,x16006))
% 168.60/168.40 [1601]~E(x16011,x16012)+E(f620(x16013,x16011,x16014,x16015,x16016),f620(x16013,x16012,x16014,x16015,x16016))
% 168.60/168.40 [1602]~E(x16021,x16022)+E(f620(x16023,x16024,x16021,x16025,x16026),f620(x16023,x16024,x16022,x16025,x16026))
% 168.60/168.40 [1603]~E(x16031,x16032)+E(f620(x16033,x16034,x16035,x16031,x16036),f620(x16033,x16034,x16035,x16032,x16036))
% 168.60/168.40 [1604]~E(x16041,x16042)+E(f620(x16043,x16044,x16045,x16046,x16041),f620(x16043,x16044,x16045,x16046,x16042))
% 168.60/168.40 [1605]~E(x16051,x16052)+E(f677(x16051,x16053,x16054,x16055,x16056),f677(x16052,x16053,x16054,x16055,x16056))
% 168.60/168.40 [1606]~E(x16061,x16062)+E(f677(x16063,x16061,x16064,x16065,x16066),f677(x16063,x16062,x16064,x16065,x16066))
% 168.60/168.40 [1607]~E(x16071,x16072)+E(f677(x16073,x16074,x16071,x16075,x16076),f677(x16073,x16074,x16072,x16075,x16076))
% 168.60/168.40 [1608]~E(x16081,x16082)+E(f677(x16083,x16084,x16085,x16081,x16086),f677(x16083,x16084,x16085,x16082,x16086))
% 168.60/168.40 [1609]~E(x16091,x16092)+E(f677(x16093,x16094,x16095,x16096,x16091),f677(x16093,x16094,x16095,x16096,x16092))
% 168.60/168.40 [1610]~E(x16101,x16102)+E(f750(x16101,x16103,x16104,x16105),f750(x16102,x16103,x16104,x16105))
% 168.60/168.40 [1611]~E(x16111,x16112)+E(f750(x16113,x16111,x16114,x16115),f750(x16113,x16112,x16114,x16115))
% 168.60/168.40 [1612]~E(x16121,x16122)+E(f750(x16123,x16124,x16121,x16125),f750(x16123,x16124,x16122,x16125))
% 168.60/168.40 [1613]~E(x16131,x16132)+E(f750(x16133,x16134,x16135,x16131),f750(x16133,x16134,x16135,x16132))
% 168.60/168.40 [1614]~E(x16141,x16142)+E(f713(x16141,x16143),f713(x16142,x16143))
% 168.60/168.40 [1615]~E(x16151,x16152)+E(f713(x16153,x16151),f713(x16153,x16152))
% 168.60/168.40 [1616]~E(x16161,x16162)+E(f657(x16161,x16163),f657(x16162,x16163))
% 168.60/168.40 [1617]~E(x16171,x16172)+E(f657(x16173,x16171),f657(x16173,x16172))
% 168.60/168.40 [1618]~E(x16181,x16182)+E(f606(x16181,x16183,x16184,x16185,x16186),f606(x16182,x16183,x16184,x16185,x16186))
% 168.60/168.40 [1619]~E(x16191,x16192)+E(f606(x16193,x16191,x16194,x16195,x16196),f606(x16193,x16192,x16194,x16195,x16196))
% 168.60/168.40 [1620]~E(x16201,x16202)+E(f606(x16203,x16204,x16201,x16205,x16206),f606(x16203,x16204,x16202,x16205,x16206))
% 168.60/168.40 [1621]~E(x16211,x16212)+E(f606(x16213,x16214,x16215,x16211,x16216),f606(x16213,x16214,x16215,x16212,x16216))
% 168.60/168.40 [1622]~E(x16221,x16222)+E(f606(x16223,x16224,x16225,x16226,x16221),f606(x16223,x16224,x16225,x16226,x16222))
% 168.60/168.40 [1623]~E(x16231,x16232)+E(f745(x16231,x16233,x16234),f745(x16232,x16233,x16234))
% 168.60/168.40 [1624]~E(x16241,x16242)+E(f745(x16243,x16241,x16244),f745(x16243,x16242,x16244))
% 168.60/168.40 [1625]~E(x16251,x16252)+E(f745(x16253,x16254,x16251),f745(x16253,x16254,x16252))
% 168.60/168.40 [1626]~E(x16261,x16262)+E(f527(x16261,x16263,x16264),f527(x16262,x16263,x16264))
% 168.60/168.40 [1627]~E(x16271,x16272)+E(f527(x16273,x16271,x16274),f527(x16273,x16272,x16274))
% 168.60/168.40 [1628]~E(x16281,x16282)+E(f527(x16283,x16284,x16281),f527(x16283,x16284,x16282))
% 168.60/168.40 [1629]~E(x16291,x16292)+E(f664(x16291,x16293,x16294,x16295,x16296),f664(x16292,x16293,x16294,x16295,x16296))
% 168.60/168.40 [1630]~E(x16301,x16302)+E(f664(x16303,x16301,x16304,x16305,x16306),f664(x16303,x16302,x16304,x16305,x16306))
% 168.60/168.40 [1631]~E(x16311,x16312)+E(f664(x16313,x16314,x16311,x16315,x16316),f664(x16313,x16314,x16312,x16315,x16316))
% 168.60/168.40 [1632]~E(x16321,x16322)+E(f664(x16323,x16324,x16325,x16321,x16326),f664(x16323,x16324,x16325,x16322,x16326))
% 168.60/168.40 [1633]~E(x16331,x16332)+E(f664(x16333,x16334,x16335,x16336,x16331),f664(x16333,x16334,x16335,x16336,x16332))
% 168.60/168.40 [1634]~E(x16341,x16342)+E(f693(x16341,x16343),f693(x16342,x16343))
% 168.60/168.40 [1635]~E(x16351,x16352)+E(f693(x16353,x16351),f693(x16353,x16352))
% 168.60/168.40 [1636]~E(x16361,x16362)+E(f685(x16361,x16363,x16364),f685(x16362,x16363,x16364))
% 168.60/168.40 [1637]~E(x16371,x16372)+E(f685(x16373,x16371,x16374),f685(x16373,x16372,x16374))
% 168.60/168.40 [1638]~E(x16381,x16382)+E(f685(x16383,x16384,x16381),f685(x16383,x16384,x16382))
% 168.60/168.40 [1639]~E(x16391,x16392)+E(f600(x16391,x16393,x16394),f600(x16392,x16393,x16394))
% 168.60/168.40 [1640]~E(x16401,x16402)+E(f600(x16403,x16401,x16404),f600(x16403,x16402,x16404))
% 168.60/168.40 [1641]~E(x16411,x16412)+E(f600(x16413,x16414,x16411),f600(x16413,x16414,x16412))
% 168.60/168.40 [1642]~E(x16421,x16422)+E(f837(x16421,x16423,x16424),f837(x16422,x16423,x16424))
% 168.60/168.40 [1643]~E(x16431,x16432)+E(f837(x16433,x16431,x16434),f837(x16433,x16432,x16434))
% 168.60/168.40 [1644]~E(x16441,x16442)+E(f837(x16443,x16444,x16441),f837(x16443,x16444,x16442))
% 168.60/168.40 [1645]~E(x16451,x16452)+E(f651(x16451,x16453,x16454,x16455),f651(x16452,x16453,x16454,x16455))
% 168.60/168.40 [1646]~E(x16461,x16462)+E(f651(x16463,x16461,x16464,x16465),f651(x16463,x16462,x16464,x16465))
% 168.60/168.40 [1647]~E(x16471,x16472)+E(f651(x16473,x16474,x16471,x16475),f651(x16473,x16474,x16472,x16475))
% 168.60/168.40 [1648]~E(x16481,x16482)+E(f651(x16483,x16484,x16485,x16481),f651(x16483,x16484,x16485,x16482))
% 168.60/168.40 [1649]~E(x16491,x16492)+E(f710(x16491,x16493,x16494),f710(x16492,x16493,x16494))
% 168.60/168.40 [1650]~E(x16501,x16502)+E(f710(x16503,x16501,x16504),f710(x16503,x16502,x16504))
% 168.60/168.40 [1651]~E(x16511,x16512)+E(f710(x16513,x16514,x16511),f710(x16513,x16514,x16512))
% 168.60/168.40 [1652]~E(x16521,x16522)+E(f47(x16521,x16523),f47(x16522,x16523))
% 168.60/168.40 [1653]~E(x16531,x16532)+E(f47(x16533,x16531),f47(x16533,x16532))
% 168.60/168.40 [1654]~E(x16541,x16542)+E(f163(x16541,x16543,x16544),f163(x16542,x16543,x16544))
% 168.60/168.40 [1655]~E(x16551,x16552)+E(f163(x16553,x16551,x16554),f163(x16553,x16552,x16554))
% 168.60/168.40 [1656]~E(x16561,x16562)+E(f163(x16563,x16564,x16561),f163(x16563,x16564,x16562))
% 168.60/168.40 [1657]~E(x16571,x16572)+E(f255(x16571),f255(x16572))
% 168.60/168.40 [1658]~E(x16581,x16582)+E(f854(x16581,x16583,x16584,x16585,x16586),f854(x16582,x16583,x16584,x16585,x16586))
% 168.60/168.40 [1659]~E(x16591,x16592)+E(f854(x16593,x16591,x16594,x16595,x16596),f854(x16593,x16592,x16594,x16595,x16596))
% 168.60/168.40 [1660]~E(x16601,x16602)+E(f854(x16603,x16604,x16601,x16605,x16606),f854(x16603,x16604,x16602,x16605,x16606))
% 168.60/168.40 [1661]~E(x16611,x16612)+E(f854(x16613,x16614,x16615,x16611,x16616),f854(x16613,x16614,x16615,x16612,x16616))
% 168.60/168.40 [1662]~E(x16621,x16622)+E(f854(x16623,x16624,x16625,x16626,x16621),f854(x16623,x16624,x16625,x16626,x16622))
% 168.60/168.40 [1663]~E(x16631,x16632)+E(f888(x16631,x16633,x16634,x16635),f888(x16632,x16633,x16634,x16635))
% 168.60/168.40 [1664]~E(x16641,x16642)+E(f888(x16643,x16641,x16644,x16645),f888(x16643,x16642,x16644,x16645))
% 168.60/168.40 [1665]~E(x16651,x16652)+E(f888(x16653,x16654,x16651,x16655),f888(x16653,x16654,x16652,x16655))
% 168.60/168.40 [1666]~E(x16661,x16662)+E(f888(x16663,x16664,x16665,x16661),f888(x16663,x16664,x16665,x16662))
% 168.60/168.40 [1667]~E(x16671,x16672)+E(f191(x16671,x16673),f191(x16672,x16673))
% 168.60/168.40 [1668]~E(x16681,x16682)+E(f191(x16683,x16681),f191(x16683,x16682))
% 168.60/168.40 [1669]~E(x16691,x16692)+E(f362(x16691,x16693,x16694),f362(x16692,x16693,x16694))
% 168.60/168.40 [1670]~E(x16701,x16702)+E(f362(x16703,x16701,x16704),f362(x16703,x16702,x16704))
% 168.60/168.40 [1671]~E(x16711,x16712)+E(f362(x16713,x16714,x16711),f362(x16713,x16714,x16712))
% 168.60/168.40 [1672]~E(x16721,x16722)+E(f579(x16721,x16723),f579(x16722,x16723))
% 168.60/168.40 [1673]~E(x16731,x16732)+E(f579(x16733,x16731),f579(x16733,x16732))
% 168.60/168.40 [1674]~E(x16741,x16742)+E(f715(x16741,x16743,x16744,x16745,x16746,x16747,x16748,x16749),f715(x16742,x16743,x16744,x16745,x16746,x16747,x16748,x16749))
% 168.60/168.40 [1675]~E(x16751,x16752)+E(f715(x16753,x16751,x16754,x16755,x16756,x16757,x16758,x16759),f715(x16753,x16752,x16754,x16755,x16756,x16757,x16758,x16759))
% 168.60/168.40 [1676]~E(x16761,x16762)+E(f715(x16763,x16764,x16761,x16765,x16766,x16767,x16768,x16769),f715(x16763,x16764,x16762,x16765,x16766,x16767,x16768,x16769))
% 168.60/168.40 [1677]~E(x16771,x16772)+E(f715(x16773,x16774,x16775,x16771,x16776,x16777,x16778,x16779),f715(x16773,x16774,x16775,x16772,x16776,x16777,x16778,x16779))
% 168.60/168.40 [1678]~E(x16781,x16782)+E(f715(x16783,x16784,x16785,x16786,x16781,x16787,x16788,x16789),f715(x16783,x16784,x16785,x16786,x16782,x16787,x16788,x16789))
% 168.60/168.40 [1679]~E(x16791,x16792)+E(f715(x16793,x16794,x16795,x16796,x16797,x16791,x16798,x16799),f715(x16793,x16794,x16795,x16796,x16797,x16792,x16798,x16799))
% 168.60/168.40 [1680]~E(x16801,x16802)+E(f715(x16803,x16804,x16805,x16806,x16807,x16808,x16801,x16809),f715(x16803,x16804,x16805,x16806,x16807,x16808,x16802,x16809))
% 168.60/168.40 [1681]~E(x16811,x16812)+E(f715(x16813,x16814,x16815,x16816,x16817,x16818,x16819,x16811),f715(x16813,x16814,x16815,x16816,x16817,x16818,x16819,x16812))
% 168.60/168.40 [1682]~E(x16821,x16822)+E(f686(x16821,x16823,x16824),f686(x16822,x16823,x16824))
% 168.60/168.40 [1683]~E(x16831,x16832)+E(f686(x16833,x16831,x16834),f686(x16833,x16832,x16834))
% 168.60/168.40 [1684]~E(x16841,x16842)+E(f686(x16843,x16844,x16841),f686(x16843,x16844,x16842))
% 168.60/168.40 [1685]~E(x16851,x16852)+E(f585(x16851,x16853,x16854,x16855,x16856,x16857),f585(x16852,x16853,x16854,x16855,x16856,x16857))
% 168.60/168.40 [1686]~E(x16861,x16862)+E(f585(x16863,x16861,x16864,x16865,x16866,x16867),f585(x16863,x16862,x16864,x16865,x16866,x16867))
% 168.60/168.40 [1687]~E(x16871,x16872)+E(f585(x16873,x16874,x16871,x16875,x16876,x16877),f585(x16873,x16874,x16872,x16875,x16876,x16877))
% 168.60/168.40 [1688]~E(x16881,x16882)+E(f585(x16883,x16884,x16885,x16881,x16886,x16887),f585(x16883,x16884,x16885,x16882,x16886,x16887))
% 168.60/168.40 [1689]~E(x16891,x16892)+E(f585(x16893,x16894,x16895,x16896,x16891,x16897),f585(x16893,x16894,x16895,x16896,x16892,x16897))
% 168.60/168.40 [1690]~E(x16901,x16902)+E(f585(x16903,x16904,x16905,x16906,x16907,x16901),f585(x16903,x16904,x16905,x16906,x16907,x16902))
% 168.60/168.40 [1691]~E(x16911,x16912)+E(f152(x16911,x16913,x16914,x16915),f152(x16912,x16913,x16914,x16915))
% 168.60/168.40 [1692]~E(x16921,x16922)+E(f152(x16923,x16921,x16924,x16925),f152(x16923,x16922,x16924,x16925))
% 168.60/168.40 [1693]~E(x16931,x16932)+E(f152(x16933,x16934,x16931,x16935),f152(x16933,x16934,x16932,x16935))
% 168.60/168.40 [1694]~E(x16941,x16942)+E(f152(x16943,x16944,x16945,x16941),f152(x16943,x16944,x16945,x16942))
% 168.60/168.40 [1695]~E(x16951,x16952)+E(f492(x16951,x16953,x16954,x16955,x16956),f492(x16952,x16953,x16954,x16955,x16956))
% 168.60/168.40 [1696]~E(x16961,x16962)+E(f492(x16963,x16961,x16964,x16965,x16966),f492(x16963,x16962,x16964,x16965,x16966))
% 168.60/168.40 [1697]~E(x16971,x16972)+E(f492(x16973,x16974,x16971,x16975,x16976),f492(x16973,x16974,x16972,x16975,x16976))
% 168.60/168.40 [1698]~E(x16981,x16982)+E(f492(x16983,x16984,x16985,x16981,x16986),f492(x16983,x16984,x16985,x16982,x16986))
% 168.60/168.40 [1699]~E(x16991,x16992)+E(f492(x16993,x16994,x16995,x16996,x16991),f492(x16993,x16994,x16995,x16996,x16992))
% 168.60/168.40 [1700]~E(x17001,x17002)+E(f437(x17001,x17003,x17004,x17005),f437(x17002,x17003,x17004,x17005))
% 168.60/168.40 [1701]~E(x17011,x17012)+E(f437(x17013,x17011,x17014,x17015),f437(x17013,x17012,x17014,x17015))
% 168.60/168.40 [1702]~E(x17021,x17022)+E(f437(x17023,x17024,x17021,x17025),f437(x17023,x17024,x17022,x17025))
% 168.60/168.40 [1703]~E(x17031,x17032)+E(f437(x17033,x17034,x17035,x17031),f437(x17033,x17034,x17035,x17032))
% 168.60/168.40 [1704]~E(x17041,x17042)+E(f778(x17041,x17043,x17044),f778(x17042,x17043,x17044))
% 168.60/168.40 [1705]~E(x17051,x17052)+E(f778(x17053,x17051,x17054),f778(x17053,x17052,x17054))
% 168.60/168.40 [1706]~E(x17061,x17062)+E(f778(x17063,x17064,x17061),f778(x17063,x17064,x17062))
% 168.60/168.40 [1707]~E(x17071,x17072)+E(f825(x17071,x17073,x17074,x17075,x17076,x17077,x17078,x17079),f825(x17072,x17073,x17074,x17075,x17076,x17077,x17078,x17079))
% 168.60/168.40 [1708]~E(x17081,x17082)+E(f825(x17083,x17081,x17084,x17085,x17086,x17087,x17088,x17089),f825(x17083,x17082,x17084,x17085,x17086,x17087,x17088,x17089))
% 168.60/168.40 [1709]~E(x17091,x17092)+E(f825(x17093,x17094,x17091,x17095,x17096,x17097,x17098,x17099),f825(x17093,x17094,x17092,x17095,x17096,x17097,x17098,x17099))
% 168.60/168.40 [1710]~E(x17101,x17102)+E(f825(x17103,x17104,x17105,x17101,x17106,x17107,x17108,x17109),f825(x17103,x17104,x17105,x17102,x17106,x17107,x17108,x17109))
% 168.60/168.40 [1711]~E(x17111,x17112)+E(f825(x17113,x17114,x17115,x17116,x17111,x17117,x17118,x17119),f825(x17113,x17114,x17115,x17116,x17112,x17117,x17118,x17119))
% 168.60/168.40 [1712]~E(x17121,x17122)+E(f825(x17123,x17124,x17125,x17126,x17127,x17121,x17128,x17129),f825(x17123,x17124,x17125,x17126,x17127,x17122,x17128,x17129))
% 168.60/168.40 [1713]~E(x17131,x17132)+E(f825(x17133,x17134,x17135,x17136,x17137,x17138,x17131,x17139),f825(x17133,x17134,x17135,x17136,x17137,x17138,x17132,x17139))
% 168.60/168.40 [1714]~E(x17141,x17142)+E(f825(x17143,x17144,x17145,x17146,x17147,x17148,x17149,x17141),f825(x17143,x17144,x17145,x17146,x17147,x17148,x17149,x17142))
% 168.60/168.40 [1715]~E(x17151,x17152)+E(f34(x17151),f34(x17152))
% 168.60/168.40 [1716]~E(x17161,x17162)+E(f266(x17161),f266(x17162))
% 168.60/168.40 [1717]~E(x17171,x17172)+E(f378(x17171,x17173,x17174),f378(x17172,x17173,x17174))
% 168.60/168.40 [1718]~E(x17181,x17182)+E(f378(x17183,x17181,x17184),f378(x17183,x17182,x17184))
% 168.60/168.40 [1719]~E(x17191,x17192)+E(f378(x17193,x17194,x17191),f378(x17193,x17194,x17192))
% 168.60/168.40 [1720]~E(x17201,x17202)+E(f608(x17201,x17203,x17204),f608(x17202,x17203,x17204))
% 168.60/168.40 [1721]~E(x17211,x17212)+E(f608(x17213,x17211,x17214),f608(x17213,x17212,x17214))
% 168.60/168.40 [1722]~E(x17221,x17222)+E(f608(x17223,x17224,x17221),f608(x17223,x17224,x17222))
% 168.60/168.40 [1723]~E(x17231,x17232)+E(f540(x17231,x17233),f540(x17232,x17233))
% 168.60/168.40 [1724]~E(x17241,x17242)+E(f540(x17243,x17241),f540(x17243,x17242))
% 168.60/168.40 [1725]~E(x17251,x17252)+E(f573(x17251,x17253,x17254,x17255,x17256,x17257),f573(x17252,x17253,x17254,x17255,x17256,x17257))
% 168.60/168.40 [1726]~E(x17261,x17262)+E(f573(x17263,x17261,x17264,x17265,x17266,x17267),f573(x17263,x17262,x17264,x17265,x17266,x17267))
% 168.60/168.40 [1727]~E(x17271,x17272)+E(f573(x17273,x17274,x17271,x17275,x17276,x17277),f573(x17273,x17274,x17272,x17275,x17276,x17277))
% 168.60/168.40 [1728]~E(x17281,x17282)+E(f573(x17283,x17284,x17285,x17281,x17286,x17287),f573(x17283,x17284,x17285,x17282,x17286,x17287))
% 168.60/168.40 [1729]~E(x17291,x17292)+E(f573(x17293,x17294,x17295,x17296,x17291,x17297),f573(x17293,x17294,x17295,x17296,x17292,x17297))
% 168.60/168.40 [1730]~E(x17301,x17302)+E(f573(x17303,x17304,x17305,x17306,x17307,x17301),f573(x17303,x17304,x17305,x17306,x17307,x17302))
% 168.60/168.40 [1731]~E(x17311,x17312)+E(f106(x17311,x17313,x17314),f106(x17312,x17313,x17314))
% 168.60/168.40 [1732]~E(x17321,x17322)+E(f106(x17323,x17321,x17324),f106(x17323,x17322,x17324))
% 168.60/168.40 [1733]~E(x17331,x17332)+E(f106(x17333,x17334,x17331),f106(x17333,x17334,x17332))
% 168.60/168.40 [1734]~E(x17341,x17342)+E(f113(x17341),f113(x17342))
% 168.60/168.40 [1735]~E(x17351,x17352)+E(f616(x17351,x17353,x17354,x17355,x17356),f616(x17352,x17353,x17354,x17355,x17356))
% 168.60/168.40 [1736]~E(x17361,x17362)+E(f616(x17363,x17361,x17364,x17365,x17366),f616(x17363,x17362,x17364,x17365,x17366))
% 168.60/168.40 [1737]~E(x17371,x17372)+E(f616(x17373,x17374,x17371,x17375,x17376),f616(x17373,x17374,x17372,x17375,x17376))
% 168.60/168.40 [1738]~E(x17381,x17382)+E(f616(x17383,x17384,x17385,x17381,x17386),f616(x17383,x17384,x17385,x17382,x17386))
% 168.60/168.40 [1739]~E(x17391,x17392)+E(f616(x17393,x17394,x17395,x17396,x17391),f616(x17393,x17394,x17395,x17396,x17392))
% 168.60/168.40 [1740]~E(x17401,x17402)+E(f502(x17401,x17403,x17404,x17405),f502(x17402,x17403,x17404,x17405))
% 168.60/168.40 [1741]~E(x17411,x17412)+E(f502(x17413,x17411,x17414,x17415),f502(x17413,x17412,x17414,x17415))
% 168.60/168.40 [1742]~E(x17421,x17422)+E(f502(x17423,x17424,x17421,x17425),f502(x17423,x17424,x17422,x17425))
% 168.60/168.40 [1743]~E(x17431,x17432)+E(f502(x17433,x17434,x17435,x17431),f502(x17433,x17434,x17435,x17432))
% 168.60/168.40 [1744]~E(x17441,x17442)+E(f610(x17441,x17443),f610(x17442,x17443))
% 168.60/168.40 [1745]~E(x17451,x17452)+E(f610(x17453,x17451),f610(x17453,x17452))
% 168.60/168.40 [1746]~E(x17461,x17462)+E(f707(x17461,x17463),f707(x17462,x17463))
% 168.60/168.40 [1747]~E(x17471,x17472)+E(f707(x17473,x17471),f707(x17473,x17472))
% 168.60/168.40 [1748]~E(x17481,x17482)+E(f866(x17481,x17483,x17484,x17485,x17486),f866(x17482,x17483,x17484,x17485,x17486))
% 168.60/168.40 [1749]~E(x17491,x17492)+E(f866(x17493,x17491,x17494,x17495,x17496),f866(x17493,x17492,x17494,x17495,x17496))
% 168.60/168.40 [1750]~E(x17501,x17502)+E(f866(x17503,x17504,x17501,x17505,x17506),f866(x17503,x17504,x17502,x17505,x17506))
% 168.60/168.40 [1751]~E(x17511,x17512)+E(f866(x17513,x17514,x17515,x17511,x17516),f866(x17513,x17514,x17515,x17512,x17516))
% 168.60/168.40 [1752]~E(x17521,x17522)+E(f866(x17523,x17524,x17525,x17526,x17521),f866(x17523,x17524,x17525,x17526,x17522))
% 168.60/168.40 [1753]~E(x17531,x17532)+E(f770(x17531,x17533),f770(x17532,x17533))
% 168.60/168.40 [1754]~E(x17541,x17542)+E(f770(x17543,x17541),f770(x17543,x17542))
% 168.60/168.40 [1755]~E(x17551,x17552)+E(f895(x17551,x17553,x17554),f895(x17552,x17553,x17554))
% 168.60/168.40 [1756]~E(x17561,x17562)+E(f895(x17563,x17561,x17564),f895(x17563,x17562,x17564))
% 168.60/168.40 [1757]~E(x17571,x17572)+E(f895(x17573,x17574,x17571),f895(x17573,x17574,x17572))
% 168.60/168.40 [1758]~E(x17581,x17582)+E(f574(x17581,x17583,x17584,x17585,x17586,x17587),f574(x17582,x17583,x17584,x17585,x17586,x17587))
% 168.60/168.40 [1759]~E(x17591,x17592)+E(f574(x17593,x17591,x17594,x17595,x17596,x17597),f574(x17593,x17592,x17594,x17595,x17596,x17597))
% 168.60/168.40 [1760]~E(x17601,x17602)+E(f574(x17603,x17604,x17601,x17605,x17606,x17607),f574(x17603,x17604,x17602,x17605,x17606,x17607))
% 168.60/168.40 [1761]~E(x17611,x17612)+E(f574(x17613,x17614,x17615,x17611,x17616,x17617),f574(x17613,x17614,x17615,x17612,x17616,x17617))
% 168.60/168.40 [1762]~E(x17621,x17622)+E(f574(x17623,x17624,x17625,x17626,x17621,x17627),f574(x17623,x17624,x17625,x17626,x17622,x17627))
% 168.60/168.40 [1763]~E(x17631,x17632)+E(f574(x17633,x17634,x17635,x17636,x17637,x17631),f574(x17633,x17634,x17635,x17636,x17637,x17632))
% 168.60/168.40 [1764]~E(x17641,x17642)+E(f348(x17641,x17643),f348(x17642,x17643))
% 168.60/168.40 [1765]~E(x17651,x17652)+E(f348(x17653,x17651),f348(x17653,x17652))
% 168.60/168.40 [1766]~E(x17661,x17662)+E(f324(x17661),f324(x17662))
% 168.60/168.40 [1767]~E(x17671,x17672)+E(f806(x17671,x17673),f806(x17672,x17673))
% 168.60/168.40 [1768]~E(x17681,x17682)+E(f806(x17683,x17681),f806(x17683,x17682))
% 168.60/168.40 [1769]~E(x17691,x17692)+E(f263(x17691,x17693),f263(x17692,x17693))
% 168.60/168.40 [1770]~E(x17701,x17702)+E(f263(x17703,x17701),f263(x17703,x17702))
% 168.60/168.40 [1771]~E(x17711,x17712)+E(f571(x17711,x17713,x17714,x17715,x17716,x17717),f571(x17712,x17713,x17714,x17715,x17716,x17717))
% 168.60/168.40 [1772]~E(x17721,x17722)+E(f571(x17723,x17721,x17724,x17725,x17726,x17727),f571(x17723,x17722,x17724,x17725,x17726,x17727))
% 168.60/168.40 [1773]~E(x17731,x17732)+E(f571(x17733,x17734,x17731,x17735,x17736,x17737),f571(x17733,x17734,x17732,x17735,x17736,x17737))
% 168.60/168.40 [1774]~E(x17741,x17742)+E(f571(x17743,x17744,x17745,x17741,x17746,x17747),f571(x17743,x17744,x17745,x17742,x17746,x17747))
% 168.60/168.40 [1775]~E(x17751,x17752)+E(f571(x17753,x17754,x17755,x17756,x17751,x17757),f571(x17753,x17754,x17755,x17756,x17752,x17757))
% 168.60/168.40 [1776]~E(x17761,x17762)+E(f571(x17763,x17764,x17765,x17766,x17767,x17761),f571(x17763,x17764,x17765,x17766,x17767,x17762))
% 168.60/168.40 [1777]~E(x17771,x17772)+E(f371(x17771,x17773,x17774),f371(x17772,x17773,x17774))
% 168.60/168.40 [1778]~E(x17781,x17782)+E(f371(x17783,x17781,x17784),f371(x17783,x17782,x17784))
% 168.60/168.40 [1779]~E(x17791,x17792)+E(f371(x17793,x17794,x17791),f371(x17793,x17794,x17792))
% 168.60/168.40 [1780]~E(x17801,x17802)+E(f336(x17801,x17803,x17804),f336(x17802,x17803,x17804))
% 168.60/168.40 [1781]~E(x17811,x17812)+E(f336(x17813,x17811,x17814),f336(x17813,x17812,x17814))
% 168.60/168.40 [1782]~E(x17821,x17822)+E(f336(x17823,x17824,x17821),f336(x17823,x17824,x17822))
% 168.60/168.40 [1783]~E(x17831,x17832)+E(f569(x17831,x17833,x17834),f569(x17832,x17833,x17834))
% 168.60/168.40 [1784]~E(x17841,x17842)+E(f569(x17843,x17841,x17844),f569(x17843,x17842,x17844))
% 168.60/168.40 [1785]~E(x17851,x17852)+E(f569(x17853,x17854,x17851),f569(x17853,x17854,x17852))
% 168.60/168.40 [1786]~E(x17861,x17862)+E(f529(x17861,x17863,x17864,x17865,x17866),f529(x17862,x17863,x17864,x17865,x17866))
% 168.60/168.40 [1787]~E(x17871,x17872)+E(f529(x17873,x17871,x17874,x17875,x17876),f529(x17873,x17872,x17874,x17875,x17876))
% 168.60/168.40 [1788]~E(x17881,x17882)+E(f529(x17883,x17884,x17881,x17885,x17886),f529(x17883,x17884,x17882,x17885,x17886))
% 168.60/168.40 [1789]~E(x17891,x17892)+E(f529(x17893,x17894,x17895,x17891,x17896),f529(x17893,x17894,x17895,x17892,x17896))
% 168.60/168.40 [1790]~E(x17901,x17902)+E(f529(x17903,x17904,x17905,x17906,x17901),f529(x17903,x17904,x17905,x17906,x17902))
% 168.60/168.40 [1791]~E(x17911,x17912)+E(f337(x17911,x17913,x17914),f337(x17912,x17913,x17914))
% 168.60/168.40 [1792]~E(x17921,x17922)+E(f337(x17923,x17921,x17924),f337(x17923,x17922,x17924))
% 168.60/168.40 [1793]~E(x17931,x17932)+E(f337(x17933,x17934,x17931),f337(x17933,x17934,x17932))
% 168.60/168.40 [1794]~E(x17941,x17942)+E(f680(x17941,x17943,x17944,x17945),f680(x17942,x17943,x17944,x17945))
% 168.60/168.40 [1795]~E(x17951,x17952)+E(f680(x17953,x17951,x17954,x17955),f680(x17953,x17952,x17954,x17955))
% 168.60/168.40 [1796]~E(x17961,x17962)+E(f680(x17963,x17964,x17961,x17965),f680(x17963,x17964,x17962,x17965))
% 168.60/168.40 [1797]~E(x17971,x17972)+E(f680(x17973,x17974,x17975,x17971),f680(x17973,x17974,x17975,x17972))
% 168.60/168.40 [1798]~E(x17981,x17982)+E(f656(x17981,x17983,x17984),f656(x17982,x17983,x17984))
% 168.60/168.40 [1799]~E(x17991,x17992)+E(f656(x17993,x17991,x17994),f656(x17993,x17992,x17994))
% 168.60/168.40 [1800]~E(x18001,x18002)+E(f656(x18003,x18004,x18001),f656(x18003,x18004,x18002))
% 168.60/168.40 [1801]~E(x18011,x18012)+E(f860(x18011,x18013),f860(x18012,x18013))
% 168.60/168.40 [1802]~E(x18021,x18022)+E(f860(x18023,x18021),f860(x18023,x18022))
% 168.60/168.40 [1803]~E(x18031,x18032)+E(f758(x18031,x18033,x18034,x18035),f758(x18032,x18033,x18034,x18035))
% 168.60/168.40 [1804]~E(x18041,x18042)+E(f758(x18043,x18041,x18044,x18045),f758(x18043,x18042,x18044,x18045))
% 168.60/168.40 [1805]~E(x18051,x18052)+E(f758(x18053,x18054,x18051,x18055),f758(x18053,x18054,x18052,x18055))
% 168.60/168.40 [1806]~E(x18061,x18062)+E(f758(x18063,x18064,x18065,x18061),f758(x18063,x18064,x18065,x18062))
% 168.60/168.40 [1807]~E(x18071,x18072)+E(f886(x18071,x18073,x18074,x18075),f886(x18072,x18073,x18074,x18075))
% 168.60/168.40 [1808]~E(x18081,x18082)+E(f886(x18083,x18081,x18084,x18085),f886(x18083,x18082,x18084,x18085))
% 168.60/168.40 [1809]~E(x18091,x18092)+E(f886(x18093,x18094,x18091,x18095),f886(x18093,x18094,x18092,x18095))
% 168.60/168.40 [1810]~E(x18101,x18102)+E(f886(x18103,x18104,x18105,x18101),f886(x18103,x18104,x18105,x18102))
% 168.60/168.40 [1811]~E(x18111,x18112)+E(f783(x18111,x18113),f783(x18112,x18113))
% 168.60/168.40 [1812]~E(x18121,x18122)+E(f783(x18123,x18121),f783(x18123,x18122))
% 168.60/168.40 [1813]~E(x18131,x18132)+E(f373(x18131,x18133),f373(x18132,x18133))
% 168.60/168.40 [1814]~E(x18141,x18142)+E(f373(x18143,x18141),f373(x18143,x18142))
% 168.60/168.40 [1815]~E(x18151,x18152)+E(f124(x18151),f124(x18152))
% 168.60/168.40 [1816]~E(x18161,x18162)+E(f682(x18161,x18163,x18164,x18165,x18166),f682(x18162,x18163,x18164,x18165,x18166))
% 168.60/168.40 [1817]~E(x18171,x18172)+E(f682(x18173,x18171,x18174,x18175,x18176),f682(x18173,x18172,x18174,x18175,x18176))
% 168.60/168.40 [1818]~E(x18181,x18182)+E(f682(x18183,x18184,x18181,x18185,x18186),f682(x18183,x18184,x18182,x18185,x18186))
% 168.60/168.40 [1819]~E(x18191,x18192)+E(f682(x18193,x18194,x18195,x18191,x18196),f682(x18193,x18194,x18195,x18192,x18196))
% 168.60/168.40 [1820]~E(x18201,x18202)+E(f682(x18203,x18204,x18205,x18206,x18201),f682(x18203,x18204,x18205,x18206,x18202))
% 168.60/168.40 [1821]~E(x18211,x18212)+E(f834(x18211,x18213,x18214,x18215,x18216,x18217),f834(x18212,x18213,x18214,x18215,x18216,x18217))
% 168.60/168.40 [1822]~E(x18221,x18222)+E(f834(x18223,x18221,x18224,x18225,x18226,x18227),f834(x18223,x18222,x18224,x18225,x18226,x18227))
% 168.60/168.40 [1823]~E(x18231,x18232)+E(f834(x18233,x18234,x18231,x18235,x18236,x18237),f834(x18233,x18234,x18232,x18235,x18236,x18237))
% 168.60/168.40 [1824]~E(x18241,x18242)+E(f834(x18243,x18244,x18245,x18241,x18246,x18247),f834(x18243,x18244,x18245,x18242,x18246,x18247))
% 168.60/168.40 [1825]~E(x18251,x18252)+E(f834(x18253,x18254,x18255,x18256,x18251,x18257),f834(x18253,x18254,x18255,x18256,x18252,x18257))
% 168.60/168.40 [1826]~E(x18261,x18262)+E(f834(x18263,x18264,x18265,x18266,x18267,x18261),f834(x18263,x18264,x18265,x18266,x18267,x18262))
% 168.60/168.40 [1827]~E(x18271,x18272)+E(f243(x18271,x18273,x18274,x18275),f243(x18272,x18273,x18274,x18275))
% 168.60/168.40 [1828]~E(x18281,x18282)+E(f243(x18283,x18281,x18284,x18285),f243(x18283,x18282,x18284,x18285))
% 168.60/168.40 [1829]~E(x18291,x18292)+E(f243(x18293,x18294,x18291,x18295),f243(x18293,x18294,x18292,x18295))
% 168.60/168.40 [1830]~E(x18301,x18302)+E(f243(x18303,x18304,x18305,x18301),f243(x18303,x18304,x18305,x18302))
% 168.60/168.40 [1831]~E(x18311,x18312)+E(f443(x18311,x18313,x18314,x18315),f443(x18312,x18313,x18314,x18315))
% 168.60/168.40 [1832]~E(x18321,x18322)+E(f443(x18323,x18321,x18324,x18325),f443(x18323,x18322,x18324,x18325))
% 168.60/168.40 [1833]~E(x18331,x18332)+E(f443(x18333,x18334,x18331,x18335),f443(x18333,x18334,x18332,x18335))
% 168.60/168.40 [1834]~E(x18341,x18342)+E(f443(x18343,x18344,x18345,x18341),f443(x18343,x18344,x18345,x18342))
% 168.60/168.40 [1835]~E(x18351,x18352)+E(f634(x18351,x18353,x18354,x18355,x18356),f634(x18352,x18353,x18354,x18355,x18356))
% 168.60/168.40 [1836]~E(x18361,x18362)+E(f634(x18363,x18361,x18364,x18365,x18366),f634(x18363,x18362,x18364,x18365,x18366))
% 168.60/168.40 [1837]~E(x18371,x18372)+E(f634(x18373,x18374,x18371,x18375,x18376),f634(x18373,x18374,x18372,x18375,x18376))
% 168.60/168.40 [1838]~E(x18381,x18382)+E(f634(x18383,x18384,x18385,x18381,x18386),f634(x18383,x18384,x18385,x18382,x18386))
% 168.60/168.40 [1839]~E(x18391,x18392)+E(f634(x18393,x18394,x18395,x18396,x18391),f634(x18393,x18394,x18395,x18396,x18392))
% 168.60/168.40 [1840]~E(x18401,x18402)+E(f676(x18401,x18403,x18404),f676(x18402,x18403,x18404))
% 168.60/168.40 [1841]~E(x18411,x18412)+E(f676(x18413,x18411,x18414),f676(x18413,x18412,x18414))
% 168.60/168.40 [1842]~E(x18421,x18422)+E(f676(x18423,x18424,x18421),f676(x18423,x18424,x18422))
% 168.60/168.40 [1843]~E(x18431,x18432)+E(f852(x18431,x18433),f852(x18432,x18433))
% 168.60/168.40 [1844]~E(x18441,x18442)+E(f852(x18443,x18441),f852(x18443,x18442))
% 168.60/168.40 [1845]~E(x18451,x18452)+E(f330(x18451),f330(x18452))
% 168.60/168.40 [1846]~E(x18461,x18462)+E(f786(x18461,x18463),f786(x18462,x18463))
% 168.60/168.40 [1847]~E(x18471,x18472)+E(f786(x18473,x18471),f786(x18473,x18472))
% 168.60/168.40 [1848]~E(x18481,x18482)+E(f451(x18481,x18483,x18484,x18485),f451(x18482,x18483,x18484,x18485))
% 168.60/168.40 [1849]~E(x18491,x18492)+E(f451(x18493,x18491,x18494,x18495),f451(x18493,x18492,x18494,x18495))
% 168.60/168.40 [1850]~E(x18501,x18502)+E(f451(x18503,x18504,x18501,x18505),f451(x18503,x18504,x18502,x18505))
% 168.60/168.40 [1851]~E(x18511,x18512)+E(f451(x18513,x18514,x18515,x18511),f451(x18513,x18514,x18515,x18512))
% 168.60/168.40 [1852]~E(x18521,x18522)+E(f61(x18521,x18523,x18524),f61(x18522,x18523,x18524))
% 168.60/168.40 [1853]~E(x18531,x18532)+E(f61(x18533,x18531,x18534),f61(x18533,x18532,x18534))
% 168.60/168.40 [1854]~E(x18541,x18542)+E(f61(x18543,x18544,x18541),f61(x18543,x18544,x18542))
% 168.60/168.40 [1855]~E(x18551,x18552)+E(f560(x18551,x18553,x18554,x18555),f560(x18552,x18553,x18554,x18555))
% 168.60/168.40 [1856]~E(x18561,x18562)+E(f560(x18563,x18561,x18564,x18565),f560(x18563,x18562,x18564,x18565))
% 168.60/168.40 [1857]~E(x18571,x18572)+E(f560(x18573,x18574,x18571,x18575),f560(x18573,x18574,x18572,x18575))
% 168.60/168.40 [1858]~E(x18581,x18582)+E(f560(x18583,x18584,x18585,x18581),f560(x18583,x18584,x18585,x18582))
% 168.60/168.40 [1859]~E(x18591,x18592)+E(f369(x18591,x18593,x18594),f369(x18592,x18593,x18594))
% 168.60/168.40 [1860]~E(x18601,x18602)+E(f369(x18603,x18601,x18604),f369(x18603,x18602,x18604))
% 168.60/168.40 [1861]~E(x18611,x18612)+E(f369(x18613,x18614,x18611),f369(x18613,x18614,x18612))
% 168.60/168.40 [1862]~E(x18621,x18622)+E(f414(x18621,x18623,x18624,x18625,x18626),f414(x18622,x18623,x18624,x18625,x18626))
% 168.60/168.40 [1863]~E(x18631,x18632)+E(f414(x18633,x18631,x18634,x18635,x18636),f414(x18633,x18632,x18634,x18635,x18636))
% 168.60/168.40 [1864]~E(x18641,x18642)+E(f414(x18643,x18644,x18641,x18645,x18646),f414(x18643,x18644,x18642,x18645,x18646))
% 168.60/168.40 [1865]~E(x18651,x18652)+E(f414(x18653,x18654,x18655,x18651,x18656),f414(x18653,x18654,x18655,x18652,x18656))
% 168.60/168.40 [1866]~E(x18661,x18662)+E(f414(x18663,x18664,x18665,x18666,x18661),f414(x18663,x18664,x18665,x18666,x18662))
% 168.60/168.40 [1867]~E(x18671,x18672)+E(f507(x18671,x18673,x18674),f507(x18672,x18673,x18674))
% 168.60/168.40 [1868]~E(x18681,x18682)+E(f507(x18683,x18681,x18684),f507(x18683,x18682,x18684))
% 168.60/168.40 [1869]~E(x18691,x18692)+E(f507(x18693,x18694,x18691),f507(x18693,x18694,x18692))
% 168.60/168.40 [1870]~E(x18701,x18702)+E(f382(x18701,x18703,x18704),f382(x18702,x18703,x18704))
% 168.60/168.40 [1871]~E(x18711,x18712)+E(f382(x18713,x18711,x18714),f382(x18713,x18712,x18714))
% 168.60/168.40 [1872]~E(x18721,x18722)+E(f382(x18723,x18724,x18721),f382(x18723,x18724,x18722))
% 168.60/168.40 [1873]~E(x18731,x18732)+E(f862(x18731,x18733),f862(x18732,x18733))
% 168.60/168.40 [1874]~E(x18741,x18742)+E(f862(x18743,x18741),f862(x18743,x18742))
% 168.60/168.40 [1875]~E(x18751,x18752)+E(f863(x18751,x18753,x18754),f863(x18752,x18753,x18754))
% 168.60/168.40 [1876]~E(x18761,x18762)+E(f863(x18763,x18761,x18764),f863(x18763,x18762,x18764))
% 168.60/168.40 [1877]~E(x18771,x18772)+E(f863(x18773,x18774,x18771),f863(x18773,x18774,x18772))
% 168.60/168.40 [1878]~E(x18781,x18782)+E(f735(x18781,x18783,x18784,x18785),f735(x18782,x18783,x18784,x18785))
% 168.60/168.40 [1879]~E(x18791,x18792)+E(f735(x18793,x18791,x18794,x18795),f735(x18793,x18792,x18794,x18795))
% 168.60/168.40 [1880]~E(x18801,x18802)+E(f735(x18803,x18804,x18801,x18805),f735(x18803,x18804,x18802,x18805))
% 168.60/168.40 [1881]~E(x18811,x18812)+E(f735(x18813,x18814,x18815,x18811),f735(x18813,x18814,x18815,x18812))
% 168.60/168.40 [1882]~E(x18821,x18822)+E(f759(x18821,x18823,x18824,x18825),f759(x18822,x18823,x18824,x18825))
% 168.60/168.40 [1883]~E(x18831,x18832)+E(f759(x18833,x18831,x18834,x18835),f759(x18833,x18832,x18834,x18835))
% 168.60/168.40 [1884]~E(x18841,x18842)+E(f759(x18843,x18844,x18841,x18845),f759(x18843,x18844,x18842,x18845))
% 168.60/168.40 [1885]~E(x18851,x18852)+E(f759(x18853,x18854,x18855,x18851),f759(x18853,x18854,x18855,x18852))
% 168.60/168.40 [1886]~E(x18861,x18862)+E(f630(x18861,x18863,x18864,x18865),f630(x18862,x18863,x18864,x18865))
% 168.60/168.40 [1887]~E(x18871,x18872)+E(f630(x18873,x18871,x18874,x18875),f630(x18873,x18872,x18874,x18875))
% 168.60/168.40 [1888]~E(x18881,x18882)+E(f630(x18883,x18884,x18881,x18885),f630(x18883,x18884,x18882,x18885))
% 168.60/168.40 [1889]~E(x18891,x18892)+E(f630(x18893,x18894,x18895,x18891),f630(x18893,x18894,x18895,x18892))
% 168.60/168.40 [1890]~E(x18901,x18902)+E(f841(x18901,x18903),f841(x18902,x18903))
% 168.60/168.40 [1891]~E(x18911,x18912)+E(f841(x18913,x18911),f841(x18913,x18912))
% 168.60/168.40 [1892]~E(x18921,x18922)+E(f513(x18921,x18923),f513(x18922,x18923))
% 168.60/168.40 [1893]~E(x18931,x18932)+E(f513(x18933,x18931),f513(x18933,x18932))
% 168.60/168.40 [1894]~E(x18941,x18942)+E(f406(x18941,x18943,x18944,x18945,x18946),f406(x18942,x18943,x18944,x18945,x18946))
% 168.60/168.40 [1895]~E(x18951,x18952)+E(f406(x18953,x18951,x18954,x18955,x18956),f406(x18953,x18952,x18954,x18955,x18956))
% 168.60/168.40 [1896]~E(x18961,x18962)+E(f406(x18963,x18964,x18961,x18965,x18966),f406(x18963,x18964,x18962,x18965,x18966))
% 168.60/168.40 [1897]~E(x18971,x18972)+E(f406(x18973,x18974,x18975,x18971,x18976),f406(x18973,x18974,x18975,x18972,x18976))
% 168.60/168.40 [1898]~E(x18981,x18982)+E(f406(x18983,x18984,x18985,x18986,x18981),f406(x18983,x18984,x18985,x18986,x18982))
% 168.60/168.40 [1899]~E(x18991,x18992)+E(f691(x18991,x18993),f691(x18992,x18993))
% 168.60/168.40 [1900]~E(x19001,x19002)+E(f691(x19003,x19001),f691(x19003,x19002))
% 168.60/168.40 [1901]~E(x19011,x19012)+E(f820(x19011,x19013,x19014),f820(x19012,x19013,x19014))
% 168.60/168.40 [1902]~E(x19021,x19022)+E(f820(x19023,x19021,x19024),f820(x19023,x19022,x19024))
% 168.60/168.40 [1903]~E(x19031,x19032)+E(f820(x19033,x19034,x19031),f820(x19033,x19034,x19032))
% 168.60/168.40 [1904]~E(x19041,x19042)+E(f510(x19041,x19043,x19044),f510(x19042,x19043,x19044))
% 168.60/168.40 [1905]~E(x19051,x19052)+E(f510(x19053,x19051,x19054),f510(x19053,x19052,x19054))
% 168.60/168.40 [1906]~E(x19061,x19062)+E(f510(x19063,x19064,x19061),f510(x19063,x19064,x19062))
% 168.60/168.40 [1907]~E(x19071,x19072)+E(f445(x19071,x19073,x19074,x19075,x19076),f445(x19072,x19073,x19074,x19075,x19076))
% 168.60/168.40 [1908]~E(x19081,x19082)+E(f445(x19083,x19081,x19084,x19085,x19086),f445(x19083,x19082,x19084,x19085,x19086))
% 168.60/168.40 [1909]~E(x19091,x19092)+E(f445(x19093,x19094,x19091,x19095,x19096),f445(x19093,x19094,x19092,x19095,x19096))
% 168.60/168.40 [1910]~E(x19101,x19102)+E(f445(x19103,x19104,x19105,x19101,x19106),f445(x19103,x19104,x19105,x19102,x19106))
% 168.60/168.40 [1911]~E(x19111,x19112)+E(f445(x19113,x19114,x19115,x19116,x19111),f445(x19113,x19114,x19115,x19116,x19112))
% 168.60/168.40 [1912]~E(x19121,x19122)+E(f35(x19121),f35(x19122))
% 168.60/168.40 [1913]~E(x19131,x19132)+E(f842(x19131,x19133,x19134),f842(x19132,x19133,x19134))
% 168.60/168.40 [1914]~E(x19141,x19142)+E(f842(x19143,x19141,x19144),f842(x19143,x19142,x19144))
% 168.60/168.40 [1915]~E(x19151,x19152)+E(f842(x19153,x19154,x19151),f842(x19153,x19154,x19152))
% 168.60/168.40 [1916]~E(x19161,x19162)+E(f409(x19161,x19163),f409(x19162,x19163))
% 168.60/168.40 [1917]~E(x19171,x19172)+E(f409(x19173,x19171),f409(x19173,x19172))
% 168.60/168.40 [1918]~E(x19181,x19182)+E(f514(x19181,x19183,x19184),f514(x19182,x19183,x19184))
% 168.60/168.40 [1919]~E(x19191,x19192)+E(f514(x19193,x19191,x19194),f514(x19193,x19192,x19194))
% 168.60/168.40 [1920]~E(x19201,x19202)+E(f514(x19203,x19204,x19201),f514(x19203,x19204,x19202))
% 168.60/168.40 [1921]~E(x19211,x19212)+E(f488(x19211,x19213,x19214,x19215),f488(x19212,x19213,x19214,x19215))
% 168.60/168.40 [1922]~E(x19221,x19222)+E(f488(x19223,x19221,x19224,x19225),f488(x19223,x19222,x19224,x19225))
% 168.60/168.40 [1923]~E(x19231,x19232)+E(f488(x19233,x19234,x19231,x19235),f488(x19233,x19234,x19232,x19235))
% 168.60/168.40 [1924]~E(x19241,x19242)+E(f488(x19243,x19244,x19245,x19241),f488(x19243,x19244,x19245,x19242))
% 168.60/168.40 [1925]~E(x19251,x19252)+E(f450(x19251,x19253,x19254,x19255),f450(x19252,x19253,x19254,x19255))
% 168.60/168.40 [1926]~E(x19261,x19262)+E(f450(x19263,x19261,x19264,x19265),f450(x19263,x19262,x19264,x19265))
% 168.60/168.40 [1927]~E(x19271,x19272)+E(f450(x19273,x19274,x19271,x19275),f450(x19273,x19274,x19272,x19275))
% 168.60/168.40 [1928]~E(x19281,x19282)+E(f450(x19283,x19284,x19285,x19281),f450(x19283,x19284,x19285,x19282))
% 168.60/168.40 [1929]~E(x19291,x19292)+E(f757(x19291,x19293,x19294,x19295),f757(x19292,x19293,x19294,x19295))
% 168.60/168.40 [1930]~E(x19301,x19302)+E(f757(x19303,x19301,x19304,x19305),f757(x19303,x19302,x19304,x19305))
% 168.60/168.40 [1931]~E(x19311,x19312)+E(f757(x19313,x19314,x19311,x19315),f757(x19313,x19314,x19312,x19315))
% 168.60/168.40 [1932]~E(x19321,x19322)+E(f757(x19323,x19324,x19325,x19321),f757(x19323,x19324,x19325,x19322))
% 168.60/168.40 [1933]~E(x19331,x19332)+E(f777(x19331,x19333,x19334),f777(x19332,x19333,x19334))
% 168.60/168.40 [1934]~E(x19341,x19342)+E(f777(x19343,x19341,x19344),f777(x19343,x19342,x19344))
% 168.60/168.40 [1935]~E(x19351,x19352)+E(f777(x19353,x19354,x19351),f777(x19353,x19354,x19352))
% 168.60/168.40 [1936]~E(x19361,x19362)+E(f754(x19361,x19363,x19364),f754(x19362,x19363,x19364))
% 168.60/168.40 [1937]~E(x19371,x19372)+E(f754(x19373,x19371,x19374),f754(x19373,x19372,x19374))
% 168.60/168.40 [1938]~E(x19381,x19382)+E(f754(x19383,x19384,x19381),f754(x19383,x19384,x19382))
% 168.60/168.40 [1939]~E(x19391,x19392)+E(f525(x19391),f525(x19392))
% 168.60/168.40 [1940]~E(x19401,x19402)+E(f353(x19401,x19403,x19404),f353(x19402,x19403,x19404))
% 168.60/168.40 [1941]~E(x19411,x19412)+E(f353(x19413,x19411,x19414),f353(x19413,x19412,x19414))
% 168.60/168.40 [1942]~E(x19421,x19422)+E(f353(x19423,x19424,x19421),f353(x19423,x19424,x19422))
% 168.60/168.40 [1943]~E(x19431,x19432)+E(f567(x19431,x19433,x19434,x19435),f567(x19432,x19433,x19434,x19435))
% 168.60/168.40 [1944]~E(x19441,x19442)+E(f567(x19443,x19441,x19444,x19445),f567(x19443,x19442,x19444,x19445))
% 168.60/168.40 [1945]~E(x19451,x19452)+E(f567(x19453,x19454,x19451,x19455),f567(x19453,x19454,x19452,x19455))
% 168.60/168.40 [1946]~E(x19461,x19462)+E(f567(x19463,x19464,x19465,x19461),f567(x19463,x19464,x19465,x19462))
% 168.60/168.40 [1947]~E(x19471,x19472)+E(f712(x19471,x19473),f712(x19472,x19473))
% 168.60/168.40 [1948]~E(x19481,x19482)+E(f712(x19483,x19481),f712(x19483,x19482))
% 168.60/168.40 [1949]~E(x19491,x19492)+E(f808(x19491,x19493,x19494,x19495,x19496,x19497),f808(x19492,x19493,x19494,x19495,x19496,x19497))
% 168.60/168.40 [1950]~E(x19501,x19502)+E(f808(x19503,x19501,x19504,x19505,x19506,x19507),f808(x19503,x19502,x19504,x19505,x19506,x19507))
% 168.60/168.40 [1951]~E(x19511,x19512)+E(f808(x19513,x19514,x19511,x19515,x19516,x19517),f808(x19513,x19514,x19512,x19515,x19516,x19517))
% 168.60/168.40 [1952]~E(x19521,x19522)+E(f808(x19523,x19524,x19525,x19521,x19526,x19527),f808(x19523,x19524,x19525,x19522,x19526,x19527))
% 168.60/168.40 [1953]~E(x19531,x19532)+E(f808(x19533,x19534,x19535,x19536,x19531,x19537),f808(x19533,x19534,x19535,x19536,x19532,x19537))
% 168.60/168.40 [1954]~E(x19541,x19542)+E(f808(x19543,x19544,x19545,x19546,x19547,x19541),f808(x19543,x19544,x19545,x19546,x19547,x19542))
% 168.60/168.40 [1955]~E(x19551,x19552)+E(f405(x19551,x19553,x19554),f405(x19552,x19553,x19554))
% 168.60/168.40 [1956]~E(x19561,x19562)+E(f405(x19563,x19561,x19564),f405(x19563,x19562,x19564))
% 168.60/168.40 [1957]~E(x19571,x19572)+E(f405(x19573,x19574,x19571),f405(x19573,x19574,x19572))
% 168.60/168.40 [1958]~E(x19581,x19582)+E(f739(x19581,x19583,x19584),f739(x19582,x19583,x19584))
% 168.60/168.40 [1959]~E(x19591,x19592)+E(f739(x19593,x19591,x19594),f739(x19593,x19592,x19594))
% 168.60/168.40 [1960]~E(x19601,x19602)+E(f739(x19603,x19604,x19601),f739(x19603,x19604,x19602))
% 168.60/168.40 [1961]~E(x19611,x19612)+E(f19(x19611,x19613,x19614,x19615),f19(x19612,x19613,x19614,x19615))
% 168.60/168.40 [1962]~E(x19621,x19622)+E(f19(x19623,x19621,x19624,x19625),f19(x19623,x19622,x19624,x19625))
% 168.60/168.40 [1963]~E(x19631,x19632)+E(f19(x19633,x19634,x19631,x19635),f19(x19633,x19634,x19632,x19635))
% 168.60/168.40 [1964]~E(x19641,x19642)+E(f19(x19643,x19644,x19645,x19641),f19(x19643,x19644,x19645,x19642))
% 168.60/168.40 [1965]~E(x19651,x19652)+E(f678(x19651,x19653),f678(x19652,x19653))
% 168.60/168.40 [1966]~E(x19661,x19662)+E(f678(x19663,x19661),f678(x19663,x19662))
% 168.60/168.40 [1967]~E(x19671,x19672)+E(f742(x19671,x19673,x19674),f742(x19672,x19673,x19674))
% 168.60/168.40 [1968]~E(x19681,x19682)+E(f742(x19683,x19681,x19684),f742(x19683,x19682,x19684))
% 168.60/168.40 [1969]~E(x19691,x19692)+E(f742(x19693,x19694,x19691),f742(x19693,x19694,x19692))
% 168.60/168.40 [1970]~E(x19701,x19702)+E(f696(x19701,x19703,x19704),f696(x19702,x19703,x19704))
% 168.60/168.40 [1971]~E(x19711,x19712)+E(f696(x19713,x19711,x19714),f696(x19713,x19712,x19714))
% 168.60/168.40 [1972]~E(x19721,x19722)+E(f696(x19723,x19724,x19721),f696(x19723,x19724,x19722))
% 168.60/168.40 [1973]~E(x19731,x19732)+E(f211(x19731,x19733,x19734),f211(x19732,x19733,x19734))
% 168.60/168.40 [1974]~E(x19741,x19742)+E(f211(x19743,x19741,x19744),f211(x19743,x19742,x19744))
% 168.60/168.40 [1975]~E(x19751,x19752)+E(f211(x19753,x19754,x19751),f211(x19753,x19754,x19752))
% 168.60/168.40 [1976]~E(x19761,x19762)+E(f618(x19761,x19763,x19764,x19765,x19766),f618(x19762,x19763,x19764,x19765,x19766))
% 168.60/168.40 [1977]~E(x19771,x19772)+E(f618(x19773,x19771,x19774,x19775,x19776),f618(x19773,x19772,x19774,x19775,x19776))
% 168.60/168.40 [1978]~E(x19781,x19782)+E(f618(x19783,x19784,x19781,x19785,x19786),f618(x19783,x19784,x19782,x19785,x19786))
% 168.60/168.40 [1979]~E(x19791,x19792)+E(f618(x19793,x19794,x19795,x19791,x19796),f618(x19793,x19794,x19795,x19792,x19796))
% 168.60/168.40 [1980]~E(x19801,x19802)+E(f618(x19803,x19804,x19805,x19806,x19801),f618(x19803,x19804,x19805,x19806,x19802))
% 168.60/168.40 [1981]~E(x19811,x19812)+E(f857(x19811,x19813,x19814,x19815,x19816),f857(x19812,x19813,x19814,x19815,x19816))
% 168.60/168.40 [1982]~E(x19821,x19822)+E(f857(x19823,x19821,x19824,x19825,x19826),f857(x19823,x19822,x19824,x19825,x19826))
% 168.60/168.40 [1983]~E(x19831,x19832)+E(f857(x19833,x19834,x19831,x19835,x19836),f857(x19833,x19834,x19832,x19835,x19836))
% 168.60/168.40 [1984]~E(x19841,x19842)+E(f857(x19843,x19844,x19845,x19841,x19846),f857(x19843,x19844,x19845,x19842,x19846))
% 168.60/168.40 [1985]~E(x19851,x19852)+E(f857(x19853,x19854,x19855,x19856,x19851),f857(x19853,x19854,x19855,x19856,x19852))
% 168.60/168.40 [1986]~E(x19861,x19862)+E(f596(x19861,x19863),f596(x19862,x19863))
% 168.60/168.40 [1987]~E(x19871,x19872)+E(f596(x19873,x19871),f596(x19873,x19872))
% 168.60/168.40 [1988]~E(x19881,x19882)+E(f194(x19881,x19883,x19884,x19885),f194(x19882,x19883,x19884,x19885))
% 168.60/168.40 [1989]~E(x19891,x19892)+E(f194(x19893,x19891,x19894,x19895),f194(x19893,x19892,x19894,x19895))
% 168.60/168.40 [1990]~E(x19901,x19902)+E(f194(x19903,x19904,x19901,x19905),f194(x19903,x19904,x19902,x19905))
% 168.60/168.40 [1991]~E(x19911,x19912)+E(f194(x19913,x19914,x19915,x19911),f194(x19913,x19914,x19915,x19912))
% 168.60/168.40 [1992]~E(x19921,x19922)+E(f116(x19921,x19923,x19924,x19925,x19926),f116(x19922,x19923,x19924,x19925,x19926))
% 168.60/168.40 [1993]~E(x19931,x19932)+E(f116(x19933,x19931,x19934,x19935,x19936),f116(x19933,x19932,x19934,x19935,x19936))
% 168.60/168.40 [1994]~E(x19941,x19942)+E(f116(x19943,x19944,x19941,x19945,x19946),f116(x19943,x19944,x19942,x19945,x19946))
% 168.60/168.40 [1995]~E(x19951,x19952)+E(f116(x19953,x19954,x19955,x19951,x19956),f116(x19953,x19954,x19955,x19952,x19956))
% 168.60/168.40 [1996]~E(x19961,x19962)+E(f116(x19963,x19964,x19965,x19966,x19961),f116(x19963,x19964,x19965,x19966,x19962))
% 168.60/168.40 [1997]~E(x19971,x19972)+E(f120(x19971,x19973,x19974,x19975),f120(x19972,x19973,x19974,x19975))
% 168.60/168.40 [1998]~E(x19981,x19982)+E(f120(x19983,x19981,x19984,x19985),f120(x19983,x19982,x19984,x19985))
% 168.60/168.40 [1999]~E(x19991,x19992)+E(f120(x19993,x19994,x19991,x19995),f120(x19993,x19994,x19992,x19995))
% 168.60/168.40 [2000]~E(x20001,x20002)+E(f120(x20003,x20004,x20005,x20001),f120(x20003,x20004,x20005,x20002))
% 168.60/168.40 [2001]~E(x20011,x20012)+E(f706(x20011,x20013,x20014,x20015),f706(x20012,x20013,x20014,x20015))
% 168.60/168.40 [2002]~E(x20021,x20022)+E(f706(x20023,x20021,x20024,x20025),f706(x20023,x20022,x20024,x20025))
% 168.60/168.40 [2003]~E(x20031,x20032)+E(f706(x20033,x20034,x20031,x20035),f706(x20033,x20034,x20032,x20035))
% 168.60/168.40 [2004]~E(x20041,x20042)+E(f706(x20043,x20044,x20045,x20041),f706(x20043,x20044,x20045,x20042))
% 168.60/168.40 [2005]~E(x20051,x20052)+E(f268(x20051,x20053,x20054,x20055),f268(x20052,x20053,x20054,x20055))
% 168.60/168.40 [2006]~E(x20061,x20062)+E(f268(x20063,x20061,x20064,x20065),f268(x20063,x20062,x20064,x20065))
% 168.60/168.40 [2007]~E(x20071,x20072)+E(f268(x20073,x20074,x20071,x20075),f268(x20073,x20074,x20072,x20075))
% 168.60/168.40 [2008]~E(x20081,x20082)+E(f268(x20083,x20084,x20085,x20081),f268(x20083,x20084,x20085,x20082))
% 168.60/168.40 [2009]~E(x20091,x20092)+E(f399(x20091,x20093),f399(x20092,x20093))
% 168.60/168.40 [2010]~E(x20101,x20102)+E(f399(x20103,x20101),f399(x20103,x20102))
% 168.60/168.40 [2011]~E(x20111,x20112)+E(f358(x20111,x20113,x20114),f358(x20112,x20113,x20114))
% 168.60/168.40 [2012]~E(x20121,x20122)+E(f358(x20123,x20121,x20124),f358(x20123,x20122,x20124))
% 168.60/168.40 [2013]~E(x20131,x20132)+E(f358(x20133,x20134,x20131),f358(x20133,x20134,x20132))
% 168.60/168.40 [2014]~E(x20141,x20142)+E(f366(x20141,x20143),f366(x20142,x20143))
% 168.60/168.40 [2015]~E(x20151,x20152)+E(f366(x20153,x20151),f366(x20153,x20152))
% 168.60/168.40 [2016]~E(x20161,x20162)+E(f749(x20161,x20163,x20164),f749(x20162,x20163,x20164))
% 168.60/168.40 [2017]~E(x20171,x20172)+E(f749(x20173,x20171,x20174),f749(x20173,x20172,x20174))
% 168.60/168.40 [2018]~E(x20181,x20182)+E(f749(x20183,x20184,x20181),f749(x20183,x20184,x20182))
% 168.60/168.40 [2019]~E(x20191,x20192)+E(f300(x20191,x20193),f300(x20192,x20193))
% 168.60/168.40 [2020]~E(x20201,x20202)+E(f300(x20203,x20201),f300(x20203,x20202))
% 168.60/168.40 [2021]~E(x20211,x20212)+E(f408(x20211,x20213),f408(x20212,x20213))
% 168.60/168.40 [2022]~E(x20221,x20222)+E(f408(x20223,x20221),f408(x20223,x20222))
% 168.60/168.40 [2023]~E(x20231,x20232)+E(f666(x20231,x20233,x20234,x20235),f666(x20232,x20233,x20234,x20235))
% 168.60/168.40 [2024]~E(x20241,x20242)+E(f666(x20243,x20241,x20244,x20245),f666(x20243,x20242,x20244,x20245))
% 168.60/168.40 [2025]~E(x20251,x20252)+E(f666(x20253,x20254,x20251,x20255),f666(x20253,x20254,x20252,x20255))
% 168.60/168.40 [2026]~E(x20261,x20262)+E(f666(x20263,x20264,x20265,x20261),f666(x20263,x20264,x20265,x20262))
% 168.60/168.40 [2027]~E(x20271,x20272)+E(f891(x20271,x20273,x20274),f891(x20272,x20273,x20274))
% 168.60/168.40 [2028]~E(x20281,x20282)+E(f891(x20283,x20281,x20284),f891(x20283,x20282,x20284))
% 168.60/168.40 [2029]~E(x20291,x20292)+E(f891(x20293,x20294,x20291),f891(x20293,x20294,x20292))
% 168.60/168.40 [2030]~E(x20301,x20302)+E(f767(x20301,x20303,x20304),f767(x20302,x20303,x20304))
% 168.60/168.40 [2031]~E(x20311,x20312)+E(f767(x20313,x20311,x20314),f767(x20313,x20312,x20314))
% 168.60/168.40 [2032]~E(x20321,x20322)+E(f767(x20323,x20324,x20321),f767(x20323,x20324,x20322))
% 168.60/168.40 [2033]~E(x20331,x20332)+E(f481(x20331,x20333,x20334,x20335),f481(x20332,x20333,x20334,x20335))
% 168.60/168.40 [2034]~E(x20341,x20342)+E(f481(x20343,x20341,x20344,x20345),f481(x20343,x20342,x20344,x20345))
% 168.60/168.40 [2035]~E(x20351,x20352)+E(f481(x20353,x20354,x20351,x20355),f481(x20353,x20354,x20352,x20355))
% 168.60/168.40 [2036]~E(x20361,x20362)+E(f481(x20363,x20364,x20365,x20361),f481(x20363,x20364,x20365,x20362))
% 168.60/168.40 [2037]~E(x20371,x20372)+E(f765(x20371),f765(x20372))
% 168.60/168.40 [2038]~E(x20381,x20382)+E(f826(x20381,x20383,x20384,x20385,x20386,x20387,x20388,x20389),f826(x20382,x20383,x20384,x20385,x20386,x20387,x20388,x20389))
% 168.60/168.40 [2039]~E(x20391,x20392)+E(f826(x20393,x20391,x20394,x20395,x20396,x20397,x20398,x20399),f826(x20393,x20392,x20394,x20395,x20396,x20397,x20398,x20399))
% 168.60/168.40 [2040]~E(x20401,x20402)+E(f826(x20403,x20404,x20401,x20405,x20406,x20407,x20408,x20409),f826(x20403,x20404,x20402,x20405,x20406,x20407,x20408,x20409))
% 168.60/168.40 [2041]~E(x20411,x20412)+E(f826(x20413,x20414,x20415,x20411,x20416,x20417,x20418,x20419),f826(x20413,x20414,x20415,x20412,x20416,x20417,x20418,x20419))
% 168.60/168.40 [2042]~E(x20421,x20422)+E(f826(x20423,x20424,x20425,x20426,x20421,x20427,x20428,x20429),f826(x20423,x20424,x20425,x20426,x20422,x20427,x20428,x20429))
% 168.60/168.40 [2043]~E(x20431,x20432)+E(f826(x20433,x20434,x20435,x20436,x20437,x20431,x20438,x20439),f826(x20433,x20434,x20435,x20436,x20437,x20432,x20438,x20439))
% 168.60/168.40 [2044]~E(x20441,x20442)+E(f826(x20443,x20444,x20445,x20446,x20447,x20448,x20441,x20449),f826(x20443,x20444,x20445,x20446,x20447,x20448,x20442,x20449))
% 168.60/168.40 [2045]~E(x20451,x20452)+E(f826(x20453,x20454,x20455,x20456,x20457,x20458,x20459,x20451),f826(x20453,x20454,x20455,x20456,x20457,x20458,x20459,x20452))
% 168.60/168.40 [2046]~E(x20461,x20462)+E(f509(x20461,x20463,x20464),f509(x20462,x20463,x20464))
% 168.60/168.40 [2047]~E(x20471,x20472)+E(f509(x20473,x20471,x20474),f509(x20473,x20472,x20474))
% 168.60/168.40 [2048]~E(x20481,x20482)+E(f509(x20483,x20484,x20481),f509(x20483,x20484,x20482))
% 168.60/168.40 [2049]~E(x20491,x20492)+E(f436(x20491,x20493,x20494),f436(x20492,x20493,x20494))
% 168.60/168.40 [2050]~E(x20501,x20502)+E(f436(x20503,x20501,x20504),f436(x20503,x20502,x20504))
% 168.60/168.40 [2051]~E(x20511,x20512)+E(f436(x20513,x20514,x20511),f436(x20513,x20514,x20512))
% 168.60/168.40 [2052]~E(x20521,x20522)+E(f545(x20521,x20523),f545(x20522,x20523))
% 168.60/168.40 [2053]~E(x20531,x20532)+E(f545(x20533,x20531),f545(x20533,x20532))
% 168.60/168.40 [2054]~E(x20541,x20542)+E(f465(x20541,x20543,x20544,x20545),f465(x20542,x20543,x20544,x20545))
% 168.60/168.40 [2055]~E(x20551,x20552)+E(f465(x20553,x20551,x20554,x20555),f465(x20553,x20552,x20554,x20555))
% 168.60/168.40 [2056]~E(x20561,x20562)+E(f465(x20563,x20564,x20561,x20565),f465(x20563,x20564,x20562,x20565))
% 168.60/168.40 [2057]~E(x20571,x20572)+E(f465(x20573,x20574,x20575,x20571),f465(x20573,x20574,x20575,x20572))
% 168.60/168.40 [2058]~E(x20581,x20582)+E(f363(x20581,x20583,x20584),f363(x20582,x20583,x20584))
% 168.60/168.40 [2059]~E(x20591,x20592)+E(f363(x20593,x20591,x20594),f363(x20593,x20592,x20594))
% 168.60/168.40 [2060]~E(x20601,x20602)+E(f363(x20603,x20604,x20601),f363(x20603,x20604,x20602))
% 168.60/168.40 [2061]~E(x20611,x20612)+E(f424(x20611,x20613),f424(x20612,x20613))
% 168.60/168.40 [2062]~E(x20621,x20622)+E(f424(x20623,x20621),f424(x20623,x20622))
% 168.60/168.40 [2063]~E(x20631,x20632)+E(f562(x20631),f562(x20632))
% 168.60/168.40 [2064]~E(x20641,x20642)+E(f772(x20641,x20643,x20644,x20645,x20646,x20647,x20648),f772(x20642,x20643,x20644,x20645,x20646,x20647,x20648))
% 168.60/168.40 [2065]~E(x20651,x20652)+E(f772(x20653,x20651,x20654,x20655,x20656,x20657,x20658),f772(x20653,x20652,x20654,x20655,x20656,x20657,x20658))
% 168.60/168.40 [2066]~E(x20661,x20662)+E(f772(x20663,x20664,x20661,x20665,x20666,x20667,x20668),f772(x20663,x20664,x20662,x20665,x20666,x20667,x20668))
% 168.60/168.40 [2067]~E(x20671,x20672)+E(f772(x20673,x20674,x20675,x20671,x20676,x20677,x20678),f772(x20673,x20674,x20675,x20672,x20676,x20677,x20678))
% 168.60/168.40 [2068]~E(x20681,x20682)+E(f772(x20683,x20684,x20685,x20686,x20681,x20687,x20688),f772(x20683,x20684,x20685,x20686,x20682,x20687,x20688))
% 168.60/168.40 [2069]~E(x20691,x20692)+E(f772(x20693,x20694,x20695,x20696,x20697,x20691,x20698),f772(x20693,x20694,x20695,x20696,x20697,x20692,x20698))
% 168.60/168.40 [2070]~E(x20701,x20702)+E(f772(x20703,x20704,x20705,x20706,x20707,x20708,x20701),f772(x20703,x20704,x20705,x20706,x20707,x20708,x20702))
% 168.60/168.40 [2071]~E(x20711,x20712)+E(f346(x20711,x20713),f346(x20712,x20713))
% 168.60/168.40 [2072]~E(x20721,x20722)+E(f346(x20723,x20721),f346(x20723,x20722))
% 168.60/168.40 [2073]~E(x20731,x20732)+E(f411(x20731,x20733,x20734,x20735,x20736),f411(x20732,x20733,x20734,x20735,x20736))
% 168.60/168.40 [2074]~E(x20741,x20742)+E(f411(x20743,x20741,x20744,x20745,x20746),f411(x20743,x20742,x20744,x20745,x20746))
% 168.60/168.40 [2075]~E(x20751,x20752)+E(f411(x20753,x20754,x20751,x20755,x20756),f411(x20753,x20754,x20752,x20755,x20756))
% 168.60/168.40 [2076]~E(x20761,x20762)+E(f411(x20763,x20764,x20765,x20761,x20766),f411(x20763,x20764,x20765,x20762,x20766))
% 168.60/168.40 [2077]~E(x20771,x20772)+E(f411(x20773,x20774,x20775,x20776,x20771),f411(x20773,x20774,x20775,x20776,x20772))
% 168.60/168.40 [2078]~E(x20781,x20782)+E(f781(x20781,x20783,x20784,x20785,x20786),f781(x20782,x20783,x20784,x20785,x20786))
% 168.60/168.40 [2079]~E(x20791,x20792)+E(f781(x20793,x20791,x20794,x20795,x20796),f781(x20793,x20792,x20794,x20795,x20796))
% 168.60/168.40 [2080]~E(x20801,x20802)+E(f781(x20803,x20804,x20801,x20805,x20806),f781(x20803,x20804,x20802,x20805,x20806))
% 168.60/168.40 [2081]~E(x20811,x20812)+E(f781(x20813,x20814,x20815,x20811,x20816),f781(x20813,x20814,x20815,x20812,x20816))
% 168.60/168.40 [2082]~E(x20821,x20822)+E(f781(x20823,x20824,x20825,x20826,x20821),f781(x20823,x20824,x20825,x20826,x20822))
% 168.60/168.40 [2083]~E(x20831,x20832)+E(f215(x20831,x20833,x20834,x20835,x20836),f215(x20832,x20833,x20834,x20835,x20836))
% 168.60/168.40 [2084]~E(x20841,x20842)+E(f215(x20843,x20841,x20844,x20845,x20846),f215(x20843,x20842,x20844,x20845,x20846))
% 168.60/168.40 [2085]~E(x20851,x20852)+E(f215(x20853,x20854,x20851,x20855,x20856),f215(x20853,x20854,x20852,x20855,x20856))
% 168.60/168.40 [2086]~E(x20861,x20862)+E(f215(x20863,x20864,x20865,x20861,x20866),f215(x20863,x20864,x20865,x20862,x20866))
% 168.60/168.40 [2087]~E(x20871,x20872)+E(f215(x20873,x20874,x20875,x20876,x20871),f215(x20873,x20874,x20875,x20876,x20872))
% 168.60/168.40 [2088]~E(x20881,x20882)+E(f351(x20881,x20883),f351(x20882,x20883))
% 168.60/168.40 [2089]~E(x20891,x20892)+E(f351(x20893,x20891),f351(x20893,x20892))
% 168.60/168.40 [2090]~E(x20901,x20902)+E(f641(x20901,x20903,x20904),f641(x20902,x20903,x20904))
% 168.60/168.40 [2091]~E(x20911,x20912)+E(f641(x20913,x20911,x20914),f641(x20913,x20912,x20914))
% 168.60/168.40 [2092]~E(x20921,x20922)+E(f641(x20923,x20924,x20921),f641(x20923,x20924,x20922))
% 168.60/168.40 [2093]~E(x20931,x20932)+E(f372(x20931,x20933,x20934),f372(x20932,x20933,x20934))
% 168.60/168.40 [2094]~E(x20941,x20942)+E(f372(x20943,x20941,x20944),f372(x20943,x20942,x20944))
% 168.60/168.40 [2095]~E(x20951,x20952)+E(f372(x20953,x20954,x20951),f372(x20953,x20954,x20952))
% 168.60/168.40 [2096]~E(x20961,x20962)+E(f203(x20961,x20963),f203(x20962,x20963))
% 168.60/168.40 [2097]~E(x20971,x20972)+E(f203(x20973,x20971),f203(x20973,x20972))
% 168.60/168.40 [2098]~E(x20981,x20982)+E(f687(x20981,x20983,x20984),f687(x20982,x20983,x20984))
% 168.60/168.40 [2099]~E(x20991,x20992)+E(f687(x20993,x20991,x20994),f687(x20993,x20992,x20994))
% 168.60/168.40 [2100]~E(x21001,x21002)+E(f687(x21003,x21004,x21001),f687(x21003,x21004,x21002))
% 168.60/168.40 [2101]~E(x21011,x21012)+E(f407(x21011,x21013,x21014,x21015,x21016,x21017),f407(x21012,x21013,x21014,x21015,x21016,x21017))
% 168.60/168.40 [2102]~E(x21021,x21022)+E(f407(x21023,x21021,x21024,x21025,x21026,x21027),f407(x21023,x21022,x21024,x21025,x21026,x21027))
% 168.60/168.40 [2103]~E(x21031,x21032)+E(f407(x21033,x21034,x21031,x21035,x21036,x21037),f407(x21033,x21034,x21032,x21035,x21036,x21037))
% 168.60/168.40 [2104]~E(x21041,x21042)+E(f407(x21043,x21044,x21045,x21041,x21046,x21047),f407(x21043,x21044,x21045,x21042,x21046,x21047))
% 168.60/168.40 [2105]~E(x21051,x21052)+E(f407(x21053,x21054,x21055,x21056,x21051,x21057),f407(x21053,x21054,x21055,x21056,x21052,x21057))
% 168.60/168.40 [2106]~E(x21061,x21062)+E(f407(x21063,x21064,x21065,x21066,x21067,x21061),f407(x21063,x21064,x21065,x21066,x21067,x21062))
% 168.60/168.40 [2107]~E(x21071,x21072)+E(f872(x21071,x21073,x21074),f872(x21072,x21073,x21074))
% 168.60/168.40 [2108]~E(x21081,x21082)+E(f872(x21083,x21081,x21084),f872(x21083,x21082,x21084))
% 168.60/168.40 [2109]~E(x21091,x21092)+E(f872(x21093,x21094,x21091),f872(x21093,x21094,x21092))
% 168.60/168.40 [2110]~E(x21101,x21102)+E(f169(x21101),f169(x21102))
% 168.60/168.40 [2111]~E(x21111,x21112)+E(f588(x21111,x21113,x21114,x21115),f588(x21112,x21113,x21114,x21115))
% 168.60/168.40 [2112]~E(x21121,x21122)+E(f588(x21123,x21121,x21124,x21125),f588(x21123,x21122,x21124,x21125))
% 168.60/168.40 [2113]~E(x21131,x21132)+E(f588(x21133,x21134,x21131,x21135),f588(x21133,x21134,x21132,x21135))
% 168.60/168.40 [2114]~E(x21141,x21142)+E(f588(x21143,x21144,x21145,x21141),f588(x21143,x21144,x21145,x21142))
% 168.60/168.40 [2115]~E(x21151,x21152)+E(f731(x21151,x21153),f731(x21152,x21153))
% 168.60/168.40 [2116]~E(x21161,x21162)+E(f731(x21163,x21161),f731(x21163,x21162))
% 168.60/168.40 [2117]~E(x21171,x21172)+E(f584(x21171,x21173,x21174),f584(x21172,x21173,x21174))
% 168.60/168.40 [2118]~E(x21181,x21182)+E(f584(x21183,x21181,x21184),f584(x21183,x21182,x21184))
% 168.60/168.40 [2119]~E(x21191,x21192)+E(f584(x21193,x21194,x21191),f584(x21193,x21194,x21192))
% 168.60/168.40 [2120]~E(x21201,x21202)+E(f893(x21201,x21203,x21204),f893(x21202,x21203,x21204))
% 168.60/168.40 [2121]~E(x21211,x21212)+E(f893(x21213,x21211,x21214),f893(x21213,x21212,x21214))
% 168.60/168.40 [2122]~E(x21221,x21222)+E(f893(x21223,x21224,x21221),f893(x21223,x21224,x21222))
% 168.60/168.40 [2123]~E(x21231,x21232)+E(f756(x21231,x21233,x21234,x21235,x21236),f756(x21232,x21233,x21234,x21235,x21236))
% 168.60/168.40 [2124]~E(x21241,x21242)+E(f756(x21243,x21241,x21244,x21245,x21246),f756(x21243,x21242,x21244,x21245,x21246))
% 168.60/168.40 [2125]~E(x21251,x21252)+E(f756(x21253,x21254,x21251,x21255,x21256),f756(x21253,x21254,x21252,x21255,x21256))
% 168.60/168.40 [2126]~E(x21261,x21262)+E(f756(x21263,x21264,x21265,x21261,x21266),f756(x21263,x21264,x21265,x21262,x21266))
% 168.60/168.40 [2127]~E(x21271,x21272)+E(f756(x21273,x21274,x21275,x21276,x21271),f756(x21273,x21274,x21275,x21276,x21272))
% 168.60/168.40 [2128]~E(x21281,x21282)+E(f639(x21281,x21283,x21284,x21285),f639(x21282,x21283,x21284,x21285))
% 168.60/168.40 [2129]~E(x21291,x21292)+E(f639(x21293,x21291,x21294,x21295),f639(x21293,x21292,x21294,x21295))
% 168.60/168.40 [2130]~E(x21301,x21302)+E(f639(x21303,x21304,x21301,x21305),f639(x21303,x21304,x21302,x21305))
% 168.60/168.40 [2131]~E(x21311,x21312)+E(f639(x21313,x21314,x21315,x21311),f639(x21313,x21314,x21315,x21312))
% 168.60/168.40 [2132]~E(x21321,x21322)+E(f840(x21321,x21323,x21324),f840(x21322,x21323,x21324))
% 168.60/168.40 [2133]~E(x21331,x21332)+E(f840(x21333,x21331,x21334),f840(x21333,x21332,x21334))
% 168.60/168.40 [2134]~E(x21341,x21342)+E(f840(x21343,x21344,x21341),f840(x21343,x21344,x21342))
% 168.60/168.40 [2135]~E(x21351,x21352)+E(f283(x21351,x21353,x21354),f283(x21352,x21353,x21354))
% 168.60/168.40 [2136]~E(x21361,x21362)+E(f283(x21363,x21361,x21364),f283(x21363,x21362,x21364))
% 168.60/168.40 [2137]~E(x21371,x21372)+E(f283(x21373,x21374,x21371),f283(x21373,x21374,x21372))
% 168.60/168.40 [2138]~E(x21381,x21382)+E(f822(x21381,x21383,x21384,x21385,x21386,x21387,x21388,x21389),f822(x21382,x21383,x21384,x21385,x21386,x21387,x21388,x21389))
% 168.60/168.40 [2139]~E(x21391,x21392)+E(f822(x21393,x21391,x21394,x21395,x21396,x21397,x21398,x21399),f822(x21393,x21392,x21394,x21395,x21396,x21397,x21398,x21399))
% 168.60/168.40 [2140]~E(x21401,x21402)+E(f822(x21403,x21404,x21401,x21405,x21406,x21407,x21408,x21409),f822(x21403,x21404,x21402,x21405,x21406,x21407,x21408,x21409))
% 168.60/168.40 [2141]~E(x21411,x21412)+E(f822(x21413,x21414,x21415,x21411,x21416,x21417,x21418,x21419),f822(x21413,x21414,x21415,x21412,x21416,x21417,x21418,x21419))
% 168.60/168.40 [2142]~E(x21421,x21422)+E(f822(x21423,x21424,x21425,x21426,x21421,x21427,x21428,x21429),f822(x21423,x21424,x21425,x21426,x21422,x21427,x21428,x21429))
% 168.60/168.40 [2143]~E(x21431,x21432)+E(f822(x21433,x21434,x21435,x21436,x21437,x21431,x21438,x21439),f822(x21433,x21434,x21435,x21436,x21437,x21432,x21438,x21439))
% 168.60/168.40 [2144]~E(x21441,x21442)+E(f822(x21443,x21444,x21445,x21446,x21447,x21448,x21441,x21449),f822(x21443,x21444,x21445,x21446,x21447,x21448,x21442,x21449))
% 168.60/168.40 [2145]~E(x21451,x21452)+E(f822(x21453,x21454,x21455,x21456,x21457,x21458,x21459,x21451),f822(x21453,x21454,x21455,x21456,x21457,x21458,x21459,x21452))
% 168.60/168.40 [2146]~E(x21461,x21462)+E(f464(x21461,x21463,x21464,x21465),f464(x21462,x21463,x21464,x21465))
% 168.60/168.40 [2147]~E(x21471,x21472)+E(f464(x21473,x21471,x21474,x21475),f464(x21473,x21472,x21474,x21475))
% 168.60/168.40 [2148]~E(x21481,x21482)+E(f464(x21483,x21484,x21481,x21485),f464(x21483,x21484,x21482,x21485))
% 168.60/168.40 [2149]~E(x21491,x21492)+E(f464(x21493,x21494,x21495,x21491),f464(x21493,x21494,x21495,x21492))
% 168.60/168.40 [2150]~E(x21501,x21502)+E(f404(x21501,x21503),f404(x21502,x21503))
% 168.60/168.40 [2151]~E(x21511,x21512)+E(f404(x21513,x21511),f404(x21513,x21512))
% 168.60/168.40 [2152]~E(x21521,x21522)+E(f832(x21521,x21523,x21524,x21525,x21526,x21527,x21528),f832(x21522,x21523,x21524,x21525,x21526,x21527,x21528))
% 168.60/168.40 [2153]~E(x21531,x21532)+E(f832(x21533,x21531,x21534,x21535,x21536,x21537,x21538),f832(x21533,x21532,x21534,x21535,x21536,x21537,x21538))
% 168.60/168.40 [2154]~E(x21541,x21542)+E(f832(x21543,x21544,x21541,x21545,x21546,x21547,x21548),f832(x21543,x21544,x21542,x21545,x21546,x21547,x21548))
% 168.60/168.40 [2155]~E(x21551,x21552)+E(f832(x21553,x21554,x21555,x21551,x21556,x21557,x21558),f832(x21553,x21554,x21555,x21552,x21556,x21557,x21558))
% 168.60/168.40 [2156]~E(x21561,x21562)+E(f832(x21563,x21564,x21565,x21566,x21561,x21567,x21568),f832(x21563,x21564,x21565,x21566,x21562,x21567,x21568))
% 168.60/168.40 [2157]~E(x21571,x21572)+E(f832(x21573,x21574,x21575,x21576,x21577,x21571,x21578),f832(x21573,x21574,x21575,x21576,x21577,x21572,x21578))
% 168.60/168.40 [2158]~E(x21581,x21582)+E(f832(x21583,x21584,x21585,x21586,x21587,x21588,x21581),f832(x21583,x21584,x21585,x21586,x21587,x21588,x21582))
% 168.60/168.40 [2159]~E(x21591,x21592)+E(f543(x21591,x21593,x21594,x21595,x21596,x21597),f543(x21592,x21593,x21594,x21595,x21596,x21597))
% 168.60/168.40 [2160]~E(x21601,x21602)+E(f543(x21603,x21601,x21604,x21605,x21606,x21607),f543(x21603,x21602,x21604,x21605,x21606,x21607))
% 168.60/168.40 [2161]~E(x21611,x21612)+E(f543(x21613,x21614,x21611,x21615,x21616,x21617),f543(x21613,x21614,x21612,x21615,x21616,x21617))
% 168.60/168.40 [2162]~E(x21621,x21622)+E(f543(x21623,x21624,x21625,x21621,x21626,x21627),f543(x21623,x21624,x21625,x21622,x21626,x21627))
% 168.60/168.40 [2163]~E(x21631,x21632)+E(f543(x21633,x21634,x21635,x21636,x21631,x21637),f543(x21633,x21634,x21635,x21636,x21632,x21637))
% 168.60/168.40 [2164]~E(x21641,x21642)+E(f543(x21643,x21644,x21645,x21646,x21647,x21641),f543(x21643,x21644,x21645,x21646,x21647,x21642))
% 168.60/168.40 [2165]~E(x21651,x21652)+E(f235(x21651,x21653,x21654),f235(x21652,x21653,x21654))
% 168.60/168.40 [2166]~E(x21661,x21662)+E(f235(x21663,x21661,x21664),f235(x21663,x21662,x21664))
% 168.60/168.40 [2167]~E(x21671,x21672)+E(f235(x21673,x21674,x21671),f235(x21673,x21674,x21672))
% 168.60/168.40 [2168]~E(x21681,x21682)+E(f532(x21681,x21683,x21684,x21685,x21686,x21687),f532(x21682,x21683,x21684,x21685,x21686,x21687))
% 168.60/168.40 [2169]~E(x21691,x21692)+E(f532(x21693,x21691,x21694,x21695,x21696,x21697),f532(x21693,x21692,x21694,x21695,x21696,x21697))
% 168.60/168.40 [2170]~E(x21701,x21702)+E(f532(x21703,x21704,x21701,x21705,x21706,x21707),f532(x21703,x21704,x21702,x21705,x21706,x21707))
% 168.60/168.40 [2171]~E(x21711,x21712)+E(f532(x21713,x21714,x21715,x21711,x21716,x21717),f532(x21713,x21714,x21715,x21712,x21716,x21717))
% 168.60/168.40 [2172]~E(x21721,x21722)+E(f532(x21723,x21724,x21725,x21726,x21721,x21727),f532(x21723,x21724,x21725,x21726,x21722,x21727))
% 168.60/168.40 [2173]~E(x21731,x21732)+E(f532(x21733,x21734,x21735,x21736,x21737,x21731),f532(x21733,x21734,x21735,x21736,x21737,x21732))
% 168.60/168.40 [2174]~E(x21741,x21742)+E(f725(x21741,x21743,x21744,x21745,x21746),f725(x21742,x21743,x21744,x21745,x21746))
% 168.60/168.40 [2175]~E(x21751,x21752)+E(f725(x21753,x21751,x21754,x21755,x21756),f725(x21753,x21752,x21754,x21755,x21756))
% 168.60/168.40 [2176]~E(x21761,x21762)+E(f725(x21763,x21764,x21761,x21765,x21766),f725(x21763,x21764,x21762,x21765,x21766))
% 168.60/168.40 [2177]~E(x21771,x21772)+E(f725(x21773,x21774,x21775,x21771,x21776),f725(x21773,x21774,x21775,x21772,x21776))
% 168.60/168.40 [2178]~E(x21781,x21782)+E(f725(x21783,x21784,x21785,x21786,x21781),f725(x21783,x21784,x21785,x21786,x21782))
% 168.60/168.40 [2179]~E(x21791,x21792)+E(f661(x21791,x21793,x21794),f661(x21792,x21793,x21794))
% 168.60/168.40 [2180]~E(x21801,x21802)+E(f661(x21803,x21801,x21804),f661(x21803,x21802,x21804))
% 168.60/168.40 [2181]~E(x21811,x21812)+E(f661(x21813,x21814,x21811),f661(x21813,x21814,x21812))
% 168.60/168.40 [2182]~E(x21821,x21822)+E(f738(x21821,x21823,x21824),f738(x21822,x21823,x21824))
% 168.60/168.40 [2183]~E(x21831,x21832)+E(f738(x21833,x21831,x21834),f738(x21833,x21832,x21834))
% 168.60/168.40 [2184]~E(x21841,x21842)+E(f738(x21843,x21844,x21841),f738(x21843,x21844,x21842))
% 168.60/168.40 [2185]~E(x21851,x21852)+E(f500(x21851),f500(x21852))
% 168.60/168.40 [2186]~E(x21861,x21862)+E(f536(x21861,x21863,x21864,x21865,x21866,x21867,x21868,x21869),f536(x21862,x21863,x21864,x21865,x21866,x21867,x21868,x21869))
% 168.60/168.40 [2187]~E(x21871,x21872)+E(f536(x21873,x21871,x21874,x21875,x21876,x21877,x21878,x21879),f536(x21873,x21872,x21874,x21875,x21876,x21877,x21878,x21879))
% 168.60/168.40 [2188]~E(x21881,x21882)+E(f536(x21883,x21884,x21881,x21885,x21886,x21887,x21888,x21889),f536(x21883,x21884,x21882,x21885,x21886,x21887,x21888,x21889))
% 168.60/168.40 [2189]~E(x21891,x21892)+E(f536(x21893,x21894,x21895,x21891,x21896,x21897,x21898,x21899),f536(x21893,x21894,x21895,x21892,x21896,x21897,x21898,x21899))
% 168.60/168.40 [2190]~E(x21901,x21902)+E(f536(x21903,x21904,x21905,x21906,x21901,x21907,x21908,x21909),f536(x21903,x21904,x21905,x21906,x21902,x21907,x21908,x21909))
% 168.60/168.40 [2191]~E(x21911,x21912)+E(f536(x21913,x21914,x21915,x21916,x21917,x21911,x21918,x21919),f536(x21913,x21914,x21915,x21916,x21917,x21912,x21918,x21919))
% 168.60/168.40 [2192]~E(x21921,x21922)+E(f536(x21923,x21924,x21925,x21926,x21927,x21928,x21921,x21929),f536(x21923,x21924,x21925,x21926,x21927,x21928,x21922,x21929))
% 168.60/168.40 [2193]~E(x21931,x21932)+E(f536(x21933,x21934,x21935,x21936,x21937,x21938,x21939,x21931),f536(x21933,x21934,x21935,x21936,x21937,x21938,x21939,x21932))
% 168.60/168.40 [2194]~E(x21941,x21942)+E(f774(x21941,x21943),f774(x21942,x21943))
% 168.60/168.40 [2195]~E(x21951,x21952)+E(f774(x21953,x21951),f774(x21953,x21952))
% 168.60/168.40 [2196]~E(x21961,x21962)+E(f611(x21961,x21963),f611(x21962,x21963))
% 168.60/168.40 [2197]~E(x21971,x21972)+E(f611(x21973,x21971),f611(x21973,x21972))
% 168.60/168.40 [2198]~E(x21981,x21982)+E(f508(x21981,x21983,x21984),f508(x21982,x21983,x21984))
% 168.60/168.40 [2199]~E(x21991,x21992)+E(f508(x21993,x21991,x21994),f508(x21993,x21992,x21994))
% 168.60/168.40 [2200]~E(x22001,x22002)+E(f508(x22003,x22004,x22001),f508(x22003,x22004,x22002))
% 168.60/168.40 [2201]~E(x22011,x22012)+E(f524(x22011,x22013,x22014,x22015,x22016,x22017),f524(x22012,x22013,x22014,x22015,x22016,x22017))
% 168.60/168.40 [2202]~E(x22021,x22022)+E(f524(x22023,x22021,x22024,x22025,x22026,x22027),f524(x22023,x22022,x22024,x22025,x22026,x22027))
% 168.60/168.40 [2203]~E(x22031,x22032)+E(f524(x22033,x22034,x22031,x22035,x22036,x22037),f524(x22033,x22034,x22032,x22035,x22036,x22037))
% 168.60/168.40 [2204]~E(x22041,x22042)+E(f524(x22043,x22044,x22045,x22041,x22046,x22047),f524(x22043,x22044,x22045,x22042,x22046,x22047))
% 168.60/168.40 [2205]~E(x22051,x22052)+E(f524(x22053,x22054,x22055,x22056,x22051,x22057),f524(x22053,x22054,x22055,x22056,x22052,x22057))
% 168.60/168.40 [2206]~E(x22061,x22062)+E(f524(x22063,x22064,x22065,x22066,x22067,x22061),f524(x22063,x22064,x22065,x22066,x22067,x22062))
% 168.60/168.40 [2207]~E(x22071,x22072)+E(f395(x22071,x22073),f395(x22072,x22073))
% 168.60/168.40 [2208]~E(x22081,x22082)+E(f395(x22083,x22081),f395(x22083,x22082))
% 168.60/168.40 [2209]~E(x22091,x22092)+E(f589(x22091,x22093,x22094,x22095,x22096),f589(x22092,x22093,x22094,x22095,x22096))
% 168.60/168.40 [2210]~E(x22101,x22102)+E(f589(x22103,x22101,x22104,x22105,x22106),f589(x22103,x22102,x22104,x22105,x22106))
% 168.60/168.40 [2211]~E(x22111,x22112)+E(f589(x22113,x22114,x22111,x22115,x22116),f589(x22113,x22114,x22112,x22115,x22116))
% 168.60/168.40 [2212]~E(x22121,x22122)+E(f589(x22123,x22124,x22125,x22121,x22126),f589(x22123,x22124,x22125,x22122,x22126))
% 168.60/168.40 [2213]~E(x22131,x22132)+E(f589(x22133,x22134,x22135,x22136,x22131),f589(x22133,x22134,x22135,x22136,x22132))
% 168.60/168.40 [2214]~E(x22141,x22142)+E(f748(x22141,x22143,x22144),f748(x22142,x22143,x22144))
% 168.60/168.40 [2215]~E(x22151,x22152)+E(f748(x22153,x22151,x22154),f748(x22153,x22152,x22154))
% 168.60/168.40 [2216]~E(x22161,x22162)+E(f748(x22163,x22164,x22161),f748(x22163,x22164,x22162))
% 168.60/168.40 [2217]~E(x22171,x22172)+E(f434(x22171,x22173,x22174),f434(x22172,x22173,x22174))
% 168.60/168.40 [2218]~E(x22181,x22182)+E(f434(x22183,x22181,x22184),f434(x22183,x22182,x22184))
% 168.60/168.40 [2219]~E(x22191,x22192)+E(f434(x22193,x22194,x22191),f434(x22193,x22194,x22192))
% 168.60/168.40 [2220]~E(x22201,x22202)+E(f869(x22201,x22203,x22204,x22205,x22206),f869(x22202,x22203,x22204,x22205,x22206))
% 168.60/168.40 [2221]~E(x22211,x22212)+E(f869(x22213,x22211,x22214,x22215,x22216),f869(x22213,x22212,x22214,x22215,x22216))
% 168.60/168.40 [2222]~E(x22221,x22222)+E(f869(x22223,x22224,x22221,x22225,x22226),f869(x22223,x22224,x22222,x22225,x22226))
% 168.60/168.40 [2223]~E(x22231,x22232)+E(f869(x22233,x22234,x22235,x22231,x22236),f869(x22233,x22234,x22235,x22232,x22236))
% 168.60/168.40 [2224]~E(x22241,x22242)+E(f869(x22243,x22244,x22245,x22246,x22241),f869(x22243,x22244,x22245,x22246,x22242))
% 168.60/168.40 [2225]~E(x22251,x22252)+E(f515(x22251,x22253,x22254),f515(x22252,x22253,x22254))
% 168.60/168.40 [2226]~E(x22261,x22262)+E(f515(x22263,x22261,x22264),f515(x22263,x22262,x22264))
% 168.60/168.40 [2227]~E(x22271,x22272)+E(f515(x22273,x22274,x22271),f515(x22273,x22274,x22272))
% 168.60/168.40 [2228]~E(x22281,x22282)+E(f504(x22281,x22283,x22284),f504(x22282,x22283,x22284))
% 168.60/168.40 [2229]~E(x22291,x22292)+E(f504(x22293,x22291,x22294),f504(x22293,x22292,x22294))
% 168.60/168.40 [2230]~E(x22301,x22302)+E(f504(x22303,x22304,x22301),f504(x22303,x22304,x22302))
% 168.60/168.40 [2231]~E(x22311,x22312)+E(f280(x22311,x22313),f280(x22312,x22313))
% 168.60/168.40 [2232]~E(x22321,x22322)+E(f280(x22323,x22321),f280(x22323,x22322))
% 168.60/168.40 [2233]~E(x22331,x22332)+E(f792(x22331,x22333,x22334),f792(x22332,x22333,x22334))
% 168.60/168.40 [2234]~E(x22341,x22342)+E(f792(x22343,x22341,x22344),f792(x22343,x22342,x22344))
% 168.60/168.40 [2235]~E(x22351,x22352)+E(f792(x22353,x22354,x22351),f792(x22353,x22354,x22352))
% 168.60/168.40 [2236]~E(x22361,x22362)+E(f576(x22361,x22363,x22364,x22365,x22366,x22367),f576(x22362,x22363,x22364,x22365,x22366,x22367))
% 168.60/168.40 [2237]~E(x22371,x22372)+E(f576(x22373,x22371,x22374,x22375,x22376,x22377),f576(x22373,x22372,x22374,x22375,x22376,x22377))
% 168.60/168.40 [2238]~E(x22381,x22382)+E(f576(x22383,x22384,x22381,x22385,x22386,x22387),f576(x22383,x22384,x22382,x22385,x22386,x22387))
% 168.60/168.40 [2239]~E(x22391,x22392)+E(f576(x22393,x22394,x22395,x22391,x22396,x22397),f576(x22393,x22394,x22395,x22392,x22396,x22397))
% 168.60/168.40 [2240]~E(x22401,x22402)+E(f576(x22403,x22404,x22405,x22406,x22401,x22407),f576(x22403,x22404,x22405,x22406,x22402,x22407))
% 168.60/168.40 [2241]~E(x22411,x22412)+E(f576(x22413,x22414,x22415,x22416,x22417,x22411),f576(x22413,x22414,x22415,x22416,x22417,x22412))
% 168.60/168.40 [2242]~E(x22421,x22422)+E(f604(x22421,x22423),f604(x22422,x22423))
% 168.60/168.40 [2243]~E(x22431,x22432)+E(f604(x22433,x22431),f604(x22433,x22432))
% 168.60/168.40 [2244]~E(x22441,x22442)+E(f544(x22441,x22443),f544(x22442,x22443))
% 168.60/168.40 [2245]~E(x22451,x22452)+E(f544(x22453,x22451),f544(x22453,x22452))
% 168.60/168.40 [2246]~E(x22461,x22462)+E(f430(x22461,x22463,x22464,x22465,x22466),f430(x22462,x22463,x22464,x22465,x22466))
% 168.60/168.40 [2247]~E(x22471,x22472)+E(f430(x22473,x22471,x22474,x22475,x22476),f430(x22473,x22472,x22474,x22475,x22476))
% 168.60/168.40 [2248]~E(x22481,x22482)+E(f430(x22483,x22484,x22481,x22485,x22486),f430(x22483,x22484,x22482,x22485,x22486))
% 168.60/168.40 [2249]~E(x22491,x22492)+E(f430(x22493,x22494,x22495,x22491,x22496),f430(x22493,x22494,x22495,x22492,x22496))
% 168.60/168.40 [2250]~E(x22501,x22502)+E(f430(x22503,x22504,x22505,x22506,x22501),f430(x22503,x22504,x22505,x22506,x22502))
% 168.60/168.40 [2251]~E(x22511,x22512)+E(f516(x22511,x22513,x22514),f516(x22512,x22513,x22514))
% 168.60/168.40 [2252]~E(x22521,x22522)+E(f516(x22523,x22521,x22524),f516(x22523,x22522,x22524))
% 168.60/168.40 [2253]~E(x22531,x22532)+E(f516(x22533,x22534,x22531),f516(x22533,x22534,x22532))
% 168.60/168.40 [2254]~E(x22541,x22542)+E(f572(x22541,x22543,x22544,x22545,x22546,x22547),f572(x22542,x22543,x22544,x22545,x22546,x22547))
% 168.60/168.40 [2255]~E(x22551,x22552)+E(f572(x22553,x22551,x22554,x22555,x22556,x22557),f572(x22553,x22552,x22554,x22555,x22556,x22557))
% 168.60/168.40 [2256]~E(x22561,x22562)+E(f572(x22563,x22564,x22561,x22565,x22566,x22567),f572(x22563,x22564,x22562,x22565,x22566,x22567))
% 168.60/168.40 [2257]~E(x22571,x22572)+E(f572(x22573,x22574,x22575,x22571,x22576,x22577),f572(x22573,x22574,x22575,x22572,x22576,x22577))
% 168.60/168.40 [2258]~E(x22581,x22582)+E(f572(x22583,x22584,x22585,x22586,x22581,x22587),f572(x22583,x22584,x22585,x22586,x22582,x22587))
% 168.60/168.40 [2259]~E(x22591,x22592)+E(f572(x22593,x22594,x22595,x22596,x22597,x22591),f572(x22593,x22594,x22595,x22596,x22597,x22592))
% 168.60/168.40 [2260]~E(x22601,x22602)+E(f511(x22601,x22603,x22604),f511(x22602,x22603,x22604))
% 168.60/168.40 [2261]~E(x22611,x22612)+E(f511(x22613,x22611,x22614),f511(x22613,x22612,x22614))
% 168.60/168.40 [2262]~E(x22621,x22622)+E(f511(x22623,x22624,x22621),f511(x22623,x22624,x22622))
% 168.60/168.40 [2263]~E(x22631,x22632)+E(f658(x22631,x22633,x22634),f658(x22632,x22633,x22634))
% 168.60/168.40 [2264]~E(x22641,x22642)+E(f658(x22643,x22641,x22644),f658(x22643,x22642,x22644))
% 168.60/168.40 [2265]~E(x22651,x22652)+E(f658(x22653,x22654,x22651),f658(x22653,x22654,x22652))
% 168.60/168.40 [2266]~E(x22661,x22662)+E(f422(x22661,x22663),f422(x22662,x22663))
% 168.60/168.40 [2267]~E(x22671,x22672)+E(f422(x22673,x22671),f422(x22673,x22672))
% 168.60/168.40 [2268]~E(x22681,x22682)+E(f21(x22681,x22683,x22684,x22685),f21(x22682,x22683,x22684,x22685))
% 168.60/168.40 [2269]~E(x22691,x22692)+E(f21(x22693,x22691,x22694,x22695),f21(x22693,x22692,x22694,x22695))
% 168.60/168.40 [2270]~E(x22701,x22702)+E(f21(x22703,x22704,x22701,x22705),f21(x22703,x22704,x22702,x22705))
% 168.60/168.40 [2271]~E(x22711,x22712)+E(f21(x22713,x22714,x22715,x22711),f21(x22713,x22714,x22715,x22712))
% 168.60/168.40 [2272]~E(x22721,x22722)+E(f482(x22721,x22723,x22724,x22725,x22726),f482(x22722,x22723,x22724,x22725,x22726))
% 168.60/168.40 [2273]~E(x22731,x22732)+E(f482(x22733,x22731,x22734,x22735,x22736),f482(x22733,x22732,x22734,x22735,x22736))
% 168.60/168.40 [2274]~E(x22741,x22742)+E(f482(x22743,x22744,x22741,x22745,x22746),f482(x22743,x22744,x22742,x22745,x22746))
% 168.60/168.40 [2275]~E(x22751,x22752)+E(f482(x22753,x22754,x22755,x22751,x22756),f482(x22753,x22754,x22755,x22752,x22756))
% 168.60/168.40 [2276]~E(x22761,x22762)+E(f482(x22763,x22764,x22765,x22766,x22761),f482(x22763,x22764,x22765,x22766,x22762))
% 168.60/168.40 [2277]~E(x22771,x22772)+E(f261(x22771,x22773,x22774,x22775),f261(x22772,x22773,x22774,x22775))
% 168.60/168.40 [2278]~E(x22781,x22782)+E(f261(x22783,x22781,x22784,x22785),f261(x22783,x22782,x22784,x22785))
% 168.60/168.40 [2279]~E(x22791,x22792)+E(f261(x22793,x22794,x22791,x22795),f261(x22793,x22794,x22792,x22795))
% 168.60/168.40 [2280]~E(x22801,x22802)+E(f261(x22803,x22804,x22805,x22801),f261(x22803,x22804,x22805,x22802))
% 168.60/168.40 [2281]~E(x22811,x22812)+E(f587(x22811,x22813,x22814,x22815),f587(x22812,x22813,x22814,x22815))
% 168.60/168.40 [2282]~E(x22821,x22822)+E(f587(x22823,x22821,x22824,x22825),f587(x22823,x22822,x22824,x22825))
% 168.60/168.40 [2283]~E(x22831,x22832)+E(f587(x22833,x22834,x22831,x22835),f587(x22833,x22834,x22832,x22835))
% 168.60/168.40 [2284]~E(x22841,x22842)+E(f587(x22843,x22844,x22845,x22841),f587(x22843,x22844,x22845,x22842))
% 168.60/168.40 [2285]~E(x22851,x22852)+E(f331(x22851,x22853),f331(x22852,x22853))
% 168.60/168.40 [2286]~E(x22861,x22862)+E(f331(x22863,x22861),f331(x22863,x22862))
% 168.60/168.40 [2287]~E(x22871,x22872)+E(f287(x22871,x22873,x22874,x22875),f287(x22872,x22873,x22874,x22875))
% 168.60/168.41 [2288]~E(x22881,x22882)+E(f287(x22883,x22881,x22884,x22885),f287(x22883,x22882,x22884,x22885))
% 168.60/168.41 [2289]~E(x22891,x22892)+E(f287(x22893,x22894,x22891,x22895),f287(x22893,x22894,x22892,x22895))
% 168.60/168.41 [2290]~E(x22901,x22902)+E(f287(x22903,x22904,x22905,x22901),f287(x22903,x22904,x22905,x22902))
% 168.60/168.41 [2291]~E(x22911,x22912)+E(f519(x22911,x22913,x22914,x22915,x22916),f519(x22912,x22913,x22914,x22915,x22916))
% 168.60/168.41 [2292]~E(x22921,x22922)+E(f519(x22923,x22921,x22924,x22925,x22926),f519(x22923,x22922,x22924,x22925,x22926))
% 168.60/168.41 [2293]~E(x22931,x22932)+E(f519(x22933,x22934,x22931,x22935,x22936),f519(x22933,x22934,x22932,x22935,x22936))
% 168.60/168.41 [2294]~E(x22941,x22942)+E(f519(x22943,x22944,x22945,x22941,x22946),f519(x22943,x22944,x22945,x22942,x22946))
% 168.60/168.41 [2295]~E(x22951,x22952)+E(f519(x22953,x22954,x22955,x22956,x22951),f519(x22953,x22954,x22955,x22956,x22952))
% 168.60/168.41 [2296]~E(x22961,x22962)+E(f220(x22961,x22963,x22964,x22965),f220(x22962,x22963,x22964,x22965))
% 168.60/168.41 [2297]~E(x22971,x22972)+E(f220(x22973,x22971,x22974,x22975),f220(x22973,x22972,x22974,x22975))
% 168.60/168.41 [2298]~E(x22981,x22982)+E(f220(x22983,x22984,x22981,x22985),f220(x22983,x22984,x22982,x22985))
% 168.60/168.41 [2299]~E(x22991,x22992)+E(f220(x22993,x22994,x22995,x22991),f220(x22993,x22994,x22995,x22992))
% 168.60/168.41 [2300]~E(x23001,x23002)+E(f701(x23001,x23003,x23004),f701(x23002,x23003,x23004))
% 168.60/168.41 [2301]~E(x23011,x23012)+E(f701(x23013,x23011,x23014),f701(x23013,x23012,x23014))
% 168.60/168.41 [2302]~E(x23021,x23022)+E(f701(x23023,x23024,x23021),f701(x23023,x23024,x23022))
% 168.60/168.41 [2303]~E(x23031,x23032)+E(f262(x23031,x23033,x23034),f262(x23032,x23033,x23034))
% 168.60/168.41 [2304]~E(x23041,x23042)+E(f262(x23043,x23041,x23044),f262(x23043,x23042,x23044))
% 168.60/168.41 [2305]~E(x23051,x23052)+E(f262(x23053,x23054,x23051),f262(x23053,x23054,x23052))
% 168.60/168.41 [2306]~E(x23061,x23062)+E(f389(x23061,x23063,x23064),f389(x23062,x23063,x23064))
% 168.60/168.41 [2307]~E(x23071,x23072)+E(f389(x23073,x23071,x23074),f389(x23073,x23072,x23074))
% 168.60/168.41 [2308]~E(x23081,x23082)+E(f389(x23083,x23084,x23081),f389(x23083,x23084,x23082))
% 168.60/168.41 [2309]~E(x23091,x23092)+E(f423(x23091,x23093),f423(x23092,x23093))
% 168.60/168.41 [2310]~E(x23101,x23102)+E(f423(x23103,x23101),f423(x23103,x23102))
% 168.60/168.41 [2311]~E(x23111,x23112)+E(f381(x23111,x23113,x23114),f381(x23112,x23113,x23114))
% 168.60/168.41 [2312]~E(x23121,x23122)+E(f381(x23123,x23121,x23124),f381(x23123,x23122,x23124))
% 168.60/168.41 [2313]~E(x23131,x23132)+E(f381(x23133,x23134,x23131),f381(x23133,x23134,x23132))
% 168.60/168.41 [2314]~E(x23141,x23142)+E(f566(x23141,x23143),f566(x23142,x23143))
% 168.60/168.41 [2315]~E(x23151,x23152)+E(f566(x23153,x23151),f566(x23153,x23152))
% 168.60/168.41 [2316]~E(x23161,x23162)+E(f418(x23161,x23163,x23164,x23165,x23166),f418(x23162,x23163,x23164,x23165,x23166))
% 168.60/168.41 [2317]~E(x23171,x23172)+E(f418(x23173,x23171,x23174,x23175,x23176),f418(x23173,x23172,x23174,x23175,x23176))
% 168.60/168.41 [2318]~E(x23181,x23182)+E(f418(x23183,x23184,x23181,x23185,x23186),f418(x23183,x23184,x23182,x23185,x23186))
% 168.60/168.41 [2319]~E(x23191,x23192)+E(f418(x23193,x23194,x23195,x23191,x23196),f418(x23193,x23194,x23195,x23192,x23196))
% 168.60/168.41 [2320]~E(x23201,x23202)+E(f418(x23203,x23204,x23205,x23206,x23201),f418(x23203,x23204,x23205,x23206,x23202))
% 168.60/168.41 [2321]~E(x23211,x23212)+E(f503(x23211,x23213,x23214,x23215),f503(x23212,x23213,x23214,x23215))
% 168.60/168.41 [2322]~E(x23221,x23222)+E(f503(x23223,x23221,x23224,x23225),f503(x23223,x23222,x23224,x23225))
% 168.60/168.41 [2323]~E(x23231,x23232)+E(f503(x23233,x23234,x23231,x23235),f503(x23233,x23234,x23232,x23235))
% 168.60/168.41 [2324]~E(x23241,x23242)+E(f503(x23243,x23244,x23245,x23241),f503(x23243,x23244,x23245,x23242))
% 168.60/168.41 [2325]~E(x23251,x23252)+E(f702(x23251,x23253,x23254,x23255,x23256),f702(x23252,x23253,x23254,x23255,x23256))
% 168.60/168.41 [2326]~E(x23261,x23262)+E(f702(x23263,x23261,x23264,x23265,x23266),f702(x23263,x23262,x23264,x23265,x23266))
% 168.60/168.41 [2327]~E(x23271,x23272)+E(f702(x23273,x23274,x23271,x23275,x23276),f702(x23273,x23274,x23272,x23275,x23276))
% 168.60/168.41 [2328]~E(x23281,x23282)+E(f702(x23283,x23284,x23285,x23281,x23286),f702(x23283,x23284,x23285,x23282,x23286))
% 168.60/168.41 [2329]~E(x23291,x23292)+E(f702(x23293,x23294,x23295,x23296,x23291),f702(x23293,x23294,x23295,x23296,x23292))
% 168.60/168.41 [2330]~E(x23301,x23302)+E(f193(x23301),f193(x23302))
% 168.60/168.41 [2331]~E(x23311,x23312)+E(f319(x23311,x23313,x23314,x23315),f319(x23312,x23313,x23314,x23315))
% 168.60/168.41 [2332]~E(x23321,x23322)+E(f319(x23323,x23321,x23324,x23325),f319(x23323,x23322,x23324,x23325))
% 168.60/168.41 [2333]~E(x23331,x23332)+E(f319(x23333,x23334,x23331,x23335),f319(x23333,x23334,x23332,x23335))
% 168.60/168.41 [2334]~E(x23341,x23342)+E(f319(x23343,x23344,x23345,x23341),f319(x23343,x23344,x23345,x23342))
% 168.60/168.41 [2335]~E(x23351,x23352)+E(f873(x23351,x23353,x23354),f873(x23352,x23353,x23354))
% 168.60/168.41 [2336]~E(x23361,x23362)+E(f873(x23363,x23361,x23364),f873(x23363,x23362,x23364))
% 168.60/168.41 [2337]~E(x23371,x23372)+E(f873(x23373,x23374,x23371),f873(x23373,x23374,x23372))
% 168.60/168.41 [2338]~E(x23381,x23382)+E(f394(x23381,x23383),f394(x23382,x23383))
% 168.60/168.41 [2339]~E(x23391,x23392)+E(f394(x23393,x23391),f394(x23393,x23392))
% 168.60/168.41 [2340]~E(x23401,x23402)+E(f814(x23401,x23403,x23404,x23405),f814(x23402,x23403,x23404,x23405))
% 168.60/168.41 [2341]~E(x23411,x23412)+E(f814(x23413,x23411,x23414,x23415),f814(x23413,x23412,x23414,x23415))
% 168.60/168.41 [2342]~E(x23421,x23422)+E(f814(x23423,x23424,x23421,x23425),f814(x23423,x23424,x23422,x23425))
% 168.60/168.41 [2343]~E(x23431,x23432)+E(f814(x23433,x23434,x23435,x23431),f814(x23433,x23434,x23435,x23432))
% 168.60/168.41 [2344]~E(x23441,x23442)+E(f683(x23441,x23443,x23444,x23445,x23446),f683(x23442,x23443,x23444,x23445,x23446))
% 168.60/168.41 [2345]~E(x23451,x23452)+E(f683(x23453,x23451,x23454,x23455,x23456),f683(x23453,x23452,x23454,x23455,x23456))
% 168.60/168.41 [2346]~E(x23461,x23462)+E(f683(x23463,x23464,x23461,x23465,x23466),f683(x23463,x23464,x23462,x23465,x23466))
% 168.60/168.41 [2347]~E(x23471,x23472)+E(f683(x23473,x23474,x23475,x23471,x23476),f683(x23473,x23474,x23475,x23472,x23476))
% 168.60/168.41 [2348]~E(x23481,x23482)+E(f683(x23483,x23484,x23485,x23486,x23481),f683(x23483,x23484,x23485,x23486,x23482))
% 168.60/168.41 [2349]~E(x23491,x23492)+E(f184(x23491,x23493,x23494,x23495),f184(x23492,x23493,x23494,x23495))
% 168.60/168.41 [2350]~E(x23501,x23502)+E(f184(x23503,x23501,x23504,x23505),f184(x23503,x23502,x23504,x23505))
% 168.60/168.41 [2351]~E(x23511,x23512)+E(f184(x23513,x23514,x23511,x23515),f184(x23513,x23514,x23512,x23515))
% 168.60/168.41 [2352]~E(x23521,x23522)+E(f184(x23523,x23524,x23525,x23521),f184(x23523,x23524,x23525,x23522))
% 168.60/168.41 [2353]~E(x23531,x23532)+E(f111(x23531,x23533,x23534,x23535),f111(x23532,x23533,x23534,x23535))
% 168.60/168.41 [2354]~E(x23541,x23542)+E(f111(x23543,x23541,x23544,x23545),f111(x23543,x23542,x23544,x23545))
% 168.60/168.41 [2355]~E(x23551,x23552)+E(f111(x23553,x23554,x23551,x23555),f111(x23553,x23554,x23552,x23555))
% 168.60/168.41 [2356]~E(x23561,x23562)+E(f111(x23563,x23564,x23565,x23561),f111(x23563,x23564,x23565,x23562))
% 168.60/168.41 [2357]~E(x23571,x23572)+E(f828(x23571,x23573,x23574,x23575,x23576,x23577,x23578),f828(x23572,x23573,x23574,x23575,x23576,x23577,x23578))
% 168.60/168.41 [2358]~E(x23581,x23582)+E(f828(x23583,x23581,x23584,x23585,x23586,x23587,x23588),f828(x23583,x23582,x23584,x23585,x23586,x23587,x23588))
% 168.60/168.41 [2359]~E(x23591,x23592)+E(f828(x23593,x23594,x23591,x23595,x23596,x23597,x23598),f828(x23593,x23594,x23592,x23595,x23596,x23597,x23598))
% 168.60/168.41 [2360]~E(x23601,x23602)+E(f828(x23603,x23604,x23605,x23601,x23606,x23607,x23608),f828(x23603,x23604,x23605,x23602,x23606,x23607,x23608))
% 168.60/168.41 [2361]~E(x23611,x23612)+E(f828(x23613,x23614,x23615,x23616,x23611,x23617,x23618),f828(x23613,x23614,x23615,x23616,x23612,x23617,x23618))
% 168.60/168.41 [2362]~E(x23621,x23622)+E(f828(x23623,x23624,x23625,x23626,x23627,x23621,x23628),f828(x23623,x23624,x23625,x23626,x23627,x23622,x23628))
% 168.60/168.41 [2363]~E(x23631,x23632)+E(f828(x23633,x23634,x23635,x23636,x23637,x23638,x23631),f828(x23633,x23634,x23635,x23636,x23637,x23638,x23632))
% 168.60/168.41 [2364]~E(x23641,x23642)+E(f392(x23641),f392(x23642))
% 168.60/168.41 [2365]~E(x23651,x23652)+E(f843(x23651,x23653,x23654),f843(x23652,x23653,x23654))
% 168.60/168.41 [2366]~E(x23661,x23662)+E(f843(x23663,x23661,x23664),f843(x23663,x23662,x23664))
% 168.60/168.41 [2367]~E(x23671,x23672)+E(f843(x23673,x23674,x23671),f843(x23673,x23674,x23672))
% 168.60/168.41 [2368]~E(x23681,x23682)+E(f438(x23681,x23683,x23684,x23685),f438(x23682,x23683,x23684,x23685))
% 168.60/168.41 [2369]~E(x23691,x23692)+E(f438(x23693,x23691,x23694,x23695),f438(x23693,x23692,x23694,x23695))
% 168.60/168.41 [2370]~E(x23701,x23702)+E(f438(x23703,x23704,x23701,x23705),f438(x23703,x23704,x23702,x23705))
% 168.60/168.41 [2371]~E(x23711,x23712)+E(f438(x23713,x23714,x23715,x23711),f438(x23713,x23714,x23715,x23712))
% 168.60/168.41 [2372]~E(x23721,x23722)+E(f859(x23721,x23723,x23724,x23725,x23726),f859(x23722,x23723,x23724,x23725,x23726))
% 168.60/168.41 [2373]~E(x23731,x23732)+E(f859(x23733,x23731,x23734,x23735,x23736),f859(x23733,x23732,x23734,x23735,x23736))
% 168.60/168.41 [2374]~E(x23741,x23742)+E(f859(x23743,x23744,x23741,x23745,x23746),f859(x23743,x23744,x23742,x23745,x23746))
% 168.60/168.41 [2375]~E(x23751,x23752)+E(f859(x23753,x23754,x23755,x23751,x23756),f859(x23753,x23754,x23755,x23752,x23756))
% 168.60/168.41 [2376]~E(x23761,x23762)+E(f859(x23763,x23764,x23765,x23766,x23761),f859(x23763,x23764,x23765,x23766,x23762))
% 168.60/168.41 [2377]~E(x23771,x23772)+E(f697(x23771,x23773,x23774),f697(x23772,x23773,x23774))
% 168.60/168.41 [2378]~E(x23781,x23782)+E(f697(x23783,x23781,x23784),f697(x23783,x23782,x23784))
% 168.60/168.41 [2379]~E(x23791,x23792)+E(f697(x23793,x23794,x23791),f697(x23793,x23794,x23792))
% 168.60/168.41 [2380]~E(x23801,x23802)+E(f402(x23801,x23803,x23804,x23805),f402(x23802,x23803,x23804,x23805))
% 168.60/168.41 [2381]~E(x23811,x23812)+E(f402(x23813,x23811,x23814,x23815),f402(x23813,x23812,x23814,x23815))
% 168.60/168.41 [2382]~E(x23821,x23822)+E(f402(x23823,x23824,x23821,x23825),f402(x23823,x23824,x23822,x23825))
% 168.60/168.41 [2383]~E(x23831,x23832)+E(f402(x23833,x23834,x23835,x23831),f402(x23833,x23834,x23835,x23832))
% 168.60/168.41 [2384]~E(x23841,x23842)+E(f668(x23841,x23843,x23844,x23845),f668(x23842,x23843,x23844,x23845))
% 168.60/168.41 [2385]~E(x23851,x23852)+E(f668(x23853,x23851,x23854,x23855),f668(x23853,x23852,x23854,x23855))
% 168.60/168.41 [2386]~E(x23861,x23862)+E(f668(x23863,x23864,x23861,x23865),f668(x23863,x23864,x23862,x23865))
% 168.60/168.41 [2387]~E(x23871,x23872)+E(f668(x23873,x23874,x23875,x23871),f668(x23873,x23874,x23875,x23872))
% 168.60/168.41 [2388]~E(x23881,x23882)+E(f551(x23881,x23883),f551(x23882,x23883))
% 168.60/168.41 [2389]~E(x23891,x23892)+E(f551(x23893,x23891),f551(x23893,x23892))
% 168.60/168.41 [2390]~E(x23901,x23902)+E(f597(x23901,x23903,x23904),f597(x23902,x23903,x23904))
% 168.60/168.41 [2391]~E(x23911,x23912)+E(f597(x23913,x23911,x23914),f597(x23913,x23912,x23914))
% 168.60/168.41 [2392]~E(x23921,x23922)+E(f597(x23923,x23924,x23921),f597(x23923,x23924,x23922))
% 168.60/168.41 [2393]~E(x23931,x23932)+E(f345(x23931,x23933,x23934,x23935),f345(x23932,x23933,x23934,x23935))
% 168.60/168.41 [2394]~E(x23941,x23942)+E(f345(x23943,x23941,x23944,x23945),f345(x23943,x23942,x23944,x23945))
% 168.60/168.41 [2395]~E(x23951,x23952)+E(f345(x23953,x23954,x23951,x23955),f345(x23953,x23954,x23952,x23955))
% 168.60/168.41 [2396]~E(x23961,x23962)+E(f345(x23963,x23964,x23965,x23961),f345(x23963,x23964,x23965,x23962))
% 168.60/168.41 [2397]~E(x23971,x23972)+E(f192(x23971,x23973,x23974),f192(x23972,x23973,x23974))
% 168.60/168.41 [2398]~E(x23981,x23982)+E(f192(x23983,x23981,x23984),f192(x23983,x23982,x23984))
% 168.60/168.41 [2399]~E(x23991,x23992)+E(f192(x23993,x23994,x23991),f192(x23993,x23994,x23992))
% 168.60/168.41 [2400]~E(x24001,x24002)+E(f421(x24001,x24003,x24004,x24005,x24006,x24007,x24008),f421(x24002,x24003,x24004,x24005,x24006,x24007,x24008))
% 168.60/168.41 [2401]~E(x24011,x24012)+E(f421(x24013,x24011,x24014,x24015,x24016,x24017,x24018),f421(x24013,x24012,x24014,x24015,x24016,x24017,x24018))
% 168.60/168.41 [2402]~E(x24021,x24022)+E(f421(x24023,x24024,x24021,x24025,x24026,x24027,x24028),f421(x24023,x24024,x24022,x24025,x24026,x24027,x24028))
% 168.60/168.41 [2403]~E(x24031,x24032)+E(f421(x24033,x24034,x24035,x24031,x24036,x24037,x24038),f421(x24033,x24034,x24035,x24032,x24036,x24037,x24038))
% 168.60/168.41 [2404]~E(x24041,x24042)+E(f421(x24043,x24044,x24045,x24046,x24041,x24047,x24048),f421(x24043,x24044,x24045,x24046,x24042,x24047,x24048))
% 168.60/168.41 [2405]~E(x24051,x24052)+E(f421(x24053,x24054,x24055,x24056,x24057,x24051,x24058),f421(x24053,x24054,x24055,x24056,x24057,x24052,x24058))
% 168.60/168.41 [2406]~E(x24061,x24062)+E(f421(x24063,x24064,x24065,x24066,x24067,x24068,x24061),f421(x24063,x24064,x24065,x24066,x24067,x24068,x24062))
% 168.60/168.41 [2407]~E(x24071,x24072)+E(f819(x24071,x24073,x24074),f819(x24072,x24073,x24074))
% 168.60/168.41 [2408]~E(x24081,x24082)+E(f819(x24083,x24081,x24084),f819(x24083,x24082,x24084))
% 168.60/168.41 [2409]~E(x24091,x24092)+E(f819(x24093,x24094,x24091),f819(x24093,x24094,x24092))
% 168.60/168.41 [2410]~E(x24101,x24102)+E(f539(x24101,x24103),f539(x24102,x24103))
% 168.60/168.41 [2411]~E(x24111,x24112)+E(f539(x24113,x24111),f539(x24113,x24112))
% 168.60/168.41 [2412]~E(x24121,x24122)+E(f226(x24121,x24123),f226(x24122,x24123))
% 168.60/168.41 [2413]~E(x24131,x24132)+E(f226(x24133,x24131),f226(x24133,x24132))
% 168.60/168.41 [2414]~E(x24141,x24142)+E(f647(x24141,x24143),f647(x24142,x24143))
% 168.60/168.41 [2415]~E(x24151,x24152)+E(f647(x24153,x24151),f647(x24153,x24152))
% 168.60/168.41 [2416]~E(x24161,x24162)+E(f196(x24161,x24163,x24164,x24165,x24166,x24167,x24168),f196(x24162,x24163,x24164,x24165,x24166,x24167,x24168))
% 168.60/168.41 [2417]~E(x24171,x24172)+E(f196(x24173,x24171,x24174,x24175,x24176,x24177,x24178),f196(x24173,x24172,x24174,x24175,x24176,x24177,x24178))
% 168.60/168.41 [2418]~E(x24181,x24182)+E(f196(x24183,x24184,x24181,x24185,x24186,x24187,x24188),f196(x24183,x24184,x24182,x24185,x24186,x24187,x24188))
% 168.60/168.41 [2419]~E(x24191,x24192)+E(f196(x24193,x24194,x24195,x24191,x24196,x24197,x24198),f196(x24193,x24194,x24195,x24192,x24196,x24197,x24198))
% 168.60/168.41 [2420]~E(x24201,x24202)+E(f196(x24203,x24204,x24205,x24206,x24201,x24207,x24208),f196(x24203,x24204,x24205,x24206,x24202,x24207,x24208))
% 168.60/168.41 [2421]~E(x24211,x24212)+E(f196(x24213,x24214,x24215,x24216,x24217,x24211,x24218),f196(x24213,x24214,x24215,x24216,x24217,x24212,x24218))
% 168.60/168.41 [2422]~E(x24221,x24222)+E(f196(x24223,x24224,x24225,x24226,x24227,x24228,x24221),f196(x24223,x24224,x24225,x24226,x24227,x24228,x24222))
% 168.60/168.41 [2423]~E(x24231,x24232)+E(f830(x24231,x24233,x24234,x24235,x24236,x24237,x24238,x24239),f830(x24232,x24233,x24234,x24235,x24236,x24237,x24238,x24239))
% 168.60/168.41 [2424]~E(x24241,x24242)+E(f830(x24243,x24241,x24244,x24245,x24246,x24247,x24248,x24249),f830(x24243,x24242,x24244,x24245,x24246,x24247,x24248,x24249))
% 168.60/168.41 [2425]~E(x24251,x24252)+E(f830(x24253,x24254,x24251,x24255,x24256,x24257,x24258,x24259),f830(x24253,x24254,x24252,x24255,x24256,x24257,x24258,x24259))
% 168.60/168.41 [2426]~E(x24261,x24262)+E(f830(x24263,x24264,x24265,x24261,x24266,x24267,x24268,x24269),f830(x24263,x24264,x24265,x24262,x24266,x24267,x24268,x24269))
% 168.60/168.41 [2427]~E(x24271,x24272)+E(f830(x24273,x24274,x24275,x24276,x24271,x24277,x24278,x24279),f830(x24273,x24274,x24275,x24276,x24272,x24277,x24278,x24279))
% 168.60/168.41 [2428]~E(x24281,x24282)+E(f830(x24283,x24284,x24285,x24286,x24287,x24281,x24288,x24289),f830(x24283,x24284,x24285,x24286,x24287,x24282,x24288,x24289))
% 168.60/168.41 [2429]~E(x24291,x24292)+E(f830(x24293,x24294,x24295,x24296,x24297,x24298,x24291,x24299),f830(x24293,x24294,x24295,x24296,x24297,x24298,x24292,x24299))
% 168.60/168.41 [2430]~E(x24301,x24302)+E(f830(x24303,x24304,x24305,x24306,x24307,x24308,x24309,x24301),f830(x24303,x24304,x24305,x24306,x24307,x24308,x24309,x24302))
% 168.60/168.41 [2431]~E(x24311,x24312)+E(f512(x24311,x24313,x24314),f512(x24312,x24313,x24314))
% 168.60/168.41 [2432]~E(x24321,x24322)+E(f512(x24323,x24321,x24324),f512(x24323,x24322,x24324))
% 168.60/168.41 [2433]~E(x24331,x24332)+E(f512(x24333,x24334,x24331),f512(x24333,x24334,x24332))
% 168.60/168.41 [2434]~E(x24341,x24342)+E(f747(x24341,x24343,x24344),f747(x24342,x24343,x24344))
% 168.60/168.41 [2435]~E(x24351,x24352)+E(f747(x24353,x24351,x24354),f747(x24353,x24352,x24354))
% 168.60/168.41 [2436]~E(x24361,x24362)+E(f747(x24363,x24364,x24361),f747(x24363,x24364,x24362))
% 168.60/168.41 [2437]~E(x24371,x24372)+E(f537(x24371),f537(x24372))
% 168.60/168.41 [2438]~E(x24381,x24382)+E(f623(x24381,x24383,x24384,x24385),f623(x24382,x24383,x24384,x24385))
% 168.60/168.41 [2439]~E(x24391,x24392)+E(f623(x24393,x24391,x24394,x24395),f623(x24393,x24392,x24394,x24395))
% 168.60/168.41 [2440]~E(x24401,x24402)+E(f623(x24403,x24404,x24401,x24405),f623(x24403,x24404,x24402,x24405))
% 168.60/168.41 [2441]~E(x24411,x24412)+E(f623(x24413,x24414,x24415,x24411),f623(x24413,x24414,x24415,x24412))
% 168.60/168.41 [2442]~E(x24421,x24422)+E(f645(x24421,x24423,x24424),f645(x24422,x24423,x24424))
% 168.60/168.41 [2443]~E(x24431,x24432)+E(f645(x24433,x24431,x24434),f645(x24433,x24432,x24434))
% 168.60/168.41 [2444]~E(x24441,x24442)+E(f645(x24443,x24444,x24441),f645(x24443,x24444,x24442))
% 168.60/168.41 [2445]~E(x24451,x24452)+E(f495(x24451,x24453,x24454,x24455),f495(x24452,x24453,x24454,x24455))
% 168.60/168.41 [2446]~E(x24461,x24462)+E(f495(x24463,x24461,x24464,x24465),f495(x24463,x24462,x24464,x24465))
% 168.60/168.41 [2447]~E(x24471,x24472)+E(f495(x24473,x24474,x24471,x24475),f495(x24473,x24474,x24472,x24475))
% 168.60/168.41 [2448]~E(x24481,x24482)+E(f495(x24483,x24484,x24485,x24481),f495(x24483,x24484,x24485,x24482))
% 168.60/168.41 [2449]~E(x24491,x24492)+E(f370(x24491,x24493,x24494),f370(x24492,x24493,x24494))
% 168.60/168.41 [2450]~E(x24501,x24502)+E(f370(x24503,x24501,x24504),f370(x24503,x24502,x24504))
% 168.60/168.41 [2451]~E(x24511,x24512)+E(f370(x24513,x24514,x24511),f370(x24513,x24514,x24512))
% 168.60/168.41 [2452]~E(x24521,x24522)+E(f559(x24521,x24523),f559(x24522,x24523))
% 168.60/168.41 [2453]~E(x24531,x24532)+E(f559(x24533,x24531),f559(x24533,x24532))
% 168.60/168.41 [2454]~E(x24541,x24542)+E(f689(x24541,x24543),f689(x24542,x24543))
% 168.60/168.41 [2455]~E(x24551,x24552)+E(f689(x24553,x24551),f689(x24553,x24552))
% 168.60/168.41 [2456]~E(x24561,x24562)+E(f805(x24561,x24563),f805(x24562,x24563))
% 168.60/168.41 [2457]~E(x24571,x24572)+E(f805(x24573,x24571),f805(x24573,x24572))
% 168.60/168.41 [2458]~E(x24581,x24582)+E(f200(x24581,x24583,x24584,x24585,x24586,x24587,x24588),f200(x24582,x24583,x24584,x24585,x24586,x24587,x24588))
% 168.60/168.41 [2459]~E(x24591,x24592)+E(f200(x24593,x24591,x24594,x24595,x24596,x24597,x24598),f200(x24593,x24592,x24594,x24595,x24596,x24597,x24598))
% 168.60/168.41 [2460]~E(x24601,x24602)+E(f200(x24603,x24604,x24601,x24605,x24606,x24607,x24608),f200(x24603,x24604,x24602,x24605,x24606,x24607,x24608))
% 168.60/168.41 [2461]~E(x24611,x24612)+E(f200(x24613,x24614,x24615,x24611,x24616,x24617,x24618),f200(x24613,x24614,x24615,x24612,x24616,x24617,x24618))
% 168.60/168.41 [2462]~E(x24621,x24622)+E(f200(x24623,x24624,x24625,x24626,x24621,x24627,x24628),f200(x24623,x24624,x24625,x24626,x24622,x24627,x24628))
% 168.60/168.41 [2463]~E(x24631,x24632)+E(f200(x24633,x24634,x24635,x24636,x24637,x24631,x24638),f200(x24633,x24634,x24635,x24636,x24637,x24632,x24638))
% 168.60/168.41 [2464]~E(x24641,x24642)+E(f200(x24643,x24644,x24645,x24646,x24647,x24648,x24641),f200(x24643,x24644,x24645,x24646,x24647,x24648,x24642))
% 168.60/168.41 [2465]~E(x24651,x24652)+E(f624(x24651,x24653,x24654,x24655),f624(x24652,x24653,x24654,x24655))
% 168.60/168.41 [2466]~E(x24661,x24662)+E(f624(x24663,x24661,x24664,x24665),f624(x24663,x24662,x24664,x24665))
% 168.60/168.41 [2467]~E(x24671,x24672)+E(f624(x24673,x24674,x24671,x24675),f624(x24673,x24674,x24672,x24675))
% 168.60/168.41 [2468]~E(x24681,x24682)+E(f624(x24683,x24684,x24685,x24681),f624(x24683,x24684,x24685,x24682))
% 168.60/168.41 [2469]~E(x24691,x24692)+E(f631(x24691,x24693),f631(x24692,x24693))
% 168.60/168.41 [2470]~E(x24701,x24702)+E(f631(x24703,x24701),f631(x24703,x24702))
% 168.60/168.41 [2471]~E(x24711,x24712)+E(f557(x24711,x24713,x24714,x24715),f557(x24712,x24713,x24714,x24715))
% 168.60/168.41 [2472]~E(x24721,x24722)+E(f557(x24723,x24721,x24724,x24725),f557(x24723,x24722,x24724,x24725))
% 168.60/168.41 [2473]~E(x24731,x24732)+E(f557(x24733,x24734,x24731,x24735),f557(x24733,x24734,x24732,x24735))
% 168.60/168.41 [2474]~E(x24741,x24742)+E(f557(x24743,x24744,x24745,x24741),f557(x24743,x24744,x24745,x24742))
% 168.60/168.41 [2475]~E(x24751,x24752)+E(f723(x24751,x24753,x24754,x24755),f723(x24752,x24753,x24754,x24755))
% 168.60/168.41 [2476]~E(x24761,x24762)+E(f723(x24763,x24761,x24764,x24765),f723(x24763,x24762,x24764,x24765))
% 168.60/168.41 [2477]~E(x24771,x24772)+E(f723(x24773,x24774,x24771,x24775),f723(x24773,x24774,x24772,x24775))
% 168.60/168.41 [2478]~E(x24781,x24782)+E(f723(x24783,x24784,x24785,x24781),f723(x24783,x24784,x24785,x24782))
% 168.60/168.41 [2479]~E(x24791,x24792)+E(f327(x24791,x24793),f327(x24792,x24793))
% 168.60/168.41 [2480]~E(x24801,x24802)+E(f327(x24803,x24801),f327(x24803,x24802))
% 168.60/168.41 [2481]~E(x24811,x24812)+E(f264(x24811,x24813,x24814,x24815),f264(x24812,x24813,x24814,x24815))
% 168.60/168.41 [2482]~E(x24821,x24822)+E(f264(x24823,x24821,x24824,x24825),f264(x24823,x24822,x24824,x24825))
% 168.60/168.41 [2483]~E(x24831,x24832)+E(f264(x24833,x24834,x24831,x24835),f264(x24833,x24834,x24832,x24835))
% 168.60/168.41 [2484]~E(x24841,x24842)+E(f264(x24843,x24844,x24845,x24841),f264(x24843,x24844,x24845,x24842))
% 168.60/168.41 [2485]~E(x24851,x24852)+E(f556(x24851,x24853,x24854,x24855),f556(x24852,x24853,x24854,x24855))
% 168.60/168.41 [2486]~E(x24861,x24862)+E(f556(x24863,x24861,x24864,x24865),f556(x24863,x24862,x24864,x24865))
% 168.60/168.41 [2487]~E(x24871,x24872)+E(f556(x24873,x24874,x24871,x24875),f556(x24873,x24874,x24872,x24875))
% 168.60/168.41 [2488]~E(x24881,x24882)+E(f556(x24883,x24884,x24885,x24881),f556(x24883,x24884,x24885,x24882))
% 168.60/168.41 [2489]~E(x24891,x24892)+E(f839(x24891),f839(x24892))
% 168.60/168.41 [2490]~E(x24901,x24902)+E(f741(x24901,x24903,x24904),f741(x24902,x24903,x24904))
% 168.60/168.41 [2491]~E(x24911,x24912)+E(f741(x24913,x24911,x24914),f741(x24913,x24912,x24914))
% 168.60/168.41 [2492]~E(x24921,x24922)+E(f741(x24923,x24924,x24921),f741(x24923,x24924,x24922))
% 168.60/168.41 [2493]~E(x24931,x24932)+E(f528(x24931,x24933,x24934,x24935),f528(x24932,x24933,x24934,x24935))
% 168.60/168.41 [2494]~E(x24941,x24942)+E(f528(x24943,x24941,x24944,x24945),f528(x24943,x24942,x24944,x24945))
% 168.60/168.41 [2495]~E(x24951,x24952)+E(f528(x24953,x24954,x24951,x24955),f528(x24953,x24954,x24952,x24955))
% 168.60/168.41 [2496]~E(x24961,x24962)+E(f528(x24963,x24964,x24965,x24961),f528(x24963,x24964,x24965,x24962))
% 168.60/168.41 [2497]~E(x24971,x24972)+E(f197(x24971),f197(x24972))
% 168.60/168.41 [2498]~E(x24981,x24982)+E(f257(x24981,x24983),f257(x24982,x24983))
% 168.60/168.41 [2499]~E(x24991,x24992)+E(f257(x24993,x24991),f257(x24993,x24992))
% 168.60/168.41 [2500]~E(x25001,x25002)+E(f717(x25001,x25003,x25004,x25005),f717(x25002,x25003,x25004,x25005))
% 168.60/168.41 [2501]~E(x25011,x25012)+E(f717(x25013,x25011,x25014,x25015),f717(x25013,x25012,x25014,x25015))
% 168.60/168.41 [2502]~E(x25021,x25022)+E(f717(x25023,x25024,x25021,x25025),f717(x25023,x25024,x25022,x25025))
% 168.60/168.41 [2503]~E(x25031,x25032)+E(f717(x25033,x25034,x25035,x25031),f717(x25033,x25034,x25035,x25032))
% 168.60/168.41 [2504]~E(x25041,x25042)+E(f626(x25041,x25043,x25044,x25045,x25046),f626(x25042,x25043,x25044,x25045,x25046))
% 168.60/168.41 [2505]~E(x25051,x25052)+E(f626(x25053,x25051,x25054,x25055,x25056),f626(x25053,x25052,x25054,x25055,x25056))
% 168.60/168.41 [2506]~E(x25061,x25062)+E(f626(x25063,x25064,x25061,x25065,x25066),f626(x25063,x25064,x25062,x25065,x25066))
% 168.60/168.41 [2507]~E(x25071,x25072)+E(f626(x25073,x25074,x25075,x25071,x25076),f626(x25073,x25074,x25075,x25072,x25076))
% 168.60/168.41 [2508]~E(x25081,x25082)+E(f626(x25083,x25084,x25085,x25086,x25081),f626(x25083,x25084,x25085,x25086,x25082))
% 168.60/168.41 [2509]~E(x25091,x25092)+E(f491(x25091,x25093,x25094,x25095,x25096),f491(x25092,x25093,x25094,x25095,x25096))
% 168.60/168.41 [2510]~E(x25101,x25102)+E(f491(x25103,x25101,x25104,x25105,x25106),f491(x25103,x25102,x25104,x25105,x25106))
% 168.60/168.41 [2511]~E(x25111,x25112)+E(f491(x25113,x25114,x25111,x25115,x25116),f491(x25113,x25114,x25112,x25115,x25116))
% 168.60/168.41 [2512]~E(x25121,x25122)+E(f491(x25123,x25124,x25125,x25121,x25126),f491(x25123,x25124,x25125,x25122,x25126))
% 168.60/168.41 [2513]~E(x25131,x25132)+E(f491(x25133,x25134,x25135,x25136,x25131),f491(x25133,x25134,x25135,x25136,x25132))
% 168.60/168.41 [2514]~E(x25141,x25142)+E(f577(x25141,x25143,x25144,x25145,x25146,x25147),f577(x25142,x25143,x25144,x25145,x25146,x25147))
% 168.60/168.41 [2515]~E(x25151,x25152)+E(f577(x25153,x25151,x25154,x25155,x25156,x25157),f577(x25153,x25152,x25154,x25155,x25156,x25157))
% 168.60/168.41 [2516]~E(x25161,x25162)+E(f577(x25163,x25164,x25161,x25165,x25166,x25167),f577(x25163,x25164,x25162,x25165,x25166,x25167))
% 168.60/168.41 [2517]~E(x25171,x25172)+E(f577(x25173,x25174,x25175,x25171,x25176,x25177),f577(x25173,x25174,x25175,x25172,x25176,x25177))
% 168.60/168.41 [2518]~E(x25181,x25182)+E(f577(x25183,x25184,x25185,x25186,x25181,x25187),f577(x25183,x25184,x25185,x25186,x25182,x25187))
% 168.60/168.41 [2519]~E(x25191,x25192)+E(f577(x25193,x25194,x25195,x25196,x25197,x25191),f577(x25193,x25194,x25195,x25196,x25197,x25192))
% 168.60/168.41 [2520]~E(x25201,x25202)+E(f225(x25201,x25203),f225(x25202,x25203))
% 168.60/168.41 [2521]~E(x25211,x25212)+E(f225(x25213,x25211),f225(x25213,x25212))
% 168.60/168.41 [2522]~E(x25221,x25222)+E(f391(x25221),f391(x25222))
% 168.60/168.41 [2523]~E(x25231,x25232)+E(f403(x25231,x25233),f403(x25232,x25233))
% 168.60/168.41 [2524]~E(x25241,x25242)+E(f403(x25243,x25241),f403(x25243,x25242))
% 168.60/168.41 [2525]~E(x25251,x25252)+E(f669(x25251,x25253,x25254,x25255),f669(x25252,x25253,x25254,x25255))
% 168.60/168.41 [2526]~E(x25261,x25262)+E(f669(x25263,x25261,x25264,x25265),f669(x25263,x25262,x25264,x25265))
% 168.60/168.41 [2527]~E(x25271,x25272)+E(f669(x25273,x25274,x25271,x25275),f669(x25273,x25274,x25272,x25275))
% 168.60/168.41 [2528]~E(x25281,x25282)+E(f669(x25283,x25284,x25285,x25281),f669(x25283,x25284,x25285,x25282))
% 168.60/168.41 [2529]~E(x25291,x25292)+E(f809(x25291,x25293,x25294),f809(x25292,x25293,x25294))
% 168.60/168.41 [2530]~E(x25301,x25302)+E(f809(x25303,x25301,x25304),f809(x25303,x25302,x25304))
% 168.60/168.41 [2531]~E(x25311,x25312)+E(f809(x25313,x25314,x25311),f809(x25313,x25314,x25312))
% 168.60/168.41 [2532]~E(x25321,x25322)+E(f385(x25321,x25323,x25324),f385(x25322,x25323,x25324))
% 168.60/168.41 [2533]~E(x25331,x25332)+E(f385(x25333,x25331,x25334),f385(x25333,x25332,x25334))
% 168.60/168.41 [2534]~E(x25341,x25342)+E(f385(x25343,x25344,x25341),f385(x25343,x25344,x25342))
% 168.60/168.41 [2535]~E(x25351,x25352)+E(f214(x25351,x25353,x25354,x25355,x25356),f214(x25352,x25353,x25354,x25355,x25356))
% 168.60/168.41 [2536]~E(x25361,x25362)+E(f214(x25363,x25361,x25364,x25365,x25366),f214(x25363,x25362,x25364,x25365,x25366))
% 168.60/168.41 [2537]~E(x25371,x25372)+E(f214(x25373,x25374,x25371,x25375,x25376),f214(x25373,x25374,x25372,x25375,x25376))
% 168.60/168.41 [2538]~E(x25381,x25382)+E(f214(x25383,x25384,x25385,x25381,x25386),f214(x25383,x25384,x25385,x25382,x25386))
% 168.60/168.41 [2539]~E(x25391,x25392)+E(f214(x25393,x25394,x25395,x25396,x25391),f214(x25393,x25394,x25395,x25396,x25392))
% 168.60/168.41 [2540]~E(x25401,x25402)+E(f343(x25401),f343(x25402))
% 168.60/168.41 [2541]~E(x25411,x25412)+E(f667(x25411,x25413,x25414,x25415),f667(x25412,x25413,x25414,x25415))
% 168.60/168.41 [2542]~E(x25421,x25422)+E(f667(x25423,x25421,x25424,x25425),f667(x25423,x25422,x25424,x25425))
% 168.60/168.41 [2543]~E(x25431,x25432)+E(f667(x25433,x25434,x25431,x25435),f667(x25433,x25434,x25432,x25435))
% 168.60/168.41 [2544]~E(x25441,x25442)+E(f667(x25443,x25444,x25445,x25441),f667(x25443,x25444,x25445,x25442))
% 168.60/168.41 [2545]~E(x25451,x25452)+E(f499(x25451,x25453,x25454),f499(x25452,x25453,x25454))
% 168.60/168.41 [2546]~E(x25461,x25462)+E(f499(x25463,x25461,x25464),f499(x25463,x25462,x25464))
% 168.60/168.41 [2547]~E(x25471,x25472)+E(f499(x25473,x25474,x25471),f499(x25473,x25474,x25472))
% 168.60/168.41 [2548]~E(x25481,x25482)+E(f431(x25481,x25483,x25484,x25485),f431(x25482,x25483,x25484,x25485))
% 168.60/168.41 [2549]~E(x25491,x25492)+E(f431(x25493,x25491,x25494,x25495),f431(x25493,x25492,x25494,x25495))
% 168.60/168.41 [2550]~E(x25501,x25502)+E(f431(x25503,x25504,x25501,x25505),f431(x25503,x25504,x25502,x25505))
% 168.60/168.41 [2551]~E(x25511,x25512)+E(f431(x25513,x25514,x25515,x25511),f431(x25513,x25514,x25515,x25512))
% 168.60/168.41 [2552]~E(x25521,x25522)+E(f694(x25521,x25523,x25524),f694(x25522,x25523,x25524))
% 168.60/168.41 [2553]~E(x25531,x25532)+E(f694(x25533,x25531,x25534),f694(x25533,x25532,x25534))
% 168.60/168.41 [2554]~E(x25541,x25542)+E(f694(x25543,x25544,x25541),f694(x25543,x25544,x25542))
% 168.60/168.41 [2555]~E(x25551,x25552)+E(f151(x25551,x25553),f151(x25552,x25553))
% 168.60/168.41 [2556]~E(x25561,x25562)+E(f151(x25563,x25561),f151(x25563,x25562))
% 168.60/168.41 [2557]~E(x25571,x25572)+E(f213(x25571,x25573,x25574,x25575,x25576),f213(x25572,x25573,x25574,x25575,x25576))
% 168.60/168.41 [2558]~E(x25581,x25582)+E(f213(x25583,x25581,x25584,x25585,x25586),f213(x25583,x25582,x25584,x25585,x25586))
% 168.60/168.41 [2559]~E(x25591,x25592)+E(f213(x25593,x25594,x25591,x25595,x25596),f213(x25593,x25594,x25592,x25595,x25596))
% 168.60/168.41 [2560]~E(x25601,x25602)+E(f213(x25603,x25604,x25605,x25601,x25606),f213(x25603,x25604,x25605,x25602,x25606))
% 168.60/168.41 [2561]~E(x25611,x25612)+E(f213(x25613,x25614,x25615,x25616,x25611),f213(x25613,x25614,x25615,x25616,x25612))
% 168.60/168.41 [2562]~E(x25621,x25622)+E(f793(x25621,x25623),f793(x25622,x25623))
% 168.60/168.41 [2563]~E(x25631,x25632)+E(f793(x25633,x25631),f793(x25633,x25632))
% 168.60/168.41 [2564]~E(x25641,x25642)+E(f323(x25641),f323(x25642))
% 168.60/168.41 [2565]~E(x25651,x25652)+E(f417(x25651,x25653,x25654,x25655,x25656),f417(x25652,x25653,x25654,x25655,x25656))
% 168.60/168.41 [2566]~E(x25661,x25662)+E(f417(x25663,x25661,x25664,x25665,x25666),f417(x25663,x25662,x25664,x25665,x25666))
% 168.60/168.41 [2567]~E(x25671,x25672)+E(f417(x25673,x25674,x25671,x25675,x25676),f417(x25673,x25674,x25672,x25675,x25676))
% 168.60/168.41 [2568]~E(x25681,x25682)+E(f417(x25683,x25684,x25685,x25681,x25686),f417(x25683,x25684,x25685,x25682,x25686))
% 168.60/168.41 [2569]~E(x25691,x25692)+E(f417(x25693,x25694,x25695,x25696,x25691),f417(x25693,x25694,x25695,x25696,x25692))
% 168.60/168.41 [2570]~E(x25701,x25702)+E(f628(x25701,x25703,x25704,x25705,x25706,x25707),f628(x25702,x25703,x25704,x25705,x25706,x25707))
% 168.60/168.41 [2571]~E(x25711,x25712)+E(f628(x25713,x25711,x25714,x25715,x25716,x25717),f628(x25713,x25712,x25714,x25715,x25716,x25717))
% 168.60/168.41 [2572]~E(x25721,x25722)+E(f628(x25723,x25724,x25721,x25725,x25726,x25727),f628(x25723,x25724,x25722,x25725,x25726,x25727))
% 168.60/168.41 [2573]~E(x25731,x25732)+E(f628(x25733,x25734,x25735,x25731,x25736,x25737),f628(x25733,x25734,x25735,x25732,x25736,x25737))
% 168.60/168.41 [2574]~E(x25741,x25742)+E(f628(x25743,x25744,x25745,x25746,x25741,x25747),f628(x25743,x25744,x25745,x25746,x25742,x25747))
% 168.60/168.41 [2575]~E(x25751,x25752)+E(f628(x25753,x25754,x25755,x25756,x25757,x25751),f628(x25753,x25754,x25755,x25756,x25757,x25752))
% 168.60/168.41 [2576]~E(x25761,x25762)+E(f282(x25761,x25763,x25764),f282(x25762,x25763,x25764))
% 168.60/168.41 [2577]~E(x25771,x25772)+E(f282(x25773,x25771,x25774),f282(x25773,x25772,x25774))
% 168.60/168.41 [2578]~E(x25781,x25782)+E(f282(x25783,x25784,x25781),f282(x25783,x25784,x25782))
% 168.60/168.41 [2579]~E(x25791,x25792)+E(f217(x25791,x25793,x25794),f217(x25792,x25793,x25794))
% 168.60/168.41 [2580]~E(x25801,x25802)+E(f217(x25803,x25801,x25804),f217(x25803,x25802,x25804))
% 168.60/168.41 [2581]~E(x25811,x25812)+E(f217(x25813,x25814,x25811),f217(x25813,x25814,x25812))
% 168.60/168.41 [2582]~E(x25821,x25822)+E(f897(x25821,x25823),f897(x25822,x25823))
% 168.60/168.41 [2583]~E(x25831,x25832)+E(f897(x25833,x25831),f897(x25833,x25832))
% 168.60/168.41 [2584]~E(x25841,x25842)+E(f804(x25841,x25843),f804(x25842,x25843))
% 168.60/168.41 [2585]~E(x25851,x25852)+E(f804(x25853,x25851),f804(x25853,x25852))
% 168.60/168.41 [2586]~E(x25861,x25862)+E(f439(x25861,x25863,x25864,x25865),f439(x25862,x25863,x25864,x25865))
% 168.60/168.41 [2587]~E(x25871,x25872)+E(f439(x25873,x25871,x25874,x25875),f439(x25873,x25872,x25874,x25875))
% 168.60/168.41 [2588]~E(x25881,x25882)+E(f439(x25883,x25884,x25881,x25885),f439(x25883,x25884,x25882,x25885))
% 168.60/168.41 [2589]~E(x25891,x25892)+E(f439(x25893,x25894,x25895,x25891),f439(x25893,x25894,x25895,x25892))
% 168.60/168.41 [2590]~E(x25901,x25902)+E(f446(x25901,x25903,x25904,x25905),f446(x25902,x25903,x25904,x25905))
% 168.60/168.41 [2591]~E(x25911,x25912)+E(f446(x25913,x25911,x25914,x25915),f446(x25913,x25912,x25914,x25915))
% 168.60/168.41 [2592]~E(x25921,x25922)+E(f446(x25923,x25924,x25921,x25925),f446(x25923,x25924,x25922,x25925))
% 168.60/168.41 [2593]~E(x25931,x25932)+E(f446(x25933,x25934,x25935,x25931),f446(x25933,x25934,x25935,x25932))
% 168.60/168.41 [2594]~E(x25941,x25942)+E(f751(x25941,x25943,x25944,x25945),f751(x25942,x25943,x25944,x25945))
% 168.60/168.41 [2595]~E(x25951,x25952)+E(f751(x25953,x25951,x25954,x25955),f751(x25953,x25952,x25954,x25955))
% 168.60/168.41 [2596]~E(x25961,x25962)+E(f751(x25963,x25964,x25961,x25965),f751(x25963,x25964,x25962,x25965))
% 168.60/168.41 [2597]~E(x25971,x25972)+E(f751(x25973,x25974,x25975,x25971),f751(x25973,x25974,x25975,x25972))
% 168.60/168.41 [2598]~E(x25981,x25982)+E(f199(x25981,x25983,x25984,x25985),f199(x25982,x25983,x25984,x25985))
% 168.60/168.41 [2599]~E(x25991,x25992)+E(f199(x25993,x25991,x25994,x25995),f199(x25993,x25992,x25994,x25995))
% 168.60/168.41 [2600]~E(x26001,x26002)+E(f199(x26003,x26004,x26001,x26005),f199(x26003,x26004,x26002,x26005))
% 168.60/168.41 [2601]~E(x26011,x26012)+E(f199(x26013,x26014,x26015,x26011),f199(x26013,x26014,x26015,x26012))
% 168.60/168.41 [2602]~E(x26021,x26022)+E(f582(x26021,x26023,x26024),f582(x26022,x26023,x26024))
% 168.60/168.41 [2603]~E(x26031,x26032)+E(f582(x26033,x26031,x26034),f582(x26033,x26032,x26034))
% 168.60/168.41 [2604]~E(x26041,x26042)+E(f582(x26043,x26044,x26041),f582(x26043,x26044,x26042))
% 168.60/168.41 [2605]~E(x26051,x26052)+E(f586(x26051,x26053,x26054),f586(x26052,x26053,x26054))
% 168.60/168.41 [2606]~E(x26061,x26062)+E(f586(x26063,x26061,x26064),f586(x26063,x26062,x26064))
% 168.60/168.41 [2607]~E(x26071,x26072)+E(f586(x26073,x26074,x26071),f586(x26073,x26074,x26072))
% 168.60/168.41 [2608]~E(x26081,x26082)+E(f493(x26081,x26083,x26084,x26085),f493(x26082,x26083,x26084,x26085))
% 168.60/168.41 [2609]~E(x26091,x26092)+E(f493(x26093,x26091,x26094,x26095),f493(x26093,x26092,x26094,x26095))
% 168.60/168.41 [2610]~E(x26101,x26102)+E(f493(x26103,x26104,x26101,x26105),f493(x26103,x26104,x26102,x26105))
% 168.60/168.41 [2611]~E(x26111,x26112)+E(f493(x26113,x26114,x26115,x26111),f493(x26113,x26114,x26115,x26112))
% 168.60/168.41 [2612]~E(x26121,x26122)+E(f768(x26121,x26123),f768(x26122,x26123))
% 168.60/168.41 [2613]~E(x26131,x26132)+E(f768(x26133,x26131),f768(x26133,x26132))
% 168.60/168.41 [2614]~E(x26141,x26142)+E(f558(x26141,x26143,x26144,x26145),f558(x26142,x26143,x26144,x26145))
% 168.60/168.41 [2615]~E(x26151,x26152)+E(f558(x26153,x26151,x26154,x26155),f558(x26153,x26152,x26154,x26155))
% 168.60/168.41 [2616]~E(x26161,x26162)+E(f558(x26163,x26164,x26161,x26165),f558(x26163,x26164,x26162,x26165))
% 168.60/168.41 [2617]~E(x26171,x26172)+E(f558(x26173,x26174,x26175,x26171),f558(x26173,x26174,x26175,x26172))
% 168.60/168.41 [2618]~E(x26181,x26182)+E(f744(x26181,x26183,x26184),f744(x26182,x26183,x26184))
% 168.60/168.41 [2619]~E(x26191,x26192)+E(f744(x26193,x26191,x26194),f744(x26193,x26192,x26194))
% 168.60/168.41 [2620]~E(x26201,x26202)+E(f744(x26203,x26204,x26201),f744(x26203,x26204,x26202))
% 168.60/168.41 [2621]~E(x26211,x26212)+E(f454(x26211,x26213,x26214),f454(x26212,x26213,x26214))
% 168.60/168.41 [2622]~E(x26221,x26222)+E(f454(x26223,x26221,x26224),f454(x26223,x26222,x26224))
% 168.60/168.41 [2623]~E(x26231,x26232)+E(f454(x26233,x26234,x26231),f454(x26233,x26234,x26232))
% 168.60/168.41 [2624]~E(x26241,x26242)+E(f189(x26241),f189(x26242))
% 168.60/168.41 [2625]~E(x26251,x26252)+E(f448(x26251,x26253,x26254,x26255),f448(x26252,x26253,x26254,x26255))
% 168.60/168.41 [2626]~E(x26261,x26262)+E(f448(x26263,x26261,x26264,x26265),f448(x26263,x26262,x26264,x26265))
% 168.60/168.41 [2627]~E(x26271,x26272)+E(f448(x26273,x26274,x26271,x26275),f448(x26273,x26274,x26272,x26275))
% 168.60/168.41 [2628]~E(x26281,x26282)+E(f448(x26283,x26284,x26285,x26281),f448(x26283,x26284,x26285,x26282))
% 168.60/168.41 [2629]~E(x26291,x26292)+E(f248(x26291,x26293,x26294,x26295,x26296),f248(x26292,x26293,x26294,x26295,x26296))
% 168.60/168.41 [2630]~E(x26301,x26302)+E(f248(x26303,x26301,x26304,x26305,x26306),f248(x26303,x26302,x26304,x26305,x26306))
% 168.60/168.41 [2631]~E(x26311,x26312)+E(f248(x26313,x26314,x26311,x26315,x26316),f248(x26313,x26314,x26312,x26315,x26316))
% 168.60/168.41 [2632]~E(x26321,x26322)+E(f248(x26323,x26324,x26325,x26321,x26326),f248(x26323,x26324,x26325,x26322,x26326))
% 168.60/168.41 [2633]~E(x26331,x26332)+E(f248(x26333,x26334,x26335,x26336,x26331),f248(x26333,x26334,x26335,x26336,x26332))
% 168.60/168.41 [2634]~E(x26341,x26342)+E(f386(x26341,x26343,x26344,x26345,x26346),f386(x26342,x26343,x26344,x26345,x26346))
% 168.60/168.41 [2635]~E(x26351,x26352)+E(f386(x26353,x26351,x26354,x26355,x26356),f386(x26353,x26352,x26354,x26355,x26356))
% 168.60/168.41 [2636]~E(x26361,x26362)+E(f386(x26363,x26364,x26361,x26365,x26366),f386(x26363,x26364,x26362,x26365,x26366))
% 168.60/168.41 [2637]~E(x26371,x26372)+E(f386(x26373,x26374,x26375,x26371,x26376),f386(x26373,x26374,x26375,x26372,x26376))
% 168.60/168.41 [2638]~E(x26381,x26382)+E(f386(x26383,x26384,x26385,x26386,x26381),f386(x26383,x26384,x26385,x26386,x26382))
% 168.60/168.41 [2639]~E(x26391,x26392)+E(f334(x26391,x26393,x26394,x26395),f334(x26392,x26393,x26394,x26395))
% 168.60/168.41 [2640]~E(x26401,x26402)+E(f334(x26403,x26401,x26404,x26405),f334(x26403,x26402,x26404,x26405))
% 168.60/168.41 [2641]~E(x26411,x26412)+E(f334(x26413,x26414,x26411,x26415),f334(x26413,x26414,x26412,x26415))
% 168.60/168.41 [2642]~E(x26421,x26422)+E(f334(x26423,x26424,x26425,x26421),f334(x26423,x26424,x26425,x26422))
% 168.60/168.41 [2643]~E(x26431,x26432)+E(f881(x26431,x26433,x26434,x26435),f881(x26432,x26433,x26434,x26435))
% 168.60/168.41 [2644]~E(x26441,x26442)+E(f881(x26443,x26441,x26444,x26445),f881(x26443,x26442,x26444,x26445))
% 168.60/168.41 [2645]~E(x26451,x26452)+E(f881(x26453,x26454,x26451,x26455),f881(x26453,x26454,x26452,x26455))
% 168.60/168.41 [2646]~E(x26461,x26462)+E(f881(x26463,x26464,x26465,x26461),f881(x26463,x26464,x26465,x26462))
% 168.60/168.41 [2647]~E(x26471,x26472)+E(f896(x26471,x26473),f896(x26472,x26473))
% 168.60/168.41 [2648]~E(x26481,x26482)+E(f896(x26483,x26481),f896(x26483,x26482))
% 168.60/168.41 [2649]~E(x26491,x26492)+E(f892(x26491,x26493,x26494),f892(x26492,x26493,x26494))
% 168.60/168.41 [2650]~E(x26501,x26502)+E(f892(x26503,x26501,x26504),f892(x26503,x26502,x26504))
% 168.60/168.41 [2651]~E(x26511,x26512)+E(f892(x26513,x26514,x26511),f892(x26513,x26514,x26512))
% 168.60/168.41 [2652]~E(x26521,x26522)+E(f568(x26521,x26523,x26524),f568(x26522,x26523,x26524))
% 168.60/168.41 [2653]~E(x26531,x26532)+E(f568(x26533,x26531,x26534),f568(x26533,x26532,x26534))
% 168.60/168.41 [2654]~E(x26541,x26542)+E(f568(x26543,x26544,x26541),f568(x26543,x26544,x26542))
% 168.60/168.41 [2655]~E(x26551,x26552)+E(f474(x26551,x26553,x26554,x26555),f474(x26552,x26553,x26554,x26555))
% 168.60/168.41 [2656]~E(x26561,x26562)+E(f474(x26563,x26561,x26564,x26565),f474(x26563,x26562,x26564,x26565))
% 168.60/168.41 [2657]~E(x26571,x26572)+E(f474(x26573,x26574,x26571,x26575),f474(x26573,x26574,x26572,x26575))
% 168.60/168.41 [2658]~E(x26581,x26582)+E(f474(x26583,x26584,x26585,x26581),f474(x26583,x26584,x26585,x26582))
% 168.60/168.41 [2659]~E(x26591,x26592)+E(f753(x26591,x26593,x26594,x26595),f753(x26592,x26593,x26594,x26595))
% 168.60/168.41 [2660]~E(x26601,x26602)+E(f753(x26603,x26601,x26604,x26605),f753(x26603,x26602,x26604,x26605))
% 168.60/168.41 [2661]~E(x26611,x26612)+E(f753(x26613,x26614,x26611,x26615),f753(x26613,x26614,x26612,x26615))
% 168.60/168.41 [2662]~E(x26621,x26622)+E(f753(x26623,x26624,x26625,x26621),f753(x26623,x26624,x26625,x26622))
% 168.60/168.41 [2663]~E(x26631,x26632)+E(f782(x26631),f782(x26632))
% 168.60/168.41 [2664]~E(x26641,x26642)+E(f447(x26641,x26643,x26644,x26645),f447(x26642,x26643,x26644,x26645))
% 168.60/168.41 [2665]~E(x26651,x26652)+E(f447(x26653,x26651,x26654,x26655),f447(x26653,x26652,x26654,x26655))
% 168.60/168.41 [2666]~E(x26661,x26662)+E(f447(x26663,x26664,x26661,x26665),f447(x26663,x26664,x26662,x26665))
% 168.60/168.41 [2667]~E(x26671,x26672)+E(f447(x26673,x26674,x26675,x26671),f447(x26673,x26674,x26675,x26672))
% 168.60/168.41 [2668]~E(x26681,x26682)+E(f870(x26681,x26683,x26684,x26685),f870(x26682,x26683,x26684,x26685))
% 168.60/168.41 [2669]~E(x26691,x26692)+E(f870(x26693,x26691,x26694,x26695),f870(x26693,x26692,x26694,x26695))
% 168.60/168.41 [2670]~E(x26701,x26702)+E(f870(x26703,x26704,x26701,x26705),f870(x26703,x26704,x26702,x26705))
% 168.60/168.41 [2671]~E(x26711,x26712)+E(f870(x26713,x26714,x26715,x26711),f870(x26713,x26714,x26715,x26712))
% 168.60/168.41 [2672]~E(x26721,x26722)+E(f599(x26721,x26723,x26724,x26725,x26726),f599(x26722,x26723,x26724,x26725,x26726))
% 168.60/168.41 [2673]~E(x26731,x26732)+E(f599(x26733,x26731,x26734,x26735,x26736),f599(x26733,x26732,x26734,x26735,x26736))
% 168.60/168.41 [2674]~E(x26741,x26742)+E(f599(x26743,x26744,x26741,x26745,x26746),f599(x26743,x26744,x26742,x26745,x26746))
% 168.60/168.41 [2675]~E(x26751,x26752)+E(f599(x26753,x26754,x26755,x26751,x26756),f599(x26753,x26754,x26755,x26752,x26756))
% 168.60/168.41 [2676]~E(x26761,x26762)+E(f599(x26763,x26764,x26765,x26766,x26761),f599(x26763,x26764,x26765,x26766,x26762))
% 168.60/168.41 [2677]~E(x26771,x26772)+E(f342(x26771),f342(x26772))
% 168.60/168.41 [2678]~E(x26781,x26782)+E(f249(x26781,x26783,x26784,x26785,x26786),f249(x26782,x26783,x26784,x26785,x26786))
% 168.60/168.41 [2679]~E(x26791,x26792)+E(f249(x26793,x26791,x26794,x26795,x26796),f249(x26793,x26792,x26794,x26795,x26796))
% 168.60/168.41 [2680]~E(x26801,x26802)+E(f249(x26803,x26804,x26801,x26805,x26806),f249(x26803,x26804,x26802,x26805,x26806))
% 168.60/168.41 [2681]~E(x26811,x26812)+E(f249(x26813,x26814,x26815,x26811,x26816),f249(x26813,x26814,x26815,x26812,x26816))
% 168.60/168.41 [2682]~E(x26821,x26822)+E(f249(x26823,x26824,x26825,x26826,x26821),f249(x26823,x26824,x26825,x26826,x26822))
% 168.60/168.41 [2683]~E(x26831,x26832)+E(f265(x26831,x26833,x26834,x26835),f265(x26832,x26833,x26834,x26835))
% 168.60/168.41 [2684]~E(x26841,x26842)+E(f265(x26843,x26841,x26844,x26845),f265(x26843,x26842,x26844,x26845))
% 168.60/168.41 [2685]~E(x26851,x26852)+E(f265(x26853,x26854,x26851,x26855),f265(x26853,x26854,x26852,x26855))
% 168.60/168.41 [2686]~E(x26861,x26862)+E(f265(x26863,x26864,x26865,x26861),f265(x26863,x26864,x26865,x26862))
% 168.60/168.41 [2687]~E(x26871,x26872)+E(f746(x26871,x26873,x26874),f746(x26872,x26873,x26874))
% 168.60/168.41 [2688]~E(x26881,x26882)+E(f746(x26883,x26881,x26884),f746(x26883,x26882,x26884))
% 168.60/168.41 [2689]~E(x26891,x26892)+E(f746(x26893,x26894,x26891),f746(x26893,x26894,x26892))
% 168.60/168.41 [2690]~E(x26901,x26902)+E(f594(x26901,x26903,x26904),f594(x26902,x26903,x26904))
% 168.60/168.41 [2691]~E(x26911,x26912)+E(f594(x26913,x26911,x26914),f594(x26913,x26912,x26914))
% 168.60/168.41 [2692]~E(x26921,x26922)+E(f594(x26923,x26924,x26921),f594(x26923,x26924,x26922))
% 168.60/168.41 [2693]~E(x26931,x26932)+E(f487(x26931,x26933,x26934,x26935),f487(x26932,x26933,x26934,x26935))
% 168.60/168.41 [2694]~E(x26941,x26942)+E(f487(x26943,x26941,x26944,x26945),f487(x26943,x26942,x26944,x26945))
% 168.60/168.41 [2695]~E(x26951,x26952)+E(f487(x26953,x26954,x26951,x26955),f487(x26953,x26954,x26952,x26955))
% 168.60/168.41 [2696]~E(x26961,x26962)+E(f487(x26963,x26964,x26965,x26961),f487(x26963,x26964,x26965,x26962))
% 168.60/168.41 [2697]~E(x26971,x26972)+E(f655(x26971),f655(x26972))
% 168.60/168.41 [2698]~E(x26981,x26982)+E(f496(x26981,x26983,x26984),f496(x26982,x26983,x26984))
% 168.60/168.41 [2699]~E(x26991,x26992)+E(f496(x26993,x26991,x26994),f496(x26993,x26992,x26994))
% 168.60/168.41 [2700]~E(x27001,x27002)+E(f496(x27003,x27004,x27001),f496(x27003,x27004,x27002))
% 168.60/168.41 [2701]~E(x27011,x27012)+E(f791(x27011,x27013),f791(x27012,x27013))
% 168.60/168.41 [2702]~E(x27021,x27022)+E(f791(x27023,x27021),f791(x27023,x27022))
% 168.60/168.41 [2703]~E(x27031,x27032)+E(f684(x27031,x27033,x27034),f684(x27032,x27033,x27034))
% 168.60/168.41 [2704]~E(x27041,x27042)+E(f684(x27043,x27041,x27044),f684(x27043,x27042,x27044))
% 168.60/168.41 [2705]~E(x27051,x27052)+E(f684(x27053,x27054,x27051),f684(x27053,x27054,x27052))
% 168.60/168.41 [2706]~E(x27061,x27062)+E(f807(x27061,x27063,x27064,x27065),f807(x27062,x27063,x27064,x27065))
% 168.60/168.41 [2707]~E(x27071,x27072)+E(f807(x27073,x27071,x27074,x27075),f807(x27073,x27072,x27074,x27075))
% 168.60/168.41 [2708]~E(x27081,x27082)+E(f807(x27083,x27084,x27081,x27085),f807(x27083,x27084,x27082,x27085))
% 168.60/168.41 [2709]~E(x27091,x27092)+E(f807(x27093,x27094,x27095,x27091),f807(x27093,x27094,x27095,x27092))
% 168.60/168.41 [2710]~E(x27101,x27102)+E(f580(x27101,x27103),f580(x27102,x27103))
% 168.60/168.41 [2711]~E(x27111,x27112)+E(f580(x27113,x27111),f580(x27113,x27112))
% 168.60/168.41 [2712]~E(x27121,x27122)+E(f322(x27121,x27123),f322(x27122,x27123))
% 168.60/168.41 [2713]~E(x27131,x27132)+E(f322(x27133,x27131),f322(x27133,x27132))
% 168.60/168.41 [2714]~E(x27141,x27142)+E(f555(x27141,x27143,x27144,x27145),f555(x27142,x27143,x27144,x27145))
% 168.60/168.41 [2715]~E(x27151,x27152)+E(f555(x27153,x27151,x27154,x27155),f555(x27153,x27152,x27154,x27155))
% 168.60/168.41 [2716]~E(x27161,x27162)+E(f555(x27163,x27164,x27161,x27165),f555(x27163,x27164,x27162,x27165))
% 168.60/168.41 [2717]~E(x27171,x27172)+E(f555(x27173,x27174,x27175,x27171),f555(x27173,x27174,x27175,x27172))
% 168.60/168.41 [2718]~E(x27181,x27182)+E(f890(x27181,x27183,x27184,x27185),f890(x27182,x27183,x27184,x27185))
% 168.60/168.41 [2719]~E(x27191,x27192)+E(f890(x27193,x27191,x27194,x27195),f890(x27193,x27192,x27194,x27195))
% 168.60/168.41 [2720]~E(x27201,x27202)+E(f890(x27203,x27204,x27201,x27205),f890(x27203,x27204,x27202,x27205))
% 168.60/168.41 [2721]~E(x27211,x27212)+E(f890(x27213,x27214,x27215,x27211),f890(x27213,x27214,x27215,x27212))
% 168.60/168.41 [2722]~E(x27221,x27222)+E(f23(x27221,x27223),f23(x27222,x27223))
% 168.60/168.41 [2723]~E(x27231,x27232)+E(f23(x27233,x27231),f23(x27233,x27232))
% 168.60/168.41 [2724]~E(x27241,x27242)+E(f340(x27241,x27243,x27244),f340(x27242,x27243,x27244))
% 168.60/168.41 [2725]~E(x27251,x27252)+E(f340(x27253,x27251,x27254),f340(x27253,x27252,x27254))
% 168.60/168.41 [2726]~E(x27261,x27262)+E(f340(x27263,x27264,x27261),f340(x27263,x27264,x27262))
% 168.60/168.41 [2727]~E(x27271,x27272)+E(f708(x27271,x27273),f708(x27272,x27273))
% 168.60/168.41 [2728]~E(x27281,x27282)+E(f708(x27283,x27281),f708(x27283,x27282))
% 168.60/168.41 [2729]~E(x27291,x27292)+E(f743(x27291,x27293,x27294),f743(x27292,x27293,x27294))
% 168.60/168.41 [2730]~E(x27301,x27302)+E(f743(x27303,x27301,x27304),f743(x27303,x27302,x27304))
% 168.60/168.41 [2731]~E(x27311,x27312)+E(f743(x27313,x27314,x27311),f743(x27313,x27314,x27312))
% 168.60/168.41 [2732]~E(x27321,x27322)+E(f195(x27321,x27323,x27324,x27325),f195(x27322,x27323,x27324,x27325))
% 168.60/168.41 [2733]~E(x27331,x27332)+E(f195(x27333,x27331,x27334,x27335),f195(x27333,x27332,x27334,x27335))
% 168.60/168.41 [2734]~E(x27341,x27342)+E(f195(x27343,x27344,x27341,x27345),f195(x27343,x27344,x27342,x27345))
% 168.60/168.41 [2735]~E(x27351,x27352)+E(f195(x27353,x27354,x27355,x27351),f195(x27353,x27354,x27355,x27352))
% 168.60/168.41 [2736]~E(x27361,x27362)+E(f253(x27361,x27363,x27364),f253(x27362,x27363,x27364))
% 168.60/168.41 [2737]~E(x27371,x27372)+E(f253(x27373,x27371,x27374),f253(x27373,x27372,x27374))
% 168.60/168.41 [2738]~E(x27381,x27382)+E(f253(x27383,x27384,x27381),f253(x27383,x27384,x27382))
% 168.60/168.41 [2739]~E(x27391,x27392)+E(f332(x27391,x27393,x27394),f332(x27392,x27393,x27394))
% 168.60/168.41 [2740]~E(x27401,x27402)+E(f332(x27403,x27401,x27404),f332(x27403,x27402,x27404))
% 168.60/168.41 [2741]~E(x27411,x27412)+E(f332(x27413,x27414,x27411),f332(x27413,x27414,x27412))
% 168.60/168.41 [2742]~E(x27421,x27422)+E(f379(x27421,x27423,x27424),f379(x27422,x27423,x27424))
% 168.60/168.41 [2743]~E(x27431,x27432)+E(f379(x27433,x27431,x27434),f379(x27433,x27432,x27434))
% 168.60/168.41 [2744]~E(x27441,x27442)+E(f379(x27443,x27444,x27441),f379(x27443,x27444,x27442))
% 168.60/168.41 [2745]~E(x27451,x27452)+E(f602(x27451,x27453,x27454),f602(x27452,x27453,x27454))
% 168.60/168.41 [2746]~E(x27461,x27462)+E(f602(x27463,x27461,x27464),f602(x27463,x27462,x27464))
% 168.60/168.41 [2747]~E(x27471,x27472)+E(f602(x27473,x27474,x27471),f602(x27473,x27474,x27472))
% 168.60/168.41 [2748]~E(x27481,x27482)+E(f329(x27481,x27483),f329(x27482,x27483))
% 168.60/168.41 [2749]~E(x27491,x27492)+E(f329(x27493,x27491),f329(x27493,x27492))
% 168.60/168.41 [2750]~E(x27501,x27502)+E(f780(x27501,x27503,x27504,x27505),f780(x27502,x27503,x27504,x27505))
% 168.60/168.41 [2751]~E(x27511,x27512)+E(f780(x27513,x27511,x27514,x27515),f780(x27513,x27512,x27514,x27515))
% 168.60/168.41 [2752]~E(x27521,x27522)+E(f780(x27523,x27524,x27521,x27525),f780(x27523,x27524,x27522,x27525))
% 168.60/168.41 [2753]~E(x27531,x27532)+E(f780(x27533,x27534,x27535,x27531),f780(x27533,x27534,x27535,x27532))
% 168.60/168.41 [2754]~E(x27541,x27542)+E(f320(x27541),f320(x27542))
% 168.60/168.41 [2755]~E(x27551,x27552)+E(f396(x27551),f396(x27552))
% 168.60/168.41 [2756]~E(x27561,x27562)+E(f419(x27561,x27563,x27564,x27565,x27566),f419(x27562,x27563,x27564,x27565,x27566))
% 168.60/168.41 [2757]~E(x27571,x27572)+E(f419(x27573,x27571,x27574,x27575,x27576),f419(x27573,x27572,x27574,x27575,x27576))
% 168.60/168.41 [2758]~E(x27581,x27582)+E(f419(x27583,x27584,x27581,x27585,x27586),f419(x27583,x27584,x27582,x27585,x27586))
% 168.60/168.41 [2759]~E(x27591,x27592)+E(f419(x27593,x27594,x27595,x27591,x27596),f419(x27593,x27594,x27595,x27592,x27596))
% 168.60/168.41 [2760]~E(x27601,x27602)+E(f419(x27603,x27604,x27605,x27606,x27601),f419(x27603,x27604,x27605,x27606,x27602))
% 168.60/168.41 [2761]~E(x27611,x27612)+E(f352(x27611),f352(x27612))
% 168.60/168.41 [2762]~E(x27621,x27622)+E(f721(x27621,x27623),f721(x27622,x27623))
% 168.60/168.41 [2763]~E(x27631,x27632)+E(f721(x27633,x27631),f721(x27633,x27632))
% 168.60/168.41 [2764]~E(x27641,x27642)+E(f790(x27641),f790(x27642))
% 168.60/168.41 [2765]~E(x27651,x27652)+E(f856(x27651,x27653,x27654,x27655,x27656),f856(x27652,x27653,x27654,x27655,x27656))
% 168.60/168.41 [2766]~E(x27661,x27662)+E(f856(x27663,x27661,x27664,x27665,x27666),f856(x27663,x27662,x27664,x27665,x27666))
% 168.60/168.41 [2767]~E(x27671,x27672)+E(f856(x27673,x27674,x27671,x27675,x27676),f856(x27673,x27674,x27672,x27675,x27676))
% 168.60/168.41 [2768]~E(x27681,x27682)+E(f856(x27683,x27684,x27685,x27681,x27686),f856(x27683,x27684,x27685,x27682,x27686))
% 168.60/168.41 [2769]~E(x27691,x27692)+E(f856(x27693,x27694,x27695,x27696,x27691),f856(x27693,x27694,x27695,x27696,x27692))
% 168.60/168.41 [2770]~E(x27701,x27702)+E(f37(x27701),f37(x27702))
% 168.60/168.41 [2771]~E(x27711,x27712)+E(f267(x27711,x27713,x27714,x27715),f267(x27712,x27713,x27714,x27715))
% 168.60/168.41 [2772]~E(x27721,x27722)+E(f267(x27723,x27721,x27724,x27725),f267(x27723,x27722,x27724,x27725))
% 168.60/168.41 [2773]~E(x27731,x27732)+E(f267(x27733,x27734,x27731,x27735),f267(x27733,x27734,x27732,x27735))
% 168.60/168.41 [2774]~E(x27741,x27742)+E(f267(x27743,x27744,x27745,x27741),f267(x27743,x27744,x27745,x27742))
% 168.60/168.41 [2775]~P1(x27751)+P1(x27752)+~E(x27751,x27752)
% 168.60/168.41 [2776]~P2(x27761)+P2(x27762)+~E(x27761,x27762)
% 168.60/168.41 [2777]~P110(x27771)+P110(x27772)+~E(x27771,x27772)
% 168.60/168.41 [2778]~P108(x27781)+P108(x27782)+~E(x27781,x27782)
% 168.60/168.41 [2779]~P114(x27791)+P114(x27792)+~E(x27791,x27792)
% 168.60/168.41 [2780]~P97(x27801)+P97(x27802)+~E(x27801,x27802)
% 168.60/168.41 [2781]P40(x27812,x27813)+~E(x27811,x27812)+~P40(x27811,x27813)
% 168.60/168.41 [2782]P40(x27823,x27822)+~E(x27821,x27822)+~P40(x27823,x27821)
% 168.60/168.41 [2783]~P109(x27831)+P109(x27832)+~E(x27831,x27832)
% 168.60/168.41 [2784]~P80(x27841)+P80(x27842)+~E(x27841,x27842)
% 168.60/168.41 [2785]~P103(x27851)+P103(x27852)+~E(x27851,x27852)
% 168.60/168.41 [2786]~P72(x27861)+P72(x27862)+~E(x27861,x27862)
% 168.60/168.41 [2787]~P104(x27871)+P104(x27872)+~E(x27871,x27872)
% 168.60/168.41 [2788]~P88(x27881)+P88(x27882)+~E(x27881,x27882)
% 168.60/168.41 [2789]~P78(x27891)+P78(x27892)+~E(x27891,x27892)
% 168.60/168.41 [2790]~P111(x27901)+P111(x27902)+~E(x27901,x27902)
% 168.60/168.41 [2791]~P139(x27911)+P139(x27912)+~E(x27911,x27912)
% 168.60/168.41 [2792]P33(x27922,x27923,x27924)+~E(x27921,x27922)+~P33(x27921,x27923,x27924)
% 168.60/168.41 [2793]P33(x27933,x27932,x27934)+~E(x27931,x27932)+~P33(x27933,x27931,x27934)
% 168.60/168.41 [2794]P33(x27943,x27944,x27942)+~E(x27941,x27942)+~P33(x27943,x27944,x27941)
% 168.60/168.41 [2795]~P67(x27951)+P67(x27952)+~E(x27951,x27952)
% 168.60/168.41 [2796]~P3(x27961)+P3(x27962)+~E(x27961,x27962)
% 168.60/168.41 [2797]~P68(x27971)+P68(x27972)+~E(x27971,x27972)
% 168.60/168.41 [2798]~P82(x27981)+P82(x27982)+~E(x27981,x27982)
% 168.60/168.41 [2799]~P116(x27991)+P116(x27992)+~E(x27991,x27992)
% 168.60/168.41 [2800]~P91(x28001)+P91(x28002)+~E(x28001,x28002)
% 168.60/168.41 [2801]P150(x28012,x28013,x28014)+~E(x28011,x28012)+~P150(x28011,x28013,x28014)
% 168.60/168.41 [2802]P150(x28023,x28022,x28024)+~E(x28021,x28022)+~P150(x28023,x28021,x28024)
% 168.60/168.41 [2803]P150(x28033,x28034,x28032)+~E(x28031,x28032)+~P150(x28033,x28034,x28031)
% 168.60/168.41 [2804]~P65(x28041)+P65(x28042)+~E(x28041,x28042)
% 168.60/168.41 [2805]~P81(x28051)+P81(x28052)+~E(x28051,x28052)
% 168.60/168.41 [2806]~P136(x28061)+P136(x28062)+~E(x28061,x28062)
% 168.60/168.41 [2807]~P121(x28071)+P121(x28072)+~E(x28071,x28072)
% 168.60/168.41 [2808]P21(x28082,x28083,x28084,x28085)+~E(x28081,x28082)+~P21(x28081,x28083,x28084,x28085)
% 168.60/168.41 [2809]P21(x28093,x28092,x28094,x28095)+~E(x28091,x28092)+~P21(x28093,x28091,x28094,x28095)
% 168.60/168.41 [2810]P21(x28103,x28104,x28102,x28105)+~E(x28101,x28102)+~P21(x28103,x28104,x28101,x28105)
% 168.60/168.41 [2811]P21(x28113,x28114,x28115,x28112)+~E(x28111,x28112)+~P21(x28113,x28114,x28115,x28111)
% 168.60/168.41 [2812]~P130(x28121)+P130(x28122)+~E(x28121,x28122)
% 168.60/168.41 [2813]~P4(x28131)+P4(x28132)+~E(x28131,x28132)
% 168.60/168.41 [2814]~P128(x28141)+P128(x28142)+~E(x28141,x28142)
% 168.60/168.41 [2815]~P69(x28151)+P69(x28152)+~E(x28151,x28152)
% 168.60/168.41 [2816]~P112(x28161)+P112(x28162)+~E(x28161,x28162)
% 168.60/168.41 [2817]~P70(x28171)+P70(x28172)+~E(x28171,x28172)
% 168.60/168.41 [2818]P36(x28182,x28183,x28184,x28185,x28186)+~E(x28181,x28182)+~P36(x28181,x28183,x28184,x28185,x28186)
% 168.60/168.41 [2819]P36(x28193,x28192,x28194,x28195,x28196)+~E(x28191,x28192)+~P36(x28193,x28191,x28194,x28195,x28196)
% 168.60/168.41 [2820]P36(x28203,x28204,x28202,x28205,x28206)+~E(x28201,x28202)+~P36(x28203,x28204,x28201,x28205,x28206)
% 168.60/168.41 [2821]P36(x28213,x28214,x28215,x28212,x28216)+~E(x28211,x28212)+~P36(x28213,x28214,x28215,x28211,x28216)
% 168.60/168.41 [2822]P36(x28223,x28224,x28225,x28226,x28222)+~E(x28221,x28222)+~P36(x28223,x28224,x28225,x28226,x28221)
% 168.60/168.41 [2823]P37(x28232,x28233,x28234)+~E(x28231,x28232)+~P37(x28231,x28233,x28234)
% 168.60/168.41 [2824]P37(x28243,x28242,x28244)+~E(x28241,x28242)+~P37(x28243,x28241,x28244)
% 168.60/168.41 [2825]P37(x28253,x28254,x28252)+~E(x28251,x28252)+~P37(x28253,x28254,x28251)
% 168.60/168.41 [2826]P25(x28262,x28263,x28264,x28265)+~E(x28261,x28262)+~P25(x28261,x28263,x28264,x28265)
% 168.60/168.41 [2827]P25(x28273,x28272,x28274,x28275)+~E(x28271,x28272)+~P25(x28273,x28271,x28274,x28275)
% 168.60/168.41 [2828]P25(x28283,x28284,x28282,x28285)+~E(x28281,x28282)+~P25(x28283,x28284,x28281,x28285)
% 168.60/168.41 [2829]P25(x28293,x28294,x28295,x28292)+~E(x28291,x28292)+~P25(x28293,x28294,x28295,x28291)
% 168.60/168.41 [2830]~P137(x28301)+P137(x28302)+~E(x28301,x28302)
% 168.60/168.41 [2831]~P86(x28311)+P86(x28312)+~E(x28311,x28312)
% 168.60/168.41 [2832]~P101(x28321)+P101(x28322)+~E(x28321,x28322)
% 168.60/168.41 [2833]~P96(x28331)+P96(x28332)+~E(x28331,x28332)
% 168.60/168.41 [2834]P35(x28342,x28343,x28344)+~E(x28341,x28342)+~P35(x28341,x28343,x28344)
% 168.60/168.41 [2835]P35(x28353,x28352,x28354)+~E(x28351,x28352)+~P35(x28353,x28351,x28354)
% 168.60/168.41 [2836]P35(x28363,x28364,x28362)+~E(x28361,x28362)+~P35(x28363,x28364,x28361)
% 168.60/168.41 [2837]P32(x28372,x28373,x28374)+~E(x28371,x28372)+~P32(x28371,x28373,x28374)
% 168.60/168.41 [2838]P32(x28383,x28382,x28384)+~E(x28381,x28382)+~P32(x28383,x28381,x28384)
% 168.60/168.41 [2839]P32(x28393,x28394,x28392)+~E(x28391,x28392)+~P32(x28393,x28394,x28391)
% 168.60/168.41 [2840]P26(x28402,x28403,x28404,x28405,x28406)+~E(x28401,x28402)+~P26(x28401,x28403,x28404,x28405,x28406)
% 168.60/168.41 [2841]P26(x28413,x28412,x28414,x28415,x28416)+~E(x28411,x28412)+~P26(x28413,x28411,x28414,x28415,x28416)
% 168.60/168.41 [2842]P26(x28423,x28424,x28422,x28425,x28426)+~E(x28421,x28422)+~P26(x28423,x28424,x28421,x28425,x28426)
% 168.60/168.41 [2843]P26(x28433,x28434,x28435,x28432,x28436)+~E(x28431,x28432)+~P26(x28433,x28434,x28435,x28431,x28436)
% 168.60/168.41 [2844]P26(x28443,x28444,x28445,x28446,x28442)+~E(x28441,x28442)+~P26(x28443,x28444,x28445,x28446,x28441)
% 168.60/168.41 [2845]~P143(x28451)+P143(x28452)+~E(x28451,x28452)
% 168.60/168.41 [2846]~P66(x28461)+P66(x28462)+~E(x28461,x28462)
% 168.60/168.41 [2847]P17(x28472,x28473,x28474)+~E(x28471,x28472)+~P17(x28471,x28473,x28474)
% 168.60/168.41 [2848]P17(x28483,x28482,x28484)+~E(x28481,x28482)+~P17(x28483,x28481,x28484)
% 168.60/168.41 [2849]P17(x28493,x28494,x28492)+~E(x28491,x28492)+~P17(x28493,x28494,x28491)
% 168.60/168.41 [2850]~P6(x28501)+P6(x28502)+~E(x28501,x28502)
% 168.60/168.41 [2851]~P73(x28511)+P73(x28512)+~E(x28511,x28512)
% 168.60/168.41 [2852]~P62(x28521)+P62(x28522)+~E(x28521,x28522)
% 168.60/168.41 [2853]P13(x28532,x28533)+~E(x28531,x28532)+~P13(x28531,x28533)
% 168.60/168.41 [2854]P13(x28543,x28542)+~E(x28541,x28542)+~P13(x28543,x28541)
% 168.60/168.41 [2855]~P74(x28551)+P74(x28552)+~E(x28551,x28552)
% 168.60/168.41 [2856]P39(x28562,x28563)+~E(x28561,x28562)+~P39(x28561,x28563)
% 168.60/168.41 [2857]P39(x28573,x28572)+~E(x28571,x28572)+~P39(x28573,x28571)
% 168.60/168.41 [2858]~P5(x28581)+P5(x28582)+~E(x28581,x28582)
% 168.60/168.41 [2859]~P71(x28591)+P71(x28592)+~E(x28591,x28592)
% 168.60/168.41 [2860]~P64(x28601)+P64(x28602)+~E(x28601,x28602)
% 168.60/168.41 [2861]P53(x28612,x28613)+~E(x28611,x28612)+~P53(x28611,x28613)
% 168.60/168.41 [2862]P53(x28623,x28622)+~E(x28621,x28622)+~P53(x28623,x28621)
% 168.60/168.41 [2863]~P83(x28631)+P83(x28632)+~E(x28631,x28632)
% 168.60/168.41 [2864]~P89(x28641)+P89(x28642)+~E(x28641,x28642)
% 168.60/168.41 [2865]~P113(x28651)+P113(x28652)+~E(x28651,x28652)
% 168.60/168.41 [2866]~P87(x28661)+P87(x28662)+~E(x28661,x28662)
% 168.60/168.41 [2867]~P63(x28671)+P63(x28672)+~E(x28671,x28672)
% 168.60/168.41 [2868]~P138(x28681)+P138(x28682)+~E(x28681,x28682)
% 168.60/168.41 [2869]P58(x28692,x28693,x28694,x28695,x28696)+~E(x28691,x28692)+~P58(x28691,x28693,x28694,x28695,x28696)
% 168.60/168.41 [2870]P58(x28703,x28702,x28704,x28705,x28706)+~E(x28701,x28702)+~P58(x28703,x28701,x28704,x28705,x28706)
% 168.60/168.41 [2871]P58(x28713,x28714,x28712,x28715,x28716)+~E(x28711,x28712)+~P58(x28713,x28714,x28711,x28715,x28716)
% 168.60/168.41 [2872]P58(x28723,x28724,x28725,x28722,x28726)+~E(x28721,x28722)+~P58(x28723,x28724,x28725,x28721,x28726)
% 168.60/168.41 [2873]P58(x28733,x28734,x28735,x28736,x28732)+~E(x28731,x28732)+~P58(x28733,x28734,x28735,x28736,x28731)
% 168.60/168.41 [2874]~P124(x28741)+P124(x28742)+~E(x28741,x28742)
% 168.60/168.41 [2875]~P123(x28751)+P123(x28752)+~E(x28751,x28752)
% 168.60/168.41 [2876]~P76(x28761)+P76(x28762)+~E(x28761,x28762)
% 168.60/168.41 [2877]~P77(x28771)+P77(x28772)+~E(x28771,x28772)
% 168.60/168.41 [2878]~P98(x28781)+P98(x28782)+~E(x28781,x28782)
% 168.60/168.41 [2879]P59(x28792,x28793)+~E(x28791,x28792)+~P59(x28791,x28793)
% 168.60/168.41 [2880]P59(x28803,x28802)+~E(x28801,x28802)+~P59(x28803,x28801)
% 168.60/168.41 [2881]~P84(x28811)+P84(x28812)+~E(x28811,x28812)
% 168.60/168.41 [2882]~P146(x28821)+P146(x28822)+~E(x28821,x28822)
% 168.60/168.41 [2883]~P135(x28831)+P135(x28832)+~E(x28831,x28832)
% 168.60/168.41 [2884]P7(x28842,x28843)+~E(x28841,x28842)+~P7(x28841,x28843)
% 168.60/168.41 [2885]P7(x28853,x28852)+~E(x28851,x28852)+~P7(x28853,x28851)
% 168.60/168.41 [2886]P41(x28862,x28863)+~E(x28861,x28862)+~P41(x28861,x28863)
% 168.60/168.41 [2887]P41(x28873,x28872)+~E(x28871,x28872)+~P41(x28873,x28871)
% 168.60/168.41 [2888]~P141(x28881)+P141(x28882)+~E(x28881,x28882)
% 168.60/168.41 [2889]P11(x28892,x28893,x28894,x28895)+~E(x28891,x28892)+~P11(x28891,x28893,x28894,x28895)
% 168.60/168.41 [2890]P11(x28903,x28902,x28904,x28905)+~E(x28901,x28902)+~P11(x28903,x28901,x28904,x28905)
% 168.60/168.41 [2891]P11(x28913,x28914,x28912,x28915)+~E(x28911,x28912)+~P11(x28913,x28914,x28911,x28915)
% 168.60/168.41 [2892]P11(x28923,x28924,x28925,x28922)+~E(x28921,x28922)+~P11(x28923,x28924,x28925,x28921)
% 168.60/168.41 [2893]P8(x28932,x28933,x28934)+~E(x28931,x28932)+~P8(x28931,x28933,x28934)
% 168.60/168.41 [2894]P8(x28943,x28942,x28944)+~E(x28941,x28942)+~P8(x28943,x28941,x28944)
% 168.60/168.41 [2895]P8(x28953,x28954,x28952)+~E(x28951,x28952)+~P8(x28953,x28954,x28951)
% 168.60/168.41 [2896]~P115(x28961)+P115(x28962)+~E(x28961,x28962)
% 168.60/168.41 [2897]P52(x28972,x28973)+~E(x28971,x28972)+~P52(x28971,x28973)
% 168.60/168.41 [2898]P52(x28983,x28982)+~E(x28981,x28982)+~P52(x28983,x28981)
% 168.60/168.41 [2899]P51(x28992,x28993)+~E(x28991,x28992)+~P51(x28991,x28993)
% 168.60/168.41 [2900]P51(x29003,x29002)+~E(x29001,x29002)+~P51(x29003,x29001)
% 168.60/168.41 [2901]P54(x29012,x29013,x29014)+~E(x29011,x29012)+~P54(x29011,x29013,x29014)
% 168.60/168.41 [2902]P54(x29023,x29022,x29024)+~E(x29021,x29022)+~P54(x29023,x29021,x29024)
% 168.60/168.41 [2903]P54(x29033,x29034,x29032)+~E(x29031,x29032)+~P54(x29033,x29034,x29031)
% 168.60/168.41 [2904]~P117(x29041)+P117(x29042)+~E(x29041,x29042)
% 168.60/168.41 [2905]~P42(x29051)+P42(x29052)+~E(x29051,x29052)
% 168.60/168.41 [2906]~P129(x29061)+P129(x29062)+~E(x29061,x29062)
% 168.60/168.41 [2907]~P93(x29071)+P93(x29072)+~E(x29071,x29072)
% 168.60/168.41 [2908]P18(x29082,x29083,x29084)+~E(x29081,x29082)+~P18(x29081,x29083,x29084)
% 168.60/168.41 [2909]P18(x29093,x29092,x29094)+~E(x29091,x29092)+~P18(x29093,x29091,x29094)
% 168.60/168.41 [2910]P18(x29103,x29104,x29102)+~E(x29101,x29102)+~P18(x29103,x29104,x29101)
% 168.60/168.41 [2911]~P145(x29111)+P145(x29112)+~E(x29111,x29112)
% 168.60/168.41 [2912]~P99(x29121)+P99(x29122)+~E(x29121,x29122)
% 168.60/168.41 [2913]~P131(x29131)+P131(x29132)+~E(x29131,x29132)
% 168.60/168.41 [2914]~P134(x29141)+P134(x29142)+~E(x29141,x29142)
% 168.60/168.41 [2915]P15(x29152,x29153,x29154)+~E(x29151,x29152)+~P15(x29151,x29153,x29154)
% 168.60/168.41 [2916]P15(x29163,x29162,x29164)+~E(x29161,x29162)+~P15(x29163,x29161,x29164)
% 168.60/168.41 [2917]P15(x29173,x29174,x29172)+~E(x29171,x29172)+~P15(x29173,x29174,x29171)
% 168.60/168.41 [2918]P20(x29182,x29183,x29184,x29185)+~E(x29181,x29182)+~P20(x29181,x29183,x29184,x29185)
% 168.60/168.41 [2919]P20(x29193,x29192,x29194,x29195)+~E(x29191,x29192)+~P20(x29193,x29191,x29194,x29195)
% 168.60/168.41 [2920]P20(x29203,x29204,x29202,x29205)+~E(x29201,x29202)+~P20(x29203,x29204,x29201,x29205)
% 168.60/168.41 [2921]P20(x29213,x29214,x29215,x29212)+~E(x29211,x29212)+~P20(x29213,x29214,x29215,x29211)
% 168.60/168.41 [2922]~P90(x29221)+P90(x29222)+~E(x29221,x29222)
% 168.60/168.41 [2923]~P147(x29231)+P147(x29232)+~E(x29231,x29232)
% 168.60/168.41 [2924]P56(x29242,x29243,x29244)+~E(x29241,x29242)+~P56(x29241,x29243,x29244)
% 168.60/168.41 [2925]P56(x29253,x29252,x29254)+~E(x29251,x29252)+~P56(x29253,x29251,x29254)
% 168.60/168.41 [2926]P56(x29263,x29264,x29262)+~E(x29261,x29262)+~P56(x29263,x29264,x29261)
% 168.60/168.41 [2927]~P85(x29271)+P85(x29272)+~E(x29271,x29272)
% 168.60/168.41 [2928]P12(x29282,x29283,x29284,x29285,x29286,x29287)+~E(x29281,x29282)+~P12(x29281,x29283,x29284,x29285,x29286,x29287)
% 168.60/168.41 [2929]P12(x29293,x29292,x29294,x29295,x29296,x29297)+~E(x29291,x29292)+~P12(x29293,x29291,x29294,x29295,x29296,x29297)
% 168.60/168.41 [2930]P12(x29303,x29304,x29302,x29305,x29306,x29307)+~E(x29301,x29302)+~P12(x29303,x29304,x29301,x29305,x29306,x29307)
% 168.60/168.41 [2931]P12(x29313,x29314,x29315,x29312,x29316,x29317)+~E(x29311,x29312)+~P12(x29313,x29314,x29315,x29311,x29316,x29317)
% 168.60/168.41 [2932]P12(x29323,x29324,x29325,x29326,x29322,x29327)+~E(x29321,x29322)+~P12(x29323,x29324,x29325,x29326,x29321,x29327)
% 168.60/168.41 [2933]P12(x29333,x29334,x29335,x29336,x29337,x29332)+~E(x29331,x29332)+~P12(x29333,x29334,x29335,x29336,x29337,x29331)
% 168.60/168.41 [2934]~P144(x29341)+P144(x29342)+~E(x29341,x29342)
% 168.60/168.41 [2935]P14(x29352,x29353,x29354)+~E(x29351,x29352)+~P14(x29351,x29353,x29354)
% 168.60/168.41 [2936]P14(x29363,x29362,x29364)+~E(x29361,x29362)+~P14(x29363,x29361,x29364)
% 168.60/168.41 [2937]P14(x29373,x29374,x29372)+~E(x29371,x29372)+~P14(x29373,x29374,x29371)
% 168.60/168.41 [2938]~P142(x29381)+P142(x29382)+~E(x29381,x29382)
% 168.60/168.41 [2939]P149(x29392,x29393,x29394)+~E(x29391,x29392)+~P149(x29391,x29393,x29394)
% 168.60/168.41 [2940]P149(x29403,x29402,x29404)+~E(x29401,x29402)+~P149(x29403,x29401,x29404)
% 168.60/168.41 [2941]P149(x29413,x29414,x29412)+~E(x29411,x29412)+~P149(x29413,x29414,x29411)
% 168.60/168.41 [2942]P16(x29422,x29423)+~E(x29421,x29422)+~P16(x29421,x29423)
% 168.60/168.41 [2943]P16(x29433,x29432)+~E(x29431,x29432)+~P16(x29433,x29431)
% 168.60/168.41 [2944]P57(x29442,x29443,x29444)+~E(x29441,x29442)+~P57(x29441,x29443,x29444)
% 168.60/168.41 [2945]P57(x29453,x29452,x29454)+~E(x29451,x29452)+~P57(x29453,x29451,x29454)
% 168.60/168.41 [2946]P57(x29463,x29464,x29462)+~E(x29461,x29462)+~P57(x29463,x29464,x29461)
% 168.60/168.41 [2947]P61(x29472,x29473)+~E(x29471,x29472)+~P61(x29471,x29473)
% 168.60/168.41 [2948]P61(x29483,x29482)+~E(x29481,x29482)+~P61(x29483,x29481)
% 168.60/168.41 [2949]P50(x29492,x29493,x29494)+~E(x29491,x29492)+~P50(x29491,x29493,x29494)
% 168.60/168.41 [2950]P50(x29503,x29502,x29504)+~E(x29501,x29502)+~P50(x29503,x29501,x29504)
% 168.60/168.41 [2951]P50(x29513,x29514,x29512)+~E(x29511,x29512)+~P50(x29513,x29514,x29511)
% 168.60/168.41 [2952]P34(x29522,x29523,x29524,x29525)+~E(x29521,x29522)+~P34(x29521,x29523,x29524,x29525)
% 168.60/168.41 [2953]P34(x29533,x29532,x29534,x29535)+~E(x29531,x29532)+~P34(x29533,x29531,x29534,x29535)
% 168.60/168.41 [2954]P34(x29543,x29544,x29542,x29545)+~E(x29541,x29542)+~P34(x29543,x29544,x29541,x29545)
% 168.60/168.41 [2955]P34(x29553,x29554,x29555,x29552)+~E(x29551,x29552)+~P34(x29553,x29554,x29555,x29551)
% 168.60/168.41 [2956]P24(x29562,x29563,x29564,x29565,x29566,x29567)+~E(x29561,x29562)+~P24(x29561,x29563,x29564,x29565,x29566,x29567)
% 168.60/168.41 [2957]P24(x29573,x29572,x29574,x29575,x29576,x29577)+~E(x29571,x29572)+~P24(x29573,x29571,x29574,x29575,x29576,x29577)
% 168.60/168.41 [2958]P24(x29583,x29584,x29582,x29585,x29586,x29587)+~E(x29581,x29582)+~P24(x29583,x29584,x29581,x29585,x29586,x29587)
% 168.60/168.41 [2959]P24(x29593,x29594,x29595,x29592,x29596,x29597)+~E(x29591,x29592)+~P24(x29593,x29594,x29595,x29591,x29596,x29597)
% 168.60/168.41 [2960]P24(x29603,x29604,x29605,x29606,x29602,x29607)+~E(x29601,x29602)+~P24(x29603,x29604,x29605,x29606,x29601,x29607)
% 168.60/168.41 [2961]P24(x29613,x29614,x29615,x29616,x29617,x29612)+~E(x29611,x29612)+~P24(x29613,x29614,x29615,x29616,x29617,x29611)
% 168.60/168.41 [2962]P27(x29622,x29623)+~E(x29621,x29622)+~P27(x29621,x29623)
% 168.60/168.41 [2963]P27(x29633,x29632)+~E(x29631,x29632)+~P27(x29633,x29631)
% 168.60/168.41 [2964]~P38(x29641)+P38(x29642)+~E(x29641,x29642)
% 168.60/168.41 [2965]P30(x29652,x29653)+~E(x29651,x29652)+~P30(x29651,x29653)
% 168.60/168.41 [2966]P30(x29663,x29662)+~E(x29661,x29662)+~P30(x29663,x29661)
% 168.60/168.41 [2967]~P102(x29671)+P102(x29672)+~E(x29671,x29672)
% 168.60/168.41 [2968]P60(x29682,x29683,x29684,x29685)+~E(x29681,x29682)+~P60(x29681,x29683,x29684,x29685)
% 168.60/168.41 [2969]P60(x29693,x29692,x29694,x29695)+~E(x29691,x29692)+~P60(x29693,x29691,x29694,x29695)
% 168.60/168.41 [2970]P60(x29703,x29704,x29702,x29705)+~E(x29701,x29702)+~P60(x29703,x29704,x29701,x29705)
% 168.60/168.41 [2971]P60(x29713,x29714,x29715,x29712)+~E(x29711,x29712)+~P60(x29713,x29714,x29715,x29711)
% 168.60/168.41 [2972]~P140(x29721)+P140(x29722)+~E(x29721,x29722)
% 168.60/168.41 [2973]~P95(x29731)+P95(x29732)+~E(x29731,x29732)
% 168.60/168.41 [2974]~P148(x29741)+P148(x29742)+~E(x29741,x29742)
% 168.60/168.41 [2975]P28(x29752,x29753,x29754)+~E(x29751,x29752)+~P28(x29751,x29753,x29754)
% 168.60/168.41 [2976]P28(x29763,x29762,x29764)+~E(x29761,x29762)+~P28(x29763,x29761,x29764)
% 168.60/168.41 [2977]P28(x29773,x29774,x29772)+~E(x29771,x29772)+~P28(x29773,x29774,x29771)
% 168.60/168.41 [2978]P45(x29782,x29783)+~E(x29781,x29782)+~P45(x29781,x29783)
% 168.60/168.41 [2979]P45(x29793,x29792)+~E(x29791,x29792)+~P45(x29793,x29791)
% 168.60/168.41 [2980]P46(x29802,x29803)+~E(x29801,x29802)+~P46(x29801,x29803)
% 168.60/168.41 [2981]P46(x29813,x29812)+~E(x29811,x29812)+~P46(x29813,x29811)
% 168.60/168.41 [2982]P49(x29822,x29823,x29824)+~E(x29821,x29822)+~P49(x29821,x29823,x29824)
% 168.60/168.41 [2983]P49(x29833,x29832,x29834)+~E(x29831,x29832)+~P49(x29833,x29831,x29834)
% 168.60/168.41 [2984]P49(x29843,x29844,x29842)+~E(x29841,x29842)+~P49(x29843,x29844,x29841)
% 168.60/168.41 [2985]~P120(x29851)+P120(x29852)+~E(x29851,x29852)
% 168.60/168.41 [2986]~P122(x29861)+P122(x29862)+~E(x29861,x29862)
% 168.60/168.41 [2987]P44(x29872,x29873,x29874,x29875,x29876,x29877)+~E(x29871,x29872)+~P44(x29871,x29873,x29874,x29875,x29876,x29877)
% 168.60/168.41 [2988]P44(x29883,x29882,x29884,x29885,x29886,x29887)+~E(x29881,x29882)+~P44(x29883,x29881,x29884,x29885,x29886,x29887)
% 168.60/168.41 [2989]P44(x29893,x29894,x29892,x29895,x29896,x29897)+~E(x29891,x29892)+~P44(x29893,x29894,x29891,x29895,x29896,x29897)
% 168.60/168.41 [2990]P44(x29903,x29904,x29905,x29902,x29906,x29907)+~E(x29901,x29902)+~P44(x29903,x29904,x29905,x29901,x29906,x29907)
% 168.60/168.41 [2991]P44(x29913,x29914,x29915,x29916,x29912,x29917)+~E(x29911,x29912)+~P44(x29913,x29914,x29915,x29916,x29911,x29917)
% 168.60/168.41 [2992]P44(x29923,x29924,x29925,x29926,x29927,x29922)+~E(x29921,x29922)+~P44(x29923,x29924,x29925,x29926,x29927,x29921)
% 168.60/168.41 [2993]P55(x29932,x29933)+~E(x29931,x29932)+~P55(x29931,x29933)
% 168.60/168.41 [2994]P55(x29943,x29942)+~E(x29941,x29942)+~P55(x29943,x29941)
% 168.60/168.41 [2995]P31(x29952,x29953,x29954)+~E(x29951,x29952)+~P31(x29951,x29953,x29954)
% 168.60/168.41 [2996]P31(x29963,x29962,x29964)+~E(x29961,x29962)+~P31(x29963,x29961,x29964)
% 168.60/168.41 [2997]P31(x29973,x29974,x29972)+~E(x29971,x29972)+~P31(x29973,x29974,x29971)
% 168.60/168.41 [2998]P29(x29982,x29983,x29984)+~E(x29981,x29982)+~P29(x29981,x29983,x29984)
% 168.60/168.41 [2999]P29(x29993,x29992,x29994)+~E(x29991,x29992)+~P29(x29993,x29991,x29994)
% 168.60/168.41 [3000]P29(x30003,x30004,x30002)+~E(x30001,x30002)+~P29(x30003,x30004,x30001)
% 168.60/168.41 [3001]~P125(x30011)+P125(x30012)+~E(x30011,x30012)
% 168.60/168.41 [3002]~P132(x30021)+P132(x30022)+~E(x30021,x30022)
% 168.60/168.41 [3003]~P126(x30031)+P126(x30032)+~E(x30031,x30032)
% 168.60/168.41 [3004]~P92(x30041)+P92(x30042)+~E(x30041,x30042)
% 168.60/168.41 [3005]~P133(x30051)+P133(x30052)+~E(x30051,x30052)
% 168.60/168.41 [3006]P43(x30062,x30063,x30064,x30065)+~E(x30061,x30062)+~P43(x30061,x30063,x30064,x30065)
% 168.60/168.41 [3007]P43(x30073,x30072,x30074,x30075)+~E(x30071,x30072)+~P43(x30073,x30071,x30074,x30075)
% 168.60/168.41 [3008]P43(x30083,x30084,x30082,x30085)+~E(x30081,x30082)+~P43(x30083,x30084,x30081,x30085)
% 168.60/168.41 [3009]P43(x30093,x30094,x30095,x30092)+~E(x30091,x30092)+~P43(x30093,x30094,x30095,x30091)
% 168.60/168.41 [3010]P23(x30102,x30103,x30104,x30105,x30106,x30107)+~E(x30101,x30102)+~P23(x30101,x30103,x30104,x30105,x30106,x30107)
% 168.60/168.41 [3011]P23(x30113,x30112,x30114,x30115,x30116,x30117)+~E(x30111,x30112)+~P23(x30113,x30111,x30114,x30115,x30116,x30117)
% 168.60/168.41 [3012]P23(x30123,x30124,x30122,x30125,x30126,x30127)+~E(x30121,x30122)+~P23(x30123,x30124,x30121,x30125,x30126,x30127)
% 168.60/168.41 [3013]P23(x30133,x30134,x30135,x30132,x30136,x30137)+~E(x30131,x30132)+~P23(x30133,x30134,x30135,x30131,x30136,x30137)
% 168.60/168.41 [3014]P23(x30143,x30144,x30145,x30146,x30142,x30147)+~E(x30141,x30142)+~P23(x30143,x30144,x30145,x30146,x30141,x30147)
% 168.60/168.41 [3015]P23(x30153,x30154,x30155,x30156,x30157,x30152)+~E(x30151,x30152)+~P23(x30153,x30154,x30155,x30156,x30157,x30151)
% 168.60/168.41 [3016]~P106(x30161)+P106(x30162)+~E(x30161,x30162)
% 168.60/168.41 [3017]~P105(x30171)+P105(x30172)+~E(x30171,x30172)
% 168.60/168.41 [3018]~P119(x30181)+P119(x30182)+~E(x30181,x30182)
% 168.60/168.41 [3019]~P47(x30191)+P47(x30192)+~E(x30191,x30192)
% 168.60/168.41 [3020]P22(x30202,x30203,x30204,x30205,x30206)+~E(x30201,x30202)+~P22(x30201,x30203,x30204,x30205,x30206)
% 168.60/168.41 [3021]P22(x30213,x30212,x30214,x30215,x30216)+~E(x30211,x30212)+~P22(x30213,x30211,x30214,x30215,x30216)
% 168.60/168.41 [3022]P22(x30223,x30224,x30222,x30225,x30226)+~E(x30221,x30222)+~P22(x30223,x30224,x30221,x30225,x30226)
% 168.60/168.41 [3023]P22(x30233,x30234,x30235,x30232,x30236)+~E(x30231,x30232)+~P22(x30233,x30234,x30235,x30231,x30236)
% 168.60/168.41 [3024]P22(x30243,x30244,x30245,x30246,x30242)+~E(x30241,x30242)+~P22(x30243,x30244,x30245,x30246,x30241)
% 168.60/168.41 [3025]~P107(x30251)+P107(x30252)+~E(x30251,x30252)
% 168.60/168.41 [3026]P10(x30262,x30263,x30264,x30265,x30266)+~E(x30261,x30262)+~P10(x30261,x30263,x30264,x30265,x30266)
% 168.60/168.41 [3027]P10(x30273,x30272,x30274,x30275,x30276)+~E(x30271,x30272)+~P10(x30273,x30271,x30274,x30275,x30276)
% 168.60/168.41 [3028]P10(x30283,x30284,x30282,x30285,x30286)+~E(x30281,x30282)+~P10(x30283,x30284,x30281,x30285,x30286)
% 168.60/168.41 [3029]P10(x30293,x30294,x30295,x30292,x30296)+~E(x30291,x30292)+~P10(x30293,x30294,x30295,x30291,x30296)
% 168.60/168.41 [3030]P10(x30303,x30304,x30305,x30306,x30302)+~E(x30301,x30302)+~P10(x30303,x30304,x30305,x30306,x30301)
% 168.60/168.41 [3031]~P100(x30311)+P100(x30312)+~E(x30311,x30312)
% 168.60/168.41 [3032]~P118(x30321)+P118(x30322)+~E(x30321,x30322)
% 168.60/168.41 [3033]P19(x30332,x30333,x30334)+~E(x30331,x30332)+~P19(x30331,x30333,x30334)
% 168.60/168.41 [3034]P19(x30343,x30342,x30344)+~E(x30341,x30342)+~P19(x30343,x30341,x30344)
% 168.60/168.41 [3035]P19(x30353,x30354,x30352)+~E(x30351,x30352)+~P19(x30353,x30354,x30351)
% 168.60/168.41 [3036]~P79(x30361)+P79(x30362)+~E(x30361,x30362)
% 168.60/168.41 [3037]~P94(x30371)+P94(x30372)+~E(x30371,x30372)
% 168.60/168.41 [3038]~P127(x30381)+P127(x30382)+~E(x30381,x30382)
% 168.60/168.41 [3039]P48(x30392,x30393)+~E(x30391,x30392)+~P48(x30391,x30393)
% 168.60/168.41 [3040]P48(x30403,x30402)+~E(x30401,x30402)+~P48(x30403,x30401)
% 168.60/168.41 [3041]~P75(x30411)+P75(x30412)+~E(x30411,x30412)
% 168.60/168.41 [3042]P9(x30422,x30423,x30424)+~E(x30421,x30422)+~P9(x30421,x30423,x30424)
% 168.60/168.41 [3043]P9(x30433,x30432,x30434)+~E(x30431,x30432)+~P9(x30433,x30431,x30434)
% 168.60/168.41 [3044]P9(x30443,x30444,x30442)+~E(x30441,x30442)+~P9(x30443,x30444,x30441)
% 168.60/168.41
% 168.60/168.41 %-------------------------------------------
% 168.60/168.46 cnf(10413,plain,
% 168.60/168.46 (~E(f315(a101,x104131),x104131)),
% 168.60/168.46 inference(rename_variables,[],[4583])).
% 168.60/168.46 cnf(10423,plain,
% 168.60/168.46 (~E(f315(a101,x104231),x104231)),
% 168.60/168.46 inference(rename_variables,[],[4583])).
% 168.60/168.46 cnf(10436,plain,
% 168.60/168.46 (~E(f315(a101,x104361),x104361)),
% 168.60/168.46 inference(rename_variables,[],[4583])).
% 168.60/168.46 cnf(10441,plain,
% 168.60/168.46 (~P1(f315(f315(f161(x104411),f102(x104411)),x104412))),
% 168.60/168.46 inference(rename_variables,[],[4624])).
% 168.60/168.46 cnf(10444,plain,
% 168.60/168.46 (~P1(f315(f315(f161(x104441),f102(x104441)),x104442))),
% 168.60/168.46 inference(rename_variables,[],[4624])).
% 168.60/168.46 cnf(10447,plain,
% 168.60/168.46 (~E(f315(a101,x104471),x104471)),
% 168.60/168.46 inference(rename_variables,[],[4583])).
% 168.60/168.46 cnf(10450,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),x104501),f2(a901)))),
% 168.60/168.46 inference(rename_variables,[],[4621])).
% 168.60/168.46 cnf(10453,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),x104531),f2(a901)))),
% 168.60/168.46 inference(rename_variables,[],[4621])).
% 168.60/168.46 cnf(10470,plain,
% 168.60/168.46 (~P1(f315(f315(f223(a901),f315(a101,x104701)),x104701))),
% 168.60/168.46 inference(rename_variables,[],[4625])).
% 168.60/168.46 cnf(10473,plain,
% 168.60/168.46 (~E(f315(f315(f140(x104731),x104732),x104733),x104733)),
% 168.60/168.46 inference(rename_variables,[],[4597])).
% 168.60/168.46 cnf(10479,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),x104791),f2(a901)))),
% 168.60/168.46 inference(rename_variables,[],[4621])).
% 168.60/168.46 cnf(10482,plain,
% 168.60/168.46 (E(f315(f272(x104821,x104821),f251(x104821,x104822)),x104822)),
% 168.60/168.46 inference(rename_variables,[],[3401])).
% 168.60/168.46 cnf(10485,plain,
% 168.60/168.46 (E(f315(f272(x104851,x104851),f251(x104851,x104852)),x104852)),
% 168.60/168.46 inference(rename_variables,[],[3401])).
% 168.60/168.46 cnf(10490,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),x104901),x104901))),
% 168.60/168.46 inference(rename_variables,[],[4617])).
% 168.60/168.46 cnf(10495,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),f315(f315(f73(a901),x104951),x104952)),x104952))),
% 168.60/168.46 inference(rename_variables,[],[4639])).
% 168.60/168.46 cnf(10498,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),f315(f315(f73(a901),x104981),x104982)),x104982))),
% 168.60/168.46 inference(rename_variables,[],[4639])).
% 168.60/168.46 cnf(10519,plain,
% 168.60/168.46 (~E(f315(a101,x105191),x105191)),
% 168.60/168.46 inference(rename_variables,[],[4583])).
% 168.60/168.46 cnf(10522,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),x105221),x105221))),
% 168.60/168.46 inference(rename_variables,[],[4617])).
% 168.60/168.46 cnf(10525,plain,
% 168.60/168.46 (P1(f315(f315(f223(a901),f38(a901,x105251,x105252)),x105251))),
% 168.60/168.46 inference(rename_variables,[],[3891])).
% 168.60/168.46 cnf(10546,plain,
% 168.60/168.46 (E(f315(f28(a901),f315(f270(a901),x105461)),x105461)),
% 168.60/168.46 inference(rename_variables,[],[3335])).
% 168.60/168.46 cnf(10554,plain,
% 168.60/168.46 (~E(f315(a101,x105541),x105541)),
% 168.60/168.46 inference(rename_variables,[],[4583])).
% 168.60/168.46 cnf(10557,plain,
% 168.60/168.46 (~E(f315(a101,x105571),x105571)),
% 168.60/168.46 inference(rename_variables,[],[4583])).
% 168.60/168.46 cnf(10560,plain,
% 168.60/168.46 (~E(f315(a101,x105601),x105601)),
% 168.60/168.46 inference(rename_variables,[],[4583])).
% 168.60/168.46 cnf(10562,plain,
% 168.60/168.46 (P1(f315(a182,a86))),
% 168.60/168.46 inference(scs_inference,[],[4583,10413,10423,10436,10447,10519,10554,10557,3236,3401,10482,3276,3338,3272,3299,3281,3371,4597,3335,4644,3356,3507,3424,4621,10450,10453,4016,3443,4618,4591,4624,10441,4617,10490,10522,3532,3952,3891,4625,10470,4249,4622,4609,3417,4610,4641,4639,10495,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397])).
% 168.60/168.46 cnf(10565,plain,
% 168.60/168.46 (P1(f315(f315(f224(a901),x105651),f315(a101,x105651)))),
% 168.60/168.46 inference(rename_variables,[],[3507])).
% 168.60/168.46 cnf(10574,plain,
% 168.60/168.46 (P1(f315(f315(f223(a901),x105741),x105741))),
% 168.60/168.46 inference(rename_variables,[],[3440])).
% 168.60/168.46 cnf(10581,plain,
% 168.60/168.46 (E(f315(f272(x105811,x105811),f251(x105811,x105812)),x105812)),
% 168.60/168.46 inference(rename_variables,[],[3401])).
% 168.60/168.46 cnf(10584,plain,
% 168.60/168.46 (E(f315(f272(x105841,x105841),f251(x105841,x105842)),x105842)),
% 168.60/168.46 inference(rename_variables,[],[3401])).
% 168.60/168.46 cnf(10601,plain,
% 168.60/168.46 (P1(f315(f315(f223(a1),x106011),x106011))),
% 168.60/168.46 inference(rename_variables,[],[3441])).
% 168.60/168.46 cnf(10606,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),x106061),f2(a901)))),
% 168.60/168.46 inference(rename_variables,[],[4621])).
% 168.60/168.46 cnf(10609,plain,
% 168.60/168.46 (P1(f315(f315(f223(f909(x106091,a899)),x106092),f230(f909(x106091,a899))))),
% 168.60/168.46 inference(rename_variables,[],[3817])).
% 168.60/168.46 cnf(10614,plain,
% 168.60/168.46 (~P1(f315(f315(f161(x106141),f102(x106141)),x106142))),
% 168.60/168.46 inference(rename_variables,[],[4624])).
% 168.60/168.46 cnf(10643,plain,
% 168.60/168.46 (~E(f315(f315(f140(x106431),x106432),x106433),x106433)),
% 168.60/168.46 inference(rename_variables,[],[4597])).
% 168.60/168.46 cnf(10646,plain,
% 168.60/168.46 (~E(f315(a101,x106461),f2(a901))),
% 168.60/168.46 inference(rename_variables,[],[4589])).
% 168.60/168.46 cnf(10657,plain,
% 168.60/168.46 (P1(f315(f315(f223(a1),x106571),x106571))),
% 168.60/168.46 inference(rename_variables,[],[3441])).
% 168.60/168.46 cnf(10662,plain,
% 168.60/168.46 (~E(f315(a101,x106621),x106621)),
% 168.60/168.46 inference(rename_variables,[],[4583])).
% 168.60/168.46 cnf(10665,plain,
% 168.60/168.46 (~P1(f315(f315(f177(f909(x106651,f909(x106652,a899))),x106653),x106654))),
% 168.60/168.46 inference(rename_variables,[],[4642])).
% 168.60/168.46 cnf(10672,plain,
% 168.60/168.46 (P1(f315(f315(f223(a901),x106721),x106721))),
% 168.60/168.46 inference(rename_variables,[],[3440])).
% 168.60/168.46 cnf(10685,plain,
% 168.60/168.46 (P1(f315(f315(f224(a901),x106851),f315(a101,x106851)))),
% 168.60/168.46 inference(rename_variables,[],[3507])).
% 168.60/168.46 cnf(10706,plain,
% 168.60/168.46 (P1(f315(f315(f223(f909(x107061,a899)),x107062),f230(f909(x107061,a899))))),
% 168.60/168.46 inference(rename_variables,[],[3817])).
% 168.60/168.46 cnf(10709,plain,
% 168.60/168.46 (~P1(f315(f315(f161(x107091),f102(x107091)),x107092))),
% 168.60/168.46 inference(rename_variables,[],[4624])).
% 168.60/168.46 cnf(10728,plain,
% 168.60/168.46 (~P1(f315(f315(f161(x107281),f102(x107281)),x107282))),
% 168.60/168.46 inference(rename_variables,[],[4624])).
% 168.60/168.46 cnf(10735,plain,
% 168.60/168.46 (~P1(f315(f315(f161(x107351),f102(x107351)),x107352))),
% 168.60/168.46 inference(rename_variables,[],[4624])).
% 168.60/168.46 cnf(10743,plain,
% 168.60/168.46 (E(f315(f315(f232(a901),f315(f92(a901),a86)),x107431),f315(f315(f232(a901),f2(a901)),x107431))),
% 168.60/168.46 inference(scs_inference,[],[3783,4583,10413,10423,10436,10447,10519,10554,10557,10560,4589,3236,3401,10482,10485,10581,3276,3338,3272,3299,3281,3905,3371,4597,10473,3335,4208,4644,3356,3799,3507,10565,10685,3424,4621,10450,10453,10479,10606,4632,3873,4016,3467,3469,3443,4618,4591,4624,10441,10444,10614,10709,10728,4158,3817,10609,3440,10574,10672,3441,10601,4617,10490,10522,3532,3952,3891,10525,4625,10470,4249,4622,4609,3417,3421,4611,4610,4641,4642,3914,4639,10495,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928])).
% 168.60/168.46 cnf(10746,plain,
% 168.60/168.46 (~E(f315(a101,x107461),f2(a901))),
% 168.60/168.46 inference(rename_variables,[],[4589])).
% 168.60/168.46 cnf(10751,plain,
% 168.60/168.46 (P1(f315(f315(f317(x107511),x107512),f230(f909(x107511,a899))))),
% 168.60/168.46 inference(rename_variables,[],[3590])).
% 168.60/168.46 cnf(10755,plain,
% 168.60/168.46 (P1(f315(f315(f224(a901),f2(a901)),f315(a93,f71(a1))))),
% 168.60/168.46 inference(scs_inference,[],[3783,4583,10413,10423,10436,10447,10519,10554,10557,10560,4589,10646,3236,3401,10482,10485,10581,3276,3338,3272,3299,3281,3905,3371,4597,10473,3335,4208,4644,3356,3799,3507,10565,10685,3424,4621,10450,10453,10479,10606,4632,3873,4016,3467,3469,3443,4618,4591,4624,10441,10444,10614,10709,10728,4158,3817,10609,3440,10574,10672,3441,10601,4617,10490,10522,3590,3532,3952,3891,10525,4625,10470,4249,4622,4609,3417,3421,4611,4610,4641,4642,3914,4639,10495,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928,5930,5935,5943,5981,5996])).
% 168.60/168.46 cnf(10758,plain,
% 168.60/168.46 (~P1(f315(f315(f161(x107581),f102(x107581)),x107582))),
% 168.60/168.46 inference(rename_variables,[],[4624])).
% 168.60/168.46 cnf(10763,plain,
% 168.60/168.46 (P1(f315(f315(f224(a901),x107631),f315(a101,x107631)))),
% 168.60/168.46 inference(rename_variables,[],[3507])).
% 168.60/168.46 cnf(10766,plain,
% 168.60/168.46 (~P1(f315(f315(f161(x107661),f102(x107661)),x107662))),
% 168.60/168.46 inference(rename_variables,[],[4624])).
% 168.60/168.46 cnf(10769,plain,
% 168.60/168.46 (~P1(f315(f315(f161(x107691),f102(x107691)),x107692))),
% 168.60/168.46 inference(rename_variables,[],[4624])).
% 168.60/168.46 cnf(10772,plain,
% 168.60/168.46 (~P1(f315(f55(x107721,x107722,f177(f909(x107721,a899))),x107723))),
% 168.60/168.46 inference(rename_variables,[],[4638])).
% 168.60/168.46 cnf(10775,plain,
% 168.60/168.46 (~P1(f315(f55(x107751,x107752,f177(f909(x107751,a899))),x107753))),
% 168.60/168.46 inference(rename_variables,[],[4638])).
% 168.60/168.46 cnf(10778,plain,
% 168.60/168.46 (~P1(f315(f315(f177(f909(x107781,f909(x107782,a899))),x107783),x107784))),
% 168.60/168.46 inference(rename_variables,[],[4642])).
% 168.60/168.46 cnf(10781,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),x107811),f2(a901)))),
% 168.60/168.46 inference(rename_variables,[],[4621])).
% 168.60/168.46 cnf(10786,plain,
% 168.60/168.46 (~P1(f315(f315(f161(x107861),f102(x107861)),x107862))),
% 168.60/168.46 inference(rename_variables,[],[4624])).
% 168.60/168.46 cnf(10796,plain,
% 168.60/168.46 (~E(f315(f157(x107961),f315(a101,f315(f315(f123(x107961),f315(f157(x107961),x107962)),f315(f315(f140(x107961),x107963),f102(x107961))))),f315(f315(f140(x107961),x107963),x107962))),
% 168.60/168.46 inference(scs_inference,[],[3783,4583,10413,10423,10436,10447,10519,10554,10557,10560,10662,4589,10646,3236,3401,10482,10485,10581,3276,3338,3272,3299,3281,3905,3371,4597,10473,3335,4208,4644,3356,3799,3507,10565,10685,10763,3424,4621,10450,10453,10479,10606,4632,3873,4016,3467,3469,3443,4618,4591,4624,10441,10444,10614,10709,10728,10735,10758,10766,10769,4158,3817,10609,3440,10574,10672,3441,10601,4617,10490,10522,3590,3532,3952,3891,10525,4625,10470,4249,4622,4609,3417,3421,4611,4610,4638,10772,4641,4642,10665,3914,4639,10495,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928,5930,5935,5943,5981,5996,6005,6008,6017,6021,6022,6023,6024,6025,6030,6035,6045,6051,6069,6073,6082,6112])).
% 168.60/168.46 cnf(10797,plain,
% 168.60/168.46 (~E(f315(a101,x107971),x107971)),
% 168.60/168.46 inference(rename_variables,[],[4583])).
% 168.60/168.46 cnf(10822,plain,
% 168.60/168.46 (P1(f315(f315(f223(a901),x108221),x108221))),
% 168.60/168.46 inference(rename_variables,[],[3440])).
% 168.60/168.46 cnf(10825,plain,
% 168.60/168.46 (P1(f315(f315(f223(a901),x108251),f315(f315(f74(a901),x108251),x108251)))),
% 168.60/168.46 inference(rename_variables,[],[3697])).
% 168.60/168.46 cnf(10828,plain,
% 168.60/168.46 (P1(f315(f315(f223(a901),x108281),f315(f315(f74(a901),x108281),x108281)))),
% 168.60/168.46 inference(rename_variables,[],[3697])).
% 168.60/168.46 cnf(10831,plain,
% 168.60/168.46 (P1(f315(f315(f224(a901),x108311),f315(a101,f315(f315(f73(a901),x108312),x108311))))),
% 168.60/168.46 inference(rename_variables,[],[3884])).
% 168.60/168.46 cnf(10836,plain,
% 168.60/168.46 (P1(f315(f315(f224(a901),x108361),f315(a101,x108361)))),
% 168.60/168.46 inference(rename_variables,[],[3507])).
% 168.60/168.46 cnf(10839,plain,
% 168.60/168.46 (P1(f315(f315(f224(a901),x108391),f315(a101,x108391)))),
% 168.60/168.46 inference(rename_variables,[],[3507])).
% 168.60/168.46 cnf(10842,plain,
% 168.60/168.46 (P1(f315(f315(f317(x108421),x108422),f230(f909(x108421,a899))))),
% 168.60/168.46 inference(rename_variables,[],[3590])).
% 168.60/168.46 cnf(10861,plain,
% 168.60/168.46 (~P1(f315(f315(f223(a901),f315(a101,x108611)),x108611))),
% 168.60/168.46 inference(rename_variables,[],[4625])).
% 168.60/168.46 cnf(10864,plain,
% 168.60/168.46 (~P1(f315(f315(f223(a901),f315(a101,x108641)),x108641))),
% 168.60/168.46 inference(rename_variables,[],[4625])).
% 168.60/168.46 cnf(10867,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),f315(f315(f73(a901),x108671),x108672)),x108672))),
% 168.60/168.46 inference(rename_variables,[],[4639])).
% 168.60/168.46 cnf(10870,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),f315(f315(f73(a901),x108701),x108702)),x108702))),
% 168.60/168.46 inference(rename_variables,[],[4639])).
% 168.60/168.46 cnf(10873,plain,
% 168.60/168.46 (P1(f315(f230(f909(x108731,a899)),x108732))),
% 168.60/168.46 inference(rename_variables,[],[3500])).
% 168.60/168.46 cnf(10876,plain,
% 168.60/168.46 (E(f315(f28(a901),f315(f270(a901),x108761)),x108761)),
% 168.60/168.46 inference(rename_variables,[],[3335])).
% 168.60/168.46 cnf(10879,plain,
% 168.60/168.46 (P1(f315(f315(f224(a901),x108791),f315(a101,x108791)))),
% 168.60/168.46 inference(rename_variables,[],[3507])).
% 168.60/168.46 cnf(10886,plain,
% 168.60/168.46 (P1(f315(f315(f223(a901),x108861),x108861))),
% 168.60/168.46 inference(rename_variables,[],[3440])).
% 168.60/168.46 cnf(10891,plain,
% 168.60/168.46 (P1(f315(f315(f223(a1),x108911),x108911))),
% 168.60/168.46 inference(rename_variables,[],[3441])).
% 168.60/168.46 cnf(10900,plain,
% 168.60/168.46 (E(f315(f272(x109001,x109001),f251(x109001,x109002)),x109002)),
% 168.60/168.46 inference(rename_variables,[],[3401])).
% 168.60/168.46 cnf(10903,plain,
% 168.60/168.46 (P1(f315(f230(f909(x109031,a899)),x109032))),
% 168.60/168.46 inference(rename_variables,[],[3500])).
% 168.60/168.46 cnf(10906,plain,
% 168.60/168.46 (P1(f315(f315(f223(a901),f2(a901)),x109061))),
% 168.60/168.46 inference(rename_variables,[],[3461])).
% 168.60/168.46 cnf(10909,plain,
% 168.60/168.46 (P1(f315(f315(f223(f909(x109091,a899)),f177(f909(x109091,a899))),x109092))),
% 168.60/168.46 inference(rename_variables,[],[3883])).
% 168.60/168.46 cnf(10912,plain,
% 168.60/168.46 (P1(f315(f230(f909(x109121,a899)),x109122))),
% 168.60/168.46 inference(rename_variables,[],[3500])).
% 168.60/168.46 cnf(10915,plain,
% 168.60/168.46 (P1(f315(f230(f909(x109151,a899)),x109152))),
% 168.60/168.46 inference(rename_variables,[],[3500])).
% 168.60/168.46 cnf(10918,plain,
% 168.60/168.46 (P1(f315(f230(f909(x109181,a899)),x109182))),
% 168.60/168.46 inference(rename_variables,[],[3500])).
% 168.60/168.46 cnf(10920,plain,
% 168.60/168.46 (~P1(f315(f315(f223(a901),f315(f315(f74(a901),f315(a101,x109201)),f315(a101,x109201))),x109201))),
% 168.60/168.46 inference(scs_inference,[],[3783,4583,10413,10423,10436,10447,10519,10554,10557,10560,10662,4589,10646,3236,3401,10482,10485,10581,10584,3276,3338,3272,3299,3281,3905,3371,4597,10473,3335,10546,4208,4644,3356,3799,3734,3507,10565,10685,10763,10836,10839,3886,3424,4621,10450,10453,10479,10606,4632,3873,3643,4016,3467,3469,3443,4618,4591,4624,10441,10444,10614,10709,10728,10735,10758,10766,10769,4158,3817,10609,3440,10574,10672,10822,3441,10601,10657,4617,10490,10522,3590,10751,3500,10873,10903,10912,10915,3532,3952,3891,10525,4625,10470,10861,3461,4249,4622,4609,3417,3421,4611,4610,4638,10772,4643,3883,3697,10825,10828,4641,4642,10665,3914,4639,10495,10498,10867,3884,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928,5930,5935,5943,5981,5996,6005,6008,6017,6021,6022,6023,6024,6025,6030,6035,6045,6051,6069,6073,6082,6112,6128,6154,6171,6172,6175,6190,6192,6194,6196,6211,6212,6215,6217,6220,6221,6238,6246,6247,6248,6250,6252,6290,6291,6296,6299,6305,6309,6343,6345,6347,6349,6359,6361,6364,6370,6372,6377,6380,6388,6396,6398,6399,6406,6429,6430,6431,6432,6433,6435,6442])).
% 168.60/168.46 cnf(10921,plain,
% 168.60/168.46 (P1(f315(f315(f223(a901),x109211),f315(f315(f74(a901),x109211),x109211)))),
% 168.60/168.46 inference(rename_variables,[],[3697])).
% 168.60/168.46 cnf(10930,plain,
% 168.60/168.46 (~P1(f315(f315(f223(a901),f315(a101,f315(a101,f315(f315(f73(a901),x109301),x109302)))),f315(a101,x109302)))),
% 168.60/168.46 inference(scs_inference,[],[3783,4583,10413,10423,10436,10447,10519,10554,10557,10560,10662,4589,10646,3236,3401,10482,10485,10581,10584,3378,3276,3338,3272,3299,3281,3905,3371,4597,10473,3335,10546,4208,4644,3356,3799,3734,3507,10565,10685,10763,10836,10839,10879,3886,3424,4621,10450,10453,10479,10606,4632,3873,3643,4016,3467,3469,3443,4618,4591,4624,10441,10444,10614,10709,10728,10735,10758,10766,10769,4158,3817,10609,3440,10574,10672,10822,3441,10601,10657,4617,10490,10522,3590,10751,3500,10873,10903,10912,10915,3532,3952,3891,10525,4625,10470,10861,3461,4249,4622,4609,3417,3421,4611,4610,4638,10772,4643,3883,3697,10825,10828,4641,4642,10665,3914,4639,10495,10498,10867,3884,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928,5930,5935,5943,5981,5996,6005,6008,6017,6021,6022,6023,6024,6025,6030,6035,6045,6051,6069,6073,6082,6112,6128,6154,6171,6172,6175,6190,6192,6194,6196,6211,6212,6215,6217,6220,6221,6238,6246,6247,6248,6250,6252,6290,6291,6296,6299,6305,6309,6343,6345,6347,6349,6359,6361,6364,6370,6372,6377,6380,6388,6396,6398,6399,6406,6429,6430,6431,6432,6433,6435,6442,6447,6481,6482,6485])).
% 168.60/168.46 cnf(10938,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a88),f315(a5,x109381)),f315(a5,f2(a901))))),
% 168.60/168.46 inference(scs_inference,[],[3783,4583,10413,10423,10436,10447,10519,10554,10557,10560,10662,4589,10646,3236,3401,10482,10485,10581,10584,3378,3276,3338,3272,3299,3281,3905,3371,4597,10473,3335,10546,4208,4644,3356,3799,3734,3507,10565,10685,10763,10836,10839,10879,3886,3424,4621,10450,10453,10479,10606,10781,4632,3873,3643,4016,3467,3469,3443,4618,4591,4624,10441,10444,10614,10709,10728,10735,10758,10766,10769,4158,3817,10609,3440,10574,10672,10822,3441,10601,10657,4617,10490,10522,3590,10751,3500,10873,10903,10912,10915,3532,3952,3891,10525,4625,10470,10861,10864,3461,4249,4622,4609,3417,3421,4611,4610,4638,10772,4643,3883,3697,10825,10828,4641,4642,10665,3914,4639,10495,10498,10867,3884,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928,5930,5935,5943,5981,5996,6005,6008,6017,6021,6022,6023,6024,6025,6030,6035,6045,6051,6069,6073,6082,6112,6128,6154,6171,6172,6175,6190,6192,6194,6196,6211,6212,6215,6217,6220,6221,6238,6246,6247,6248,6250,6252,6290,6291,6296,6299,6305,6309,6343,6345,6347,6349,6359,6361,6364,6370,6372,6377,6380,6388,6396,6398,6399,6406,6429,6430,6431,6432,6433,6435,6442,6447,6481,6482,6485,6486,6487,6489,6490])).
% 168.60/168.46 cnf(10961,plain,
% 168.60/168.46 (P1(f315(f315(f223(a901),x109611),x109611))),
% 168.60/168.46 inference(rename_variables,[],[3440])).
% 168.60/168.46 cnf(10972,plain,
% 168.60/168.46 (~P1(f315(f315(f161(x109721),f102(x109721)),x109722))),
% 168.60/168.46 inference(rename_variables,[],[4624])).
% 168.60/168.46 cnf(10979,plain,
% 168.60/168.46 (P1(f315(f315(f224(a901),x109791),f315(a101,x109791)))),
% 168.60/168.46 inference(rename_variables,[],[3507])).
% 168.60/168.46 cnf(10981,plain,
% 168.60/168.46 (P1(f315(f315(f224(a1),f315(f315(f3(a1),x109811),f71(a1))),x109811))),
% 168.60/168.46 inference(scs_inference,[],[3783,4583,10413,10423,10436,10447,10519,10554,10557,10560,10662,4589,10646,3236,3401,10482,10485,10581,10584,3378,3276,3338,3272,3299,3281,3905,3371,4597,10473,3335,10546,4208,4644,3356,3799,3734,3507,10565,10685,10763,10836,10839,10879,3886,3424,4621,10450,10453,10479,10606,10781,4632,3873,3643,4016,3467,3469,3443,4618,4591,4624,10441,10444,10614,10709,10728,10735,10758,10766,10769,10786,4158,3817,10609,3440,10574,10672,10822,10886,10961,3441,10601,10657,10891,4617,10490,10522,3590,10751,4628,3500,10873,10903,10912,10915,3532,3952,3891,10525,4625,10470,10861,10864,3461,4249,4622,4609,4612,3417,3421,4611,4610,4638,10772,4643,3883,3697,10825,10828,4641,4642,10665,3914,4639,10495,10498,10867,3884,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928,5930,5935,5943,5981,5996,6005,6008,6017,6021,6022,6023,6024,6025,6030,6035,6045,6051,6069,6073,6082,6112,6128,6154,6171,6172,6175,6190,6192,6194,6196,6211,6212,6215,6217,6220,6221,6238,6246,6247,6248,6250,6252,6290,6291,6296,6299,6305,6309,6343,6345,6347,6349,6359,6361,6364,6370,6372,6377,6380,6388,6396,6398,6399,6406,6429,6430,6431,6432,6433,6435,6442,6447,6481,6482,6485,6486,6487,6489,6490,6491,6492,6499,6535,6536,6545,6567,6568,6592,6594,6606,6607,6613,6643,6645,6660,6700,6703,6704,6760])).
% 168.60/168.46 cnf(10982,plain,
% 168.60/168.46 (P1(f315(f315(f223(a1),x109821),x109821))),
% 168.60/168.46 inference(rename_variables,[],[3441])).
% 168.60/168.46 cnf(10987,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),x109871),f2(a901)))),
% 168.60/168.46 inference(rename_variables,[],[4621])).
% 168.60/168.46 cnf(11002,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),x110021),f2(a901)))),
% 168.60/168.46 inference(rename_variables,[],[4621])).
% 168.60/168.46 cnf(11005,plain,
% 168.60/168.46 (~P1(f315(f315(f224(f909(x110051,a899)),x110052),f177(f909(x110051,a899))))),
% 168.60/168.46 inference(rename_variables,[],[4636])).
% 168.60/168.46 cnf(11008,plain,
% 168.60/168.46 (P1(f315(f315(f223(a901),x110081),x110081))),
% 168.60/168.46 inference(rename_variables,[],[3440])).
% 168.60/168.46 cnf(11011,plain,
% 168.60/168.46 (P1(f315(f315(f223(a901),x110111),x110111))),
% 168.60/168.46 inference(rename_variables,[],[3440])).
% 168.60/168.46 cnf(11026,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),x110261),x110261))),
% 168.60/168.46 inference(rename_variables,[],[4617])).
% 168.60/168.46 cnf(11035,plain,
% 168.60/168.46 (~P1(f315(f315(f317(x110351),x110352),f177(f909(x110351,a899))))),
% 168.60/168.46 inference(rename_variables,[],[4628])).
% 168.60/168.46 cnf(11042,plain,
% 168.60/168.46 (P1(f315(f315(f223(a901),x110421),x110421))),
% 168.60/168.46 inference(rename_variables,[],[3440])).
% 168.60/168.46 cnf(11045,plain,
% 168.60/168.46 (~P1(f315(f315(f317(x110451),x110452),f177(f909(x110451,a899))))),
% 168.60/168.46 inference(rename_variables,[],[4628])).
% 168.60/168.46 cnf(11048,plain,
% 168.60/168.46 (P1(f315(f315(f223(f909(x110481,a899)),f315(f298(x110482,x110481,x110483),f315(f299(x110482,x110481,x110483),x110484))),x110484))),
% 168.60/168.46 inference(rename_variables,[],[4304])).
% 168.60/168.46 cnf(11057,plain,
% 168.60/168.46 (P1(f315(f315(f223(f909(x110571,a899)),f315(f161(x110571),f315(f125(x110571,x110572),x110573))),f315(f161(x110571),x110573)))),
% 168.60/168.46 inference(rename_variables,[],[4077])).
% 168.60/168.46 cnf(11060,plain,
% 168.60/168.46 (E(f315(f298(x110601,x110601,f7(x110601)),x110602),x110602)),
% 168.60/168.46 inference(rename_variables,[],[3496])).
% 168.60/168.46 cnf(11065,plain,
% 168.60/168.46 (P1(f315(f315(f223(a901),f2(a901)),x110651))),
% 168.60/168.46 inference(rename_variables,[],[3461])).
% 168.60/168.46 cnf(11068,plain,
% 168.60/168.46 (P1(f315(f315(f223(a901),x110681),x110681))),
% 168.60/168.46 inference(rename_variables,[],[3440])).
% 168.60/168.46 cnf(11071,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),x110711),x110711))),
% 168.60/168.46 inference(rename_variables,[],[4617])).
% 168.60/168.46 cnf(11080,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),x110801),x110801))),
% 168.60/168.46 inference(rename_variables,[],[4617])).
% 168.60/168.46 cnf(11091,plain,
% 168.60/168.46 (P1(f315(f315(f223(a901),x110911),f315(f315(f74(a901),x110911),x110911)))),
% 168.60/168.46 inference(rename_variables,[],[3697])).
% 168.60/168.46 cnf(11097,plain,
% 168.60/168.46 (P1(f315(f315(f224(a901),x110971),f315(a101,f315(f315(f73(a901),x110972),x110971))))),
% 168.60/168.46 inference(rename_variables,[],[3884])).
% 168.60/168.46 cnf(11104,plain,
% 168.60/168.46 (P1(f315(f315(f223(a901),x111041),x111041))),
% 168.60/168.46 inference(rename_variables,[],[3440])).
% 168.60/168.46 cnf(11107,plain,
% 168.60/168.46 (P1(f315(f315(f223(a1),x111071),x111071))),
% 168.60/168.46 inference(rename_variables,[],[3441])).
% 168.60/168.46 cnf(11110,plain,
% 168.60/168.46 (~E(f315(a101,x111101),x111101)),
% 168.60/168.46 inference(rename_variables,[],[4583])).
% 168.60/168.46 cnf(11115,plain,
% 168.60/168.46 (P1(f315(f315(f317(x111151),x111152),f230(f909(x111151,a899))))),
% 168.60/168.46 inference(rename_variables,[],[3590])).
% 168.60/168.46 cnf(11120,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),x111201),f2(a901)))),
% 168.60/168.46 inference(rename_variables,[],[4621])).
% 168.60/168.46 cnf(11135,plain,
% 168.60/168.46 (P1(f315(f315(f223(a901),f2(a901)),x111351))),
% 168.60/168.46 inference(rename_variables,[],[3461])).
% 168.60/168.46 cnf(11142,plain,
% 168.60/168.46 (P1(f315(f315(f223(a901),x111421),x111421))),
% 168.60/168.46 inference(rename_variables,[],[3440])).
% 168.60/168.46 cnf(11151,plain,
% 168.60/168.46 (~P1(f315(f315(f317(x111511),x111512),f177(f909(x111511,a899))))),
% 168.60/168.46 inference(rename_variables,[],[4628])).
% 168.60/168.46 cnf(11153,plain,
% 168.60/168.46 (P1(f315(f315(f223(f909(x111531,a899)),f31(f909(x111531,a899),f315(f296(x111531),x111532))),x111532))),
% 168.60/168.46 inference(scs_inference,[],[3783,4583,10413,10423,10436,10447,10519,10554,10557,10560,10662,10797,4589,10646,3236,3401,10482,10485,10581,10584,3378,3276,3338,3272,3299,3281,3905,3496,3371,4597,10473,3335,10546,4208,4068,4644,3356,3634,3799,3734,3948,3507,10565,10685,10763,10836,10839,10879,10979,3886,3424,4621,10450,10453,10479,10606,10781,10987,11002,4632,3873,3643,4016,3467,3469,3443,4618,4591,4624,10441,10444,10614,10709,10728,10735,10758,10766,10769,10786,4170,4077,11057,3800,4158,3817,10609,4636,3440,10574,10672,10822,10886,10961,11008,11011,11042,11068,11104,3441,10601,10657,10891,10982,3442,4617,10490,10522,11026,11071,3590,10751,10842,11115,4628,11035,11045,3500,10873,10903,10912,10915,3532,3952,3891,10525,4625,10470,10861,10864,3461,10906,11065,4249,4622,3960,4609,4612,3417,3421,4611,4610,4638,10772,4643,3883,3697,10825,10828,10921,11091,4641,4642,10665,4304,3914,4639,10495,10498,10867,3884,10831,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928,5930,5935,5943,5981,5996,6005,6008,6017,6021,6022,6023,6024,6025,6030,6035,6045,6051,6069,6073,6082,6112,6128,6154,6171,6172,6175,6190,6192,6194,6196,6211,6212,6215,6217,6220,6221,6238,6246,6247,6248,6250,6252,6290,6291,6296,6299,6305,6309,6343,6345,6347,6349,6359,6361,6364,6370,6372,6377,6380,6388,6396,6398,6399,6406,6429,6430,6431,6432,6433,6435,6442,6447,6481,6482,6485,6486,6487,6489,6490,6491,6492,6499,6535,6536,6545,6567,6568,6592,6594,6606,6607,6613,6643,6645,6660,6700,6703,6704,6760,6783,6826,6841,6849,6858,6859,6860,6861,6882,6883,6890,6902,6905,6907,6909,6910,6911,6913,6927,6938,6939,6940,6953,7008,7019,7021,7026,7045,7046,7082,7089,7096,7126,7157,7213,7242,7299,7320,7329,7332,7392,7402,7465,7467,7481,7490,7491,7492,7509,7513,7515,7562,7572,7575,7590,7638,7640,7643,7687,7688,7706,7776,7794,7818,7842,7854,7868,7879,7890,7891,7917,7919])).
% 168.60/168.46 cnf(11159,plain,
% 168.60/168.46 (P1(f315(f315(f317(x111591),x111592),f230(f909(x111591,a899))))),
% 168.60/168.46 inference(rename_variables,[],[3590])).
% 168.60/168.46 cnf(11162,plain,
% 168.60/168.46 (~P1(f315(f315(f317(f908(f902(x111621),f902(x111621))),f315(f315(f240(f902(x111621),f902(x111621)),x111622),f102(x111621))),f134(x111621,x111623)))),
% 168.60/168.46 inference(rename_variables,[],[4644])).
% 168.60/168.46 cnf(11171,plain,
% 168.60/168.46 (~P1(f315(f315(f317(f908(x111711,x111711)),x111712),f251(x111711,f177(f909(x111711,a899)))))),
% 168.60/168.46 inference(scs_inference,[],[3783,4583,10413,10423,10436,10447,10519,10554,10557,10560,10662,10797,4589,10646,3236,3401,10482,10485,10581,10584,3378,3276,3338,3272,3299,3281,3905,3496,3371,4597,10473,3335,10546,4208,4068,4644,3356,3634,3799,3734,3948,3507,10565,10685,10763,10836,10839,10879,10979,3886,3424,4621,10450,10453,10479,10606,10781,10987,11002,4632,3873,3643,4016,3467,3469,3443,4618,4591,4624,10441,10444,10614,10709,10728,10735,10758,10766,10769,10786,4170,4077,11057,3800,4158,3817,10609,4636,3440,10574,10672,10822,10886,10961,11008,11011,11042,11068,11104,3441,10601,10657,10891,10982,3442,4617,10490,10522,11026,11071,3590,10751,10842,11115,4628,11035,11045,11151,3500,10873,10903,10912,10915,3532,3952,3891,10525,4625,10470,10861,10864,3461,10906,11065,4249,4622,3960,4609,4612,3417,3421,4611,4610,4638,10772,4643,3883,3591,3697,10825,10828,10921,11091,4641,4642,10665,4304,3914,4639,10495,10498,10867,3884,10831,4144,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928,5930,5935,5943,5981,5996,6005,6008,6017,6021,6022,6023,6024,6025,6030,6035,6045,6051,6069,6073,6082,6112,6128,6154,6171,6172,6175,6190,6192,6194,6196,6211,6212,6215,6217,6220,6221,6238,6246,6247,6248,6250,6252,6290,6291,6296,6299,6305,6309,6343,6345,6347,6349,6359,6361,6364,6370,6372,6377,6380,6388,6396,6398,6399,6406,6429,6430,6431,6432,6433,6435,6442,6447,6481,6482,6485,6486,6487,6489,6490,6491,6492,6499,6535,6536,6545,6567,6568,6592,6594,6606,6607,6613,6643,6645,6660,6700,6703,6704,6760,6783,6826,6841,6849,6858,6859,6860,6861,6882,6883,6890,6902,6905,6907,6909,6910,6911,6913,6927,6938,6939,6940,6953,7008,7019,7021,7026,7045,7046,7082,7089,7096,7126,7157,7213,7242,7299,7320,7329,7332,7392,7402,7465,7467,7481,7490,7491,7492,7509,7513,7515,7562,7572,7575,7590,7638,7640,7643,7687,7688,7706,7776,7794,7818,7842,7854,7868,7879,7890,7891,7917,7919,7921,7931,7969,7980,8005,8032,8065])).
% 168.60/168.46 cnf(11172,plain,
% 168.60/168.46 (~P1(f315(f315(f317(x111721),x111722),f177(f909(x111721,a899))))),
% 168.60/168.46 inference(rename_variables,[],[4628])).
% 168.60/168.46 cnf(11175,plain,
% 168.60/168.46 (~P1(f315(f315(f317(x111751),x111752),f177(f909(x111751,a899))))),
% 168.60/168.46 inference(rename_variables,[],[4628])).
% 168.60/168.46 cnf(11178,plain,
% 168.60/168.46 (P1(f315(f315(f223(f909(x111781,a899)),x111782),f315(f315(f297(x111781),x111783),x111782)))),
% 168.60/168.46 inference(rename_variables,[],[3881])).
% 168.60/168.46 cnf(11181,plain,
% 168.60/168.46 (P1(f315(f315(f223(a901),x111811),x111811))),
% 168.60/168.46 inference(rename_variables,[],[3440])).
% 168.60/168.46 cnf(11184,plain,
% 168.60/168.46 (P1(f315(f315(f223(f909(x111841,a899)),x111842),f315(f315(f297(x111841),x111843),x111842)))),
% 168.60/168.46 inference(rename_variables,[],[3881])).
% 168.60/168.46 cnf(11187,plain,
% 168.60/168.46 (E(f315(f298(x111871,x111871,f7(x111871)),x111872),x111872)),
% 168.60/168.46 inference(rename_variables,[],[3496])).
% 168.60/168.46 cnf(11189,plain,
% 168.60/168.46 (P36(x111891,x111892,x111893,f103(x111891,f102(x111891)),f102(x111892))),
% 168.60/168.46 inference(scs_inference,[],[3783,4583,10413,10423,10436,10447,10519,10554,10557,10560,10662,10797,4589,10646,3236,3286,3401,10482,10485,10581,10584,3378,3276,3338,3272,3299,3281,3905,3496,11060,3371,4597,10473,3335,10546,4208,4068,4644,3356,3634,3799,3734,3948,3507,10565,10685,10763,10836,10839,10879,10979,3886,3424,4621,10450,10453,10479,10606,10781,10987,11002,4632,3873,3643,4016,3467,3469,3443,4618,4591,4624,10441,10444,10614,10709,10728,10735,10758,10766,10769,10786,4170,4077,11057,3800,4158,3817,10609,4636,3440,10574,10672,10822,10886,10961,11008,11011,11042,11068,11104,11142,3441,10601,10657,10891,10982,3442,4617,10490,10522,11026,11071,3590,10751,10842,11115,4628,11035,11045,11151,11172,3500,10873,10903,10912,10915,3532,3952,3891,10525,4625,10470,10861,10864,3461,10906,11065,4249,4622,3960,4609,4612,3417,3421,4611,4610,4638,10772,4643,3881,11178,3883,3591,3697,10825,10828,10921,11091,4641,4642,10665,4304,3914,4639,10495,10498,10867,3884,10831,4144,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928,5930,5935,5943,5981,5996,6005,6008,6017,6021,6022,6023,6024,6025,6030,6035,6045,6051,6069,6073,6082,6112,6128,6154,6171,6172,6175,6190,6192,6194,6196,6211,6212,6215,6217,6220,6221,6238,6246,6247,6248,6250,6252,6290,6291,6296,6299,6305,6309,6343,6345,6347,6349,6359,6361,6364,6370,6372,6377,6380,6388,6396,6398,6399,6406,6429,6430,6431,6432,6433,6435,6442,6447,6481,6482,6485,6486,6487,6489,6490,6491,6492,6499,6535,6536,6545,6567,6568,6592,6594,6606,6607,6613,6643,6645,6660,6700,6703,6704,6760,6783,6826,6841,6849,6858,6859,6860,6861,6882,6883,6890,6902,6905,6907,6909,6910,6911,6913,6927,6938,6939,6940,6953,7008,7019,7021,7026,7045,7046,7082,7089,7096,7126,7157,7213,7242,7299,7320,7329,7332,7392,7402,7465,7467,7481,7490,7491,7492,7509,7513,7515,7562,7572,7575,7590,7638,7640,7643,7687,7688,7706,7776,7794,7818,7842,7854,7868,7879,7890,7891,7917,7919,7921,7931,7969,7980,8005,8032,8065,8096,8130,8169,8186,8188,8204])).
% 168.60/168.46 cnf(11202,plain,
% 168.60/168.46 (P1(f315(f315(f223(f909(x112021,a899)),x112022),f315(f315(f297(x112021),x112023),x112022)))),
% 168.60/168.46 inference(rename_variables,[],[3881])).
% 168.60/168.46 cnf(11213,plain,
% 168.60/168.46 (~E(f315(a101,x112131),f2(a901))),
% 168.60/168.46 inference(rename_variables,[],[4589])).
% 168.60/168.46 cnf(11216,plain,
% 168.60/168.46 (~P1(f315(f315(f161(x112161),f102(x112161)),x112162))),
% 168.60/168.46 inference(rename_variables,[],[4624])).
% 168.60/168.46 cnf(11229,plain,
% 168.60/168.46 (P1(f315(f315(f224(a901),x112291),f315(a101,x112291)))),
% 168.60/168.46 inference(rename_variables,[],[3507])).
% 168.60/168.46 cnf(11239,plain,
% 168.60/168.46 (~E(f315(f298(x112391,f909(x112391,a899),x112392),x112393),f315(f296(x112391),x112393))),
% 168.60/168.46 inference(rename_variables,[],[4626])).
% 168.60/168.46 cnf(11242,plain,
% 168.60/168.46 (~P1(f315(f315(f317(x112421),x112422),f177(f909(x112421,a899))))),
% 168.60/168.46 inference(rename_variables,[],[4628])).
% 168.60/168.46 cnf(11245,plain,
% 168.60/168.46 (~P1(f315(f315(f317(x112451),x112452),f177(f909(x112451,a899))))),
% 168.60/168.46 inference(rename_variables,[],[4628])).
% 168.60/168.46 cnf(11248,plain,
% 168.60/168.46 (~P1(f315(f315(f317(f908(x112481,x112481)),f315(f315(f240(x112481,x112481),x112482),x112483)),f142(x112481,f102(f909(x112481,a901)))))),
% 168.60/168.46 inference(rename_variables,[],[4643])).
% 168.60/168.46 cnf(11251,plain,
% 168.60/168.46 (~P1(f315(f315(f317(f908(x112511,x112511)),f315(f315(f240(x112511,x112511),x112512),x112513)),f142(x112511,f102(f909(x112511,a901)))))),
% 168.60/168.46 inference(rename_variables,[],[4643])).
% 168.60/168.46 cnf(11256,plain,
% 168.60/168.46 (~P1(f315(f315(f317(x112561),x112562),f177(f909(x112561,a899))))),
% 168.60/168.46 inference(rename_variables,[],[4628])).
% 168.60/168.46 cnf(11259,plain,
% 168.60/168.46 (P1(f315(f315(f317(f908(x112591,x112591)),f315(f315(f240(x112591,x112591),x112592),x112592)),f295(x112591,x112593)))),
% 168.60/168.46 inference(rename_variables,[],[4068])).
% 168.60/168.46 cnf(11262,plain,
% 168.60/168.46 (P1(f315(f315(f223(f909(x112621,a899)),x112622),f230(f909(x112621,a899))))),
% 168.60/168.46 inference(rename_variables,[],[3817])).
% 168.60/168.46 cnf(11265,plain,
% 168.60/168.46 (P1(f315(f315(f223(f909(x112651,a899)),f315(f161(x112651),f165(x112651,x112652,x112653))),f315(f161(x112651),x112652)))),
% 168.60/168.46 inference(rename_variables,[],[4124])).
% 168.60/168.46 cnf(11281,plain,
% 168.60/168.46 (P1(f315(f315(f223(f909(x112811,a899)),f177(f909(x112811,a899))),x112812))),
% 168.60/168.46 inference(rename_variables,[],[3883])).
% 168.60/168.46 cnf(11292,plain,
% 168.60/168.46 (~P1(f315(f315(f317(f908(f902(x112921),f902(x112921))),f315(f315(f240(f902(x112921),f902(x112921)),x112922),f102(x112921))),f136(x112921,x112923)))),
% 168.60/168.46 inference(rename_variables,[],[4645])).
% 168.60/168.46 cnf(11303,plain,
% 168.60/168.46 (~E(f315(a101,x113031),x113031)),
% 168.60/168.46 inference(rename_variables,[],[4583])).
% 168.60/168.46 cnf(11306,plain,
% 168.60/168.46 (~E(f315(a101,x113061),x113061)),
% 168.60/168.46 inference(rename_variables,[],[4583])).
% 168.60/168.46 cnf(11310,plain,
% 168.60/168.46 (P1(f315(f315(f317(f908(f902(x113101),f902(x113101))),f315(f315(f240(f902(x113101),f902(x113101)),f102(x113101)),f102(x113101))),f315(f315(f277(f902(x113101),f902(x113101),f902(x113101)),f147(x113101,x113102)),f295(f902(x113101),f147(x113101,x113102)))))),
% 168.60/168.46 inference(scs_inference,[],[3783,4583,10413,10423,10436,10447,10519,10554,10557,10560,10662,10797,11110,11303,11306,4589,10646,10746,3236,3286,3401,10482,10485,10581,10584,3378,3893,3276,3338,3272,3299,3281,3905,3496,11060,3371,4066,4597,10473,4626,3335,10546,4208,4068,11259,4644,11162,4645,3356,3634,3799,3734,3948,3507,10565,10685,10763,10836,10839,10879,10979,3886,3424,4621,10450,10453,10479,10606,10781,10987,11002,11120,4632,3873,3643,4016,3467,3469,3443,4618,4591,4624,10441,10444,10614,10709,10728,10735,10758,10766,10769,10786,10972,4170,4077,11057,4124,3800,4158,3817,10609,10706,4636,3440,10574,10672,10822,10886,10961,11008,11011,11042,11068,11104,11142,3441,10601,10657,10891,10982,3442,4617,10490,10522,11026,11071,3590,10751,10842,11115,11159,4628,11035,11045,11151,11172,11175,11242,11245,3500,10873,10903,10912,10915,3532,3952,3891,10525,4625,10470,10861,10864,3461,10906,11065,4249,4622,3960,4609,4612,3417,3421,4611,4610,4638,10772,4643,11248,4034,3881,11178,11184,3883,10909,3591,3697,10825,10828,10921,11091,4641,4642,10665,4304,3914,4639,10495,10498,10867,3884,10831,4144,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928,5930,5935,5943,5981,5996,6005,6008,6017,6021,6022,6023,6024,6025,6030,6035,6045,6051,6069,6073,6082,6112,6128,6154,6171,6172,6175,6190,6192,6194,6196,6211,6212,6215,6217,6220,6221,6238,6246,6247,6248,6250,6252,6290,6291,6296,6299,6305,6309,6343,6345,6347,6349,6359,6361,6364,6370,6372,6377,6380,6388,6396,6398,6399,6406,6429,6430,6431,6432,6433,6435,6442,6447,6481,6482,6485,6486,6487,6489,6490,6491,6492,6499,6535,6536,6545,6567,6568,6592,6594,6606,6607,6613,6643,6645,6660,6700,6703,6704,6760,6783,6826,6841,6849,6858,6859,6860,6861,6882,6883,6890,6902,6905,6907,6909,6910,6911,6913,6927,6938,6939,6940,6953,7008,7019,7021,7026,7045,7046,7082,7089,7096,7126,7157,7213,7242,7299,7320,7329,7332,7392,7402,7465,7467,7481,7490,7491,7492,7509,7513,7515,7562,7572,7575,7590,7638,7640,7643,7687,7688,7706,7776,7794,7818,7842,7854,7868,7879,7890,7891,7917,7919,7921,7931,7969,7980,8005,8032,8065,8096,8130,8169,8186,8188,8204,8205,8273,8284,8349,8373,8392,8419,8458,8459,8476,8516,8518,8520,8526,8542,8546,8561,8582,8590,8592,8602,8607,8611,8612,8613,8614,8615,8616,8635,8650,8651,8669,8671,8675,8676,8677,8678,8679,8697,8698,8699,8709,8722,8725,8736,8741,8743,8745,8746,8747,8754])).
% 168.60/168.46 cnf(11313,plain,
% 168.60/168.46 (~E(f315(a101,x113131),f2(a901))),
% 168.60/168.46 inference(rename_variables,[],[4589])).
% 168.60/168.46 cnf(11315,plain,
% 168.60/168.46 (E(f315(x113151,f315(f84(x113152,x113153,f230(f909(x113152,a899)),x113151),f315(x113151,x113154))),f315(x113151,x113154))),
% 168.60/168.46 inference(scs_inference,[],[3783,4583,10413,10423,10436,10447,10519,10554,10557,10560,10662,10797,11110,11303,11306,4589,10646,10746,11213,3236,3286,3401,10482,10485,10581,10584,3378,3893,3276,3338,3272,3299,3281,3905,3496,11060,3371,4066,4597,10473,4626,3335,10546,4208,4068,11259,4644,11162,4645,3356,3634,3799,3734,3948,3507,10565,10685,10763,10836,10839,10879,10979,3886,3424,4621,10450,10453,10479,10606,10781,10987,11002,11120,4632,3873,3643,4016,3467,3469,3443,4618,4591,4624,10441,10444,10614,10709,10728,10735,10758,10766,10769,10786,10972,4170,4077,11057,4124,3800,4158,3817,10609,10706,4636,3440,10574,10672,10822,10886,10961,11008,11011,11042,11068,11104,11142,3441,10601,10657,10891,10982,3442,4617,10490,10522,11026,11071,3590,10751,10842,11115,11159,4628,11035,11045,11151,11172,11175,11242,11245,3500,10873,10903,10912,10915,3532,3952,3891,10525,4625,10470,10861,10864,3461,10906,11065,4249,4622,3960,4609,4612,3417,3421,4611,4610,4638,10772,4643,11248,4034,3881,11178,11184,3883,10909,3591,3697,10825,10828,10921,11091,4641,4642,10665,4304,3914,4639,10495,10498,10867,3884,10831,4144,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928,5930,5935,5943,5981,5996,6005,6008,6017,6021,6022,6023,6024,6025,6030,6035,6045,6051,6069,6073,6082,6112,6128,6154,6171,6172,6175,6190,6192,6194,6196,6211,6212,6215,6217,6220,6221,6238,6246,6247,6248,6250,6252,6290,6291,6296,6299,6305,6309,6343,6345,6347,6349,6359,6361,6364,6370,6372,6377,6380,6388,6396,6398,6399,6406,6429,6430,6431,6432,6433,6435,6442,6447,6481,6482,6485,6486,6487,6489,6490,6491,6492,6499,6535,6536,6545,6567,6568,6592,6594,6606,6607,6613,6643,6645,6660,6700,6703,6704,6760,6783,6826,6841,6849,6858,6859,6860,6861,6882,6883,6890,6902,6905,6907,6909,6910,6911,6913,6927,6938,6939,6940,6953,7008,7019,7021,7026,7045,7046,7082,7089,7096,7126,7157,7213,7242,7299,7320,7329,7332,7392,7402,7465,7467,7481,7490,7491,7492,7509,7513,7515,7562,7572,7575,7590,7638,7640,7643,7687,7688,7706,7776,7794,7818,7842,7854,7868,7879,7890,7891,7917,7919,7921,7931,7969,7980,8005,8032,8065,8096,8130,8169,8186,8188,8204,8205,8273,8284,8349,8373,8392,8419,8458,8459,8476,8516,8518,8520,8526,8542,8546,8561,8582,8590,8592,8602,8607,8611,8612,8613,8614,8615,8616,8635,8650,8651,8669,8671,8675,8676,8677,8678,8679,8697,8698,8699,8709,8722,8725,8736,8741,8743,8745,8746,8747,8754,8760,8768])).
% 168.60/168.46 cnf(11318,plain,
% 168.60/168.46 (P1(f315(f315(f223(f909(x113181,a899)),x113182),x113182))),
% 168.60/168.46 inference(rename_variables,[],[3730])).
% 168.60/168.46 cnf(11325,plain,
% 168.60/168.46 (~E(f315(a101,x113251),x113251)),
% 168.60/168.46 inference(rename_variables,[],[4583])).
% 168.60/168.46 cnf(11328,plain,
% 168.60/168.46 (~E(f315(a101,x113281),x113281)),
% 168.60/168.46 inference(rename_variables,[],[4583])).
% 168.60/168.46 cnf(11330,plain,
% 168.60/168.46 (~P26(x113301,f909(x113301,a899),x113302,x113303,f315(f296(x113301),x113303))),
% 168.60/168.46 inference(scs_inference,[],[3783,4583,10413,10423,10436,10447,10519,10554,10557,10560,10662,10797,11110,11303,11306,11325,4589,10646,10746,11213,3236,3286,3401,10482,10485,10581,10584,3378,3893,3276,3338,3272,3299,3281,3905,3496,11060,3371,4066,4597,10473,4626,11239,3335,10546,4208,4068,11259,4644,11162,4645,3356,3634,3799,3734,3948,3507,10565,10685,10763,10836,10839,10879,10979,3886,3424,4621,10450,10453,10479,10606,10781,10987,11002,11120,4632,3873,3643,4016,3467,3469,3443,4618,4591,4624,10441,10444,10614,10709,10728,10735,10758,10766,10769,10786,10972,4170,4077,11057,4124,3800,4158,3817,10609,10706,4636,3440,10574,10672,10822,10886,10961,11008,11011,11042,11068,11104,11142,3441,10601,10657,10891,10982,3442,4617,10490,10522,11026,11071,3590,10751,10842,11115,11159,4628,11035,11045,11151,11172,11175,11242,11245,3500,10873,10903,10912,10915,3532,3952,3891,10525,4625,10470,10861,10864,3461,10906,11065,4249,4622,3960,4609,4612,3417,3421,4611,4610,4638,10772,4643,11248,4034,3881,11178,11184,3730,3883,10909,3591,3697,10825,10828,10921,11091,4641,4642,10665,4304,3914,4639,10495,10498,10867,3884,10831,4144,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928,5930,5935,5943,5981,5996,6005,6008,6017,6021,6022,6023,6024,6025,6030,6035,6045,6051,6069,6073,6082,6112,6128,6154,6171,6172,6175,6190,6192,6194,6196,6211,6212,6215,6217,6220,6221,6238,6246,6247,6248,6250,6252,6290,6291,6296,6299,6305,6309,6343,6345,6347,6349,6359,6361,6364,6370,6372,6377,6380,6388,6396,6398,6399,6406,6429,6430,6431,6432,6433,6435,6442,6447,6481,6482,6485,6486,6487,6489,6490,6491,6492,6499,6535,6536,6545,6567,6568,6592,6594,6606,6607,6613,6643,6645,6660,6700,6703,6704,6760,6783,6826,6841,6849,6858,6859,6860,6861,6882,6883,6890,6902,6905,6907,6909,6910,6911,6913,6927,6938,6939,6940,6953,7008,7019,7021,7026,7045,7046,7082,7089,7096,7126,7157,7213,7242,7299,7320,7329,7332,7392,7402,7465,7467,7481,7490,7491,7492,7509,7513,7515,7562,7572,7575,7590,7638,7640,7643,7687,7688,7706,7776,7794,7818,7842,7854,7868,7879,7890,7891,7917,7919,7921,7931,7969,7980,8005,8032,8065,8096,8130,8169,8186,8188,8204,8205,8273,8284,8349,8373,8392,8419,8458,8459,8476,8516,8518,8520,8526,8542,8546,8561,8582,8590,8592,8602,8607,8611,8612,8613,8614,8615,8616,8635,8650,8651,8669,8671,8675,8676,8677,8678,8679,8697,8698,8699,8709,8722,8725,8736,8741,8743,8745,8746,8747,8754,8760,8768,8771,8788,8789,8798,8799,8807])).
% 168.60/168.46 cnf(11333,plain,
% 168.60/168.46 (P25(x113331,x113331,f7(x113331),x113332)),
% 168.60/168.46 inference(rename_variables,[],[3674])).
% 168.60/168.46 cnf(11338,plain,
% 168.60/168.46 (~E(f315(f298(x113381,f909(x113381,a899),x113382),x113383),f315(f296(x113381),x113383))),
% 168.60/168.46 inference(rename_variables,[],[4626])).
% 168.60/168.46 cnf(11343,plain,
% 168.60/168.46 (P1(f315(f315(f223(f909(x113431,a899)),x113432),f230(f909(x113431,a899))))),
% 168.60/168.46 inference(rename_variables,[],[3817])).
% 168.60/168.46 cnf(11359,plain,
% 168.60/168.46 (~P1(f315(f315(f317(x113591),x113592),f177(f909(x113591,a899))))),
% 168.60/168.46 inference(rename_variables,[],[4628])).
% 168.60/168.46 cnf(11362,plain,
% 168.60/168.46 (~P1(f315(f315(f223(a901),f315(a101,x113621)),x113621))),
% 168.60/168.46 inference(rename_variables,[],[4625])).
% 168.60/168.46 cnf(11367,plain,
% 168.60/168.46 (~P1(f315(f315(f317(x113671),x113672),f177(f909(x113671,a899))))),
% 168.60/168.46 inference(rename_variables,[],[4628])).
% 168.60/168.46 cnf(11377,plain,
% 168.60/168.46 (~P1(f315(f315(f317(a901),f315(a101,f315(f131(a901,a901,f73(a901),f2(a901)),x113771))),f315(f161(a901),x113771)))),
% 168.60/168.46 inference(scs_inference,[],[3783,3674,4583,10413,10423,10436,10447,10519,10554,10557,10560,10662,10797,11110,11303,11306,11325,4589,10646,10746,11213,3236,3286,3401,10482,10485,10581,10584,3378,3893,3276,3338,3272,3299,3281,3905,3496,11060,3371,4066,4597,10473,4626,11239,3543,3335,10546,4208,4068,11259,4644,11162,4645,3356,3634,3799,3734,3948,3507,10565,10685,10763,10836,10839,10879,10979,11229,3886,3424,4621,10450,10453,10479,10606,10781,10987,11002,11120,4632,3873,3643,4016,3467,3469,3443,4618,4591,4624,10441,10444,10614,10709,10728,10735,10758,10766,10769,10786,10972,4170,4077,11057,4124,3800,4158,3817,10609,10706,11262,4636,3440,10574,10672,10822,10886,10961,11008,11011,11042,11068,11104,11142,3441,10601,10657,10891,10982,3442,4617,10490,10522,11026,11071,3590,10751,10842,11115,11159,4628,11035,11045,11151,11172,11175,11242,11245,11256,11359,3500,10873,10903,10912,10915,3532,3952,3891,10525,4625,10470,10861,10864,11362,3461,10906,11065,4249,4622,3960,4609,4612,3417,3421,4611,4610,4638,10772,4643,11248,4034,3881,11178,11184,3730,3883,10909,3591,3697,10825,10828,10921,11091,4641,4642,10665,4304,3914,4639,10495,10498,10867,3884,10831,4144,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928,5930,5935,5943,5981,5996,6005,6008,6017,6021,6022,6023,6024,6025,6030,6035,6045,6051,6069,6073,6082,6112,6128,6154,6171,6172,6175,6190,6192,6194,6196,6211,6212,6215,6217,6220,6221,6238,6246,6247,6248,6250,6252,6290,6291,6296,6299,6305,6309,6343,6345,6347,6349,6359,6361,6364,6370,6372,6377,6380,6388,6396,6398,6399,6406,6429,6430,6431,6432,6433,6435,6442,6447,6481,6482,6485,6486,6487,6489,6490,6491,6492,6499,6535,6536,6545,6567,6568,6592,6594,6606,6607,6613,6643,6645,6660,6700,6703,6704,6760,6783,6826,6841,6849,6858,6859,6860,6861,6882,6883,6890,6902,6905,6907,6909,6910,6911,6913,6927,6938,6939,6940,6953,7008,7019,7021,7026,7045,7046,7082,7089,7096,7126,7157,7213,7242,7299,7320,7329,7332,7392,7402,7465,7467,7481,7490,7491,7492,7509,7513,7515,7562,7572,7575,7590,7638,7640,7643,7687,7688,7706,7776,7794,7818,7842,7854,7868,7879,7890,7891,7917,7919,7921,7931,7969,7980,8005,8032,8065,8096,8130,8169,8186,8188,8204,8205,8273,8284,8349,8373,8392,8419,8458,8459,8476,8516,8518,8520,8526,8542,8546,8561,8582,8590,8592,8602,8607,8611,8612,8613,8614,8615,8616,8635,8650,8651,8669,8671,8675,8676,8677,8678,8679,8697,8698,8699,8709,8722,8725,8736,8741,8743,8745,8746,8747,8754,8760,8768,8771,8788,8789,8798,8799,8807,8826,8839,8843,8864,8886,8887,8890,8891,8897,8906,8907,8930,8941,8951,8952,8953,8956,8979,8980,8991])).
% 168.60/168.46 cnf(11378,plain,
% 168.60/168.46 (~P1(f315(f315(f223(a901),f315(a101,x113781)),x113781))),
% 168.60/168.46 inference(rename_variables,[],[4625])).
% 168.60/168.46 cnf(11381,plain,
% 168.60/168.46 (~P1(f315(f315(f317(x113811),x113812),f177(f909(x113811,a899))))),
% 168.60/168.46 inference(rename_variables,[],[4628])).
% 168.60/168.46 cnf(11387,plain,
% 168.60/168.46 (E(f315(f125(x113871,f230(f909(x113872,a899))),f724(x113873,x113874,f315(f315(f140(x113871),x113874),x113873),f230(f909(x113872,a899)),x113871)),x113873)),
% 168.60/168.46 inference(scs_inference,[],[3783,3674,4583,10413,10423,10436,10447,10519,10554,10557,10560,10662,10797,11110,11303,11306,11325,4589,10646,10746,11213,3236,3286,3401,10482,10485,10581,10584,3378,3893,3276,3338,3272,3299,3281,3905,3496,11060,3371,4066,4597,10473,4626,11239,3543,3335,10546,4208,4068,11259,4644,11162,4645,3356,3634,3799,3734,3948,3507,10565,10685,10763,10836,10839,10879,10979,11229,3886,3424,4621,10450,10453,10479,10606,10781,10987,11002,11120,4632,3873,3643,4016,3467,3469,3443,4618,4591,4624,10441,10444,10614,10709,10728,10735,10758,10766,10769,10786,10972,4170,4077,11057,4124,3800,4158,3817,10609,10706,11262,4636,3440,10574,10672,10822,10886,10961,11008,11011,11042,11068,11104,11142,3441,10601,10657,10891,10982,3442,4617,10490,10522,11026,11071,3590,10751,10842,11115,11159,4628,11035,11045,11151,11172,11175,11242,11245,11256,11359,11367,3500,10873,10903,10912,10915,3532,3952,3891,10525,4625,10470,10861,10864,11362,3461,10906,11065,4249,4622,3960,4609,4612,3417,3421,4611,4610,4638,10772,4643,11248,4034,3881,11178,11184,3730,3883,10909,3591,3697,10825,10828,10921,11091,4641,4642,10665,4304,3914,4639,10495,10498,10867,3884,10831,4144,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928,5930,5935,5943,5981,5996,6005,6008,6017,6021,6022,6023,6024,6025,6030,6035,6045,6051,6069,6073,6082,6112,6128,6154,6171,6172,6175,6190,6192,6194,6196,6211,6212,6215,6217,6220,6221,6238,6246,6247,6248,6250,6252,6290,6291,6296,6299,6305,6309,6343,6345,6347,6349,6359,6361,6364,6370,6372,6377,6380,6388,6396,6398,6399,6406,6429,6430,6431,6432,6433,6435,6442,6447,6481,6482,6485,6486,6487,6489,6490,6491,6492,6499,6535,6536,6545,6567,6568,6592,6594,6606,6607,6613,6643,6645,6660,6700,6703,6704,6760,6783,6826,6841,6849,6858,6859,6860,6861,6882,6883,6890,6902,6905,6907,6909,6910,6911,6913,6927,6938,6939,6940,6953,7008,7019,7021,7026,7045,7046,7082,7089,7096,7126,7157,7213,7242,7299,7320,7329,7332,7392,7402,7465,7467,7481,7490,7491,7492,7509,7513,7515,7562,7572,7575,7590,7638,7640,7643,7687,7688,7706,7776,7794,7818,7842,7854,7868,7879,7890,7891,7917,7919,7921,7931,7969,7980,8005,8032,8065,8096,8130,8169,8186,8188,8204,8205,8273,8284,8349,8373,8392,8419,8458,8459,8476,8516,8518,8520,8526,8542,8546,8561,8582,8590,8592,8602,8607,8611,8612,8613,8614,8615,8616,8635,8650,8651,8669,8671,8675,8676,8677,8678,8679,8697,8698,8699,8709,8722,8725,8736,8741,8743,8745,8746,8747,8754,8760,8768,8771,8788,8789,8798,8799,8807,8826,8839,8843,8864,8886,8887,8890,8891,8897,8906,8907,8930,8941,8951,8952,8953,8956,8979,8980,8991,9041,9051,9053,9069])).
% 168.60/168.46 cnf(11390,plain,
% 168.60/168.46 (P1(f315(f315(f317(f908(x113901,x113901)),f315(f315(f240(x113901,x113901),x113902),x113902)),f295(x113901,x113903)))),
% 168.60/168.46 inference(rename_variables,[],[4068])).
% 168.60/168.46 cnf(11393,plain,
% 168.60/168.46 (P1(f315(f315(f317(x113931),x113932),f230(f909(x113931,a899))))),
% 168.60/168.46 inference(rename_variables,[],[3590])).
% 168.60/168.46 cnf(11396,plain,
% 168.60/168.46 (P1(f315(f315(f317(x113961),x113962),f230(f909(x113961,a899))))),
% 168.60/168.46 inference(rename_variables,[],[3590])).
% 168.60/168.46 cnf(11403,plain,
% 168.60/168.46 (~P1(f315(f315(f317(f908(f902(x114031),f902(x114031))),f315(f315(f240(f902(x114031),f902(x114031)),x114032),f102(x114031))),f134(x114031,x114033)))),
% 168.60/168.46 inference(rename_variables,[],[4644])).
% 168.60/168.46 cnf(11406,plain,
% 168.60/168.46 (~P1(f315(f315(f317(f908(f902(x114061),f902(x114061))),f315(f315(f240(f902(x114061),f902(x114061)),x114062),f102(x114061))),f136(x114061,x114063)))),
% 168.60/168.46 inference(rename_variables,[],[4645])).
% 168.60/168.46 cnf(11409,plain,
% 168.60/168.46 (~P1(f315(f315(f317(f908(f902(x114091),f902(x114091))),f315(f315(f240(f902(x114091),f902(x114091)),x114092),f102(x114091))),f146(x114091,x114093)))),
% 168.60/168.46 inference(rename_variables,[],[4646])).
% 168.60/168.46 cnf(11414,plain,
% 168.60/168.46 (~P1(f315(f315(f224(f909(x114141,a899)),x114142),f177(f909(x114141,a899))))),
% 168.60/168.46 inference(rename_variables,[],[4636])).
% 168.60/168.46 cnf(11417,plain,
% 168.60/168.46 (~P1(f315(f315(f317(x114171),x114172),f177(f909(x114171,a899))))),
% 168.60/168.46 inference(rename_variables,[],[4628])).
% 168.60/168.46 cnf(11422,plain,
% 168.60/168.46 (P1(f315(f315(f223(f909(x114221,a899)),x114222),f230(f909(x114221,a899))))),
% 168.60/168.46 inference(rename_variables,[],[3817])).
% 168.60/168.46 cnf(11424,plain,
% 168.60/168.46 (~P59(f902(x114241),f147(x114241,x114242))),
% 168.60/168.46 inference(scs_inference,[],[3783,3674,4583,10413,10423,10436,10447,10519,10554,10557,10560,10662,10797,11110,11303,11306,11325,4589,10646,10746,11213,3236,3286,3401,10482,10485,10581,10584,3378,3893,3276,3338,3272,3299,3281,3905,3496,11060,3371,4066,4597,10473,4626,11239,3543,3335,10546,4208,4068,11259,4644,11162,11403,4645,11292,4646,3356,3634,3799,3734,3948,3507,10565,10685,10763,10836,10839,10879,10979,11229,3886,3424,4621,10450,10453,10479,10606,10781,10987,11002,11120,4632,3873,3643,4016,3467,3469,3443,4618,4591,4624,10441,10444,10614,10709,10728,10735,10758,10766,10769,10786,10972,4170,4077,11057,4124,3800,4158,3817,10609,10706,11262,11343,4636,11005,3440,10574,10672,10822,10886,10961,11008,11011,11042,11068,11104,11142,3441,10601,10657,10891,10982,3442,4617,10490,10522,11026,11071,3590,10751,10842,11115,11159,11393,4628,11035,11045,11151,11172,11175,11242,11245,11256,11359,11367,11381,3500,10873,10903,10912,10915,3532,3952,3891,10525,4625,10470,10861,10864,11362,3461,10906,11065,4249,4622,3960,4609,4612,3417,3421,4611,4610,4638,10772,4643,11248,4034,3881,11178,11184,3730,3883,10909,3591,3697,10825,10828,10921,11091,4641,4642,10665,4304,3914,4639,10495,10498,10867,3884,10831,4144,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928,5930,5935,5943,5981,5996,6005,6008,6017,6021,6022,6023,6024,6025,6030,6035,6045,6051,6069,6073,6082,6112,6128,6154,6171,6172,6175,6190,6192,6194,6196,6211,6212,6215,6217,6220,6221,6238,6246,6247,6248,6250,6252,6290,6291,6296,6299,6305,6309,6343,6345,6347,6349,6359,6361,6364,6370,6372,6377,6380,6388,6396,6398,6399,6406,6429,6430,6431,6432,6433,6435,6442,6447,6481,6482,6485,6486,6487,6489,6490,6491,6492,6499,6535,6536,6545,6567,6568,6592,6594,6606,6607,6613,6643,6645,6660,6700,6703,6704,6760,6783,6826,6841,6849,6858,6859,6860,6861,6882,6883,6890,6902,6905,6907,6909,6910,6911,6913,6927,6938,6939,6940,6953,7008,7019,7021,7026,7045,7046,7082,7089,7096,7126,7157,7213,7242,7299,7320,7329,7332,7392,7402,7465,7467,7481,7490,7491,7492,7509,7513,7515,7562,7572,7575,7590,7638,7640,7643,7687,7688,7706,7776,7794,7818,7842,7854,7868,7879,7890,7891,7917,7919,7921,7931,7969,7980,8005,8032,8065,8096,8130,8169,8186,8188,8204,8205,8273,8284,8349,8373,8392,8419,8458,8459,8476,8516,8518,8520,8526,8542,8546,8561,8582,8590,8592,8602,8607,8611,8612,8613,8614,8615,8616,8635,8650,8651,8669,8671,8675,8676,8677,8678,8679,8697,8698,8699,8709,8722,8725,8736,8741,8743,8745,8746,8747,8754,8760,8768,8771,8788,8789,8798,8799,8807,8826,8839,8843,8864,8886,8887,8890,8891,8897,8906,8907,8930,8941,8951,8952,8953,8956,8979,8980,8991,9041,9051,9053,9069,9081,9082,9083,9094,9158,9189,9190,9191,9206,9223,9231,9259,9260,9329])).
% 168.60/168.46 cnf(11429,plain,
% 168.60/168.46 (~P1(f315(f315(f161(x114291),f102(x114291)),x114292))),
% 168.60/168.46 inference(rename_variables,[],[4624])).
% 168.60/168.46 cnf(11434,plain,
% 168.60/168.46 (~P1(f315(f315(f317(x114341),x114342),f177(f909(x114341,a899))))),
% 168.60/168.46 inference(rename_variables,[],[4628])).
% 168.60/168.46 cnf(11437,plain,
% 168.60/168.46 (~P1(f315(f315(f317(f908(x114371,x114371)),f315(f315(f240(x114371,x114371),x114372),x114373)),f142(x114371,f102(f909(x114371,a901)))))),
% 168.60/168.46 inference(rename_variables,[],[4643])).
% 168.60/168.46 cnf(11440,plain,
% 168.60/168.46 (P1(f315(f315(f223(f909(x114401,a899)),x114402),x114402))),
% 168.60/168.46 inference(rename_variables,[],[3730])).
% 168.60/168.46 cnf(11443,plain,
% 168.60/168.46 (~P1(f315(f315(f317(x114431),x114432),f177(f909(x114431,a899))))),
% 168.60/168.46 inference(rename_variables,[],[4628])).
% 168.60/168.46 cnf(11445,plain,
% 168.60/168.46 (P1(f315(f315(f223(f909(x114451,a899)),f315(f273(x114452,x114451,f177(f909(f908(x114452,x114451),a899))),x114453)),x114454))),
% 168.60/168.46 inference(scs_inference,[],[3783,3674,4583,10413,10423,10436,10447,10519,10554,10557,10560,10662,10797,11110,11303,11306,11325,4589,10646,10746,11213,3236,3286,3401,10482,10485,10581,10584,3378,3893,3276,3338,3272,3299,3281,3905,3496,11060,3371,4066,4597,10473,4626,11239,3543,3335,10546,4208,4068,11259,4644,11162,11403,4645,11292,4646,3356,3634,3799,3734,3948,3507,10565,10685,10763,10836,10839,10879,10979,11229,3886,3424,4621,10450,10453,10479,10606,10781,10987,11002,11120,4632,3873,3643,4016,3467,3469,3443,4618,4591,4624,10441,10444,10614,10709,10728,10735,10758,10766,10769,10786,10972,11216,4170,4077,11057,4124,3800,4158,3817,10609,10706,11262,11343,4636,11005,3440,10574,10672,10822,10886,10961,11008,11011,11042,11068,11104,11142,3441,10601,10657,10891,10982,3442,4617,10490,10522,11026,11071,3590,10751,10842,11115,11159,11393,4628,11035,11045,11151,11172,11175,11242,11245,11256,11359,11367,11381,11417,11434,3500,10873,10903,10912,10915,3532,3952,3891,10525,4625,10470,10861,10864,11362,3461,10906,11065,4249,4622,3960,4609,4612,3417,3421,4611,4610,4638,10772,4643,11248,11251,4034,3881,11178,11184,3730,11318,3883,10909,11281,3591,3697,10825,10828,10921,11091,4641,4642,10665,4304,3914,4639,10495,10498,10867,3884,10831,4144,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928,5930,5935,5943,5981,5996,6005,6008,6017,6021,6022,6023,6024,6025,6030,6035,6045,6051,6069,6073,6082,6112,6128,6154,6171,6172,6175,6190,6192,6194,6196,6211,6212,6215,6217,6220,6221,6238,6246,6247,6248,6250,6252,6290,6291,6296,6299,6305,6309,6343,6345,6347,6349,6359,6361,6364,6370,6372,6377,6380,6388,6396,6398,6399,6406,6429,6430,6431,6432,6433,6435,6442,6447,6481,6482,6485,6486,6487,6489,6490,6491,6492,6499,6535,6536,6545,6567,6568,6592,6594,6606,6607,6613,6643,6645,6660,6700,6703,6704,6760,6783,6826,6841,6849,6858,6859,6860,6861,6882,6883,6890,6902,6905,6907,6909,6910,6911,6913,6927,6938,6939,6940,6953,7008,7019,7021,7026,7045,7046,7082,7089,7096,7126,7157,7213,7242,7299,7320,7329,7332,7392,7402,7465,7467,7481,7490,7491,7492,7509,7513,7515,7562,7572,7575,7590,7638,7640,7643,7687,7688,7706,7776,7794,7818,7842,7854,7868,7879,7890,7891,7917,7919,7921,7931,7969,7980,8005,8032,8065,8096,8130,8169,8186,8188,8204,8205,8273,8284,8349,8373,8392,8419,8458,8459,8476,8516,8518,8520,8526,8542,8546,8561,8582,8590,8592,8602,8607,8611,8612,8613,8614,8615,8616,8635,8650,8651,8669,8671,8675,8676,8677,8678,8679,8697,8698,8699,8709,8722,8725,8736,8741,8743,8745,8746,8747,8754,8760,8768,8771,8788,8789,8798,8799,8807,8826,8839,8843,8864,8886,8887,8890,8891,8897,8906,8907,8930,8941,8951,8952,8953,8956,8979,8980,8991,9041,9051,9053,9069,9081,9082,9083,9094,9158,9189,9190,9191,9206,9223,9231,9259,9260,9329,9364,9370,9380,9381,9382,9391,9421,9437])).
% 168.60/168.46 cnf(11446,plain,
% 168.60/168.46 (P1(f315(f315(f223(f909(x114461,a899)),f177(f909(x114461,a899))),x114462))),
% 168.60/168.46 inference(rename_variables,[],[3883])).
% 168.60/168.46 cnf(11449,plain,
% 168.60/168.46 (P1(f315(f315(f317(f908(x114491,x114491)),f315(f315(f240(x114491,x114491),x114492),x114492)),f295(x114491,x114493)))),
% 168.60/168.46 inference(rename_variables,[],[4068])).
% 168.60/168.46 cnf(11455,plain,
% 168.60/168.46 (P36(x114551,x114552,x114553,f315(f315(f143(x114554,x114551),x114555),f103(x114554,f102(x114554))),f102(x114552))),
% 168.60/168.46 inference(scs_inference,[],[3783,3674,4583,10413,10423,10436,10447,10519,10554,10557,10560,10662,10797,11110,11303,11306,11325,4589,10646,10746,11213,3236,3286,3401,10482,10485,10581,10584,3378,3893,3276,3338,3272,3299,3281,3905,3496,11060,3371,4066,4597,10473,4626,11239,3543,3335,10546,4208,4068,11259,11390,4644,11162,11403,4645,11292,4646,3356,3634,3799,3734,3948,3507,10565,10685,10763,10836,10839,10879,10979,11229,3886,3424,4621,10450,10453,10479,10606,10781,10987,11002,11120,4632,3873,3643,4016,3467,3469,3443,4618,4591,4624,10441,10444,10614,10709,10728,10735,10758,10766,10769,10786,10972,11216,4170,4077,11057,4124,3800,4158,3817,10609,10706,11262,11343,4636,11005,3440,10574,10672,10822,10886,10961,11008,11011,11042,11068,11104,11142,3441,10601,10657,10891,10982,3442,4617,10490,10522,11026,11071,3590,10751,10842,11115,11159,11393,4628,11035,11045,11151,11172,11175,11242,11245,11256,11359,11367,11381,11417,11434,3500,10873,10903,10912,10915,3532,3952,3891,10525,4625,10470,10861,10864,11362,3461,10906,11065,4249,4622,3960,4609,4612,3417,3421,4611,4610,4638,10772,4643,11248,11251,4034,3881,11178,11184,3730,11318,3883,10909,11281,3591,3697,10825,10828,10921,11091,4641,4642,10665,4304,3914,4639,10495,10498,10867,3884,10831,4144,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928,5930,5935,5943,5981,5996,6005,6008,6017,6021,6022,6023,6024,6025,6030,6035,6045,6051,6069,6073,6082,6112,6128,6154,6171,6172,6175,6190,6192,6194,6196,6211,6212,6215,6217,6220,6221,6238,6246,6247,6248,6250,6252,6290,6291,6296,6299,6305,6309,6343,6345,6347,6349,6359,6361,6364,6370,6372,6377,6380,6388,6396,6398,6399,6406,6429,6430,6431,6432,6433,6435,6442,6447,6481,6482,6485,6486,6487,6489,6490,6491,6492,6499,6535,6536,6545,6567,6568,6592,6594,6606,6607,6613,6643,6645,6660,6700,6703,6704,6760,6783,6826,6841,6849,6858,6859,6860,6861,6882,6883,6890,6902,6905,6907,6909,6910,6911,6913,6927,6938,6939,6940,6953,7008,7019,7021,7026,7045,7046,7082,7089,7096,7126,7157,7213,7242,7299,7320,7329,7332,7392,7402,7465,7467,7481,7490,7491,7492,7509,7513,7515,7562,7572,7575,7590,7638,7640,7643,7687,7688,7706,7776,7794,7818,7842,7854,7868,7879,7890,7891,7917,7919,7921,7931,7969,7980,8005,8032,8065,8096,8130,8169,8186,8188,8204,8205,8273,8284,8349,8373,8392,8419,8458,8459,8476,8516,8518,8520,8526,8542,8546,8561,8582,8590,8592,8602,8607,8611,8612,8613,8614,8615,8616,8635,8650,8651,8669,8671,8675,8676,8677,8678,8679,8697,8698,8699,8709,8722,8725,8736,8741,8743,8745,8746,8747,8754,8760,8768,8771,8788,8789,8798,8799,8807,8826,8839,8843,8864,8886,8887,8890,8891,8897,8906,8907,8930,8941,8951,8952,8953,8956,8979,8980,8991,9041,9051,9053,9069,9081,9082,9083,9094,9158,9189,9190,9191,9206,9223,9231,9259,9260,9329,9364,9370,9380,9381,9382,9391,9421,9437,9441,9445,9467,9468])).
% 168.60/168.46 cnf(11460,plain,
% 168.60/168.46 (~P1(f315(f315(f317(f908(f902(x114601),f902(x114601))),f315(f315(f240(f902(x114601),f902(x114601)),x114602),f102(x114601))),f146(x114601,x114603)))),
% 168.60/168.46 inference(rename_variables,[],[4646])).
% 168.60/168.46 cnf(11467,plain,
% 168.60/168.46 (~P1(f315(f315(f317(f908(f902(x114671),f902(x114671))),f315(f315(f240(f902(x114671),f902(x114671)),f102(x114671)),x114672)),f134(x114671,x114673)))),
% 168.60/168.46 inference(rename_variables,[],[4647])).
% 168.60/168.46 cnf(11475,plain,
% 168.60/168.46 (P1(f315(f315(f317(x114751),x114752),f230(f909(x114751,a899))))),
% 168.60/168.46 inference(rename_variables,[],[3590])).
% 168.60/168.46 cnf(11480,plain,
% 168.60/168.46 (P1(f315(f315(f223(f909(x114801,a899)),f177(f909(x114801,a899))),x114802))),
% 168.60/168.46 inference(rename_variables,[],[3883])).
% 168.60/168.46 cnf(11483,plain,
% 168.60/168.46 (~P1(f315(f315(f317(x114831),x114832),f177(f909(x114831,a899))))),
% 168.60/168.46 inference(rename_variables,[],[4628])).
% 168.60/168.46 cnf(11486,plain,
% 168.60/168.46 (P1(f315(f315(f223(f909(x114861,a899)),x114862),f230(f909(x114861,a899))))),
% 168.60/168.46 inference(rename_variables,[],[3817])).
% 168.60/168.46 cnf(11490,plain,
% 168.60/168.46 (P1(f315(f315(f223(f909(x114901,a899)),f315(f273(x114902,x114901,x114903),f177(f909(x114902,a899)))),x114904))),
% 168.60/168.46 inference(scs_inference,[],[3783,3674,4583,10413,10423,10436,10447,10519,10554,10557,10560,10662,10797,11110,11303,11306,11325,4589,10646,10746,11213,3236,3286,3401,10482,10485,10581,10584,3378,3893,3276,3338,3272,3299,3281,3905,3496,11060,3371,4066,4597,10473,4626,11239,3543,3335,10546,4208,4068,11259,11390,4644,11162,11403,4645,11292,4646,11409,4647,4648,3356,3634,3799,3734,3948,3507,10565,10685,10763,10836,10839,10879,10979,11229,3886,3424,4621,10450,10453,10479,10606,10781,10987,11002,11120,4632,3873,3643,4016,3467,3469,3443,4618,4591,4624,10441,10444,10614,10709,10728,10735,10758,10766,10769,10786,10972,11216,4170,4077,11057,4124,3800,4158,3817,10609,10706,11262,11343,11422,4636,11005,11414,3440,10574,10672,10822,10886,10961,11008,11011,11042,11068,11104,11142,3441,10601,10657,10891,10982,3442,4617,10490,10522,11026,11071,3590,10751,10842,11115,11159,11393,11396,4628,11035,11045,11151,11172,11175,11242,11245,11256,11359,11367,11381,11417,11434,11443,3500,10873,10903,10912,10915,3532,3952,3891,10525,4625,10470,10861,10864,11362,3461,10906,11065,4249,4622,3960,4609,4612,3417,3421,4611,4610,4638,10772,4643,11248,11251,4034,3881,11178,11184,3730,11318,3883,10909,11281,11446,11480,3591,3697,10825,10828,10921,11091,4641,4642,10665,4304,4212,3914,4639,10495,10498,10867,3884,10831,4144,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928,5930,5935,5943,5981,5996,6005,6008,6017,6021,6022,6023,6024,6025,6030,6035,6045,6051,6069,6073,6082,6112,6128,6154,6171,6172,6175,6190,6192,6194,6196,6211,6212,6215,6217,6220,6221,6238,6246,6247,6248,6250,6252,6290,6291,6296,6299,6305,6309,6343,6345,6347,6349,6359,6361,6364,6370,6372,6377,6380,6388,6396,6398,6399,6406,6429,6430,6431,6432,6433,6435,6442,6447,6481,6482,6485,6486,6487,6489,6490,6491,6492,6499,6535,6536,6545,6567,6568,6592,6594,6606,6607,6613,6643,6645,6660,6700,6703,6704,6760,6783,6826,6841,6849,6858,6859,6860,6861,6882,6883,6890,6902,6905,6907,6909,6910,6911,6913,6927,6938,6939,6940,6953,7008,7019,7021,7026,7045,7046,7082,7089,7096,7126,7157,7213,7242,7299,7320,7329,7332,7392,7402,7465,7467,7481,7490,7491,7492,7509,7513,7515,7562,7572,7575,7590,7638,7640,7643,7687,7688,7706,7776,7794,7818,7842,7854,7868,7879,7890,7891,7917,7919,7921,7931,7969,7980,8005,8032,8065,8096,8130,8169,8186,8188,8204,8205,8273,8284,8349,8373,8392,8419,8458,8459,8476,8516,8518,8520,8526,8542,8546,8561,8582,8590,8592,8602,8607,8611,8612,8613,8614,8615,8616,8635,8650,8651,8669,8671,8675,8676,8677,8678,8679,8697,8698,8699,8709,8722,8725,8736,8741,8743,8745,8746,8747,8754,8760,8768,8771,8788,8789,8798,8799,8807,8826,8839,8843,8864,8886,8887,8890,8891,8897,8906,8907,8930,8941,8951,8952,8953,8956,8979,8980,8991,9041,9051,9053,9069,9081,9082,9083,9094,9158,9189,9190,9191,9206,9223,9231,9259,9260,9329,9364,9370,9380,9381,9382,9391,9421,9437,9441,9445,9467,9468,9495,9559,9564,9567,9604,9605,9606,9634,9635,9651,9672,9678,9690,9715])).
% 168.60/168.46 cnf(11491,plain,
% 168.60/168.46 (P1(f315(f315(f223(f909(x114911,a899)),f177(f909(x114911,a899))),x114912))),
% 168.60/168.46 inference(rename_variables,[],[3883])).
% 168.60/168.46 cnf(11493,plain,
% 168.60/168.46 (~P1(f315(f59(a901,x114931,x114932,x114933,f230(f909(a901,a899))),x114934))),
% 168.60/168.46 inference(scs_inference,[],[3783,3674,4583,10413,10423,10436,10447,10519,10554,10557,10560,10662,10797,11110,11303,11306,11325,4589,10646,10746,11213,3236,3286,3401,10482,10485,10581,10584,3378,3893,3276,3338,3272,3299,3281,3905,3496,11060,3371,4066,4597,10473,4626,11239,3543,3335,10546,4208,4068,11259,11390,4644,11162,11403,4645,11292,4646,11409,4647,4648,3356,3634,3799,3734,3948,3507,10565,10685,10763,10836,10839,10879,10979,11229,3886,3424,4621,10450,10453,10479,10606,10781,10987,11002,11120,4632,3873,3643,4016,3467,3469,3443,4618,4591,4624,10441,10444,10614,10709,10728,10735,10758,10766,10769,10786,10972,11216,4170,4077,11057,4124,3800,4158,3817,10609,10706,11262,11343,11422,4636,11005,11414,3440,10574,10672,10822,10886,10961,11008,11011,11042,11068,11104,11142,3441,10601,10657,10891,10982,3442,4617,10490,10522,11026,11071,3590,10751,10842,11115,11159,11393,11396,4628,11035,11045,11151,11172,11175,11242,11245,11256,11359,11367,11381,11417,11434,11443,3500,10873,10903,10912,10915,3532,3952,3891,10525,4625,10470,10861,10864,11362,3461,10906,11065,4249,4622,3960,4609,4612,3417,3421,4611,4610,4638,10772,4643,11248,11251,4034,3881,11178,11184,3730,11318,3883,10909,11281,11446,11480,3591,3697,10825,10828,10921,11091,4641,4642,10665,4304,4212,3914,4639,10495,10498,10867,3884,10831,4144,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928,5930,5935,5943,5981,5996,6005,6008,6017,6021,6022,6023,6024,6025,6030,6035,6045,6051,6069,6073,6082,6112,6128,6154,6171,6172,6175,6190,6192,6194,6196,6211,6212,6215,6217,6220,6221,6238,6246,6247,6248,6250,6252,6290,6291,6296,6299,6305,6309,6343,6345,6347,6349,6359,6361,6364,6370,6372,6377,6380,6388,6396,6398,6399,6406,6429,6430,6431,6432,6433,6435,6442,6447,6481,6482,6485,6486,6487,6489,6490,6491,6492,6499,6535,6536,6545,6567,6568,6592,6594,6606,6607,6613,6643,6645,6660,6700,6703,6704,6760,6783,6826,6841,6849,6858,6859,6860,6861,6882,6883,6890,6902,6905,6907,6909,6910,6911,6913,6927,6938,6939,6940,6953,7008,7019,7021,7026,7045,7046,7082,7089,7096,7126,7157,7213,7242,7299,7320,7329,7332,7392,7402,7465,7467,7481,7490,7491,7492,7509,7513,7515,7562,7572,7575,7590,7638,7640,7643,7687,7688,7706,7776,7794,7818,7842,7854,7868,7879,7890,7891,7917,7919,7921,7931,7969,7980,8005,8032,8065,8096,8130,8169,8186,8188,8204,8205,8273,8284,8349,8373,8392,8419,8458,8459,8476,8516,8518,8520,8526,8542,8546,8561,8582,8590,8592,8602,8607,8611,8612,8613,8614,8615,8616,8635,8650,8651,8669,8671,8675,8676,8677,8678,8679,8697,8698,8699,8709,8722,8725,8736,8741,8743,8745,8746,8747,8754,8760,8768,8771,8788,8789,8798,8799,8807,8826,8839,8843,8864,8886,8887,8890,8891,8897,8906,8907,8930,8941,8951,8952,8953,8956,8979,8980,8991,9041,9051,9053,9069,9081,9082,9083,9094,9158,9189,9190,9191,9206,9223,9231,9259,9260,9329,9364,9370,9380,9381,9382,9391,9421,9437,9441,9445,9467,9468,9495,9559,9564,9567,9604,9605,9606,9634,9635,9651,9672,9678,9690,9715,9736])).
% 168.60/168.46 cnf(11504,plain,
% 168.60/168.46 (P1(f315(f230(f909(x115041,a899)),x115042))),
% 168.60/168.46 inference(rename_variables,[],[3500])).
% 168.60/168.46 cnf(11512,plain,
% 168.60/168.46 (~P1(f315(f315(f317(f908(f902(x115121),f902(x115121))),f315(f315(f240(f902(x115121),f902(x115121)),x115122),f102(x115121))),f134(x115121,x115123)))),
% 168.60/168.46 inference(rename_variables,[],[4644])).
% 168.60/168.46 cnf(11515,plain,
% 168.60/168.46 (~P1(f315(f315(f317(f908(f902(x115151),f902(x115151))),f315(f315(f240(f902(x115151),f902(x115151)),x115152),f102(x115151))),f136(x115151,x115153)))),
% 168.60/168.46 inference(rename_variables,[],[4645])).
% 168.60/168.46 cnf(11518,plain,
% 168.60/168.46 (~E(f315(f315(f140(x115181),x115182),x115183),x115183)),
% 168.60/168.46 inference(rename_variables,[],[4597])).
% 168.60/168.46 cnf(11521,plain,
% 168.60/168.46 (~E(f315(a101,x115211),x115211)),
% 168.60/168.46 inference(rename_variables,[],[4583])).
% 168.60/168.46 cnf(11524,plain,
% 168.60/168.46 (~P1(f315(f315(f317(x115241),x115242),f177(f909(x115241,a899))))),
% 168.60/168.46 inference(rename_variables,[],[4628])).
% 168.60/168.46 cnf(11529,plain,
% 168.60/168.46 (~P1(f315(f315(f317(x115291),x115292),f177(f909(x115291,a899))))),
% 168.60/168.46 inference(rename_variables,[],[4628])).
% 168.60/168.46 cnf(11532,plain,
% 168.60/168.46 (~P1(f315(f315(f317(x115321),x115322),f177(f909(x115321,a899))))),
% 168.60/168.46 inference(rename_variables,[],[4628])).
% 168.60/168.46 cnf(11535,plain,
% 168.60/168.46 (P1(f315(f315(f317(f908(f902(x115351),f902(x115351))),f315(f315(f240(f902(x115351),f902(x115351)),x115352),x115352)),f147(x115351,f295(x115351,x115353))))),
% 168.60/168.46 inference(rename_variables,[],[4201])).
% 168.60/168.46 cnf(11538,plain,
% 168.60/168.46 (~P1(f315(f315(f317(f908(f902(x115381),f902(x115381))),f315(f315(f240(f902(x115381),f902(x115381)),x115382),f102(x115381))),f134(x115381,x115383)))),
% 168.60/168.46 inference(rename_variables,[],[4644])).
% 168.60/168.46 cnf(11542,plain,
% 168.60/168.46 (E(f315(f315(f140(x115421),f636(f295(x115421,x115422),f315(f315(f140(x115421),x115423),x115424),x115424,x115423,x115421)),f637(f295(x115421,x115422),f315(f315(f140(x115421),x115423),x115424),x115424,x115423,x115421)),f315(f315(f140(x115421),x115423),x115424))),
% 168.60/168.46 inference(scs_inference,[],[3783,3674,4583,10413,10423,10436,10447,10519,10554,10557,10560,10662,10797,11110,11303,11306,11325,11328,4589,10646,10746,11213,3236,3286,3401,10482,10485,10581,10584,3378,3893,3276,3338,3272,3299,3281,3905,3496,11060,3371,4066,4597,10473,10643,4626,11239,3543,3335,10546,4208,4068,11259,11390,4644,11162,11403,11512,4645,11292,11406,4646,11409,4647,11467,4648,3356,3634,3799,3734,3948,3507,10565,10685,10763,10836,10839,10879,10979,11229,3886,3424,4621,10450,10453,10479,10606,10781,10987,11002,11120,4632,3873,3643,4016,3467,3469,3443,4618,4591,4201,11535,4624,10441,10444,10614,10709,10728,10735,10758,10766,10769,10786,10972,11216,4170,4077,11057,4124,3800,4158,3817,10609,10706,11262,11343,11422,4636,11005,11414,3440,10574,10672,10822,10886,10961,11008,11011,11042,11068,11104,11142,3441,10601,10657,10891,10982,3442,4617,10490,10522,11026,11071,3590,10751,10842,11115,11159,11393,11396,4628,11035,11045,11151,11172,11175,11242,11245,11256,11359,11367,11381,11417,11434,11443,11483,11524,11529,3500,10873,10903,10912,10915,10918,3532,3952,3891,10525,4625,10470,10861,10864,11362,3461,10906,11065,4249,4622,3960,4609,4612,3417,3421,4611,4610,4638,10772,4643,11248,11251,4034,3881,11178,11184,3730,11318,3883,10909,11281,11446,11480,3591,3697,10825,10828,10921,11091,4641,4642,10665,4304,4212,3914,4639,10495,10498,10867,3884,10831,4144,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928,5930,5935,5943,5981,5996,6005,6008,6017,6021,6022,6023,6024,6025,6030,6035,6045,6051,6069,6073,6082,6112,6128,6154,6171,6172,6175,6190,6192,6194,6196,6211,6212,6215,6217,6220,6221,6238,6246,6247,6248,6250,6252,6290,6291,6296,6299,6305,6309,6343,6345,6347,6349,6359,6361,6364,6370,6372,6377,6380,6388,6396,6398,6399,6406,6429,6430,6431,6432,6433,6435,6442,6447,6481,6482,6485,6486,6487,6489,6490,6491,6492,6499,6535,6536,6545,6567,6568,6592,6594,6606,6607,6613,6643,6645,6660,6700,6703,6704,6760,6783,6826,6841,6849,6858,6859,6860,6861,6882,6883,6890,6902,6905,6907,6909,6910,6911,6913,6927,6938,6939,6940,6953,7008,7019,7021,7026,7045,7046,7082,7089,7096,7126,7157,7213,7242,7299,7320,7329,7332,7392,7402,7465,7467,7481,7490,7491,7492,7509,7513,7515,7562,7572,7575,7590,7638,7640,7643,7687,7688,7706,7776,7794,7818,7842,7854,7868,7879,7890,7891,7917,7919,7921,7931,7969,7980,8005,8032,8065,8096,8130,8169,8186,8188,8204,8205,8273,8284,8349,8373,8392,8419,8458,8459,8476,8516,8518,8520,8526,8542,8546,8561,8582,8590,8592,8602,8607,8611,8612,8613,8614,8615,8616,8635,8650,8651,8669,8671,8675,8676,8677,8678,8679,8697,8698,8699,8709,8722,8725,8736,8741,8743,8745,8746,8747,8754,8760,8768,8771,8788,8789,8798,8799,8807,8826,8839,8843,8864,8886,8887,8890,8891,8897,8906,8907,8930,8941,8951,8952,8953,8956,8979,8980,8991,9041,9051,9053,9069,9081,9082,9083,9094,9158,9189,9190,9191,9206,9223,9231,9259,9260,9329,9364,9370,9380,9381,9382,9391,9421,9437,9441,9445,9467,9468,9495,9559,9564,9567,9604,9605,9606,9634,9635,9651,9672,9678,9690,9715,9736,9745,9746,9747,9748,9763,9765,9770,9800,9801,9807,9808,9852,9853,9864,9865,9889,9907,9909,9910])).
% 168.60/168.46 cnf(11548,plain,
% 168.60/168.46 (~P1(f315(f315(f317(f908(x115481,x115481)),f315(f315(f240(x115481,x115481),x115482),x115483)),f142(x115481,f102(f909(x115481,a901)))))),
% 168.60/168.46 inference(rename_variables,[],[4643])).
% 168.60/168.46 cnf(11551,plain,
% 168.60/168.46 (~P1(f315(f315(f317(x115511),x115512),f177(f909(x115511,a899))))),
% 168.60/168.46 inference(rename_variables,[],[4628])).
% 168.60/168.46 cnf(11554,plain,
% 168.60/168.46 (~P1(f315(f315(f317(x115541),x115542),f177(f909(x115541,a899))))),
% 168.60/168.46 inference(rename_variables,[],[4628])).
% 168.60/168.46 cnf(11557,plain,
% 168.60/168.46 (P1(f315(f315(f317(x115571),x115572),f230(f909(x115571,a899))))),
% 168.60/168.46 inference(rename_variables,[],[3590])).
% 168.60/168.46 cnf(11560,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),x115601),f2(a901)))),
% 168.60/168.46 inference(rename_variables,[],[4621])).
% 168.60/168.46 cnf(11565,plain,
% 168.60/168.46 (~P1(f315(f315(f317(f908(x115651,x115651)),f315(f315(f240(x115651,x115651),x115652),x115653)),f142(x115651,f102(f909(x115651,a901)))))),
% 168.60/168.46 inference(rename_variables,[],[4643])).
% 168.60/168.46 cnf(11574,plain,
% 168.60/168.46 (~E(f315(f298(x115741,f909(x115741,a899),x115742),x115743),f315(f296(x115741),x115743))),
% 168.60/168.46 inference(rename_variables,[],[4626])).
% 168.60/168.46 cnf(11577,plain,
% 168.60/168.46 (~E(f315(f298(x115771,f909(x115771,a899),x115772),x115773),f315(f296(x115771),x115773))),
% 168.60/168.46 inference(rename_variables,[],[4626])).
% 168.60/168.46 cnf(11582,plain,
% 168.60/168.46 (~P1(f315(f315(f317(f908(f902(x115821),f902(x115821))),f315(f315(f240(f902(x115821),f902(x115821)),x115822),f102(x115821))),f134(x115821,x115823)))),
% 168.60/168.46 inference(rename_variables,[],[4644])).
% 168.60/168.46 cnf(11588,plain,
% 168.60/168.46 (~P1(f315(f315(f317(f908(f902(x115881),f902(x115881))),f315(f315(f240(f902(x115881),f902(x115881)),x115882),f102(x115881))),f134(x115881,x115883)))),
% 168.60/168.46 inference(rename_variables,[],[4644])).
% 168.60/168.46 cnf(11591,plain,
% 168.60/168.46 (~P1(f315(f315(f317(x115911),x115912),f177(f909(x115911,a899))))),
% 168.60/168.46 inference(rename_variables,[],[4628])).
% 168.60/168.46 cnf(11593,plain,
% 168.60/168.46 (P1(f315(f315(f317(f908(x115931,x115932)),f315(f315(f240(x115931,x115932),f315(x115933,x115934)),f315(x115935,x115934))),f315(f298(f908(x115936,x115936),f908(x115931,x115932),f246(x115936,x115931,x115936,x115932,x115933,x115935)),f295(x115936,x115937))))),
% 168.60/168.46 inference(scs_inference,[],[3783,3674,4583,10413,10423,10436,10447,10519,10554,10557,10560,10662,10797,11110,11303,11306,11325,11328,4589,10646,10746,11213,3236,3286,3401,10482,10485,10581,10584,3378,3893,3276,3338,3272,3299,3281,3905,3496,11060,3371,4066,4597,10473,10643,4626,11239,11338,11574,3543,3335,10546,4208,4068,11259,11390,11449,4644,11162,11403,11512,11538,11582,4645,11292,11406,11515,4646,11409,4647,11467,4648,3356,3634,3799,3734,3948,3507,10565,10685,10763,10836,10839,10879,10979,11229,3886,3424,4621,10450,10453,10479,10606,10781,10987,11002,11120,4632,3873,3643,4016,3467,3469,3443,4618,4591,4201,11535,4624,10441,10444,10614,10709,10728,10735,10758,10766,10769,10786,10972,11216,4170,4077,11057,4124,3800,4158,3817,10609,10706,11262,11343,11422,4636,11005,11414,3440,10574,10672,10822,10886,10961,11008,11011,11042,11068,11104,11142,3441,10601,10657,10891,10982,3442,4617,10490,10522,11026,11071,3590,10751,10842,11115,11159,11393,11396,11475,4628,11035,11045,11151,11172,11175,11242,11245,11256,11359,11367,11381,11417,11434,11443,11483,11524,11529,11532,11551,11554,3500,10873,10903,10912,10915,10918,3532,3952,3891,10525,4625,10470,10861,10864,11362,3461,10906,11065,4249,4622,3960,4609,4612,3417,3421,4611,4610,4638,10772,4643,11248,11251,11437,11548,4034,3881,11178,11184,3730,11318,3883,10909,11281,11446,11480,3591,3697,10825,10828,10921,11091,4641,4642,10665,4304,4212,3914,4639,10495,10498,10867,3884,10831,4144,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928,5930,5935,5943,5981,5996,6005,6008,6017,6021,6022,6023,6024,6025,6030,6035,6045,6051,6069,6073,6082,6112,6128,6154,6171,6172,6175,6190,6192,6194,6196,6211,6212,6215,6217,6220,6221,6238,6246,6247,6248,6250,6252,6290,6291,6296,6299,6305,6309,6343,6345,6347,6349,6359,6361,6364,6370,6372,6377,6380,6388,6396,6398,6399,6406,6429,6430,6431,6432,6433,6435,6442,6447,6481,6482,6485,6486,6487,6489,6490,6491,6492,6499,6535,6536,6545,6567,6568,6592,6594,6606,6607,6613,6643,6645,6660,6700,6703,6704,6760,6783,6826,6841,6849,6858,6859,6860,6861,6882,6883,6890,6902,6905,6907,6909,6910,6911,6913,6927,6938,6939,6940,6953,7008,7019,7021,7026,7045,7046,7082,7089,7096,7126,7157,7213,7242,7299,7320,7329,7332,7392,7402,7465,7467,7481,7490,7491,7492,7509,7513,7515,7562,7572,7575,7590,7638,7640,7643,7687,7688,7706,7776,7794,7818,7842,7854,7868,7879,7890,7891,7917,7919,7921,7931,7969,7980,8005,8032,8065,8096,8130,8169,8186,8188,8204,8205,8273,8284,8349,8373,8392,8419,8458,8459,8476,8516,8518,8520,8526,8542,8546,8561,8582,8590,8592,8602,8607,8611,8612,8613,8614,8615,8616,8635,8650,8651,8669,8671,8675,8676,8677,8678,8679,8697,8698,8699,8709,8722,8725,8736,8741,8743,8745,8746,8747,8754,8760,8768,8771,8788,8789,8798,8799,8807,8826,8839,8843,8864,8886,8887,8890,8891,8897,8906,8907,8930,8941,8951,8952,8953,8956,8979,8980,8991,9041,9051,9053,9069,9081,9082,9083,9094,9158,9189,9190,9191,9206,9223,9231,9259,9260,9329,9364,9370,9380,9381,9382,9391,9421,9437,9441,9445,9467,9468,9495,9559,9564,9567,9604,9605,9606,9634,9635,9651,9672,9678,9690,9715,9736,9745,9746,9747,9748,9763,9765,9770,9800,9801,9807,9808,9852,9853,9864,9865,9889,9907,9909,9910,9918,9923,9930,9954,9988,9990,9994,10044,10078,10088,10090,10094,10095,10097,10106,10107,10127,10132,10225])).
% 168.60/168.46 cnf(11596,plain,
% 168.60/168.46 (~P1(f315(f315(f317(x115961),x115962),f177(f909(x115961,a899))))),
% 168.60/168.46 inference(rename_variables,[],[4628])).
% 168.60/168.46 cnf(11599,plain,
% 168.60/168.46 (~P1(f315(f315(f317(x115991),x115992),f177(f909(x115991,a899))))),
% 168.60/168.46 inference(rename_variables,[],[4628])).
% 168.60/168.46 cnf(11602,plain,
% 168.60/168.46 (~P1(f315(f315(f317(x116021),x116022),f177(f909(x116021,a899))))),
% 168.60/168.46 inference(rename_variables,[],[4628])).
% 168.60/168.46 cnf(11605,plain,
% 168.60/168.46 (~P1(f315(f315(f317(x116051),x116052),f177(f909(x116051,a899))))),
% 168.60/168.46 inference(rename_variables,[],[4628])).
% 168.60/168.46 cnf(11608,plain,
% 168.60/168.46 (P1(f315(f315(f317(x116081),f315(x116082,x116083)),f315(f298(x116084,x116081,x116082),f230(f909(x116084,a899)))))),
% 168.60/168.46 inference(rename_variables,[],[4034])).
% 168.60/168.46 cnf(11610,plain,
% 168.60/168.46 (~P1(f315(f315(f317(f908(x116101,x116102)),x116103),f315(f298(f908(x116104,x116104),f908(x116101,x116102),f246(x116104,x116101,x116104,x116102,x116105,x116106)),f142(x116104,f102(f909(x116104,a901))))))),
% 168.60/168.46 inference(scs_inference,[],[3783,3674,4583,10413,10423,10436,10447,10519,10554,10557,10560,10662,10797,11110,11303,11306,11325,11328,4589,10646,10746,11213,3236,3286,3401,10482,10485,10581,10584,3378,3893,3276,3338,3272,3299,3281,3905,3496,11060,3371,4066,4597,10473,10643,4626,11239,11338,11574,3543,3335,10546,4208,4068,11259,11390,11449,4644,11162,11403,11512,11538,11582,4645,11292,11406,11515,4646,11409,4647,11467,4648,3356,3634,3799,3734,3948,3507,10565,10685,10763,10836,10839,10879,10979,11229,3886,3424,4621,10450,10453,10479,10606,10781,10987,11002,11120,4632,3873,3643,4016,3467,3469,3443,4618,4591,4201,11535,4624,10441,10444,10614,10709,10728,10735,10758,10766,10769,10786,10972,11216,4170,4077,11057,4124,3800,4158,3817,10609,10706,11262,11343,11422,4636,11005,11414,3440,10574,10672,10822,10886,10961,11008,11011,11042,11068,11104,11142,3441,10601,10657,10891,10982,3442,4617,10490,10522,11026,11071,3590,10751,10842,11115,11159,11393,11396,11475,4628,11035,11045,11151,11172,11175,11242,11245,11256,11359,11367,11381,11417,11434,11443,11483,11524,11529,11532,11551,11554,11591,11596,11599,11602,3500,10873,10903,10912,10915,10918,3532,3952,3891,10525,4625,10470,10861,10864,11362,3461,10906,11065,4249,4622,3960,4609,4612,3417,3421,4611,4610,4638,10772,4643,11248,11251,11437,11548,11565,4034,3881,11178,11184,3730,11318,3883,10909,11281,11446,11480,3591,3697,10825,10828,10921,11091,4641,4642,10665,4304,4212,3914,4639,10495,10498,10867,3884,10831,4144,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928,5930,5935,5943,5981,5996,6005,6008,6017,6021,6022,6023,6024,6025,6030,6035,6045,6051,6069,6073,6082,6112,6128,6154,6171,6172,6175,6190,6192,6194,6196,6211,6212,6215,6217,6220,6221,6238,6246,6247,6248,6250,6252,6290,6291,6296,6299,6305,6309,6343,6345,6347,6349,6359,6361,6364,6370,6372,6377,6380,6388,6396,6398,6399,6406,6429,6430,6431,6432,6433,6435,6442,6447,6481,6482,6485,6486,6487,6489,6490,6491,6492,6499,6535,6536,6545,6567,6568,6592,6594,6606,6607,6613,6643,6645,6660,6700,6703,6704,6760,6783,6826,6841,6849,6858,6859,6860,6861,6882,6883,6890,6902,6905,6907,6909,6910,6911,6913,6927,6938,6939,6940,6953,7008,7019,7021,7026,7045,7046,7082,7089,7096,7126,7157,7213,7242,7299,7320,7329,7332,7392,7402,7465,7467,7481,7490,7491,7492,7509,7513,7515,7562,7572,7575,7590,7638,7640,7643,7687,7688,7706,7776,7794,7818,7842,7854,7868,7879,7890,7891,7917,7919,7921,7931,7969,7980,8005,8032,8065,8096,8130,8169,8186,8188,8204,8205,8273,8284,8349,8373,8392,8419,8458,8459,8476,8516,8518,8520,8526,8542,8546,8561,8582,8590,8592,8602,8607,8611,8612,8613,8614,8615,8616,8635,8650,8651,8669,8671,8675,8676,8677,8678,8679,8697,8698,8699,8709,8722,8725,8736,8741,8743,8745,8746,8747,8754,8760,8768,8771,8788,8789,8798,8799,8807,8826,8839,8843,8864,8886,8887,8890,8891,8897,8906,8907,8930,8941,8951,8952,8953,8956,8979,8980,8991,9041,9051,9053,9069,9081,9082,9083,9094,9158,9189,9190,9191,9206,9223,9231,9259,9260,9329,9364,9370,9380,9381,9382,9391,9421,9437,9441,9445,9467,9468,9495,9559,9564,9567,9604,9605,9606,9634,9635,9651,9672,9678,9690,9715,9736,9745,9746,9747,9748,9763,9765,9770,9800,9801,9807,9808,9852,9853,9864,9865,9889,9907,9909,9910,9918,9923,9930,9954,9988,9990,9994,10044,10078,10088,10090,10094,10095,10097,10106,10107,10127,10132,10225,10317,10318,10319,10320,10379,10397])).
% 168.60/168.46 cnf(11611,plain,
% 168.60/168.46 (~P1(f315(f315(f317(f908(x116111,x116111)),f315(f315(f240(x116111,x116111),x116112),x116113)),f142(x116111,f102(f909(x116111,a901)))))),
% 168.60/168.46 inference(rename_variables,[],[4643])).
% 168.60/168.46 cnf(11619,plain,
% 168.60/168.46 (E(f103(x116191,f102(x116191)),f102(x116191))),
% 168.60/168.46 inference(rename_variables,[],[3286])).
% 168.60/168.46 cnf(11622,plain,
% 168.60/168.46 (~E(f315(a101,x116221),x116221)),
% 168.60/168.46 inference(rename_variables,[],[4583])).
% 168.60/168.46 cnf(11629,plain,
% 168.60/168.46 (~E(f315(a101,x116291),x116291)),
% 168.60/168.46 inference(rename_variables,[],[4583])).
% 168.60/168.46 cnf(11634,plain,
% 168.60/168.46 (E(f315(f272(x116341,x116341),f251(x116341,x116342)),x116342)),
% 168.60/168.46 inference(rename_variables,[],[3401])).
% 168.60/168.46 cnf(11637,plain,
% 168.60/168.46 (E(f315(f272(x116371,x116371),f251(x116371,x116372)),x116372)),
% 168.60/168.46 inference(rename_variables,[],[3401])).
% 168.60/168.46 cnf(11643,plain,
% 168.60/168.46 (~E(f315(a101,x116431),x116431)),
% 168.60/168.46 inference(rename_variables,[],[4583])).
% 168.60/168.46 cnf(11648,plain,
% 168.60/168.46 (~E(f315(f315(f73(a1),x116481),x116481),a86)),
% 168.60/168.46 inference(rename_variables,[],[4594])).
% 168.60/168.46 cnf(11655,plain,
% 168.60/168.46 (E(f315(f315(f3(a901),f2(a901)),x116551),f2(a901))),
% 168.60/168.46 inference(rename_variables,[],[3357])).
% 168.60/168.46 cnf(11658,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),x116581),f2(a901)))),
% 168.60/168.46 inference(rename_variables,[],[4621])).
% 168.60/168.46 cnf(11665,plain,
% 168.60/168.46 (E(f315(f315(f73(a1),f315(f315(f74(a1),x116651),f315(f315(f29(a1),x116652),x116651))),f38(a1,x116652,x116651)),x116652)),
% 168.60/168.46 inference(rename_variables,[],[3984])).
% 168.60/168.46 cnf(11689,plain,
% 168.60/168.46 (~E(f315(a101,x116891),x116891)),
% 168.60/168.46 inference(rename_variables,[],[4583])).
% 168.60/168.46 cnf(11692,plain,
% 168.60/168.46 (~E(f315(a101,x116921),x116921)),
% 168.60/168.46 inference(rename_variables,[],[4583])).
% 168.60/168.46 cnf(11718,plain,
% 168.60/168.46 (~P1(f315(f315(f161(x117181),f102(x117181)),x117182))),
% 168.60/168.46 inference(rename_variables,[],[4624])).
% 168.60/168.46 cnf(11724,plain,
% 168.60/168.46 (P1(f315(f315(f224(a901),f2(a901)),f315(a101,x117241)))),
% 168.60/168.46 inference(rename_variables,[],[3519])).
% 168.60/168.46 cnf(11725,plain,
% 168.60/168.46 (~E(f315(a101,x117251),x117251)),
% 168.60/168.46 inference(rename_variables,[],[4583])).
% 168.60/168.46 cnf(11728,plain,
% 168.60/168.46 (P1(f315(f315(f317(x117281),x117282),f230(f909(x117281,a899))))),
% 168.60/168.46 inference(rename_variables,[],[3590])).
% 168.60/168.46 cnf(11740,plain,
% 168.60/168.46 (~E(f315(a101,x117401),x117401)),
% 168.60/168.46 inference(rename_variables,[],[4583])).
% 168.60/168.46 cnf(11743,plain,
% 168.60/168.46 (P1(f315(f315(f223(a1),x117431),x117431))),
% 168.60/168.46 inference(rename_variables,[],[3441])).
% 168.60/168.46 cnf(11750,plain,
% 168.60/168.46 (P1(f315(f59(x117501,x117502,x117503,x117504,f177(f909(x117501,a899))),x117504))),
% 168.60/168.46 inference(rename_variables,[],[4343])).
% 168.60/168.46 cnf(11751,plain,
% 168.60/168.46 (E(f315(f272(x117511,x117511),f251(x117511,x117512)),x117512)),
% 168.60/168.46 inference(rename_variables,[],[3401])).
% 168.60/168.46 cnf(11764,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),f315(f315(f73(a901),x117641),x117642)),x117642))),
% 168.60/168.46 inference(rename_variables,[],[4639])).
% 168.60/168.46 cnf(11767,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a1),f315(f89(a1),x117671)),f2(a1)))),
% 168.60/168.46 inference(rename_variables,[],[4632])).
% 168.60/168.46 cnf(11783,plain,
% 168.60/168.46 (~E(f315(f315(f90(a901),f315(a101,x117831)),x117831),f315(a101,x117831))),
% 168.60/168.46 inference(scs_inference,[],[3783,3674,4583,10413,10423,10436,10447,10519,10554,10557,10560,10662,10797,11110,11303,11306,11325,11328,11521,11622,11629,11643,11689,11692,11725,3361,4589,10646,10746,11213,3053,3059,3063,3064,3071,3075,3086,3091,3097,3115,3116,3123,3136,3137,3148,3181,3190,3191,3201,3222,3236,4581,3286,11619,3401,10482,10485,10581,10584,10900,11634,11637,3378,3893,3276,3984,11665,3338,3272,3299,3281,3905,3496,11060,3371,4066,4597,10473,10643,4626,11239,11338,11574,11577,3543,3335,10546,10876,3336,3254,3357,11655,4208,4068,11259,11390,11449,4644,11162,11403,11512,11538,11582,11588,4645,11292,11406,11515,4646,11409,4647,11467,4648,3356,3634,3799,4594,3734,3948,3507,10565,10685,10763,10836,10839,10879,10979,11229,3886,3424,3519,4621,10450,10453,10479,10606,10781,10987,11002,11120,11560,11658,4632,3873,3643,4016,3467,3469,3443,4618,4591,3627,4633,4201,11535,3757,4624,10441,10444,10614,10709,10728,10735,10758,10766,10769,10786,10972,11216,11429,4170,4077,11057,4124,3800,4158,3817,10609,10706,11262,11343,11422,4636,11005,11414,3440,10574,10672,10822,10886,10961,11008,11011,11042,11068,11104,11142,3441,10601,10657,10891,10982,11107,3442,4617,10490,10522,11026,11071,3590,10751,10842,11115,11159,11393,11396,11475,11557,4628,11035,11045,11151,11172,11175,11242,11245,11256,11359,11367,11381,11417,11434,11443,11483,11524,11529,11532,11551,11554,11591,11596,11599,11602,3500,10873,10903,10912,10915,10918,3532,3952,3891,10525,4625,10470,10861,10864,11362,11378,3461,10906,11065,4249,4622,3960,4609,4612,3417,3421,4611,4610,4343,4638,10772,10775,4643,11248,11251,11437,11548,11565,4034,3881,11178,11184,3730,11318,3883,10909,11281,11446,11480,3591,3697,10825,10828,10921,11091,4641,4642,10665,4304,4212,3914,4639,10495,10498,10867,10870,3884,10831,4144,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928,5930,5935,5943,5981,5996,6005,6008,6017,6021,6022,6023,6024,6025,6030,6035,6045,6051,6069,6073,6082,6112,6128,6154,6171,6172,6175,6190,6192,6194,6196,6211,6212,6215,6217,6220,6221,6238,6246,6247,6248,6250,6252,6290,6291,6296,6299,6305,6309,6343,6345,6347,6349,6359,6361,6364,6370,6372,6377,6380,6388,6396,6398,6399,6406,6429,6430,6431,6432,6433,6435,6442,6447,6481,6482,6485,6486,6487,6489,6490,6491,6492,6499,6535,6536,6545,6567,6568,6592,6594,6606,6607,6613,6643,6645,6660,6700,6703,6704,6760,6783,6826,6841,6849,6858,6859,6860,6861,6882,6883,6890,6902,6905,6907,6909,6910,6911,6913,6927,6938,6939,6940,6953,7008,7019,7021,7026,7045,7046,7082,7089,7096,7126,7157,7213,7242,7299,7320,7329,7332,7392,7402,7465,7467,7481,7490,7491,7492,7509,7513,7515,7562,7572,7575,7590,7638,7640,7643,7687,7688,7706,7776,7794,7818,7842,7854,7868,7879,7890,7891,7917,7919,7921,7931,7969,7980,8005,8032,8065,8096,8130,8169,8186,8188,8204,8205,8273,8284,8349,8373,8392,8419,8458,8459,8476,8516,8518,8520,8526,8542,8546,8561,8582,8590,8592,8602,8607,8611,8612,8613,8614,8615,8616,8635,8650,8651,8669,8671,8675,8676,8677,8678,8679,8697,8698,8699,8709,8722,8725,8736,8741,8743,8745,8746,8747,8754,8760,8768,8771,8788,8789,8798,8799,8807,8826,8839,8843,8864,8886,8887,8890,8891,8897,8906,8907,8930,8941,8951,8952,8953,8956,8979,8980,8991,9041,9051,9053,9069,9081,9082,9083,9094,9158,9189,9190,9191,9206,9223,9231,9259,9260,9329,9364,9370,9380,9381,9382,9391,9421,9437,9441,9445,9467,9468,9495,9559,9564,9567,9604,9605,9606,9634,9635,9651,9672,9678,9690,9715,9736,9745,9746,9747,9748,9763,9765,9770,9800,9801,9807,9808,9852,9853,9864,9865,9889,9907,9909,9910,9918,9923,9930,9954,9988,9990,9994,10044,10078,10088,10090,10094,10095,10097,10106,10107,10127,10132,10225,10317,10318,10319,10320,10379,10397,2,8,9,4668,4669,4687,4729,4731,4732,4755,4757,4758,4768,4813,4815,4863,4993,4994,5011,5035,5092,5093,5099,5100,5102,5104,5113,5116,5117,5125,5138,5139,5145,5166,5167,5185,5190,5191,5192,5193,5197,5205,5208,5215,5270,5275,5276,5281,5288,5319,5329,5334,5344,5362,5364,5371,5372,5374,5385,5403,5405,5406,5413,5420,5421,5433,5434,5435,5436,5438,5439,5444,5445])).
% 168.60/168.46 cnf(11790,plain,
% 168.60/168.46 (E(f315(f272(x117901,x117901),f251(x117901,x117902)),x117902)),
% 168.60/168.46 inference(rename_variables,[],[3401])).
% 168.60/168.46 cnf(11795,plain,
% 168.60/168.46 (E(f315(f272(x117951,x117951),f251(x117951,x117952)),x117952)),
% 168.60/168.46 inference(rename_variables,[],[3401])).
% 168.60/168.46 cnf(11798,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a1),f315(f89(a1),x117981)),f2(a1)))),
% 168.60/168.46 inference(rename_variables,[],[4632])).
% 168.60/168.46 cnf(11803,plain,
% 168.60/168.46 (~E(f315(a101,x118031),x118031)),
% 168.60/168.46 inference(rename_variables,[],[4583])).
% 168.60/168.46 cnf(11812,plain,
% 168.60/168.46 (~P1(f315(f315(f161(x118121),f102(x118121)),x118122))),
% 168.60/168.46 inference(rename_variables,[],[4624])).
% 168.60/168.46 cnf(11835,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a1),f315(f89(a1),x118351)),f2(a1)))),
% 168.60/168.46 inference(rename_variables,[],[4632])).
% 168.60/168.46 cnf(11838,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),x118381),f2(a901)))),
% 168.60/168.46 inference(rename_variables,[],[4621])).
% 168.60/168.46 cnf(11839,plain,
% 168.60/168.46 (P1(f315(f315(f224(a901),x118391),f315(a101,x118391)))),
% 168.60/168.46 inference(rename_variables,[],[3507])).
% 168.60/168.46 cnf(11842,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a1),f315(f89(a1),x118421)),f2(a1)))),
% 168.60/168.46 inference(rename_variables,[],[4632])).
% 168.60/168.46 cnf(11845,plain,
% 168.60/168.46 (~P1(f315(f315(f317(x118451),x118452),f177(f909(x118451,a899))))),
% 168.60/168.46 inference(rename_variables,[],[4628])).
% 168.60/168.46 cnf(11846,plain,
% 168.60/168.46 (P1(f315(f315(f317(f909(x118461,a899)),x118462),f315(f296(x118461),x118462)))),
% 168.60/168.46 inference(rename_variables,[],[3800])).
% 168.60/168.46 cnf(11861,plain,
% 168.60/168.46 (~P1(f315(f315(f223(a901),f315(a101,x118611)),x118611))),
% 168.60/168.46 inference(rename_variables,[],[4625])).
% 168.60/168.46 cnf(11862,plain,
% 168.60/168.46 (~E(f315(a101,x118621),x118621)),
% 168.60/168.46 inference(rename_variables,[],[4583])).
% 168.60/168.46 cnf(11865,plain,
% 168.60/168.46 (E(f315(f272(x118651,x118651),f251(x118651,x118652)),x118652)),
% 168.60/168.46 inference(rename_variables,[],[3401])).
% 168.60/168.46 cnf(11875,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),f315(f315(f73(a901),x118751),x118752)),x118751))),
% 168.60/168.46 inference(rename_variables,[],[4640])).
% 168.60/168.46 cnf(11878,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a1),f315(f89(a1),x118781)),f2(a1)))),
% 168.60/168.46 inference(rename_variables,[],[4632])).
% 168.60/168.46 cnf(11881,plain,
% 168.60/168.46 (~E(f315(a101,x118811),x118811)),
% 168.60/168.46 inference(rename_variables,[],[4583])).
% 168.60/168.46 cnf(11894,plain,
% 168.60/168.46 (P1(f315(f315(f317(x118941),x118942),f315(f315(f297(x118941),x118942),x118943)))),
% 168.60/168.46 inference(rename_variables,[],[3747])).
% 168.60/168.46 cnf(11895,plain,
% 168.60/168.46 (~P1(f315(f315(f223(a1),f2(a1)),f315(f72(a1),f315(f89(a1),f315(a101,x118951)))))),
% 168.60/168.46 inference(rename_variables,[],[4641])).
% 168.60/168.46 cnf(11898,plain,
% 168.60/168.46 (P1(f315(f315(f224(a901),f315(f315(f3(a901),x118981),x118982)),f315(a101,x118981)))),
% 168.60/168.46 inference(rename_variables,[],[3886])).
% 168.60/168.46 cnf(11901,plain,
% 168.60/168.46 (P1(f315(f315(f223(a901),f38(a901,x119011,x119012)),x119011))),
% 168.60/168.46 inference(rename_variables,[],[3891])).
% 168.60/168.46 cnf(11907,plain,
% 168.60/168.46 (E(f315(f272(x119071,x119071),f251(x119071,x119072)),x119072)),
% 168.60/168.46 inference(rename_variables,[],[3401])).
% 168.60/168.46 cnf(11912,plain,
% 168.60/168.46 (E(f315(f315(f123(x119121),f158(x119121,x119122,x119123)),f158(x119121,x119124,x119123)),f315(f315(f123(x119121),f158(x119121,x119124,x119123)),f158(x119121,x119122,x119123)))),
% 168.60/168.46 inference(rename_variables,[],[3998])).
% 168.60/168.46 cnf(11917,plain,
% 168.60/168.46 (~P1(f315(f315(f223(a901),f315(a101,x119171)),x119171))),
% 168.60/168.46 inference(rename_variables,[],[4625])).
% 168.60/168.46 cnf(11926,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),x119261),x119261))),
% 168.60/168.46 inference(rename_variables,[],[4617])).
% 168.60/168.46 cnf(11929,plain,
% 168.60/168.46 (P1(f315(f315(f223(a901),f38(a901,x119291,x119292)),x119291))),
% 168.60/168.46 inference(rename_variables,[],[3891])).
% 168.60/168.46 cnf(11930,plain,
% 168.60/168.46 (P1(f315(f315(f223(a901),f2(a901)),x119301))),
% 168.60/168.46 inference(rename_variables,[],[3461])).
% 168.60/168.46 cnf(11947,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),x119471),x119471))),
% 168.60/168.46 inference(rename_variables,[],[4617])).
% 168.60/168.46 cnf(11950,plain,
% 168.60/168.46 (P1(f315(f315(f317(x119501),f315(x119502,x119503)),f315(f298(x119504,x119501,x119502),f230(f909(x119504,a899)))))),
% 168.60/168.46 inference(rename_variables,[],[4034])).
% 168.60/168.46 cnf(11951,plain,
% 168.60/168.46 (~P1(f315(f315(f223(a901),f315(a101,x119511)),x119511))),
% 168.60/168.46 inference(rename_variables,[],[4625])).
% 168.60/168.46 cnf(11954,plain,
% 168.60/168.46 (P1(f315(f315(f317(x119541),f315(x119542,x119543)),f315(f298(x119544,x119541,x119542),f230(f909(x119544,a899)))))),
% 168.60/168.46 inference(rename_variables,[],[4034])).
% 168.60/168.46 cnf(11955,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),f315(f315(f73(a901),x119551),x119552)),x119552))),
% 168.60/168.46 inference(rename_variables,[],[4639])).
% 168.60/168.46 cnf(11960,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),f315(f315(f73(a901),x119601),x119602)),x119601))),
% 168.60/168.46 inference(rename_variables,[],[4640])).
% 168.60/168.46 cnf(11963,plain,
% 168.60/168.46 (~P1(f315(f315(f161(x119631),f102(x119631)),x119632))),
% 168.60/168.46 inference(rename_variables,[],[4624])).
% 168.60/168.46 cnf(11966,plain,
% 168.60/168.46 (P1(f315(f315(f223(a901),x119661),x119661))),
% 168.60/168.46 inference(rename_variables,[],[3440])).
% 168.60/168.46 cnf(11974,plain,
% 168.60/168.46 (~P37(x119741,x119742,f102(x119741))),
% 168.60/168.46 inference(rename_variables,[],[4604])).
% 168.60/168.46 cnf(11977,plain,
% 168.60/168.46 (P1(f315(f315(f317(x119771),x119772),f230(f909(x119771,a899))))),
% 168.60/168.46 inference(rename_variables,[],[3590])).
% 168.60/168.46 cnf(11978,plain,
% 168.60/168.46 (~P1(f315(f315(f223(a901),f315(a101,x119781)),x119781))),
% 168.60/168.46 inference(rename_variables,[],[4625])).
% 168.60/168.46 cnf(11991,plain,
% 168.60/168.46 (~P1(f315(f315(f317(x119911),x119912),f177(f909(x119911,a899))))),
% 168.60/168.46 inference(rename_variables,[],[4628])).
% 168.60/168.46 cnf(11994,plain,
% 168.60/168.46 (E(f315(f315(f18(x119941,x119942),x119943),x119944),x119943)),
% 168.60/168.46 inference(rename_variables,[],[3431])).
% 168.60/168.46 cnf(11997,plain,
% 168.60/168.46 (E(f315(f315(f18(x119971,x119972),x119973),x119974),x119973)),
% 168.60/168.46 inference(rename_variables,[],[3431])).
% 168.60/168.46 cnf(12009,plain,
% 168.60/168.46 (P1(f315(f315(f224(a901),f2(a901)),f315(a101,x120091)))),
% 168.60/168.46 inference(rename_variables,[],[3519])).
% 168.60/168.46 cnf(12012,plain,
% 168.60/168.46 (P1(f315(f315(f223(a901),x120121),x120121))),
% 168.60/168.46 inference(rename_variables,[],[3440])).
% 168.60/168.46 cnf(12015,plain,
% 168.60/168.46 (P1(f315(f54(x120151),f315(f161(x120151),x120152)))),
% 168.60/168.46 inference(rename_variables,[],[3479])).
% 168.60/168.46 cnf(12018,plain,
% 168.60/168.46 (P1(f315(f54(x120181),f315(f161(x120181),x120182)))),
% 168.60/168.46 inference(rename_variables,[],[3479])).
% 168.60/168.46 cnf(12021,plain,
% 168.60/168.46 (P1(f315(f315(f223(a1),f315(f72(a1),f315(f89(a1),x120211))),f315(f89(a1),x120212)))),
% 168.60/168.46 inference(rename_variables,[],[3915])).
% 168.60/168.46 cnf(12024,plain,
% 168.60/168.46 (~P1(f315(f315(f317(x120241),x120242),f177(f909(x120241,a899))))),
% 168.60/168.46 inference(rename_variables,[],[4628])).
% 168.60/168.46 cnf(12040,plain,
% 168.60/168.46 (~P1(f315(f315(f317(a901),f2(a901)),f315(f292(a901),x120401)))),
% 168.60/168.46 inference(scs_inference,[],[3783,3674,4603,4604,4583,10413,10423,10436,10447,10519,10554,10557,10560,10662,10797,11110,11303,11306,11325,11328,11521,11622,11629,11643,11689,11692,11725,11740,11803,11862,3361,4589,10646,10746,11213,3052,3053,3056,3059,3060,3063,3064,3071,3075,3076,3086,3087,3091,3097,3115,3116,3123,3136,3137,3148,3180,3181,3190,3191,3193,3201,3202,3222,3236,4581,3998,11912,3286,11619,3401,10482,10485,10581,10584,10900,11634,11637,11751,11790,11795,11865,3378,3893,3276,3636,3984,11665,3338,3272,3299,3295,3281,3282,3905,3496,11060,3371,4066,4597,10473,10643,3431,11994,4626,11239,11338,11574,11577,3543,3335,10546,10876,3336,3595,3254,3357,11655,4208,4068,11259,11390,11449,4644,11162,11403,11512,11538,11582,11588,4645,11292,11406,11515,4646,11409,4647,11467,4648,3356,3634,3799,4479,4480,4594,3734,3948,3507,10565,10685,10763,10836,10839,10879,10979,11229,11839,3886,11898,3424,3519,11724,4621,10450,10453,10479,10606,10781,10987,11002,11120,11560,11658,11838,4632,11767,11798,11835,11842,3873,3643,4016,3467,3469,3443,4618,4591,3627,4633,4201,11535,3757,3479,12015,4624,10441,10444,10614,10709,10728,10735,10758,10766,10769,10786,10972,11216,11429,11718,11812,4170,4077,11057,4124,3800,4158,3817,10609,10706,11262,11343,11422,4636,11005,11414,3440,10574,10672,10822,10886,10961,11008,11011,11042,11068,11104,11142,11181,11966,3441,10601,10657,10891,10982,11107,3442,3515,4617,10490,10522,11026,11071,11080,11926,3590,10751,10842,11115,11159,11393,11396,11475,11557,11728,4628,11035,11045,11151,11172,11175,11242,11245,11256,11359,11367,11381,11417,11434,11443,11483,11524,11529,11532,11551,11554,11591,11596,11599,11602,11605,11845,11991,3500,10873,10903,10912,10915,10918,3539,3532,3952,3891,10525,11901,4625,10470,10861,10864,11362,11378,11861,11917,11951,11978,3461,10906,11065,11135,3915,4249,4622,3960,4609,4612,3417,3421,4611,4610,3747,4343,4638,10772,10775,4643,11248,11251,11437,11548,11565,4034,11608,11950,3881,11178,11184,3730,11318,3883,10909,11281,11446,11480,3591,3697,10825,10828,10921,11091,4641,11895,4642,10665,4304,4212,3914,3859,4639,10495,10498,10867,10870,11764,4640,11875,3884,10831,4144,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928,5930,5935,5943,5981,5996,6005,6008,6017,6021,6022,6023,6024,6025,6030,6035,6045,6051,6069,6073,6082,6112,6128,6154,6171,6172,6175,6190,6192,6194,6196,6211,6212,6215,6217,6220,6221,6238,6246,6247,6248,6250,6252,6290,6291,6296,6299,6305,6309,6343,6345,6347,6349,6359,6361,6364,6370,6372,6377,6380,6388,6396,6398,6399,6406,6429,6430,6431,6432,6433,6435,6442,6447,6481,6482,6485,6486,6487,6489,6490,6491,6492,6499,6535,6536,6545,6567,6568,6592,6594,6606,6607,6613,6643,6645,6660,6700,6703,6704,6760,6783,6826,6841,6849,6858,6859,6860,6861,6882,6883,6890,6902,6905,6907,6909,6910,6911,6913,6927,6938,6939,6940,6953,7008,7019,7021,7026,7045,7046,7082,7089,7096,7126,7157,7213,7242,7299,7320,7329,7332,7392,7402,7465,7467,7481,7490,7491,7492,7509,7513,7515,7562,7572,7575,7590,7638,7640,7643,7687,7688,7706,7776,7794,7818,7842,7854,7868,7879,7890,7891,7917,7919,7921,7931,7969,7980,8005,8032,8065,8096,8130,8169,8186,8188,8204,8205,8273,8284,8349,8373,8392,8419,8458,8459,8476,8516,8518,8520,8526,8542,8546,8561,8582,8590,8592,8602,8607,8611,8612,8613,8614,8615,8616,8635,8650,8651,8669,8671,8675,8676,8677,8678,8679,8697,8698,8699,8709,8722,8725,8736,8741,8743,8745,8746,8747,8754,8760,8768,8771,8788,8789,8798,8799,8807,8826,8839,8843,8864,8886,8887,8890,8891,8897,8906,8907,8930,8941,8951,8952,8953,8956,8979,8980,8991,9041,9051,9053,9069,9081,9082,9083,9094,9158,9189,9190,9191,9206,9223,9231,9259,9260,9329,9364,9370,9380,9381,9382,9391,9421,9437,9441,9445,9467,9468,9495,9559,9564,9567,9604,9605,9606,9634,9635,9651,9672,9678,9690,9715,9736,9745,9746,9747,9748,9763,9765,9770,9800,9801,9807,9808,9852,9853,9864,9865,9889,9907,9909,9910,9918,9923,9930,9954,9988,9990,9994,10044,10078,10088,10090,10094,10095,10097,10106,10107,10127,10132,10225,10317,10318,10319,10320,10379,10397,2,8,9,4668,4669,4687,4729,4731,4732,4755,4757,4758,4768,4813,4815,4863,4993,4994,5011,5035,5092,5093,5099,5100,5102,5104,5113,5116,5117,5125,5138,5139,5145,5166,5167,5185,5190,5191,5192,5193,5197,5205,5208,5215,5270,5275,5276,5281,5288,5319,5329,5334,5344,5362,5364,5371,5372,5374,5385,5403,5405,5406,5413,5420,5421,5433,5434,5435,5436,5438,5439,5444,5445,5446,5447,5478,5479,5480,5488,5489,5490,5491,5535,5540,5542,5578,5580,5581,5583,5584,5586,5587,5589,5598,5603,5605,5606,5607,5609,5611,5612,5613,5614,5615,5616,5625,5626,5636,5639,5650,5666,5667,5670,5681,5684,5685,5686,5713,5723,5738,5739,5748,5749,5751,5753,5758,5793,5798,5800,5859,5894,5895,5909,5915,5918,5919,5920,5921,5940,5944,5945,5954,5976,6009,6028,6029,6033,6034,6036,6059,6063,6066,6067,6068,6084,6096,6097,6130,6131,6135,6156,6159,6162,6184,6185,6213,6216,6225,6234,6236,6245,6249,6257,6258,6259])).
% 168.60/168.46 cnf(12042,plain,
% 168.60/168.46 (~P1(f315(f315(f317(a901),x120421),f315(f270(a901),f2(a901))))),
% 168.60/168.46 inference(scs_inference,[],[3783,3674,4603,4604,4583,10413,10423,10436,10447,10519,10554,10557,10560,10662,10797,11110,11303,11306,11325,11328,11521,11622,11629,11643,11689,11692,11725,11740,11803,11862,3361,4589,10646,10746,11213,3052,3053,3056,3059,3060,3063,3064,3071,3075,3076,3086,3087,3091,3097,3115,3116,3123,3136,3137,3148,3180,3181,3190,3191,3193,3201,3202,3222,3236,4581,3998,11912,3286,11619,3401,10482,10485,10581,10584,10900,11634,11637,11751,11790,11795,11865,3378,3893,3276,3636,3984,11665,3338,3272,3299,3295,3281,3282,3905,3496,11060,3371,4066,4597,10473,10643,3431,11994,4626,11239,11338,11574,11577,3543,3335,10546,10876,3336,3595,3254,3357,11655,4208,4068,11259,11390,11449,4644,11162,11403,11512,11538,11582,11588,4645,11292,11406,11515,4646,11409,4647,11467,4648,3356,3634,3799,4479,4480,4594,3734,3948,3507,10565,10685,10763,10836,10839,10879,10979,11229,11839,3886,11898,3424,3519,11724,4621,10450,10453,10479,10606,10781,10987,11002,11120,11560,11658,11838,4632,11767,11798,11835,11842,3873,3643,4016,3467,3469,3443,4618,4591,3627,4633,4201,11535,3757,3479,12015,4624,10441,10444,10614,10709,10728,10735,10758,10766,10769,10786,10972,11216,11429,11718,11812,4170,4077,11057,4124,3800,4158,3817,10609,10706,11262,11343,11422,4636,11005,11414,3440,10574,10672,10822,10886,10961,11008,11011,11042,11068,11104,11142,11181,11966,3441,10601,10657,10891,10982,11107,3442,3515,4617,10490,10522,11026,11071,11080,11926,3590,10751,10842,11115,11159,11393,11396,11475,11557,11728,4628,11035,11045,11151,11172,11175,11242,11245,11256,11359,11367,11381,11417,11434,11443,11483,11524,11529,11532,11551,11554,11591,11596,11599,11602,11605,11845,11991,3500,10873,10903,10912,10915,10918,3539,3532,3952,3891,10525,11901,4625,10470,10861,10864,11362,11378,11861,11917,11951,11978,3461,10906,11065,11135,3915,4249,4622,3960,4609,4612,3417,3421,4611,4610,3747,4343,4638,10772,10775,4643,11248,11251,11437,11548,11565,4034,11608,11950,3881,11178,11184,3730,11318,3883,10909,11281,11446,11480,3591,3697,10825,10828,10921,11091,4641,11895,4642,10665,4304,4212,3914,3859,4639,10495,10498,10867,10870,11764,4640,11875,3884,10831,4144,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928,5930,5935,5943,5981,5996,6005,6008,6017,6021,6022,6023,6024,6025,6030,6035,6045,6051,6069,6073,6082,6112,6128,6154,6171,6172,6175,6190,6192,6194,6196,6211,6212,6215,6217,6220,6221,6238,6246,6247,6248,6250,6252,6290,6291,6296,6299,6305,6309,6343,6345,6347,6349,6359,6361,6364,6370,6372,6377,6380,6388,6396,6398,6399,6406,6429,6430,6431,6432,6433,6435,6442,6447,6481,6482,6485,6486,6487,6489,6490,6491,6492,6499,6535,6536,6545,6567,6568,6592,6594,6606,6607,6613,6643,6645,6660,6700,6703,6704,6760,6783,6826,6841,6849,6858,6859,6860,6861,6882,6883,6890,6902,6905,6907,6909,6910,6911,6913,6927,6938,6939,6940,6953,7008,7019,7021,7026,7045,7046,7082,7089,7096,7126,7157,7213,7242,7299,7320,7329,7332,7392,7402,7465,7467,7481,7490,7491,7492,7509,7513,7515,7562,7572,7575,7590,7638,7640,7643,7687,7688,7706,7776,7794,7818,7842,7854,7868,7879,7890,7891,7917,7919,7921,7931,7969,7980,8005,8032,8065,8096,8130,8169,8186,8188,8204,8205,8273,8284,8349,8373,8392,8419,8458,8459,8476,8516,8518,8520,8526,8542,8546,8561,8582,8590,8592,8602,8607,8611,8612,8613,8614,8615,8616,8635,8650,8651,8669,8671,8675,8676,8677,8678,8679,8697,8698,8699,8709,8722,8725,8736,8741,8743,8745,8746,8747,8754,8760,8768,8771,8788,8789,8798,8799,8807,8826,8839,8843,8864,8886,8887,8890,8891,8897,8906,8907,8930,8941,8951,8952,8953,8956,8979,8980,8991,9041,9051,9053,9069,9081,9082,9083,9094,9158,9189,9190,9191,9206,9223,9231,9259,9260,9329,9364,9370,9380,9381,9382,9391,9421,9437,9441,9445,9467,9468,9495,9559,9564,9567,9604,9605,9606,9634,9635,9651,9672,9678,9690,9715,9736,9745,9746,9747,9748,9763,9765,9770,9800,9801,9807,9808,9852,9853,9864,9865,9889,9907,9909,9910,9918,9923,9930,9954,9988,9990,9994,10044,10078,10088,10090,10094,10095,10097,10106,10107,10127,10132,10225,10317,10318,10319,10320,10379,10397,2,8,9,4668,4669,4687,4729,4731,4732,4755,4757,4758,4768,4813,4815,4863,4993,4994,5011,5035,5092,5093,5099,5100,5102,5104,5113,5116,5117,5125,5138,5139,5145,5166,5167,5185,5190,5191,5192,5193,5197,5205,5208,5215,5270,5275,5276,5281,5288,5319,5329,5334,5344,5362,5364,5371,5372,5374,5385,5403,5405,5406,5413,5420,5421,5433,5434,5435,5436,5438,5439,5444,5445,5446,5447,5478,5479,5480,5488,5489,5490,5491,5535,5540,5542,5578,5580,5581,5583,5584,5586,5587,5589,5598,5603,5605,5606,5607,5609,5611,5612,5613,5614,5615,5616,5625,5626,5636,5639,5650,5666,5667,5670,5681,5684,5685,5686,5713,5723,5738,5739,5748,5749,5751,5753,5758,5793,5798,5800,5859,5894,5895,5909,5915,5918,5919,5920,5921,5940,5944,5945,5954,5976,6009,6028,6029,6033,6034,6036,6059,6063,6066,6067,6068,6084,6096,6097,6130,6131,6135,6156,6159,6162,6184,6185,6213,6216,6225,6234,6236,6245,6249,6257,6258,6259,6260])).
% 168.60/168.46 cnf(12045,plain,
% 168.60/168.46 (P1(f315(f315(f223(a1),x120451),x120451))),
% 168.60/168.46 inference(rename_variables,[],[3441])).
% 168.60/168.46 cnf(12048,plain,
% 168.60/168.46 (P1(f315(f315(f223(a1),x120481),x120481))),
% 168.60/168.46 inference(rename_variables,[],[3441])).
% 168.60/168.46 cnf(12059,plain,
% 168.60/168.46 (P1(f315(f315(f223(a1),x120591),x120591))),
% 168.60/168.46 inference(rename_variables,[],[3441])).
% 168.60/168.46 cnf(12062,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),x120621),f2(a901)))),
% 168.60/168.46 inference(rename_variables,[],[4621])).
% 168.60/168.46 cnf(12067,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),x120671),f2(a901)))),
% 168.60/168.46 inference(rename_variables,[],[4621])).
% 168.60/168.46 cnf(12076,plain,
% 168.60/168.46 (P1(f315(f315(f223(a901),f2(a901)),x120761))),
% 168.60/168.46 inference(rename_variables,[],[3461])).
% 168.60/168.46 cnf(12077,plain,
% 168.60/168.46 (~P1(f315(f315(f223(a901),f315(a101,x120771)),x120771))),
% 168.60/168.46 inference(rename_variables,[],[4625])).
% 168.60/168.46 cnf(12080,plain,
% 168.60/168.46 (~P1(f315(f315(f161(x120801),f102(x120801)),x120802))),
% 168.60/168.46 inference(rename_variables,[],[4624])).
% 168.60/168.46 cnf(12083,plain,
% 168.60/168.46 (~P1(f315(f315(f161(x120831),f102(x120831)),x120832))),
% 168.60/168.46 inference(rename_variables,[],[4624])).
% 168.60/168.46 cnf(12090,plain,
% 168.60/168.46 (P1(f315(f315(f224(a901),x120901),f315(a101,f315(f315(f73(a901),x120902),x120901))))),
% 168.60/168.46 inference(rename_variables,[],[3884])).
% 168.60/168.46 cnf(12091,plain,
% 168.60/168.46 (P1(f315(f315(f224(a901),x120911),f315(a101,x120911)))),
% 168.60/168.46 inference(rename_variables,[],[3507])).
% 168.60/168.46 cnf(12103,plain,
% 168.60/168.46 (P1(f315(f315(f224(a1),f315(f72(a1),f71(a1))),f2(a1)))),
% 168.60/168.46 inference(scs_inference,[],[3783,3674,4603,4604,4583,10413,10423,10436,10447,10519,10554,10557,10560,10662,10797,11110,11303,11306,11325,11328,11521,11622,11629,11643,11689,11692,11725,11740,11803,11862,3361,4589,10646,10746,11213,3052,3053,3056,3059,3060,3063,3064,3071,3075,3076,3077,3086,3087,3091,3097,3115,3116,3123,3130,3136,3137,3148,3180,3181,3186,3190,3191,3193,3201,3202,3222,3236,4581,3998,11912,3286,11619,3401,10482,10485,10581,10584,10900,11634,11637,11751,11790,11795,11865,3378,3893,3276,3636,3984,11665,3338,3272,3299,3295,3281,3282,3905,3496,11060,3371,4066,4597,10473,10643,3431,11994,4626,11239,11338,11574,11577,3543,3335,10546,10876,3336,3595,3254,3357,11655,4208,4068,11259,11390,11449,4644,11162,11403,11512,11538,11582,11588,4645,11292,11406,11515,4646,11409,4647,11467,4648,3356,3634,3799,4479,4480,4594,3734,3948,3507,10565,10685,10763,10836,10839,10879,10979,11229,11839,3886,11898,3424,3519,11724,4621,10450,10453,10479,10606,10781,10987,11002,11120,11560,11658,11838,12062,12067,4632,11767,11798,11835,11842,11878,3873,3643,4016,3467,3469,3443,4618,4591,3627,4633,4201,11535,3757,3479,12015,4624,10441,10444,10614,10709,10728,10735,10758,10766,10769,10786,10972,11216,11429,11718,11812,11963,12080,4170,4077,11057,4124,3800,4158,3817,10609,10706,11262,11343,11422,4636,11005,11414,3440,10574,10672,10822,10886,10961,11008,11011,11042,11068,11104,11142,11181,11966,3441,10601,10657,10891,10982,11107,11743,12045,12048,3442,3515,4617,10490,10522,11026,11071,11080,11926,3590,10751,10842,11115,11159,11393,11396,11475,11557,11728,4628,11035,11045,11151,11172,11175,11242,11245,11256,11359,11367,11381,11417,11434,11443,11483,11524,11529,11532,11551,11554,11591,11596,11599,11602,11605,11845,11991,3500,10873,10903,10912,10915,10918,3539,3532,3952,3891,10525,11901,11929,4625,10470,10861,10864,11362,11378,11861,11917,11951,11978,3461,10906,11065,11135,11930,3915,4249,4622,3960,4609,4612,3417,3421,4611,4610,3747,4343,4638,10772,10775,4643,11248,11251,11437,11548,11565,4034,11608,11950,3881,11178,11184,3730,11318,3883,10909,11281,11446,11480,3591,3697,10825,10828,10921,11091,4641,11895,4642,10665,4304,4212,3914,3859,4639,10495,10498,10867,10870,11764,4640,11875,3884,10831,11097,4144,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928,5930,5935,5943,5981,5996,6005,6008,6017,6021,6022,6023,6024,6025,6030,6035,6045,6051,6069,6073,6082,6112,6128,6154,6171,6172,6175,6190,6192,6194,6196,6211,6212,6215,6217,6220,6221,6238,6246,6247,6248,6250,6252,6290,6291,6296,6299,6305,6309,6343,6345,6347,6349,6359,6361,6364,6370,6372,6377,6380,6388,6396,6398,6399,6406,6429,6430,6431,6432,6433,6435,6442,6447,6481,6482,6485,6486,6487,6489,6490,6491,6492,6499,6535,6536,6545,6567,6568,6592,6594,6606,6607,6613,6643,6645,6660,6700,6703,6704,6760,6783,6826,6841,6849,6858,6859,6860,6861,6882,6883,6890,6902,6905,6907,6909,6910,6911,6913,6927,6938,6939,6940,6953,7008,7019,7021,7026,7045,7046,7082,7089,7096,7126,7157,7213,7242,7299,7320,7329,7332,7392,7402,7465,7467,7481,7490,7491,7492,7509,7513,7515,7562,7572,7575,7590,7638,7640,7643,7687,7688,7706,7776,7794,7818,7842,7854,7868,7879,7890,7891,7917,7919,7921,7931,7969,7980,8005,8032,8065,8096,8130,8169,8186,8188,8204,8205,8273,8284,8349,8373,8392,8419,8458,8459,8476,8516,8518,8520,8526,8542,8546,8561,8582,8590,8592,8602,8607,8611,8612,8613,8614,8615,8616,8635,8650,8651,8669,8671,8675,8676,8677,8678,8679,8697,8698,8699,8709,8722,8725,8736,8741,8743,8745,8746,8747,8754,8760,8768,8771,8788,8789,8798,8799,8807,8826,8839,8843,8864,8886,8887,8890,8891,8897,8906,8907,8930,8941,8951,8952,8953,8956,8979,8980,8991,9041,9051,9053,9069,9081,9082,9083,9094,9158,9189,9190,9191,9206,9223,9231,9259,9260,9329,9364,9370,9380,9381,9382,9391,9421,9437,9441,9445,9467,9468,9495,9559,9564,9567,9604,9605,9606,9634,9635,9651,9672,9678,9690,9715,9736,9745,9746,9747,9748,9763,9765,9770,9800,9801,9807,9808,9852,9853,9864,9865,9889,9907,9909,9910,9918,9923,9930,9954,9988,9990,9994,10044,10078,10088,10090,10094,10095,10097,10106,10107,10127,10132,10225,10317,10318,10319,10320,10379,10397,2,8,9,4668,4669,4687,4729,4731,4732,4755,4757,4758,4768,4813,4815,4863,4993,4994,5011,5035,5092,5093,5099,5100,5102,5104,5113,5116,5117,5125,5138,5139,5145,5166,5167,5185,5190,5191,5192,5193,5197,5205,5208,5215,5270,5275,5276,5281,5288,5319,5329,5334,5344,5362,5364,5371,5372,5374,5385,5403,5405,5406,5413,5420,5421,5433,5434,5435,5436,5438,5439,5444,5445,5446,5447,5478,5479,5480,5488,5489,5490,5491,5535,5540,5542,5578,5580,5581,5583,5584,5586,5587,5589,5598,5603,5605,5606,5607,5609,5611,5612,5613,5614,5615,5616,5625,5626,5636,5639,5650,5666,5667,5670,5681,5684,5685,5686,5713,5723,5738,5739,5748,5749,5751,5753,5758,5793,5798,5800,5859,5894,5895,5909,5915,5918,5919,5920,5921,5940,5944,5945,5954,5976,6009,6028,6029,6033,6034,6036,6059,6063,6066,6067,6068,6084,6096,6097,6130,6131,6135,6156,6159,6162,6184,6185,6213,6216,6225,6234,6236,6245,6249,6257,6258,6259,6260,6293,6310,6363,6400,6402,6403,6426,6427,6434,6438,6439,6443,6457,6473,6494,6495,6500,6512,6515,6528,6548,6555,6557,6572,6573])).
% 168.60/168.46 cnf(12106,plain,
% 168.60/168.46 (~P1(f315(f315(f223(a901),f315(a101,x121061)),x121061))),
% 168.60/168.46 inference(rename_variables,[],[4625])).
% 168.60/168.46 cnf(12109,plain,
% 168.60/168.46 (~P1(f315(f315(f223(a901),f315(a101,x121091)),x121091))),
% 168.60/168.46 inference(rename_variables,[],[4625])).
% 168.60/168.46 cnf(12112,plain,
% 168.60/168.46 (~P1(f315(f315(f223(a901),f315(a101,x121121)),x121121))),
% 168.60/168.46 inference(rename_variables,[],[4625])).
% 168.60/168.46 cnf(12115,plain,
% 168.60/168.46 (~P1(f315(f315(f223(a901),f315(a101,x121151)),x121151))),
% 168.60/168.46 inference(rename_variables,[],[4625])).
% 168.60/168.46 cnf(12118,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),x121181),x121181))),
% 168.60/168.46 inference(rename_variables,[],[4617])).
% 168.60/168.46 cnf(12121,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),x121211),x121211))),
% 168.60/168.46 inference(rename_variables,[],[4617])).
% 168.60/168.46 cnf(12124,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),x121241),x121241))),
% 168.60/168.46 inference(rename_variables,[],[4617])).
% 168.60/168.46 cnf(12127,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),x121271),x121271))),
% 168.60/168.46 inference(rename_variables,[],[4617])).
% 168.60/168.46 cnf(12144,plain,
% 168.60/168.46 (P1(f315(f315(f223(a901),x121441),x121441))),
% 168.60/168.46 inference(rename_variables,[],[3440])).
% 168.60/168.46 cnf(12147,plain,
% 168.60/168.46 (P25(a901,a901,a101,x121471)),
% 168.60/168.46 inference(rename_variables,[],[3642])).
% 168.60/168.46 cnf(12150,plain,
% 168.60/168.46 (P1(f315(f315(f223(a1),x121501),x121501))),
% 168.60/168.46 inference(rename_variables,[],[3441])).
% 168.60/168.46 cnf(12161,plain,
% 168.60/168.46 (P1(f315(f315(f223(a1),x121611),x121611))),
% 168.60/168.46 inference(rename_variables,[],[3441])).
% 168.60/168.46 cnf(12163,plain,
% 168.60/168.46 (~P1(f315(f315(f161(x121631),f315(f125(x121631,x121632),f102(x121631))),x121633))),
% 168.60/168.46 inference(scs_inference,[],[3783,3674,4603,4604,4583,10413,10423,10436,10447,10519,10554,10557,10560,10662,10797,11110,11303,11306,11325,11328,11521,11622,11629,11643,11689,11692,11725,11740,11803,11862,3642,3361,4589,10646,10746,11213,3052,3053,3056,3059,3060,3063,3064,3071,3075,3076,3077,3086,3087,3091,3097,3115,3116,3123,3130,3136,3137,3148,3180,3181,3186,3190,3191,3193,3201,3202,3222,3236,4581,3998,11912,3286,11619,3401,10482,10485,10581,10584,10900,11634,11637,11751,11790,11795,11865,3378,3893,3276,3636,3984,11665,3338,3272,3299,3295,3281,3282,3905,3496,11060,3371,4066,4597,10473,10643,3431,11994,4626,11239,11338,11574,11577,3543,3335,10546,10876,3336,3595,3254,3357,11655,4208,4068,11259,11390,11449,4644,11162,11403,11512,11538,11582,11588,4645,11292,11406,11515,4646,11409,4647,11467,4648,3356,3634,3799,4479,4480,4594,3734,3948,3507,10565,10685,10763,10836,10839,10879,10979,11229,11839,12091,3886,11898,3424,3519,11724,4621,10450,10453,10479,10606,10781,10987,11002,11120,11560,11658,11838,12062,12067,4632,11767,11798,11835,11842,11878,3873,3643,4016,3467,3469,3443,4618,4591,3627,4633,4201,11535,3757,3479,12015,4624,10441,10444,10614,10709,10728,10735,10758,10766,10769,10786,10972,11216,11429,11718,11812,11963,12080,12083,4170,4077,11057,4124,3800,4158,3817,10609,10706,11262,11343,11422,4636,11005,11414,3440,10574,10672,10822,10886,10961,11008,11011,11042,11068,11104,11142,11181,11966,12012,3441,10601,10657,10891,10982,11107,11743,12045,12048,12059,12150,3442,3515,4617,10490,10522,11026,11071,11080,11926,11947,12118,12121,12124,3590,10751,10842,11115,11159,11393,11396,11475,11557,11728,4628,11035,11045,11151,11172,11175,11242,11245,11256,11359,11367,11381,11417,11434,11443,11483,11524,11529,11532,11551,11554,11591,11596,11599,11602,11605,11845,11991,3500,10873,10903,10912,10915,10918,3539,3532,3952,3891,10525,11901,11929,4625,10470,10861,10864,11362,11378,11861,11917,11951,11978,12077,12106,12109,12112,3461,10906,11065,11135,11930,3915,4249,4622,3960,4609,4612,3417,3421,4611,4610,3747,4343,4638,10772,10775,4643,11248,11251,11437,11548,11565,4034,11608,11950,3881,11178,11184,3730,11318,3883,10909,11281,11446,11480,3591,3697,10825,10828,10921,11091,4641,11895,4642,10665,4304,4212,3914,3859,4639,10495,10498,10867,10870,11764,4640,11875,3884,10831,11097,4144,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928,5930,5935,5943,5981,5996,6005,6008,6017,6021,6022,6023,6024,6025,6030,6035,6045,6051,6069,6073,6082,6112,6128,6154,6171,6172,6175,6190,6192,6194,6196,6211,6212,6215,6217,6220,6221,6238,6246,6247,6248,6250,6252,6290,6291,6296,6299,6305,6309,6343,6345,6347,6349,6359,6361,6364,6370,6372,6377,6380,6388,6396,6398,6399,6406,6429,6430,6431,6432,6433,6435,6442,6447,6481,6482,6485,6486,6487,6489,6490,6491,6492,6499,6535,6536,6545,6567,6568,6592,6594,6606,6607,6613,6643,6645,6660,6700,6703,6704,6760,6783,6826,6841,6849,6858,6859,6860,6861,6882,6883,6890,6902,6905,6907,6909,6910,6911,6913,6927,6938,6939,6940,6953,7008,7019,7021,7026,7045,7046,7082,7089,7096,7126,7157,7213,7242,7299,7320,7329,7332,7392,7402,7465,7467,7481,7490,7491,7492,7509,7513,7515,7562,7572,7575,7590,7638,7640,7643,7687,7688,7706,7776,7794,7818,7842,7854,7868,7879,7890,7891,7917,7919,7921,7931,7969,7980,8005,8032,8065,8096,8130,8169,8186,8188,8204,8205,8273,8284,8349,8373,8392,8419,8458,8459,8476,8516,8518,8520,8526,8542,8546,8561,8582,8590,8592,8602,8607,8611,8612,8613,8614,8615,8616,8635,8650,8651,8669,8671,8675,8676,8677,8678,8679,8697,8698,8699,8709,8722,8725,8736,8741,8743,8745,8746,8747,8754,8760,8768,8771,8788,8789,8798,8799,8807,8826,8839,8843,8864,8886,8887,8890,8891,8897,8906,8907,8930,8941,8951,8952,8953,8956,8979,8980,8991,9041,9051,9053,9069,9081,9082,9083,9094,9158,9189,9190,9191,9206,9223,9231,9259,9260,9329,9364,9370,9380,9381,9382,9391,9421,9437,9441,9445,9467,9468,9495,9559,9564,9567,9604,9605,9606,9634,9635,9651,9672,9678,9690,9715,9736,9745,9746,9747,9748,9763,9765,9770,9800,9801,9807,9808,9852,9853,9864,9865,9889,9907,9909,9910,9918,9923,9930,9954,9988,9990,9994,10044,10078,10088,10090,10094,10095,10097,10106,10107,10127,10132,10225,10317,10318,10319,10320,10379,10397,2,8,9,4668,4669,4687,4729,4731,4732,4755,4757,4758,4768,4813,4815,4863,4993,4994,5011,5035,5092,5093,5099,5100,5102,5104,5113,5116,5117,5125,5138,5139,5145,5166,5167,5185,5190,5191,5192,5193,5197,5205,5208,5215,5270,5275,5276,5281,5288,5319,5329,5334,5344,5362,5364,5371,5372,5374,5385,5403,5405,5406,5413,5420,5421,5433,5434,5435,5436,5438,5439,5444,5445,5446,5447,5478,5479,5480,5488,5489,5490,5491,5535,5540,5542,5578,5580,5581,5583,5584,5586,5587,5589,5598,5603,5605,5606,5607,5609,5611,5612,5613,5614,5615,5616,5625,5626,5636,5639,5650,5666,5667,5670,5681,5684,5685,5686,5713,5723,5738,5739,5748,5749,5751,5753,5758,5793,5798,5800,5859,5894,5895,5909,5915,5918,5919,5920,5921,5940,5944,5945,5954,5976,6009,6028,6029,6033,6034,6036,6059,6063,6066,6067,6068,6084,6096,6097,6130,6131,6135,6156,6159,6162,6184,6185,6213,6216,6225,6234,6236,6245,6249,6257,6258,6259,6260,6293,6310,6363,6400,6402,6403,6426,6427,6434,6438,6439,6443,6457,6473,6494,6495,6500,6512,6515,6528,6548,6555,6557,6572,6573,6576,6577,6579,6581,6582,6583,6585,6587,6593,6599,6600,6602,6603,6609,6611,6653,6659,6674,6678,6679,6680,6714,6719,6721])).
% 168.60/168.46 cnf(12164,plain,
% 168.60/168.46 (P1(f315(f315(f223(f909(x121641,a899)),f315(f161(x121641),f315(f125(x121641,x121642),x121643))),f315(f161(x121641),x121643)))),
% 168.60/168.46 inference(rename_variables,[],[4077])).
% 168.60/168.46 cnf(12171,plain,
% 168.60/168.46 (P1(f315(f315(f224(a901),x121711),f315(a101,x121711)))),
% 168.60/168.46 inference(rename_variables,[],[3507])).
% 168.60/168.46 cnf(12174,plain,
% 168.60/168.46 (P1(f315(f315(f317(f909(x121741,a899)),x121742),f315(f296(x121741),x121742)))),
% 168.60/168.46 inference(rename_variables,[],[3800])).
% 168.60/168.46 cnf(12175,plain,
% 168.60/168.46 (~E(f315(a101,x121751),x121751)),
% 168.60/168.46 inference(rename_variables,[],[4583])).
% 168.60/168.46 cnf(12180,plain,
% 168.60/168.46 (P1(f315(f315(f223(a1),x121801),x121801))),
% 168.60/168.46 inference(rename_variables,[],[3441])).
% 168.60/168.46 cnf(12185,plain,
% 168.60/168.46 (P1(f315(f315(f223(a1),x121851),x121851))),
% 168.60/168.46 inference(rename_variables,[],[3441])).
% 168.60/168.46 cnf(12196,plain,
% 168.60/168.46 (P1(f315(f315(f223(f909(x121961,a899)),x121962),f315(f315(f297(x121961),x121963),x121962)))),
% 168.60/168.46 inference(rename_variables,[],[3881])).
% 168.60/168.46 cnf(12199,plain,
% 168.60/168.46 (P1(f315(f315(f223(a901),x121991),x121991))),
% 168.60/168.46 inference(rename_variables,[],[3440])).
% 168.60/168.46 cnf(12200,plain,
% 168.60/168.46 (~E(f315(a101,x122001),x122001)),
% 168.60/168.46 inference(rename_variables,[],[4583])).
% 168.60/168.46 cnf(12215,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),x122151),x122151))),
% 168.60/168.46 inference(rename_variables,[],[4617])).
% 168.60/168.46 cnf(12216,plain,
% 168.60/168.46 (~E(f315(a101,x122161),x122161)),
% 168.60/168.46 inference(rename_variables,[],[4583])).
% 168.60/168.46 cnf(12219,plain,
% 168.60/168.46 (P1(f315(f315(f223(a901),x122191),x122191))),
% 168.60/168.46 inference(rename_variables,[],[3440])).
% 168.60/168.46 cnf(12222,plain,
% 168.60/168.46 (P1(f315(f315(f223(a901),x122221),x122221))),
% 168.60/168.46 inference(rename_variables,[],[3440])).
% 168.60/168.46 cnf(12225,plain,
% 168.60/168.46 (P1(f315(f315(f223(a901),x122251),x122251))),
% 168.60/168.46 inference(rename_variables,[],[3440])).
% 168.60/168.46 cnf(12228,plain,
% 168.60/168.46 (P1(f315(f315(f223(a901),x122281),x122281))),
% 168.60/168.46 inference(rename_variables,[],[3440])).
% 168.60/168.46 cnf(12231,plain,
% 168.60/168.46 (P1(f315(f315(f223(a1),x122311),x122311))),
% 168.60/168.46 inference(rename_variables,[],[3441])).
% 168.60/168.46 cnf(12234,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),x122341),x122341))),
% 168.60/168.46 inference(rename_variables,[],[4617])).
% 168.60/168.46 cnf(12237,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),x122371),x122371))),
% 168.60/168.46 inference(rename_variables,[],[4617])).
% 168.60/168.46 cnf(12238,plain,
% 168.60/168.46 (P1(f315(f315(f224(a901),x122381),f315(a101,x122381)))),
% 168.60/168.46 inference(rename_variables,[],[3507])).
% 168.60/168.46 cnf(12245,plain,
% 168.60/168.46 (~E(f315(a101,x122451),x122451)),
% 168.60/168.46 inference(rename_variables,[],[4583])).
% 168.60/168.46 cnf(12250,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),x122501),x122501))),
% 168.60/168.46 inference(rename_variables,[],[4617])).
% 168.60/168.46 cnf(12251,plain,
% 168.60/168.46 (~E(f315(a101,x122511),x122511)),
% 168.60/168.46 inference(rename_variables,[],[4583])).
% 168.60/168.46 cnf(12254,plain,
% 168.60/168.46 (P1(f315(f315(f223(a1),x122541),x122541))),
% 168.60/168.46 inference(rename_variables,[],[3441])).
% 168.60/168.46 cnf(12271,plain,
% 168.60/168.46 (P1(f315(f315(f223(a1),x122711),x122711))),
% 168.60/168.46 inference(rename_variables,[],[3441])).
% 168.60/168.46 cnf(12276,plain,
% 168.60/168.46 (P1(f315(f315(f223(a901),f2(a901)),x122761))),
% 168.60/168.46 inference(rename_variables,[],[3461])).
% 168.60/168.46 cnf(12292,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),x122921),f2(a901)))),
% 168.60/168.46 inference(rename_variables,[],[4621])).
% 168.60/168.46 cnf(12295,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),x122951),f2(a901)))),
% 168.60/168.46 inference(rename_variables,[],[4621])).
% 168.60/168.46 cnf(12298,plain,
% 168.60/168.46 (~P1(f315(f315(f317(x122981),x122982),f177(f909(x122981,a899))))),
% 168.60/168.46 inference(rename_variables,[],[4628])).
% 168.60/168.46 cnf(12301,plain,
% 168.60/168.46 (~P1(f315(f315(f317(x123011),x123012),f177(f909(x123011,a899))))),
% 168.60/168.46 inference(rename_variables,[],[4628])).
% 168.60/168.46 cnf(12304,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),x123041),x123041))),
% 168.60/168.46 inference(rename_variables,[],[4617])).
% 168.60/168.46 cnf(12307,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),x123071),x123071))),
% 168.60/168.46 inference(rename_variables,[],[4617])).
% 168.60/168.46 cnf(12310,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),x123101),x123101))),
% 168.60/168.46 inference(rename_variables,[],[4617])).
% 168.60/168.46 cnf(12313,plain,
% 168.60/168.46 (~P1(f315(f315(f224(a901),x123131),x123131))),
% 168.60/168.46 inference(rename_variables,[],[4617])).
% 168.60/168.46 cnf(12316,plain,
% 168.60/168.46 (P1(f315(f315(f224(a901),x123161),f315(a101,x123161)))),
% 168.60/168.46 inference(rename_variables,[],[3507])).
% 168.60/168.46 cnf(12323,plain,
% 168.60/168.46 (P1(f315(f315(f317(f909(x123231,a899)),x123232),f315(f296(x123231),x123232)))),
% 168.60/168.46 inference(rename_variables,[],[3800])).
% 168.60/168.46 cnf(12328,plain,
% 168.60/168.46 (P1(f315(f315(f223(f909(x123281,a899)),x123282),f315(f315(f297(x123281),x123283),x123282)))),
% 168.60/168.46 inference(rename_variables,[],[3881])).
% 168.60/168.46 cnf(12335,plain,
% 168.60/168.46 (~P1(f315(f315(f317(x123351),x123352),f177(f909(x123351,a899))))),
% 168.60/168.46 inference(rename_variables,[],[4628])).
% 168.60/168.46 cnf(12344,plain,
% 168.60/168.46 (P1(f315(f315(f223(f909(x123441,a899)),x123442),f230(f909(x123441,a899))))),
% 168.60/168.46 inference(rename_variables,[],[3817])).
% 168.60/168.46 cnf(12345,plain,
% 168.60/168.47 (~E(f315(a101,x123451),x123451)),
% 168.60/168.47 inference(rename_variables,[],[4583])).
% 168.60/168.47 cnf(12348,plain,
% 168.60/168.47 (P1(f315(f315(f223(f909(x123481,a899)),x123482),f230(f909(x123481,a899))))),
% 168.60/168.47 inference(rename_variables,[],[3817])).
% 168.60/168.47 cnf(12351,plain,
% 168.60/168.47 (P1(f315(f315(f223(f909(x123511,a899)),f315(f161(x123511),f315(f125(x123511,x123512),x123513))),f315(f161(x123511),x123513)))),
% 168.60/168.47 inference(rename_variables,[],[4077])).
% 168.60/168.47 cnf(12357,plain,
% 168.60/168.47 (P1(f315(f315(f224(a901),x123571),f315(a101,x123571)))),
% 168.60/168.47 inference(rename_variables,[],[3507])).
% 168.60/168.47 cnf(12366,plain,
% 168.60/168.47 (E(f315(f272(x123661,x123661),f251(x123661,x123662)),x123662)),
% 168.60/168.47 inference(rename_variables,[],[3401])).
% 168.60/168.47 cnf(12377,plain,
% 168.60/168.47 (~P1(f315(f315(f223(a901),f315(a101,x123771)),x123771))),
% 168.60/168.47 inference(rename_variables,[],[4625])).
% 168.60/168.47 cnf(12378,plain,
% 168.60/168.47 (~P1(f315(f315(f224(a901),x123781),f2(a901)))),
% 168.60/168.47 inference(rename_variables,[],[4621])).
% 168.60/168.47 cnf(12383,plain,
% 168.60/168.47 (P1(f315(f54(x123831),f177(f909(x123831,a899))))),
% 168.60/168.47 inference(rename_variables,[],[3515])).
% 168.60/168.47 cnf(12384,plain,
% 168.60/168.47 (~P1(f315(f315(f317(x123841),x123842),f177(f909(x123841,a899))))),
% 168.60/168.47 inference(rename_variables,[],[4628])).
% 168.60/168.47 cnf(12391,plain,
% 168.60/168.47 (P1(f315(f315(f223(f909(x123911,a899)),f315(f161(x123911),f165(x123911,x123912,x123913))),f315(f161(x123911),x123912)))),
% 168.60/168.47 inference(rename_variables,[],[4124])).
% 168.60/168.47 cnf(12394,plain,
% 168.60/168.47 (P25(x123941,x123941,f7(x123941),x123942)),
% 168.60/168.47 inference(rename_variables,[],[3674])).
% 168.60/168.47 cnf(12401,plain,
% 168.60/168.47 (P1(f315(f315(f317(f909(x124011,a899)),x124012),f315(f296(x124011),x124012)))),
% 168.60/168.47 inference(rename_variables,[],[3800])).
% 168.60/168.47 cnf(12410,plain,
% 168.60/168.47 (P1(f315(f315(f223(a901),x124101),x124101))),
% 168.60/168.47 inference(rename_variables,[],[3440])).
% 168.60/168.47 cnf(12413,plain,
% 168.60/168.47 (~P1(f315(f315(f317(x124131),x124132),f177(f909(x124131,a899))))),
% 168.60/168.47 inference(rename_variables,[],[4628])).
% 168.60/168.47 cnf(12416,plain,
% 168.60/168.47 (P1(f315(f315(f223(f909(x124161,a899)),x124162),f315(f315(f297(x124161),x124163),x124162)))),
% 168.60/168.47 inference(rename_variables,[],[3881])).
% 168.60/168.47 cnf(12417,plain,
% 168.60/168.47 (P1(f315(f315(f223(f909(x124171,a899)),x124172),f230(f909(x124171,a899))))),
% 168.60/168.47 inference(rename_variables,[],[3817])).
% 168.60/168.47 cnf(12424,plain,
% 168.60/168.47 (P1(f315(f315(f223(a901),x124241),x124241))),
% 168.60/168.47 inference(rename_variables,[],[3440])).
% 168.60/168.47 cnf(12427,plain,
% 168.60/168.47 (P1(f315(f315(f223(a901),x124271),x124271))),
% 168.60/168.47 inference(rename_variables,[],[3440])).
% 168.60/168.47 cnf(12430,plain,
% 168.60/168.47 (P1(f315(f315(f223(a901),x124301),x124301))),
% 168.60/168.47 inference(rename_variables,[],[3440])).
% 168.60/168.47 cnf(12433,plain,
% 168.60/168.47 (P1(f315(f315(f223(a901),x124331),x124331))),
% 168.60/168.47 inference(rename_variables,[],[3440])).
% 168.60/168.47 cnf(12436,plain,
% 168.60/168.47 (P1(f315(f315(f224(a901),x124361),f315(a101,x124361)))),
% 168.60/168.47 inference(rename_variables,[],[3507])).
% 168.60/168.47 cnf(12439,plain,
% 168.60/168.47 (P1(f315(f315(f224(a901),x124391),f315(a101,x124391)))),
% 168.60/168.47 inference(rename_variables,[],[3507])).
% 168.60/168.47 cnf(12442,plain,
% 168.60/168.47 (P1(f315(f315(f275(a901),x124421),x124421))),
% 168.60/168.47 inference(rename_variables,[],[3442])).
% 168.60/168.47 cnf(12445,plain,
% 168.60/168.47 (P1(f315(f315(f275(a901),x124451),x124451))),
% 168.60/168.47 inference(rename_variables,[],[3442])).
% 168.60/168.47 cnf(12448,plain,
% 168.60/168.47 (P1(f315(f315(f223(f909(x124481,a899)),x124482),x124482))),
% 168.60/168.47 inference(rename_variables,[],[3730])).
% 168.60/168.47 cnf(12450,plain,
% 168.60/168.47 (~P1(f315(f315(f223(a1),f315(f315(f3(a1),a76),a86)),f2(a1)))),
% 168.60/168.47 inference(scs_inference,[],[3783,3674,11333,4603,4604,4583,10413,10423,10436,10447,10519,10554,10557,10560,10662,10797,11110,11303,11306,11325,11328,11521,11622,11629,11643,11689,11692,11725,11740,11803,11862,11881,12175,12200,12216,12245,12251,3642,3361,4589,10646,10746,11213,4595,3052,3053,3055,3056,3059,3060,3062,3063,3064,3071,3075,3076,3077,3086,3087,3091,3097,3115,3116,3123,3130,3133,3136,3137,3148,3180,3181,3186,3190,3191,3193,3201,3202,3222,3332,3236,4581,3998,11912,3286,11619,3401,10482,10485,10581,10584,10900,11634,11637,11751,11790,11795,11865,11907,3378,3387,3893,4194,3276,3636,3984,11665,3338,3272,3299,3295,3281,3282,3905,3496,11060,3371,4066,4597,10473,10643,3431,11994,4626,11239,11338,11574,11577,3543,3335,10546,10876,3336,3595,3254,3357,11655,4208,4068,11259,11390,11449,4644,11162,11403,11512,11538,11582,11588,4645,11292,11406,11515,4646,11409,4647,11467,4648,3356,3634,3799,4479,4480,4594,3734,3948,3735,3620,3876,3507,10565,10685,10763,10836,10839,10879,10979,11229,11839,12091,12171,12238,12316,12357,12436,3886,11898,3424,3519,11724,3696,4621,10450,10453,10479,10606,10781,10987,11002,11120,11560,11658,11838,12062,12067,12292,12295,4632,11767,11798,11835,11842,11878,3873,3643,4016,3467,3469,3443,4618,4591,3627,4633,4201,11535,3757,3479,12015,12018,4624,10441,10444,10614,10709,10728,10735,10758,10766,10769,10786,10972,11216,11429,11718,11812,11963,12080,12083,4170,4077,11057,12164,4124,11265,3800,11846,12174,12323,4158,3817,10609,10706,11262,11343,11422,11486,12344,12348,4636,11005,11414,3440,10574,10672,10822,10886,10961,11008,11011,11042,11068,11104,11142,11181,11966,12012,12144,12199,12219,12222,12225,12228,12410,12424,12427,12430,3441,10601,10657,10891,10982,11107,11743,12045,12048,12059,12150,12161,12180,12185,12231,12254,3442,12442,3515,12383,4617,10490,10522,11026,11071,11080,11926,11947,12118,12121,12124,12127,12215,12234,12237,12250,12304,12307,12310,3590,10751,10842,11115,11159,11393,11396,11475,11557,11728,4628,11035,11045,11151,11172,11175,11242,11245,11256,11359,11367,11381,11417,11434,11443,11483,11524,11529,11532,11551,11554,11591,11596,11599,11602,11605,11845,11991,12024,12298,12301,12335,12384,3500,10873,10903,10912,10915,10918,3539,3532,3952,3891,10525,11901,11929,4625,10470,10861,10864,11362,11378,11861,11917,11951,11978,12077,12106,12109,12112,12115,3461,10906,11065,11135,11930,12076,3915,4249,4622,3926,3960,4609,4612,3417,3421,4611,4610,3747,4343,4638,10772,10775,4643,11248,11251,11437,11548,11565,4034,11608,11950,3881,11178,11184,11202,12196,12328,3730,11318,11440,3883,10909,11281,11446,11480,3591,3697,10825,10828,10921,11091,4641,11895,4642,10665,4304,4212,3914,3859,4639,10495,10498,10867,10870,11764,4640,11875,3884,10831,11097,4144,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928,5930,5935,5943,5981,5996,6005,6008,6017,6021,6022,6023,6024,6025,6030,6035,6045,6051,6069,6073,6082,6112,6128,6154,6171,6172,6175,6190,6192,6194,6196,6211,6212,6215,6217,6220,6221,6238,6246,6247,6248,6250,6252,6290,6291,6296,6299,6305,6309,6343,6345,6347,6349,6359,6361,6364,6370,6372,6377,6380,6388,6396,6398,6399,6406,6429,6430,6431,6432,6433,6435,6442,6447,6481,6482,6485,6486,6487,6489,6490,6491,6492,6499,6535,6536,6545,6567,6568,6592,6594,6606,6607,6613,6643,6645,6660,6700,6703,6704,6760,6783,6826,6841,6849,6858,6859,6860,6861,6882,6883,6890,6902,6905,6907,6909,6910,6911,6913,6927,6938,6939,6940,6953,7008,7019,7021,7026,7045,7046,7082,7089,7096,7126,7157,7213,7242,7299,7320,7329,7332,7392,7402,7465,7467,7481,7490,7491,7492,7509,7513,7515,7562,7572,7575,7590,7638,7640,7643,7687,7688,7706,7776,7794,7818,7842,7854,7868,7879,7890,7891,7917,7919,7921,7931,7969,7980,8005,8032,8065,8096,8130,8169,8186,8188,8204,8205,8273,8284,8349,8373,8392,8419,8458,8459,8476,8516,8518,8520,8526,8542,8546,8561,8582,8590,8592,8602,8607,8611,8612,8613,8614,8615,8616,8635,8650,8651,8669,8671,8675,8676,8677,8678,8679,8697,8698,8699,8709,8722,8725,8736,8741,8743,8745,8746,8747,8754,8760,8768,8771,8788,8789,8798,8799,8807,8826,8839,8843,8864,8886,8887,8890,8891,8897,8906,8907,8930,8941,8951,8952,8953,8956,8979,8980,8991,9041,9051,9053,9069,9081,9082,9083,9094,9158,9189,9190,9191,9206,9223,9231,9259,9260,9329,9364,9370,9380,9381,9382,9391,9421,9437,9441,9445,9467,9468,9495,9559,9564,9567,9604,9605,9606,9634,9635,9651,9672,9678,9690,9715,9736,9745,9746,9747,9748,9763,97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% 168.60/168.47 cnf(12455,plain,
% 168.60/168.47 (P1(f315(f315(f317(f909(x124551,a899)),x124552),f315(f296(x124551),x124552)))),
% 168.60/168.47 inference(rename_variables,[],[3800])).
% 168.60/168.47 cnf(12464,plain,
% 168.60/168.47 (~E(f315(a101,x124641),x124641)),
% 168.60/168.47 inference(rename_variables,[],[4583])).
% 168.60/168.47 cnf(12465,plain,
% 168.60/168.47 (E(f315(f298(x124651,x124651,f7(x124651)),x124652),x124652)),
% 168.60/168.47 inference(rename_variables,[],[3496])).
% 168.60/168.47 cnf(12468,plain,
% 168.60/168.47 (P34(x124681,x124682,f102(x124681),f102(x124681))),
% 168.60/168.47 inference(rename_variables,[],[3683])).
% 168.60/168.47 cnf(12471,plain,
% 168.60/168.47 (P1(f315(f315(f223(f909(x124711,a899)),f315(f161(x124711),f165(x124711,x124712,x124713))),f315(f161(x124711),x124712)))),
% 168.60/168.47 inference(rename_variables,[],[4124])).
% 168.60/168.47 cnf(12472,plain,
% 168.60/168.47 (P1(f315(f54(x124721),f315(f161(x124721),x124722)))),
% 168.60/168.47 inference(rename_variables,[],[3479])).
% 168.60/168.47 cnf(12483,plain,
% 168.60/168.47 (~P1(f315(f315(f224(a901),x124831),x124831))),
% 168.60/168.47 inference(rename_variables,[],[4617])).
% 168.60/168.47 cnf(12486,plain,
% 168.60/168.47 (~P1(f315(f315(f224(a901),x124861),x124861))),
% 168.60/168.47 inference(rename_variables,[],[4617])).
% 168.60/168.47 cnf(12491,plain,
% 168.60/168.47 (P1(f315(f315(f223(a901),f2(a901)),x124911))),
% 168.60/168.47 inference(rename_variables,[],[3461])).
% 168.60/168.47 cnf(12498,plain,
% 168.60/168.47 (P13(a901,f315(f157(a901),f315(f315(f143(f902(x124981),a901),f178(f902(x124981))),f168(x124981,x124982))))),
% 168.60/168.47 inference(rename_variables,[],[3994])).
% 168.60/168.47 cnf(12501,plain,
% 168.60/168.47 (P25(x125011,x125011,f7(x125011),x125012)),
% 168.60/168.47 inference(rename_variables,[],[3674])).
% 168.60/168.47 cnf(12504,plain,
% 168.60/168.47 (P25(x125041,x125041,f7(x125041),x125042)),
% 168.60/168.47 inference(rename_variables,[],[3674])).
% 168.60/168.47 cnf(12507,plain,
% 168.60/168.47 (P1(f315(f315(f317(f902(x125071)),f102(x125071)),f150(x125071,x125072)))),
% 168.60/168.47 inference(rename_variables,[],[3634])).
% 168.60/168.47 cnf(12510,plain,
% 168.60/168.47 (~P1(f315(f315(f177(f909(x125101,f909(x125102,a899))),x125103),x125104))),
% 168.60/168.47 inference(rename_variables,[],[4642])).
% 168.60/168.47 cnf(12515,plain,
% 168.60/168.47 (P1(f315(f315(f223(a901),x125151),x125151))),
% 168.60/168.47 inference(rename_variables,[],[3440])).
% 168.60/168.47 cnf(12516,plain,
% 168.60/168.47 (P1(f315(f315(f223(a901),f2(a901)),x125161))),
% 168.60/168.47 inference(rename_variables,[],[3461])).
% 168.60/168.47 cnf(12518,plain,
% 168.60/168.47 (P1(f315(f315(f223(a1),f2(a1)),f339(x125181,f177(f909(x125182,f909(x125183,a899))),f71(a1))))),
% 168.60/168.47 inference(scs_inference,[],[3783,3674,11333,12394,12501,3683,4603,4604,4602,4583,10413,10423,10436,10447,10519,10554,10557,10560,10662,10797,11110,11303,11306,11325,11328,11521,11622,11629,11643,11689,11692,11725,11740,11803,11862,11881,12175,12200,12216,12245,12251,12345,3642,3361,4589,10646,10746,11213,4595,3052,3053,3055,3056,3059,3060,3062,3063,3064,3071,3075,3076,3077,3086,3087,3091,3097,3115,3116,3123,3130,3133,3136,3137,3148,3180,3181,3186,3190,3191,3193,3201,3202,3222,3332,3236,4581,3998,11912,3286,11619,3401,10482,10485,10581,10584,10900,11634,11637,11751,11790,11795,11865,11907,3378,3387,3893,4194,3276,3636,3984,11665,3338,3272,3299,3295,3281,3282,3905,3319,3496,11060,11187,3371,4066,4597,10473,10643,3431,11994,4626,11239,11338,11574,11577,3543,3335,10546,10876,3336,3595,3254,3357,11655,4208,4068,11259,11390,11449,4644,11162,11403,11512,11538,11582,11588,4645,11292,11406,11515,4646,11409,4647,11467,4648,3356,3634,3799,4479,4480,4594,3734,3948,3735,3994,3620,3876,3507,10565,10685,10763,10836,10839,10879,10979,11229,11839,12091,12171,12238,12316,12357,12436,3886,11898,3424,3519,11724,3696,4621,10450,10453,10479,10606,10781,10987,11002,11120,11560,11658,11838,12062,12067,12292,12295,12378,4632,11767,11798,11835,11842,11878,3873,3643,4016,3467,3469,3443,4618,4591,3627,4633,4201,11535,3757,3479,12015,12018,4624,10441,10444,10614,10709,10728,10735,10758,10766,10769,10786,10972,11216,11429,11718,11812,11963,12080,12083,4170,4077,11057,12164,4124,11265,12391,3800,11846,12174,12323,12401,4158,3817,10609,10706,11262,11343,11422,11486,12344,12348,4636,11005,11414,3440,10574,10672,10822,10886,10961,11008,11011,11042,11068,11104,11142,11181,11966,12012,12144,12199,12219,12222,12225,12228,12410,12424,12427,12430,12433,3441,10601,10657,10891,10982,11107,11743,12045,12048,12059,12150,12161,12180,12185,12231,12254,3442,12442,3515,12383,4617,10490,10522,11026,11071,11080,11926,11947,12118,12121,12124,12127,12215,12234,12237,12250,12304,12307,12310,12313,12483,3590,10751,10842,11115,11159,11393,11396,11475,11557,11728,11977,4628,11035,11045,11151,11172,11175,11242,11245,11256,11359,11367,11381,11417,11434,11443,11483,11524,11529,11532,11551,11554,11591,11596,11599,11602,11605,11845,11991,12024,12298,12301,12335,12384,3500,10873,10903,10912,10915,10918,3539,3532,3952,3891,10525,11901,11929,4625,10470,10861,10864,11362,11378,11861,11917,11951,11978,12077,12106,12109,12112,12115,12377,3461,10906,11065,11135,11930,12076,12276,12491,3915,4249,4622,3926,3960,4609,4612,3417,3421,4611,4610,3747,4343,4638,10772,10775,4643,11248,11251,11437,11548,11565,4034,11608,11950,3881,11178,11184,11202,12196,12328,3730,11318,11440,3883,10909,11281,11446,11480,3591,3697,10825,10828,10921,11091,4641,11895,4642,10665,10778,12510,4304,4212,3914,3859,4639,10495,10498,10867,10870,11764,4640,11875,3884,10831,11097,4144,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928,5930,5935,5943,5981,5996,6005,6008,6017,6021,6022,6023,6024,6025,6030,6035,6045,6051,6069,6073,6082,6112,6128,6154,6171,6172,6175,6190,6192,6194,6196,6211,6212,6215,6217,6220,6221,6238,6246,6247,6248,6250,6252,6290,6291,6296,6299,6305,6309,6343,6345,6347,6349,6359,6361,6364,6370,6372,6377,6380,6388,6396,6398,6399,6406,6429,6430,6431,6432,6433,6435,6442,6447,6481,6482,6485,6486,6487,6489,6490,6491,6492,6499,6535,6536,6545,6567,6568,6592,6594,6606,6607,6613,6643,6645,6660,6700,6703,6704,6760,6783,6826,6841,6849,6858,6859,6860,6861,6882,6883,6890,6902,6905,6907,6909,6910,6911,6913,6927,6938,6939,6940,6953,7008,7019,7021,7026,7045,7046,7082,7089,7096,7126,7157,7213,7242,7299,7320,7329,7332,7392,7402,7465,7467,7481,7490,7491,7492,7509,7513,7515,7562,7572,7575,7590,7638,7640,7643,7687,7688,7706,7776,7794,7818,7842,7854,7868,7879,7890,7891,7917,7919,7921,7931,7969,7980,8005,8032,8065,8096,8130,8169,8186,8188,8204,8205,8273,8284,8349,8373,8392,8419,8458,8459,8476,8516,8518,8520,8526,8542,8546,8561,8582,8590,8592,8602,8607,8611,8612,8613,8614,8615,8616,8635,8650,8651,8669,8671,8675,8676,8677,8678,8679,8697,8698,8699,8709,8722,8725,8736,8741,8743,8745,8746,8747,8754,8760,8768,8771,8788,8789,8798,8799,8807,8826,8839,8843,8864,8886,8887,8890,8891,8897,8906,8907,8930,8941,8951,8952,8953,8956,8979,8980,8991,9041,9051,9053,9069,9081,9082,9083,9094,9158,9189,9190,9191,9206,9223,9231,9259,9260,9329,9364,9370,9380,9381,9382,9391,9421,9437,9441,9445,9467,9468,9495,9559,9564,9567,9604,9605,9606,9634,9635,9651,9672,9678,9690,9715,9736,9745,9746,9747,9748,9763,9765,9770,9800,9801,9807,9808,9852,9853,9864,9865,9889,9907,9909,9910,9918,9923,9930,9954,9988,9990,9994,10044,10078,10088,10090,10094,10095,10097,10106,10107,10127,10132,10225,10317,10318,10319,10320,10379,10397,2,8,9,4668,4669,4687,4729,4731,4732,4755,4757,4758,4768,4813,4815,4863,4993,4994,5011,5035,5092,5093,5099,5100,5102,5104,5113,5116,5117,5125,5138,5139,5145,5166,5167,5185,5190,5191,5192,5193,5197,5205,5208,5215,5270,5275,5276,5281,5288,5319,5329,5334,5344,5362,5364,5371,5372,5374,5385,5403,5405,5406,5413,5420,5421,5433,5434,5435,5436,5438,5439,5444,5445,5446,5447,5478,5479,5480,5488,5489,5490,5491,5535,5540,5542,5578,5580,5581,5583,5584,5586,5587,5589,5598,5603,5605,5606,5607,5609,5611,5612,5613,5614,5615,5616,5625,5626,5636,5639,5650,5666,5667,5670,5681,5684,5685,5686,5713,5723,5738,5739,5748,5749,5751,5753,5758,5793,5798,5800,5859,5894,5895,5909,5915,5918,5919,5920,5921,5940,5944,5945,5954,5976,6009,6028,6029,6033,6034,6036,6059,6063,6066,6067,6068,6084,6096,6097,6130,6131,6135,6156,6159,6162,6184,6185,6213,6216,6225,6234,6236,6245,6249,6257,6258,6259,6260,6293,6310,6363,6400,6402,6403,6426,6427,6434,6438,6439,6443,6457,6473,6494,6495,6500,6512,6515,6528,6548,6555,6557,6572,6573,6576,6577,6579,6581,6582,6583,6585,6587,6593,6599,6600,6602,6603,6609,6611,6653,6659,6674,6678,6679,6680,6714,6719,6721,6726,6727,6737,6741,6755,6778,6779,6781,6782,6793,6799,6818,6821,6842,6862,6873,6876,6877,6878,6884,6898,6917,6919,6921,6923,6928,6934,6936,6950,6955,6956,6993,6994,6995,7010,7011,7013,7014,7035,7037,7052,7080,7104,7115,7117,7119,7121,7122,7154,7155,7156,7160,7161,7168,7169,7171,7173,7195,7204,7205,7216,7226,7266,7276,7282,7289,7300,7305,7307,7314,7322,7323,7336,7353,7374,7376,7395,7450,7451,7452,7454,7456,7460,7461,7466,7530,7558,7573,7578,7589,7620,7624,7631,7646,7671,7689,7692,7693,7703,7723,7725,7727,7729,7730,7731,7732,7733,7758,7784,7785,7817,7819,7820,7821,7827,7848,7865,7870,7876,7878,7886,7898,7899,7901,7922,7929,7950,8018,8019,8020,8068,8074,8075,8099,8100])).
% 168.60/168.47 cnf(12519,plain,
% 168.60/168.47 (~P1(f315(f315(f177(f909(x125191,f909(x125192,a899))),x125193),x125194))),
% 168.60/168.47 inference(rename_variables,[],[4642])).
% 168.60/168.47 cnf(12522,plain,
% 168.60/168.47 (P1(f315(f315(f223(f909(f908(f902(x125221),f902(x125221)),a899)),f147(x125221,x125222)),f295(f902(x125221),f146(x125221,x125222))))),
% 168.60/168.47 inference(rename_variables,[],[4129])).
% 168.60/168.47 cnf(12528,plain,
% 168.60/168.47 (P1(f315(f315(f223(f909(x125281,a899)),f315(f298(x125282,x125281,x125283),f315(f299(x125282,x125281,x125283),x125284))),x125284))),
% 168.60/168.47 inference(rename_variables,[],[4304])).
% 168.60/168.47 cnf(12531,plain,
% 168.60/168.47 (P1(f315(f315(f223(f909(x125311,a899)),f315(f161(x125311),f165(x125311,x125312,x125313))),f315(f161(x125311),x125312)))),
% 168.60/168.47 inference(rename_variables,[],[4124])).
% 168.60/168.47 cnf(12532,plain,
% 168.60/168.47 (P1(f315(f315(f223(f909(x125321,a899)),f315(f161(x125321),f315(f125(x125321,x125322),x125323))),f315(f161(x125321),x125323)))),
% 168.60/168.47 inference(rename_variables,[],[4077])).
% 168.60/168.47 cnf(12535,plain,
% 168.60/168.47 (~P1(f315(f315(f224(f909(x125351,a899)),x125352),f177(f909(x125351,a899))))),
% 168.60/168.47 inference(rename_variables,[],[4636])).
% 168.60/168.47 cnf(12543,plain,
% 168.60/168.47 (P1(f315(f315(f223(f909(x125431,a899)),f315(f298(x125432,x125431,x125433),f315(f299(x125432,x125431,x125433),x125434))),x125434))),
% 168.60/168.47 inference(rename_variables,[],[4304])).
% 168.60/168.47 cnf(12548,plain,
% 168.60/168.47 (P1(f315(f315(f317(f902(x125481)),f102(x125481)),f150(x125481,x125482)))),
% 168.60/168.47 inference(rename_variables,[],[3634])).
% 168.60/168.47 cnf(12551,plain,
% 168.60/168.47 (~P1(f315(f315(f317(f908(f902(x125511),f902(x125511))),f315(f315(f240(f902(x125511),f902(x125511)),x125512),f102(x125511))),f134(x125511,x125513)))),
% 168.60/168.47 inference(rename_variables,[],[4644])).
% 168.60/168.47 cnf(12554,plain,
% 168.60/168.47 (~P1(f315(f315(f224(a901),x125541),f2(a901)))),
% 168.60/168.47 inference(rename_variables,[],[4621])).
% 168.60/168.47 cnf(12556,plain,
% 168.60/168.47 (~P1(f315(f54(x125561),f230(f909(x125561,a899))))),
% 168.60/168.47 inference(scs_inference,[],[3783,3674,11333,12394,12501,3683,3690,3411,4603,4604,3309,3312,4602,4583,10413,10423,10436,10447,10519,10554,10557,10560,10662,10797,11110,11303,11306,11325,11328,11521,11622,11629,11643,11689,11692,11725,11740,11803,11862,11881,12175,12200,12216,12245,12251,12345,3642,3361,4589,10646,10746,11213,4595,3052,3053,3055,3056,3059,3060,3062,3063,3064,3071,3075,3076,3077,3086,3087,3091,3097,3109,3115,3116,3123,3130,3133,3136,3137,3148,3180,3181,3186,3190,3191,3193,3201,3202,3222,3332,3236,4581,3998,11912,3286,11619,3401,10482,10485,10581,10584,10900,11634,11637,11751,11790,11795,11865,11907,3378,3387,3893,4194,3276,3636,3984,11665,3338,3272,3299,3295,3281,3282,3905,3319,3496,11060,11187,3371,4066,4597,10473,10643,3431,11994,4626,11239,11338,11574,11577,3543,3335,10546,10876,3336,3595,3254,3357,11655,4208,4068,11259,11390,11449,4644,11162,11403,11512,11538,11582,11588,4645,11292,11406,11515,4646,11409,4647,11467,4648,3356,3634,12507,12548,3799,4479,4480,4594,3734,3948,3735,3994,3620,3876,3507,10565,10685,10763,10836,10839,10879,10979,11229,11839,12091,12171,12238,12316,12357,12436,3886,11898,3424,3519,11724,3696,4621,10450,10453,10479,10606,10781,10987,11002,11120,11560,11658,11838,12062,12067,12292,12295,12378,4632,11767,11798,11835,11842,11878,3873,3643,4016,3467,3469,3443,4618,4591,3627,4633,4201,11535,3757,3479,12015,12018,4624,10441,10444,10614,10709,10728,10735,10758,10766,10769,10786,10972,11216,11429,11718,11812,11963,12080,12083,4170,4129,12522,4077,11057,12164,12351,4124,11265,12391,12471,3800,11846,12174,12323,12401,4158,3817,10609,10706,11262,11343,11422,11486,12344,12348,4636,11005,11414,3440,10574,10672,10822,10886,10961,11008,11011,11042,11068,11104,11142,11181,11966,12012,12144,12199,12219,12222,12225,12228,12410,12424,12427,12430,12433,3441,10601,10657,10891,10982,11107,11743,12045,12048,12059,12150,12161,12180,12185,12231,12254,3442,12442,3515,12383,4617,10490,10522,11026,11071,11080,11926,11947,12118,12121,12124,12127,12215,12234,12237,12250,12304,12307,12310,12313,12483,3590,10751,10842,11115,11159,11393,11396,11475,11557,11728,11977,4628,11035,11045,11151,11172,11175,11242,11245,11256,11359,11367,11381,11417,11434,11443,11483,11524,11529,11532,11551,11554,11591,11596,11599,11602,11605,11845,11991,12024,12298,12301,12335,12384,3500,10873,10903,10912,10915,10918,3539,3532,3952,3891,10525,11901,11929,4625,10470,10861,10864,11362,11378,11861,11917,11951,11978,12077,12106,12109,12112,12115,12377,3461,10906,11065,11135,11930,12076,12276,12491,3915,4249,4622,3926,3960,4609,4612,3417,3421,4611,4610,3747,4343,4638,10772,10775,4643,11248,11251,11437,11548,11565,4034,11608,11950,3881,11178,11184,11202,12196,12328,3730,11318,11440,12448,3883,10909,11281,11446,11480,3591,3697,10825,10828,10921,11091,4641,11895,4642,10665,10778,12510,4304,11048,12528,4212,3914,3859,4639,10495,10498,10867,10870,11764,4640,11875,3884,10831,11097,4144,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928,5930,5935,5943,5981,5996,6005,6008,6017,6021,6022,6023,6024,6025,6030,6035,6045,6051,6069,6073,6082,6112,6128,6154,6171,6172,6175,6190,6192,6194,6196,6211,6212,6215,6217,6220,6221,6238,6246,6247,6248,6250,6252,6290,6291,6296,6299,6305,6309,6343,6345,6347,6349,6359,6361,6364,6370,6372,6377,6380,6388,6396,6398,6399,6406,6429,6430,6431,6432,6433,6435,6442,6447,6481,6482,6485,6486,6487,6489,6490,6491,6492,6499,6535,6536,6545,6567,6568,6592,6594,6606,6607,6613,6643,6645,6660,6700,6703,6704,6760,6783,6826,6841,6849,6858,6859,6860,6861,6882,6883,6890,6902,6905,6907,6909,6910,6911,6913,6927,6938,6939,6940,6953,7008,7019,7021,7026,7045,7046,7082,7089,7096,7126,7157,7213,7242,7299,7320,7329,7332,7392,7402,7465,7467,7481,7490,7491,7492,7509,7513,7515,7562,7572,7575,7590,7638,7640,7643,7687,7688,7706,7776,7794,7818,7842,7854,7868,7879,7890,7891,7917,7919,7921,7931,7969,7980,8005,8032,8065,8096,8130,8169,8186,8188,8204,8205,8273,8284,8349,8373,8392,8419,8458,8459,8476,8516,8518,8520,8526,8542,8546,8561,8582,8590,8592,8602,8607,8611,8612,8613,8614,8615,8616,8635,8650,8651,8669,8671,8675,8676,8677,8678,8679,8697,8698,8699,8709,8722,8725,8736,8741,8743,8745,8746,8747,8754,8760,8768,8771,8788,8789,8798,8799,8807,8826,8839,8843,8864,8886,8887,8890,8891,8897,8906,8907,8930,8941,8951,8952,8953,8956,8979,8980,8991,9041,9051,9053,9069,9081,9082,9083,9094,9158,9189,9190,919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% 168.60/168.47 cnf(12557,plain,
% 168.60/168.47 (P1(f315(f315(f223(f909(x125571,a899)),x125572),x125572))),
% 168.60/168.47 inference(rename_variables,[],[3730])).
% 168.60/168.47 cnf(12560,plain,
% 168.60/168.47 (~P1(f315(f315(f317(x125601),x125602),f177(f909(x125601,a899))))),
% 168.60/168.47 inference(rename_variables,[],[4628])).
% 168.60/168.47 cnf(12563,plain,
% 168.60/168.47 (~P1(f315(f315(f177(f909(x125631,f909(x125632,a899))),x125633),x125634))),
% 168.60/168.47 inference(rename_variables,[],[4642])).
% 168.60/168.47 cnf(12566,plain,
% 168.60/168.47 (P1(f315(f315(f223(f909(x125661,a899)),f315(f298(x125662,x125661,x125663),f315(f299(x125662,x125661,x125663),x125664))),x125664))),
% 168.60/168.47 inference(rename_variables,[],[4304])).
% 168.60/168.47 cnf(12567,plain,
% 168.60/168.47 (P1(f315(f315(f223(f909(x125671,a899)),x125672),x125672))),
% 168.60/168.47 inference(rename_variables,[],[3730])).
% 168.60/168.47 cnf(12572,plain,
% 168.60/168.47 (E(f315(f272(x125721,x125721),f251(x125721,x125722)),x125722)),
% 168.60/168.47 inference(rename_variables,[],[3401])).
% 168.60/168.47 cnf(12575,plain,
% 168.60/168.47 (P1(f315(f315(f223(f909(x125751,a899)),f315(f161(x125751),f165(x125751,x125752,x125753))),f315(f161(x125751),x125752)))),
% 168.60/168.47 inference(rename_variables,[],[4124])).
% 168.60/168.47 cnf(12576,plain,
% 168.60/168.47 (P1(f315(f54(x125761),f315(f161(x125761),x125762)))),
% 168.60/168.47 inference(rename_variables,[],[3479])).
% 168.60/168.47 cnf(12579,plain,
% 168.60/168.47 (P1(f315(f315(f223(a901),x125791),x125791))),
% 168.60/168.47 inference(rename_variables,[],[3440])).
% 168.60/168.47 cnf(12582,plain,
% 168.60/168.47 (~P1(f315(f315(f224(a901),x125821),x125821))),
% 168.60/168.47 inference(rename_variables,[],[4617])).
% 168.60/168.47 cnf(12585,plain,
% 168.60/168.47 (~P1(f315(f315(f224(a901),x125851),x125851))),
% 168.60/168.47 inference(rename_variables,[],[4617])).
% 168.60/168.47 cnf(12596,plain,
% 168.60/168.47 (P25(x125961,x125961,f7(x125961),x125962)),
% 168.60/168.47 inference(rename_variables,[],[3674])).
% 168.60/168.47 cnf(12604,plain,
% 168.60/168.47 (~P1(f315(f315(f317(x126041),x126042),f177(f909(x126041,a899))))),
% 168.60/168.47 inference(rename_variables,[],[4628])).
% 168.60/168.47 cnf(12607,plain,
% 168.60/168.47 (P1(f315(f315(f317(f908(x126071,x126071)),f315(f315(f240(x126071,x126071),x126072),x126072)),f295(x126071,x126073)))),
% 168.60/168.47 inference(rename_variables,[],[4068])).
% 168.60/168.47 cnf(12610,plain,
% 168.60/168.47 (~P1(f315(f315(f317(x126101),x126102),f177(f909(x126101,a899))))),
% 168.60/168.47 inference(rename_variables,[],[4628])).
% 168.60/168.47 cnf(12613,plain,
% 168.60/168.47 (P1(f315(f315(f317(f908(x126131,x126131)),f315(f315(f240(x126131,x126131),x126132),x126132)),f295(x126131,x126133)))),
% 168.60/168.47 inference(rename_variables,[],[4068])).
% 168.60/168.47 cnf(12623,plain,
% 168.60/168.47 (~E(f315(f315(f140(x126231),x126232),x126233),x126233)),
% 168.60/168.47 inference(rename_variables,[],[4597])).
% 168.60/168.47 cnf(12625,plain,
% 168.60/168.47 (~P26(a901,a901,x126251,f230(f909(a901,a899)),f291(a901,x126252,x126253))),
% 168.60/168.47 inference(scs_inference,[],[3783,3674,11333,12394,12501,12504,3683,3690,3411,4603,4604,3309,3312,4602,4583,10413,10423,10436,10447,10519,10554,10557,10560,10662,10797,11110,11303,11306,11325,11328,11521,11622,11629,11643,11689,11692,11725,11740,11803,11862,11881,12175,12200,12216,12245,12251,12345,3642,12147,3361,4589,10646,10746,11213,4595,3052,3053,3055,3056,3059,3060,3062,3063,3064,3071,3075,3076,3077,3081,3086,3087,3091,3097,3109,3115,3116,3123,3130,3133,3136,3137,3148,3180,3181,3186,3190,3191,3193,3201,3202,3222,3332,3236,4581,3998,11912,3286,11619,3401,10482,10485,10581,10584,10900,11634,11637,11751,11790,11795,11865,11907,12366,3378,3387,3893,4194,3276,3636,3984,11665,3338,3272,3299,3752,3295,3281,3282,3905,3319,3496,11060,11187,3371,4066,4597,10473,10643,11518,3431,11994,4626,11239,11338,11574,11577,3543,4606,3335,10546,10876,3336,3595,3254,3357,11655,4208,4068,11259,11390,11449,12607,4644,11162,11403,11512,11538,11582,11588,12551,4645,11292,11406,11515,4646,11409,4647,11467,4648,3356,3634,12507,12548,3799,3583,4479,4480,4594,11648,3734,3948,3735,3994,3620,3876,3507,10565,10685,10763,10836,10839,10879,10979,11229,11839,12091,12171,12238,12316,12357,12436,12439,3886,11898,3424,3519,11724,3696,4621,10450,10453,10479,10606,10781,10987,11002,11120,11560,11658,11838,12062,12067,12292,12295,12378,12554,4632,11767,11798,11835,11842,11878,3873,3643,4016,3467,3469,3443,4618,4591,3627,4633,4201,11535,3757,3479,12015,12018,12472,4624,10441,10444,10614,10709,10728,10735,10758,10766,10769,10786,10972,11216,11429,11718,11812,11963,12080,12083,4170,4129,12522,4077,11057,12164,12351,4124,11265,12391,12471,12531,12575,3800,11846,12174,12323,12401,4158,3817,10609,10706,11262,11343,11422,11486,12344,12348,12417,4636,11005,11414,3440,10574,10672,10822,10886,10961,11008,11011,11042,11068,11104,11142,11181,11966,12012,12144,12199,12219,12222,12225,12228,12410,12424,12427,12430,12433,12515,3441,10601,10657,10891,10982,11107,11743,12045,12048,12059,12150,12161,12180,12185,12231,12254,3442,12442,3515,12383,4617,10490,10522,11026,11071,11080,11926,11947,12118,12121,12124,12127,12215,12234,12237,12250,12304,12307,12310,12313,12483,12486,12582,3590,10751,10842,11115,11159,11393,11396,11475,11557,11728,11977,4628,11035,11045,11151,11172,11175,11242,11245,11256,11359,11367,11381,11417,11434,11443,11483,11524,11529,11532,11551,11554,11591,11596,11599,11602,11605,11845,11991,12024,12298,12301,12335,12384,12413,12560,12604,3500,10873,10903,10912,10915,10918,3539,3532,3952,3891,10525,11901,11929,4625,10470,10861,10864,11362,11378,11861,11917,11951,11978,12077,12106,12109,12112,12115,12377,3461,10906,11065,11135,11930,12076,12276,12491,3915,4249,4622,3926,3960,4609,4612,3417,3421,4611,4610,3747,4343,4638,10772,10775,4643,11248,11251,11437,11548,11565,11611,4034,11608,11950,3881,11178,11184,11202,12196,12328,3730,11318,11440,12448,12557,3883,10909,11281,11446,11480,3591,3697,10825,10828,10921,11091,4641,11895,4642,10665,10778,12510,12519,4304,11048,12528,12543,4212,3914,3859,4639,10495,10498,10867,10870,11764,4640,11875,3884,10831,11097,4144,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928,5930,5935,5943,5981,5996,6005,6008,6017,6021,6022,6023,6024,6025,6030,6035,6045,6051,6069,6073,6082,6112,6128,6154,6171,6172,6175,6190,6192,6194,6196,6211,6212,6215,6217,6220,6221,6238,6246,6247,6248,6250,6252,6290,6291,6296,6299,6305,6309,6343,6345,6347,6349,6359,6361,6364,6370,6372,6377,6380,6388,6396,6398,6399,6406,6429,6430,6431,6432,6433,6435,6442,6447,6481,6482,6485,6486,6487,6489,6490,6491,6492,6499,6535,6536,6545,6567,6568,6592,6594,6606,6607,6613,6643,6645,6660,6700,6703,6704,6760,6783,6826,6841,6849,6858,6859,6860,6861,6882,6883,6890,6902,6905,6907,6909,6910,6911,6913,6927,6938,6939,6940,6953,7008,7019,7021,7026,7045,7046,7082,7089,7096,7126,7157,7213,7242,7299,7320,7329,7332,7392,7402,7465,7467,7481,7490,7491,7492,7509,7513,7515,7562,7572,7575,7590,7638,7640,7643,7687,7688,7706,7776,7794,7818,7842,7854,7868,7879,7890,7891,7917,7919,7921,7931,7969,7980,8005,8032,8065,8096,8130,8169,8186,8188,8204,8205,8273,8284,8349,8373,8392,8419,8458,8459,8476,8516,8518,8520,8526,8542,8546,8561,8582,8590,8592,8602,8607,8611,8612,8613,8614,8615,8616,8635,8650,8651,8669,8671,8675,8676,8677,8678,8679,8697,8698,8699,8709,8722,8725,8736,8741,8743,8745,8746,8747,8754,8760,8768,8771,8788,8789,8798,8799,8807,8826,8839,8843,8864,8886,8887,8890,8891,8897,8906,8907,8930,8941,8951,8952,8953,8956,8979,8980,8991,9041,9051,9053,9069,9081,9082,9083,9094,9158,9189,9190,9191,9206,9223,9231,9259,9260,9329,9364,9370,9380,9381,9382,9391,9421,9437,9441,9445,9467,9468,9495,9559,9564,9567,9604,9605,9606,9634,9635,9651,9672,9678,9690,9715,9736,9745,9746,9747,9748,9763,9765,9770,9800,9801,9807,9808,9852,9853,9864,9865,9889,9907,9909,9910,9918,9923,9930,9954,9988,9990,9994,10044,10078,10088,10090,10094,10095,10097,10106,10107,10127,10132,10225,10317,10318,10319,10320,10379,10397,2,8,9,4668,4669,4687,4729,4731,4732,4755,4757,4758,4768,4813,4815,4863,4993,4994,5011,5035,5092,5093,5099,5100,5102,5104,5113,5116,5117,5125,5138,5139,5145,5166,5167,5185,5190,5191,5192,5193,5197,5205,5208,5215,5270,5275,5276,5281,5288,5319,5329,5334,5344,5362,5364,5371,5372,5374,5385,5403,5405,5406,5413,5420,5421,5433,5434,5435,5436,5438,5439,5444,5445,5446,5447,5478,5479,5480,5488,5489,5490,5491,5535,5540,5542,5578,5580,5581,5583,5584,5586,5587,5589,5598,5603,5605,5606,5607,5609,5611,5612,5613,5614,5615,5616,5625,5626,5636,5639,5650,5666,5667,5670,5681,5684,5685,5686,5713,5723,5738,5739,5748,5749,5751,5753,5758,5793,5798,5800,5859,5894,5895,5909,5915,5918,5919,5920,5921,5940,5944,5945,5954,5976,6009,6028,6029,6033,6034,6036,6059,6063,6066,6067,6068,6084,6096,6097,6130,6131,6135,6156,6159,6162,6184,6185,6213,6216,6225,6234,6236,6245,6249,6257,6258,6259,6260,6293,6310,6363,6400,6402,6403,6426,6427,6434,6438,6439,6443,6457,6473,6494,6495,6500,6512,6515,6528,6548,6555,6557,6572,6573,6576,6577,6579,6581,6582,6583,6585,6587,6593,6599,6600,6602,6603,6609,6611,6653,6659,6674,6678,6679,6680,6714,6719,6721,6726,6727,6737,6741,6755,6778,6779,6781,6782,6793,6799,6818,6821,6842,6862,6873,6876,6877,6878,6884,6898,6917,6919,6921,6923,6928,6934,6936,6950,6955,6956,6993,6994,6995,7010,7011,7013,7014,7035,7037,7052,7080,7104,7115,7117,7119,7121,7122,7154,7155,7156,7160,7161,7168,7169,7171,7173,7195,7204,7205,7216,7226,7266,7276,7282,7289,7300,7305,7307,7314,7322,7323,7336,7353,7374,7376,7395,7450,7451,7452,7454,7456,7460,7461,7466,7530,7558,7573,7578,7589,7620,7624,7631,7646,7671,7689,7692,7693,7703,7723,7725,7727,7729,7730,7731,7732,7733,7758,7784,7785,7817,7819,7820,7821,7827,7848,7865,7870,7876,7878,7886,7898,7899,7901,7922,7929,7950,8018,8019,8020,8068,8074,8075,8099,8100,8117,8118,8119,8177,8178,8207,8237,8247,8261,8276,8305,8309,8315,8327,8345,8350,8372,8417,8446,8460,8480,8483,8509,8535,8593,8594,8597,8598,8667,8701,8702,8703,8704,8731,8763,8792,8800])).
% 168.60/168.47 cnf(12630,plain,
% 168.60/168.47 (P1(f315(f315(f317(x126301),x126302),f230(f909(x126301,a899))))),
% 168.60/168.47 inference(rename_variables,[],[3590])).
% 168.60/168.47 cnf(12631,plain,
% 168.60/168.47 (~E(f315(a101,x126311),x126311)),
% 168.60/168.47 inference(rename_variables,[],[4583])).
% 168.60/168.47 cnf(12634,plain,
% 168.60/168.47 (P1(f315(f315(f317(f902(x126341)),f102(x126341)),f150(x126341,x126342)))),
% 168.60/168.47 inference(rename_variables,[],[3634])).
% 168.60/168.47 cnf(12635,plain,
% 168.60/168.47 (~E(f315(f315(f140(x126351),x126352),x126353),f102(x126351))),
% 168.60/168.47 inference(rename_variables,[],[4600])).
% 168.60/168.47 cnf(12638,plain,
% 168.60/168.47 (P25(x126381,x126381,f7(x126381),x126382)),
% 168.60/168.47 inference(rename_variables,[],[3674])).
% 168.60/168.47 cnf(12641,plain,
% 168.60/168.47 (P1(f315(f315(f317(x126411),f315(x126412,x126413)),f315(f298(x126414,x126411,x126412),f230(f909(x126414,a899)))))),
% 168.60/168.47 inference(rename_variables,[],[4034])).
% 168.60/168.47 cnf(12642,plain,
% 168.60/168.47 (P25(x126421,x126421,f7(x126421),x126422)),
% 168.60/168.47 inference(rename_variables,[],[3674])).
% 168.60/168.47 cnf(12645,plain,
% 168.60/168.47 (P1(f315(f315(f223(f909(x126451,a899)),f177(f909(x126451,a899))),x126452))),
% 168.60/168.47 inference(rename_variables,[],[3883])).
% 168.60/168.47 cnf(12646,plain,
% 168.60/168.47 (P1(f315(f315(f223(f909(x126461,a899)),x126462),x126462))),
% 168.60/168.47 inference(rename_variables,[],[3730])).
% 168.60/168.47 cnf(12649,plain,
% 168.60/168.47 (P1(f315(f315(f317(x126491),f315(x126492,x126493)),f315(f298(x126494,x126491,x126492),f230(f909(x126494,a899)))))),
% 168.60/168.47 inference(rename_variables,[],[4034])).
% 168.60/168.47 cnf(12650,plain,
% 168.60/168.47 (P25(x126501,x126501,f7(x126501),x126502)),
% 168.60/168.47 inference(rename_variables,[],[3674])).
% 168.60/168.47 cnf(12653,plain,
% 168.60/168.47 (P1(f315(f315(f317(f908(f902(x126531),f902(x126531))),f315(f315(f240(f902(x126531),f902(x126531)),f102(x126531)),f102(x126531))),f147(x126531,x126532)))),
% 168.60/168.47 inference(rename_variables,[],[4208])).
% 168.60/168.47 cnf(12657,plain,
% 168.60/168.47 (~P1(f315(f315(f224(a901),x126571),f2(a901)))),
% 168.60/168.47 inference(rename_variables,[],[4621])).
% 168.60/168.47 cnf(12663,plain,
% 168.60/168.47 (E(f315(f315(f123(x126631),x126632),f102(x126631)),x126632)),
% 168.60/168.47 inference(rename_variables,[],[3372])).
% 168.60/168.47 cnf(12664,plain,
% 168.60/168.47 (~E(f315(f315(f140(x126641),x126642),x126643),x126643)),
% 168.60/168.47 inference(rename_variables,[],[4597])).
% 168.60/168.47 cnf(12667,plain,
% 168.60/168.47 (E(f315(f315(f123(x126671),x126672),f102(x126671)),x126672)),
% 168.60/168.47 inference(rename_variables,[],[3372])).
% 168.60/168.47 cnf(12668,plain,
% 168.60/168.47 (~E(f315(f315(f140(x126681),x126682),x126683),x126683)),
% 168.60/168.47 inference(rename_variables,[],[4597])).
% 168.60/168.47 cnf(12671,plain,
% 168.60/168.47 (E(f315(f315(f123(x126711),x126712),f102(x126711)),x126712)),
% 168.60/168.47 inference(rename_variables,[],[3372])).
% 168.60/168.47 cnf(12678,plain,
% 168.60/168.47 (P53(x126781,f251(x126781,x126782))),
% 168.60/168.47 inference(rename_variables,[],[3313])).
% 168.60/168.47 cnf(12681,plain,
% 168.60/168.47 (P1(f315(f315(f223(f909(x126811,a899)),f315(f161(x126811),f315(f125(x126811,x126812),x126813))),f315(f161(x126811),x126813)))),
% 168.60/168.47 inference(rename_variables,[],[4077])).
% 168.60/168.47 cnf(12682,plain,
% 168.60/168.47 (E(f315(f298(x126821,x126821,f7(x126821)),x126822),x126822)),
% 168.60/168.47 inference(rename_variables,[],[3496])).
% 168.60/168.47 cnf(12687,plain,
% 168.60/168.47 (P1(f315(f315(f223(f909(x126871,a899)),x126872),f230(f909(x126871,a899))))),
% 168.60/168.47 inference(rename_variables,[],[3817])).
% 168.60/168.47 cnf(12691,plain,
% 168.60/168.47 (~P1(f315(f315(f224(a901),x126911),x126911))),
% 168.60/168.47 inference(rename_variables,[],[4617])).
% 168.60/168.47 cnf(12692,plain,
% 168.60/168.47 (~E(f315(a101,x126921),x126921)),
% 168.60/168.47 inference(rename_variables,[],[4583])).
% 168.60/168.47 cnf(12695,plain,
% 168.60/168.47 (P1(f315(f315(f223(f909(x126951,a899)),f177(f909(x126951,a899))),x126952))),
% 168.60/168.47 inference(rename_variables,[],[3883])).
% 168.60/168.47 cnf(12698,plain,
% 168.60/168.47 (P1(f315(f315(f223(a901),x126981),x126981))),
% 168.60/168.47 inference(rename_variables,[],[3440])).
% 168.60/168.47 cnf(12701,plain,
% 168.60/168.47 (P1(f315(f315(f223(f909(x127011,a899)),x127012),x127012))),
% 168.60/168.47 inference(rename_variables,[],[3730])).
% 168.60/168.47 cnf(12706,plain,
% 168.60/168.47 (P1(f315(f315(f223(f909(x127061,a899)),x127062),f315(f315(f297(x127061),x127063),x127062)))),
% 168.60/168.47 inference(rename_variables,[],[3881])).
% 168.60/168.47 cnf(12709,plain,
% 168.60/168.47 (P1(f315(f315(f223(f909(x127091,a899)),x127092),x127092))),
% 168.60/168.47 inference(rename_variables,[],[3730])).
% 168.60/168.47 cnf(12710,plain,
% 168.60/168.47 (~P1(f315(f315(f317(x127101),x127102),f177(f909(x127101,a899))))),
% 168.60/168.47 inference(rename_variables,[],[4628])).
% 168.60/168.47 cnf(12713,plain,
% 168.60/168.47 (~P1(f315(f315(f317(x127131),x127132),f177(f909(x127131,a899))))),
% 168.60/168.47 inference(rename_variables,[],[4628])).
% 168.60/168.47 cnf(12721,plain,
% 168.60/168.47 (~P1(f315(f315(f223(f909(f908(x127211,x127211),a899)),f315(f298(f908(x127211,x127211),f908(x127211,x127211),f7(f908(x127211,x127211))),f230(f909(f908(x127211,x127211),a899)))),f315(f298(f908(x127211,x127211),f908(x127211,x127211),f7(f908(x127211,x127211))),f177(f909(f908(x127211,x127211),a899)))))),
% 168.60/168.47 inference(scs_inference,[],[3783,3674,11333,12394,12501,12504,12596,12638,12642,12650,3683,3690,3411,4603,4604,3309,3312,3313,4602,4583,10413,10423,10436,10447,10519,10554,10557,10560,10662,10797,11110,11303,11306,11325,11328,11521,11622,11629,11643,11689,11692,11725,11740,11803,11862,11881,12175,12200,12216,12245,12251,12345,12464,12631,3495,3642,12147,3361,4589,10646,10746,11213,4595,3052,3053,3055,3056,3059,3060,3062,3063,3064,3071,3075,3076,3077,3081,3086,3087,3091,3097,3109,3115,3116,3123,3130,3133,3136,3137,3148,3180,3181,3186,3190,3191,3193,3201,3202,3222,3332,3236,4581,3998,11912,3286,11619,3401,10482,10485,10581,10584,10900,11634,11637,11751,11790,11795,11865,11907,12366,3372,12663,12667,3378,3387,3893,4194,3276,3636,3984,11665,3338,3272,3299,3752,3295,3281,3282,3905,3319,3496,11060,11187,12465,12682,3371,4066,4597,10473,10643,11518,12623,12664,4600,12635,3431,11994,4626,11239,11338,11574,11577,3543,4606,3335,10546,10876,3336,3595,3254,3357,11655,4208,12653,4068,11259,11390,11449,12607,12613,4644,11162,11403,11512,11538,11582,11588,12551,4645,11292,11406,11515,4646,11409,4647,11467,4648,3356,3634,12507,12548,12634,3799,3583,4479,4480,4594,11648,3734,3948,3735,3994,3620,3876,3507,10565,10685,10763,10836,10839,10879,10979,11229,11839,12091,12171,12238,12316,12357,12436,12439,3886,11898,3424,3519,11724,3696,4621,10450,10453,10479,10606,10781,10987,11002,11120,11560,11658,11838,12062,12067,12292,12295,12378,12554,4632,11767,11798,11835,11842,11878,3873,3643,4016,3467,3469,3443,4618,4591,3825,3627,4633,4201,11535,3757,3479,12015,12018,12472,4624,10441,10444,10614,10709,10728,10735,10758,10766,10769,10786,10972,11216,11429,11718,11812,11963,12080,12083,4170,4129,12522,4077,11057,12164,12351,12532,4124,11265,12391,12471,12531,12575,3800,11846,12174,12323,12401,4158,3817,10609,10706,11262,11343,11422,11486,12344,12348,12417,4636,11005,11414,3440,10574,10672,10822,10886,10961,11008,11011,11042,11068,11104,11142,11181,11966,12012,12144,12199,12219,12222,12225,12228,12410,12424,12427,12430,12433,12515,12579,3441,10601,10657,10891,10982,11107,11743,12045,12048,12059,12150,12161,12180,12185,12231,12254,3442,12442,3515,12383,4617,10490,10522,11026,11071,11080,11926,11947,12118,12121,12124,12127,12215,12234,12237,12250,12304,12307,12310,12313,12483,12486,12582,12585,3590,10751,10842,11115,11159,11393,11396,11475,11557,11728,11977,4628,11035,11045,11151,11172,11175,11242,11245,11256,11359,11367,11381,11417,11434,11443,11483,11524,11529,11532,11551,11554,11591,11596,11599,11602,11605,11845,11991,12024,12298,12301,12335,12384,12413,12560,12604,12610,12710,3500,10873,10903,10912,10915,10918,3539,3532,3952,3891,10525,11901,11929,4625,10470,10861,10864,11362,11378,11861,11917,11951,11978,12077,12106,12109,12112,12115,12377,3461,10906,11065,11135,11930,12076,12276,12491,3915,4249,4622,3926,3960,4609,4612,3417,3421,4611,4610,3747,4343,4638,10772,10775,4643,11248,11251,11437,11548,11565,11611,4034,11608,11950,11954,12641,3881,11178,11184,11202,12196,12328,12416,3730,11318,11440,12448,12557,12567,12646,12701,3883,10909,11281,11446,11480,11491,12645,3591,3697,10825,10828,10921,11091,4641,11895,4642,10665,10778,12510,12519,4304,11048,12528,12543,4212,3914,3859,4639,10495,10498,10867,10870,11764,4640,11875,3884,10831,11097,4144,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928,5930,5935,5943,5981,5996,6005,6008,6017,6021,6022,6023,6024,6025,6030,6035,6045,6051,6069,6073,6082,6112,6128,6154,6171,6172,6175,6190,6192,6194,6196,6211,6212,6215,6217,6220,6221,6238,6246,6247,6248,6250,6252,6290,6291,6296,6299,6305,6309,6343,6345,6347,6349,6359,6361,6364,6370,6372,6377,6380,6388,6396,6398,6399,6406,6429,6430,6431,6432,6433,6435,6442,6447,6481,6482,6485,6486,6487,6489,6490,6491,6492,6499,6535,6536,6545,6567,6568,6592,6594,6606,6607,6613,6643,6645,6660,6700,6703,6704,6760,6783,6826,6841,6849,6858,6859,6860,6861,6882,6883,6890,6902,6905,6907,6909,6910,6911,6913,6927,6938,6939,6940,6953,7008,7019,7021,7026,7045,7046,7082,7089,7096,7126,7157,7213,7242,7299,7320,7329,7332,7392,7402,7465,7467,7481,7490,7491,7492,7509,7513,7515,7562,7572,7575,7590,7638,7640,7643,7687,7688,7706,7776,7794,7818,7842,7854,7868,7879,7890,7891,7917,7919,7921,7931,7969,7980,8005,8032,8065,8096,8130,8169,8186,8188,8204,8205,8273,8284,8349,8373,8392,8419,8458,8459,8476,8516,8518,8520,8526,8542,8546,8561,8582,8590,8592,8602,8607,8611,8612,8613,8614,8615,8616,8635,8650,8651,8669,8671,8675,8676,8677,8678,8679,8697,8698,8699,8709,8722,8725,8736,8741,8743,8745,8746,8747,8754,8760,8768,8771,8788,8789,8798,8799,8807,8826,8839,8843,8864,8886,8887,8890,8891,8897,8906,8907,8930,8941,8951,8952,8953,8956,8979,8980,8991,9041,9051,9053,9069,9081,9082,9083,9094,9158,9189,9190,9191,9206,9223,9231,9259,9260,9329,9364,9370,9380,9381,9382,9391,9421,9437,9441,9445,9467,9468,9495,9559,9564,9567,9604,9605,9606,9634,9635,9651,9672,9678,9690,9715,9736,9745,9746,9747,9748,9763,9765,9770,9800,9801,9807,9808,9852,9853,9864,9865,9889,9907,9909,9910,9918,9923,9930,9954,9988,9990,9994,10044,10078,10088,10090,10094,10095,10097,10106,10107,10127,10132,10225,10317,10318,10319,10320,10379,10397,2,8,9,4668,4669,4687,4729,4731,4732,4755,4757,4758,4768,4813,4815,4863,4993,4994,5011,5035,5092,5093,5099,5100,5102,5104,5113,5116,5117,5125,5138,5139,5145,5166,5167,5185,5190,5191,5192,5193,5197,5205,5208,5215,5270,5275,5276,5281,5288,5319,5329,5334,5344,5362,5364,5371,5372,5374,5385,5403,5405,5406,5413,5420,5421,5433,5434,5435,5436,5438,5439,5444,5445,5446,5447,5478,5479,5480,5488,5489,5490,5491,5535,5540,5542,5578,5580,5581,5583,5584,5586,5587,5589,5598,5603,5605,5606,5607,5609,5611,5612,5613,5614,5615,5616,5625,5626,5636,5639,5650,5666,5667,5670,5681,5684,5685,5686,5713,5723,5738,5739,5748,5749,5751,5753,5758,5793,5798,5800,5859,5894,5895,5909,5915,5918,5919,5920,5921,5940,5944,5945,5954,5976,6009,6028,6029,6033,6034,6036,6059,6063,6066,6067,6068,6084,6096,6097,6130,6131,6135,6156,6159,6162,6184,6185,6213,6216,6225,6234,6236,6245,6249,6257,6258,6259,6260,6293,6310,6363,6400,6402,6403,6426,6427,6434,6438,6439,6443,6457,6473,6494,6495,6500,6512,6515,6528,6548,6555,6557,6572,6573,6576,6577,6579,6581,6582,6583,6585,6587,6593,6599,6600,6602,6603,6609,6611,6653,6659,6674,6678,6679,6680,6714,6719,6721,6726,6727,6737,6741,6755,6778,6779,6781,6782,6793,6799,6818,6821,6842,6862,6873,6876,6877,6878,6884,6898,6917,6919,6921,6923,6928,6934,6936,6950,6955,6956,6993,6994,6995,7010,7011,7013,7014,7035,7037,7052,7080,7104,7115,7117,7119,7121,7122,7154,7155,7156,7160,7161,7168,7169,7171,7173,7195,7204,7205,7216,7226,7266,7276,7282,7289,7300,7305,7307,7314,7322,7323,7336,7353,7374,7376,7395,7450,7451,7452,7454,7456,7460,7461,7466,7530,7558,7573,7578,7589,7620,7624,7631,7646,7671,7689,7692,7693,7703,7723,7725,7727,7729,7730,7731,7732,7733,7758,7784,7785,7817,7819,7820,7821,7827,7848,7865,7870,7876,7878,7886,7898,7899,7901,7922,7929,7950,8018,8019,8020,8068,8074,8075,8099,8100,8117,8118,8119,8177,8178,8207,8237,8247,8261,8276,8305,8309,8315,8327,8345,8350,8372,8417,8446,8460,8480,8483,8509,8535,8593,8594,8597,8598,8667,8701,8702,8703,8704,8731,8763,8792,8800,8801,8842,8863,8908,8924,8970,8973,8988,8995,9038,9077,9078,9096,9097,9111,9228,9233,9237,9257,9268,9291,9293,9296,9302,9304,9305,9316,9317,9336,9344])).
% 168.60/168.47 cnf(12722,plain,
% 168.60/168.47 (P25(x127221,x127221,f7(x127221),x127222)),
% 168.60/168.47 inference(rename_variables,[],[3674])).
% 168.60/168.47 cnf(12725,plain,
% 168.60/168.47 (E(f315(f178(f902(x127251)),f158(x127251,x127252,x127253)),x127252)),
% 168.60/168.47 inference(rename_variables,[],[3506])).
% 168.60/168.47 cnf(12728,plain,
% 168.60/168.47 (P26(x127281,x127281,f25(x127281),x127282,x127282)),
% 168.60/168.47 inference(rename_variables,[],[4092])).
% 168.60/168.47 cnf(12731,plain,
% 168.60/168.47 (~P1(f315(f315(f224(a901),x127311),x127311))),
% 168.60/168.47 inference(rename_variables,[],[4617])).
% 168.60/168.47 cnf(12732,plain,
% 168.60/168.47 (P1(f315(f230(f909(x127321,a899)),x127322))),
% 168.60/168.47 inference(rename_variables,[],[3500])).
% 168.60/168.47 cnf(12735,plain,
% 168.60/168.47 (~P1(f315(f315(f317(x127351),x127352),f177(f909(x127351,a899))))),
% 168.60/168.47 inference(rename_variables,[],[4628])).
% 168.60/168.47 cnf(12738,plain,
% 168.60/168.47 (P1(f315(f315(f317(x127381),f315(x127382,x127383)),f315(f298(x127384,x127381,x127382),f230(f909(x127384,a899)))))),
% 168.60/168.47 inference(rename_variables,[],[4034])).
% 168.60/168.47 cnf(12739,plain,
% 168.60/168.47 (P1(f315(f315(f317(f908(x127391,x127391)),f315(f315(f240(x127391,x127391),x127392),x127392)),f295(x127391,x127393)))),
% 168.60/168.47 inference(rename_variables,[],[4068])).
% 168.60/168.47 cnf(12742,plain,
% 168.60/168.47 (P1(f315(f315(f317(f908(x127421,x127421)),f315(f315(f240(x127421,x127421),x127422),x127422)),f295(x127421,x127423)))),
% 168.60/168.47 inference(rename_variables,[],[4068])).
% 168.60/168.47 cnf(12745,plain,
% 168.60/168.47 (P1(f315(f315(f223(a901),x127451),x127451))),
% 168.60/168.47 inference(rename_variables,[],[3440])).
% 168.60/168.47 cnf(12746,plain,
% 168.60/168.47 (P1(f315(f230(f909(x127461,a899)),x127462))),
% 168.60/168.47 inference(rename_variables,[],[3500])).
% 168.60/168.47 cnf(12749,plain,
% 168.60/168.47 (P1(f315(f315(f223(f909(x127491,a899)),x127492),f230(f909(x127491,a899))))),
% 168.60/168.47 inference(rename_variables,[],[3817])).
% 168.60/168.47 cnf(12750,plain,
% 168.60/168.47 (P26(x127501,x127501,f25(x127501),x127502,x127502)),
% 168.60/168.47 inference(rename_variables,[],[4092])).
% 168.60/168.47 cnf(12753,plain,
% 168.60/168.47 (P1(f315(f54(x127531),f315(f161(x127531),x127532)))),
% 168.60/168.47 inference(rename_variables,[],[3479])).
% 168.60/168.47 cnf(12760,plain,
% 168.60/168.47 (P1(f315(f315(f317(f908(x127601,x127601)),f315(f315(f240(x127601,x127601),x127602),x127602)),f315(f315(f277(x127601,x127601,x127601),f295(x127601,x127603)),f295(x127601,f295(x127601,x127603)))))),
% 168.60/168.47 inference(scs_inference,[],[3783,4092,12728,3674,11333,12394,12501,12504,12596,12638,12642,12650,3683,3690,3411,4603,4604,3309,3312,3313,4602,4583,10413,10423,10436,10447,10519,10554,10557,10560,10662,10797,11110,11303,11306,11325,11328,11521,11622,11629,11643,11689,11692,11725,11740,11803,11862,11881,12175,12200,12216,12245,12251,12345,12464,12631,3495,3642,12147,3361,4589,10646,10746,11213,4595,3052,3053,3055,3056,3059,3060,3062,3063,3064,3071,3075,3076,3077,3081,3086,3087,3091,3097,3109,3115,3116,3123,3130,3133,3136,3137,3148,3180,3181,3186,3190,3191,3193,3201,3202,3222,3332,3236,4581,3998,11912,3286,11619,3401,10482,10485,10581,10584,10900,11634,11637,11751,11790,11795,11865,11907,12366,3372,12663,12667,12671,3378,3387,3893,4194,3506,3276,3636,3984,11665,3338,3272,3299,3752,3295,3281,3282,3905,3319,3496,11060,11187,12465,12682,3371,4066,4597,10473,10643,11518,12623,12664,4600,12635,3431,11994,4626,11239,11338,11574,11577,3543,4606,3335,10546,10876,3336,3595,3254,3357,11655,4208,12653,4068,11259,11390,11449,12607,12613,12739,12742,4644,11162,11403,11512,11538,11582,11588,12551,4645,11292,11406,11515,4646,11409,4647,11467,4648,3356,3634,12507,12548,12634,3799,3583,4479,4480,4594,11648,3734,3948,3735,3994,3620,3876,3507,10565,10685,10763,10836,10839,10879,10979,11229,11839,12091,12171,12238,12316,12357,12436,12439,3886,11898,3424,3519,11724,3696,4621,10450,10453,10479,10606,10781,10987,11002,11120,11560,11658,11838,12062,12067,12292,12295,12378,12554,4632,11767,11798,11835,11842,11878,3873,3643,4016,3467,3469,3443,4618,4591,3825,3627,4633,4201,11535,3757,3479,12015,12018,12472,12576,4624,10441,10444,10614,10709,10728,10735,10758,10766,10769,10786,10972,11216,11429,11718,11812,11963,12080,12083,4170,4129,12522,4077,11057,12164,12351,12532,4124,11265,12391,12471,12531,12575,3800,11846,12174,12323,12401,4158,3817,10609,10706,11262,11343,11422,11486,12344,12348,12417,12687,4636,11005,11414,3440,10574,10672,10822,10886,10961,11008,11011,11042,11068,11104,11142,11181,11966,12012,12144,12199,12219,12222,12225,12228,12410,12424,12427,12430,12433,12515,12579,12698,3441,10601,10657,10891,10982,11107,11743,12045,12048,12059,12150,12161,12180,12185,12231,12254,3442,12442,3515,12383,4617,10490,10522,11026,11071,11080,11926,11947,12118,12121,12124,12127,12215,12234,12237,12250,12304,12307,12310,12313,12483,12486,12582,12585,12691,3590,10751,10842,11115,11159,11393,11396,11475,11557,11728,11977,4628,11035,11045,11151,11172,11175,11242,11245,11256,11359,11367,11381,11417,11434,11443,11483,11524,11529,11532,11551,11554,11591,11596,11599,11602,11605,11845,11991,12024,12298,12301,12335,12384,12413,12560,12604,12610,12710,12713,3500,10873,10903,10912,10915,10918,11504,12732,3539,3532,3952,3891,10525,11901,11929,4625,10470,10861,10864,11362,11378,11861,11917,11951,11978,12077,12106,12109,12112,12115,12377,3461,10906,11065,11135,11930,12076,12276,12491,3915,4249,4622,3926,3960,4609,4612,3417,3421,4611,4610,3747,4343,4638,10772,10775,4643,11248,11251,11437,11548,11565,11611,4034,11608,11950,11954,12641,12649,3881,11178,11184,11202,12196,12328,12416,3730,11318,11440,12448,12557,12567,12646,12701,3883,10909,11281,11446,11480,11491,12645,3591,3697,10825,10828,10921,11091,4641,11895,4642,10665,10778,12510,12519,4304,11048,12528,12543,4212,3914,3859,4639,10495,10498,10867,10870,11764,4640,11875,3884,10831,11097,4144,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928,5930,5935,5943,5981,5996,6005,6008,6017,6021,6022,6023,6024,6025,6030,6035,6045,6051,6069,6073,6082,6112,6128,6154,6171,6172,6175,6190,6192,6194,6196,6211,6212,6215,6217,6220,6221,6238,6246,6247,6248,6250,6252,6290,6291,6296,6299,6305,6309,6343,6345,6347,6349,6359,6361,6364,6370,6372,6377,6380,6388,6396,6398,6399,6406,6429,6430,6431,6432,6433,6435,6442,6447,6481,6482,6485,6486,6487,6489,6490,6491,6492,6499,6535,6536,6545,6567,6568,6592,6594,6606,6607,6613,6643,6645,6660,6700,6703,6704,6760,6783,6826,6841,6849,6858,6859,6860,6861,6882,6883,6890,6902,6905,6907,6909,6910,6911,6913,6927,6938,6939,6940,6953,7008,7019,7021,7026,7045,7046,7082,7089,7096,7126,7157,7213,7242,7299,7320,7329,7332,7392,7402,7465,7467,7481,7490,7491,7492,7509,7513,7515,7562,7572,7575,7590,7638,7640,7643,7687,7688,7706,7776,7794,7818,7842,7854,7868,7879,7890,7891,7917,7919,7921,7931,7969,7980,8005,8032,8065,8096,8130,8169,8186,8188,8204,8205,8273,8284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% 168.60/168.47 cnf(12763,plain,
% 168.60/168.47 (~P1(f315(f315(f177(f909(x127631,f909(x127632,a899))),x127633),x127634))),
% 168.60/168.47 inference(rename_variables,[],[4642])).
% 168.60/168.47 cnf(12769,plain,
% 168.60/168.47 (P1(f315(f315(f223(f909(x127691,a899)),x127692),f230(f909(x127691,a899))))),
% 168.60/168.47 inference(rename_variables,[],[3817])).
% 168.60/168.47 cnf(12772,plain,
% 168.60/168.47 (P1(f315(f315(f317(f908(x127721,x127721)),f315(f315(f240(x127721,x127721),x127722),x127722)),f295(x127721,x127723)))),
% 168.60/168.47 inference(rename_variables,[],[4068])).
% 168.60/168.47 cnf(12775,plain,
% 168.60/168.47 (~P1(f315(f315(f224(a901),f315(f315(f73(a901),x127751),x127752)),x127752))),
% 168.60/168.47 inference(rename_variables,[],[4639])).
% 168.60/168.47 cnf(12776,plain,
% 168.60/168.47 (P1(f315(f315(f224(a901),x127761),f315(a101,x127761)))),
% 168.60/168.47 inference(rename_variables,[],[3507])).
% 168.60/168.47 cnf(12779,plain,
% 168.60/168.47 (P1(f315(f315(f223(f909(x127791,a899)),x127792),f230(f909(x127791,a899))))),
% 168.60/168.47 inference(rename_variables,[],[3817])).
% 168.60/168.47 cnf(12782,plain,
% 168.60/168.47 (E(f315(f272(x127821,x127821),f251(x127821,x127822)),x127822)),
% 168.60/168.47 inference(rename_variables,[],[3401])).
% 168.60/168.47 cnf(12793,plain,
% 168.60/168.47 (~P1(f315(f315(f317(x127931),x127932),f177(f909(x127931,a899))))),
% 168.60/168.47 inference(rename_variables,[],[4628])).
% 168.60/168.47 cnf(12794,plain,
% 168.60/168.47 (P1(f315(f315(f317(f908(f902(x127941),f902(x127941))),f315(f315(f240(f902(x127941),f902(x127941)),f102(x127941)),f102(x127941))),f147(x127941,x127942)))),
% 168.60/168.47 inference(rename_variables,[],[4208])).
% 168.60/168.47 cnf(12799,plain,
% 168.60/168.47 (~P1(f315(f315(f317(x127991),x127992),f177(f909(x127991,a899))))),
% 168.60/168.47 inference(rename_variables,[],[4628])).
% 168.60/168.47 cnf(12804,plain,
% 168.60/168.47 (P33(x128041,x128042,f102(x128041))),
% 168.60/168.47 inference(rename_variables,[],[3377])).
% 168.60/168.47 cnf(12807,plain,
% 168.60/168.47 (E(f315(f178(f902(x128071)),f158(x128071,x128072,x128073)),x128072)),
% 168.60/168.47 inference(rename_variables,[],[3506])).
% 168.60/168.47 cnf(12810,plain,
% 168.60/168.47 (~P1(f315(f315(f317(x128101),x128102),f177(f909(x128101,a899))))),
% 168.60/168.47 inference(rename_variables,[],[4628])).
% 168.60/168.47 cnf(12816,plain,
% 168.60/168.47 (~P1(f315(f315(f224(a901),x128161),x128161))),
% 168.60/168.47 inference(rename_variables,[],[4617])).
% 168.60/168.47 cnf(12819,plain,
% 168.60/168.47 (P1(f315(f315(f317(x128191),x128192),f230(f909(x128191,a899))))),
% 168.60/168.47 inference(rename_variables,[],[3590])).
% 168.60/168.47 cnf(12823,plain,
% 168.60/168.47 (P1(f315(f315(f223(f909(x128231,a899)),x128232),x128232))),
% 168.60/168.47 inference(rename_variables,[],[3730])).
% 168.60/168.47 cnf(12826,plain,
% 168.60/168.47 (~P1(f315(f315(f317(x128261),x128262),f177(f909(x128261,a899))))),
% 168.60/168.47 inference(rename_variables,[],[4628])).
% 168.60/168.47 cnf(12829,plain,
% 168.60/168.47 (P1(f315(f315(f223(a1),f2(a1)),f315(f315(f232(a1),f315(f69(a1),x128291)),x128292)))),
% 168.60/168.47 inference(rename_variables,[],[3914])).
% 168.60/168.47 cnf(12832,plain,
% 168.60/168.47 (~E(f315(a101,x128321),x128321)),
% 168.60/168.47 inference(rename_variables,[],[4583])).
% 168.60/168.47 cnf(12834,plain,
% 168.60/168.47 (E(f315(f272(x128341,x128341),f251(x128341,x128342)),x128342)),
% 168.60/168.47 inference(rename_variables,[],[3401])).
% 168.60/168.47 cnf(12836,plain,
% 168.60/168.47 (E(f315(f272(x128361,x128361),f251(x128361,x128362)),x128362)),
% 168.60/168.47 inference(rename_variables,[],[3401])).
% 168.60/168.47 cnf(12838,plain,
% 168.60/168.47 (P40(x128381,f251(x128381,x128382))),
% 168.60/168.47 inference(rename_variables,[],[3310])).
% 168.60/168.47 cnf(12846,plain,
% 168.60/168.47 (E(f315(f272(x128461,x128461),f251(x128461,x128462)),x128462)),
% 168.60/168.47 inference(rename_variables,[],[3401])).
% 168.60/168.47 cnf(12851,plain,
% 168.60/168.47 (E(f315(f272(x128511,x128511),f251(x128511,x128512)),x128512)),
% 168.60/168.47 inference(rename_variables,[],[3401])).
% 168.60/168.47 cnf(12853,plain,
% 168.60/168.47 (E(f315(f272(x128531,x128531),f251(x128531,x128532)),x128532)),
% 168.60/168.47 inference(rename_variables,[],[3401])).
% 168.60/168.47 cnf(12863,plain,
% 168.60/168.47 (P25(x128631,x128631,f7(x128631),x128632)),
% 168.60/168.47 inference(rename_variables,[],[3674])).
% 168.60/168.47 cnf(12865,plain,
% 168.60/168.47 (P25(x128651,x128651,f7(x128651),x128652)),
% 168.60/168.47 inference(rename_variables,[],[3674])).
% 168.60/168.47 cnf(12872,plain,
% 168.60/168.47 (P26(x128721,x128721,f25(x128721),x128722,x128722)),
% 168.60/168.47 inference(rename_variables,[],[4092])).
% 168.60/168.47 cnf(12874,plain,
% 168.60/168.47 (P26(x128741,x128741,f25(x128741),x128742,x128742)),
% 168.60/168.47 inference(rename_variables,[],[4092])).
% 168.60/168.47 cnf(12876,plain,
% 168.60/168.47 (P26(x128761,x128761,f25(x128761),x128762,x128762)),
% 168.60/168.47 inference(rename_variables,[],[4092])).
% 168.60/168.47 cnf(12880,plain,
% 168.60/168.47 (E(f315(f272(x128801,x128801),f251(x128801,x128802)),x128802)),
% 168.60/168.47 inference(rename_variables,[],[3401])).
% 168.60/168.47 cnf(12884,plain,
% 168.60/168.47 (P39(x128841,f142(x128841,x128842))),
% 168.60/168.47 inference(rename_variables,[],[3309])).
% 168.60/168.47 cnf(12888,plain,
% 168.60/168.47 (E(f315(f272(x128881,x128881),f251(x128881,x128882)),x128882)),
% 168.60/168.47 inference(rename_variables,[],[3401])).
% 168.60/168.47 cnf(12890,plain,
% 168.60/168.47 (P53(x128901,f251(x128901,x128902))),
% 168.60/168.47 inference(rename_variables,[],[3313])).
% 168.60/168.47 cnf(12897,plain,
% 168.60/168.47 (E(f315(f272(x128971,x128971),f251(x128971,x128972)),x128972)),
% 168.60/168.47 inference(rename_variables,[],[3401])).
% 168.60/168.47 cnf(12909,plain,
% 168.60/168.47 (E(f177(f909(f908(x129091,x129091),a899)),f251(x129091,f177(f909(x129091,a899))))),
% 168.60/168.47 inference(rename_variables,[],[3510])).
% 168.60/168.47 cnf(12911,plain,
% 168.60/168.47 (P54(x129111,x129112,f251(x129111,x129112))),
% 168.60/168.47 inference(rename_variables,[],[3410])).
% 168.60/168.47 cnf(12913,plain,
% 168.60/168.47 (P54(x129131,x129132,f251(x129131,x129132))),
% 168.60/168.47 inference(rename_variables,[],[3410])).
% 168.60/168.47 cnf(12915,plain,
% 168.60/168.47 (P54(x129151,x129152,f251(x129151,x129152))),
% 168.60/168.47 inference(rename_variables,[],[3410])).
% 168.60/168.47 cnf(12917,plain,
% 168.60/168.47 (E(f315(f272(x129171,x129171),f251(x129171,x129172)),x129172)),
% 168.60/168.47 inference(rename_variables,[],[3401])).
% 168.60/168.47 cnf(12919,plain,
% 168.60/168.47 (P15(x129191,f909(x129191,a899),f297(x129191))),
% 168.60/168.47 inference(rename_variables,[],[3414])).
% 168.60/168.47 cnf(12923,plain,
% 168.60/168.47 (P56(x129231,x129231,f251(x129231,x129232))),
% 168.60/168.47 inference(rename_variables,[],[3411])).
% 168.60/168.47 cnf(12931,plain,
% 168.60/168.47 (E(f177(f909(f908(x129311,x129311),a899)),f251(x129311,f177(f909(x129311,a899))))),
% 168.60/168.47 inference(rename_variables,[],[3510])).
% 168.60/168.47 cnf(12933,plain,
% 168.60/168.47 (E(f177(f909(f908(x129331,x129331),a899)),f251(x129331,f177(f909(x129331,a899))))),
% 168.60/168.47 inference(rename_variables,[],[3510])).
% 168.60/168.47 cnf(12944,plain,
% 168.60/168.47 (P57(x129441,f177(f909(x129441,a899)),x129442)),
% 168.60/168.47 inference(rename_variables,[],[3459])).
% 168.60/168.47 cnf(12950,plain,
% 168.60/168.47 (P34(x129501,x129502,f102(x129501),f102(x129501))),
% 168.60/168.47 inference(rename_variables,[],[3683])).
% 168.60/168.47 cnf(12952,plain,
% 168.60/168.47 (P34(x129521,x129522,f102(x129521),f102(x129521))),
% 168.60/168.47 inference(rename_variables,[],[3683])).
% 168.60/168.47 cnf(12957,plain,
% 168.60/168.47 (P44(x129571,x129572,x129573,x129574,f177(f909(x129571,a899)),x129574)),
% 168.60/168.47 inference(rename_variables,[],[4365])).
% 168.60/168.47 cnf(12968,plain,
% 168.60/168.47 (E(f315(f272(x129681,x129681),f251(x129681,x129682)),x129682)),
% 168.60/168.47 inference(rename_variables,[],[3401])).
% 168.60/168.47 cnf(12980,plain,
% 168.60/168.47 (~P1(f315(f315(f224(a901),x129801),f2(a901)))),
% 168.60/168.47 inference(rename_variables,[],[4621])).
% 168.60/168.47 cnf(12989,plain,
% 168.60/168.47 (~P1(f315(f315(f224(a1),f315(f89(a1),x129891)),f315(f72(a1),f315(f89(a1),x129892))))),
% 168.60/168.47 inference(rename_variables,[],[4637])).
% 168.60/168.47 cnf(12999,plain,
% 168.60/168.47 (~P1(f315(f315(f224(a901),x129991),f2(a901)))),
% 168.60/168.47 inference(rename_variables,[],[4621])).
% 168.60/168.47 cnf(13002,plain,
% 168.60/168.47 (~P1(f315(f315(f224(a901),x130021),f2(a901)))),
% 168.60/168.47 inference(rename_variables,[],[4621])).
% 168.60/168.47 cnf(13005,plain,
% 168.60/168.47 (P1(f315(f54(a901),f293(a901,x130051,x130052)))),
% 168.60/168.47 inference(rename_variables,[],[3645])).
% 168.60/168.47 cnf(13008,plain,
% 168.60/168.47 (P1(f315(f54(a901),f293(a901,x130081,x130082)))),
% 168.60/168.47 inference(rename_variables,[],[3645])).
% 168.60/168.47 cnf(13011,plain,
% 168.60/168.47 (P1(f315(f54(a901),f293(a901,x130111,x130112)))),
% 168.60/168.47 inference(rename_variables,[],[3645])).
% 168.60/168.47 cnf(13014,plain,
% 168.60/168.47 (P1(f315(f54(a901),f293(a901,x130141,x130142)))),
% 168.60/168.47 inference(rename_variables,[],[3645])).
% 168.60/168.47 cnf(13021,plain,
% 168.60/168.47 (P1(f315(f315(f223(a1),f315(f72(a1),f315(f89(a1),x130211))),f315(f89(a1),x130212)))),
% 168.60/168.47 inference(rename_variables,[],[3915])).
% 168.60/168.47 cnf(13026,plain,
% 168.60/168.47 (~P1(f315(f315(f224(a901),x130261),f2(a901)))),
% 168.60/168.47 inference(rename_variables,[],[4621])).
% 168.60/168.47 cnf(13027,plain,
% 168.60/168.47 (P1(f315(f315(f223(a901),x130271),x130271))),
% 168.60/168.47 inference(rename_variables,[],[3440])).
% 168.60/168.47 cnf(13034,plain,
% 168.60/168.47 (P1(f315(f315(f224(a901),x130341),f315(a101,x130341)))),
% 168.60/168.47 inference(rename_variables,[],[3507])).
% 168.60/168.47 cnf(13036,plain,
% 168.60/168.47 (P1(f315(f315(f223(a1),f2(a1)),a76))),
% 168.60/168.47 inference(scs_inference,[],[3783,4092,12728,12750,12872,12874,3674,11333,12394,12501,12504,12596,12638,12642,12650,12722,12863,3683,12468,12950,12952,3690,3410,12911,12913,12915,3411,12923,3377,12804,4603,4604,11974,4365,12957,3414,12919,3253,3309,12884,3310,12838,3311,3312,3313,12678,12890,4602,3732,4583,10413,10423,10436,10447,10519,10554,10557,10560,10662,10797,11110,11303,11306,11325,11328,11521,11622,11629,11643,11689,11692,11725,11740,11803,11862,11881,12175,12200,12216,12245,12251,12345,12464,12631,12692,3495,3459,12944,3642,12147,3361,4589,10646,10746,11213,4595,3052,3053,3055,3056,3059,3060,3062,3063,3064,3071,3075,3076,3077,3080,3081,3086,3087,3091,3097,3109,3115,3116,3123,3130,3133,3136,3137,3148,3180,3181,3186,3190,3191,3193,3201,3202,3212,3222,3332,4580,3236,3308,4581,3772,3998,11912,3286,11619,3422,3398,3401,10482,10485,10581,10584,10900,11634,11637,11751,11790,11795,11865,11907,12366,12572,12782,12834,12836,12846,12851,12853,12880,12888,12897,12917,3372,12663,12667,12671,3378,3387,3893,4194,3506,12725,12807,3276,3636,3984,11665,3494,3338,3272,3299,3752,3295,3403,4101,3992,3815,3281,3282,3263,3905,3319,3496,11060,11187,12465,12682,3371,4066,4597,10473,10643,11518,12623,12664,12668,4600,12635,3431,11994,4024,4626,11239,11338,11574,11577,3834,3543,3758,3516,4606,3510,12909,12931,12933,3335,10546,10876,3336,3595,3327,3254,3357,11655,4208,12653,12794,4068,11259,11390,11449,12607,12613,12739,12742,12772,4644,11162,11403,11512,11538,11582,11588,12551,4645,11292,11406,11515,4646,11409,4647,11467,4648,3356,3634,12507,12548,12634,3799,3583,4479,4480,3655,4594,11648,3776,3734,3778,3948,3735,3994,3620,3876,3507,10565,10685,10763,10836,10839,10879,10979,11229,11839,12091,12171,12238,12316,12357,12436,12439,12776,3886,11898,3424,3519,11724,3696,4621,10450,10453,10479,10606,10781,10987,11002,11120,11560,11658,11838,12062,12067,12292,12295,12378,12554,12657,12980,12999,13002,4632,11767,11798,11835,11842,11878,3873,3643,3645,13005,13008,13011,4016,3467,3469,3443,4618,3334,4591,3825,4130,3627,4633,4201,11535,3757,3479,12015,12018,12472,12576,4624,10441,10444,10614,10709,10728,10735,10758,10766,10769,10786,10972,11216,11429,11718,11812,11963,12080,12083,4170,4129,12522,4077,11057,12164,12351,12532,4124,11265,12391,12471,12531,12575,3800,11846,12174,12323,12401,4158,3817,10609,10706,11262,11343,11422,11486,12344,12348,12417,12687,12749,12769,12779,4636,11005,11414,3440,10574,10672,10822,10886,10961,11008,11011,11042,11068,11104,11142,11181,11966,12012,12144,12199,12219,12222,12225,12228,12410,12424,12427,12430,12433,12515,12579,12698,12745,3441,10601,10657,10891,10982,11107,11743,12045,12048,12059,12150,12161,12180,12185,12231,12254,3442,12442,3515,12383,4617,10490,10522,11026,11071,11080,11926,11947,12118,12121,12124,12127,12215,12234,12237,12250,12304,12307,12310,12313,12483,12486,12582,12585,12691,12731,3590,10751,10842,11115,11159,11393,11396,11475,11557,11728,11977,12630,4628,11035,11045,11151,11172,11175,11242,11245,11256,11359,11367,11381,11417,11434,11443,11483,11524,11529,11532,11551,11554,11591,11596,11599,11602,11605,11845,11991,12024,12298,12301,12335,12384,12413,12560,12604,12610,12710,12713,12735,12793,12799,12810,3500,10873,10903,10912,10915,10918,11504,12732,3539,3532,3952,3891,10525,11901,11929,4625,10470,10861,10864,11362,11378,11861,11917,11951,11978,12077,12106,12109,12112,12115,12377,3461,10906,11065,11135,11930,12076,12276,12491,3915,12021,4249,3649,4622,3926,3960,4609,4612,4613,3417,3421,4611,4610,3747,4343,11750,4638,10772,10775,4643,11248,11251,11437,11548,11565,11611,4034,11608,11950,11954,12641,12649,3881,11178,11184,11202,12196,12328,12416,3730,11318,11440,12448,12557,12567,12646,12701,12709,4206,3883,10909,11281,11446,11480,11491,12645,3591,3697,10825,10828,10921,11091,3699,4641,11895,4637,12989,4642,10665,10778,12510,12519,12563,12763,4304,11048,12528,12543,4212,3914,3859,3860,4639,10495,10498,10867,10870,11764,11955,4640,11875,3884,10831,11097,4144,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928,5930,5935,5943,5981,5996,6005,6008,6017,6021,6022,6023,6024,6025,6030,6035,6045,6051,6069,6073,6082,6112,6128,6154,6171,6172,6175,6190,6192,6194,6196,6211,6212,6215,6217,6220,6221,6238,6246,6247,6248,6250,6252,6290,6291,6296,6299,6305,6309,6343,6345,6347,6349,6359,6361,6364,6370,6372,6377,6380,6388,6396,6398,6399,6406,6429,6430,6431,643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% 168.60/168.47 cnf(13038,plain,
% 168.60/168.47 (~P1(f315(f315(f224(a1),f2(a1)),f315(f92(a1),f2(a1))))),
% 168.60/168.47 inference(scs_inference,[],[3783,4092,12728,12750,12872,12874,3674,11333,12394,12501,12504,12596,12638,12642,12650,12722,12863,3683,12468,12950,12952,3690,3410,12911,12913,12915,3411,12923,3377,12804,4603,4604,11974,4365,12957,3414,12919,3253,3309,12884,3310,12838,3311,3312,3313,12678,12890,4602,3732,4583,10413,10423,10436,10447,10519,10554,10557,10560,10662,10797,11110,11303,11306,11325,11328,11521,11622,11629,11643,11689,11692,11725,11740,11803,11862,11881,12175,12200,12216,12245,12251,12345,12464,12631,12692,3495,3459,12944,3642,12147,3361,4589,10646,10746,11213,4595,3052,3053,3055,3056,3059,3060,3062,3063,3064,3071,3075,3076,3077,3080,3081,3086,3087,3091,3097,3109,3115,3116,3123,3130,3133,3136,3137,3148,3180,3181,3186,3190,3191,3193,3201,3202,3212,3222,3332,4580,3236,3308,4581,3772,3998,11912,3286,11619,3422,3398,3401,10482,10485,10581,10584,10900,11634,11637,11751,11790,11795,11865,11907,12366,12572,12782,12834,12836,12846,12851,12853,12880,12888,12897,12917,3372,12663,12667,12671,3378,3387,3893,4194,3506,12725,12807,3276,3636,3984,11665,3494,3338,3272,3299,3752,3295,3403,4101,3992,3815,3281,3282,3263,3905,3319,3496,11060,11187,12465,12682,3371,4066,4597,10473,10643,11518,12623,12664,12668,4600,12635,3431,11994,4024,4626,11239,11338,11574,11577,3834,3543,3758,3516,4606,3510,12909,12931,12933,3335,10546,10876,3336,3595,3327,3254,3357,11655,4208,12653,12794,4068,11259,11390,11449,12607,12613,12739,12742,12772,4644,11162,11403,11512,11538,11582,11588,12551,4645,11292,11406,11515,4646,11409,4647,11467,4648,3356,3634,12507,12548,12634,3799,3583,4479,4480,3655,4594,11648,3776,3734,3778,3948,3735,3994,3620,3876,3507,10565,10685,10763,10836,10839,10879,10979,11229,11839,12091,12171,12238,12316,12357,12436,12439,12776,3886,11898,3424,3519,11724,3696,4621,10450,10453,10479,10606,10781,10987,11002,11120,11560,11658,11838,12062,12067,12292,12295,12378,12554,12657,12980,12999,13002,4632,11767,11798,11835,11842,11878,3873,3643,3645,13005,13008,13011,4016,3467,3469,3443,4618,3334,4591,3825,4130,3627,4633,4201,11535,3757,3479,12015,12018,12472,12576,4624,10441,10444,10614,10709,10728,10735,10758,10766,10769,10786,10972,11216,11429,11718,11812,11963,12080,12083,4170,4129,12522,4077,11057,12164,12351,12532,4124,11265,12391,12471,12531,12575,3800,11846,12174,12323,12401,4158,3817,10609,10706,11262,11343,11422,11486,12344,12348,12417,12687,12749,12769,12779,4636,11005,11414,3440,10574,10672,10822,10886,10961,11008,11011,11042,11068,11104,11142,11181,11966,12012,12144,12199,12219,12222,12225,12228,12410,12424,12427,12430,12433,12515,12579,12698,12745,3441,10601,10657,10891,10982,11107,11743,12045,12048,12059,12150,12161,12180,12185,12231,12254,3442,12442,3515,12383,4617,10490,10522,11026,11071,11080,11926,11947,12118,12121,12124,12127,12215,12234,12237,12250,12304,12307,12310,12313,12483,12486,12582,12585,12691,12731,3590,10751,10842,11115,11159,11393,11396,11475,11557,11728,11977,12630,4628,11035,11045,11151,11172,11175,11242,11245,11256,11359,11367,11381,11417,11434,11443,11483,11524,11529,11532,11551,11554,11591,11596,11599,11602,11605,11845,11991,12024,12298,12301,12335,12384,12413,12560,12604,12610,12710,12713,12735,12793,12799,12810,3500,10873,10903,10912,10915,10918,11504,12732,3539,3532,3952,3891,10525,11901,11929,4625,10470,10861,10864,11362,11378,11861,11917,11951,11978,12077,12106,12109,12112,12115,12377,3461,10906,11065,11135,11930,12076,12276,12491,3915,12021,4249,3649,4622,3926,3960,4609,4612,4613,3417,3421,4611,4610,3747,4343,11750,4638,10772,10775,4643,11248,11251,11437,11548,11565,11611,4034,11608,11950,11954,12641,12649,3881,11178,11184,11202,12196,12328,12416,3730,11318,11440,12448,12557,12567,12646,12701,12709,4206,3883,10909,11281,11446,11480,11491,12645,3591,3697,10825,10828,10921,11091,3699,4641,11895,4637,12989,4642,10665,10778,12510,12519,12563,12763,4304,11048,12528,12543,4212,3914,3859,3860,4639,10495,10498,10867,10870,11764,11955,4640,11875,3884,10831,11097,4144,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928,5930,5935,5943,5981,5996,6005,6008,6017,6021,6022,6023,6024,6025,6030,6035,6045,6051,6069,6073,6082,6112,6128,6154,6171,6172,6175,6190,6192,6194,6196,6211,6212,6215,6217,6220,6221,6238,6246,6247,6248,6250,6252,6290,6291,6296,6299,6305,6309,6343,6345,6347,6349,6359,6361,6364,6370,6372,6377,6380,6388,6396,6398,6399,6406,6429,6430,6431,643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% 168.60/168.47 cnf(13041,plain,
% 168.60/168.47 (P1(f315(f315(f223(a1),x130411),x130411))),
% 168.60/168.47 inference(rename_variables,[],[3441])).
% 168.60/168.47 cnf(13044,plain,
% 168.60/168.47 (P1(f315(f54(a901),f293(a901,x130441,x130442)))),
% 168.60/168.47 inference(rename_variables,[],[3645])).
% 168.60/168.47 cnf(13047,plain,
% 168.60/168.47 (P1(f315(f54(a901),f293(a901,x130471,x130472)))),
% 168.60/168.47 inference(rename_variables,[],[3645])).
% 168.60/168.47 cnf(13050,plain,
% 168.60/168.47 (P1(f315(f315(f223(a901),x130501),x130501))),
% 168.60/168.47 inference(rename_variables,[],[3440])).
% 168.60/168.47 cnf(13051,plain,
% 168.60/168.47 (~E(f315(a101,x130511),f2(a901))),
% 168.60/168.47 inference(rename_variables,[],[4589])).
% 168.60/168.47 cnf(13068,plain,
% 168.60/168.47 (P1(f315(f315(f223(a901),f38(a901,x130681,x130682)),x130681))),
% 168.60/168.47 inference(rename_variables,[],[3891])).
% 168.60/168.47 cnf(13073,plain,
% 168.60/168.47 (P1(f315(f315(f224(a901),x130731),f315(a101,x130731)))),
% 168.60/168.47 inference(rename_variables,[],[3507])).
% 168.60/168.47 cnf(13076,plain,
% 168.60/168.47 (P1(f315(f315(f224(a901),x130761),f315(a101,x130761)))),
% 168.60/168.47 inference(rename_variables,[],[3507])).
% 168.60/168.47 cnf(13077,plain,
% 168.60/168.47 (~P1(f315(f315(f224(a901),x130771),f2(a901)))),
% 168.60/168.47 inference(rename_variables,[],[4621])).
% 168.60/168.47 cnf(13086,plain,
% 168.60/168.47 (~P1(f315(f315(f224(a1),f315(f89(a1),x130861)),f2(a1)))),
% 168.60/168.47 inference(rename_variables,[],[4632])).
% 168.60/168.47 cnf(13087,plain,
% 168.60/168.47 (P1(f315(f230(f909(x130871,a899)),x130872))),
% 168.60/168.47 inference(rename_variables,[],[3500])).
% 168.60/168.47 cnf(13090,plain,
% 168.60/168.47 (~P1(f315(f315(f224(a1),f315(f89(a1),x130901)),f2(a1)))),
% 168.60/168.47 inference(rename_variables,[],[4632])).
% 168.60/168.47 cnf(13091,plain,
% 168.60/168.47 (P1(f315(f230(f909(x130911,a899)),x130912))),
% 168.60/168.47 inference(rename_variables,[],[3500])).
% 168.60/168.47 cnf(13094,plain,
% 168.60/168.47 (P1(f315(f230(f909(x130941,a899)),x130942))),
% 168.60/168.47 inference(rename_variables,[],[3500])).
% 168.60/168.47 cnf(13097,plain,
% 168.60/168.47 (P1(f315(f230(f909(x130971,a899)),x130972))),
% 168.60/168.47 inference(rename_variables,[],[3500])).
% 168.60/168.47 cnf(13105,plain,
% 168.60/168.47 (~P1(f315(f315(f317(x131051),x131052),f177(f909(x131051,a899))))),
% 168.60/168.47 inference(rename_variables,[],[4628])).
% 168.60/168.47 cnf(13106,plain,
% 168.60/168.47 (P1(f315(f54(x131061),f177(f909(x131061,a899))))),
% 168.60/168.47 inference(rename_variables,[],[3515])).
% 168.60/168.47 cnf(13109,plain,
% 168.60/168.47 (P1(f315(f315(f223(a901),x131091),x131091))),
% 168.60/168.47 inference(rename_variables,[],[3440])).
% 168.60/168.47 cnf(13118,plain,
% 168.60/168.47 (P1(f315(f315(f223(a901),f2(a901)),x131181))),
% 168.60/168.47 inference(rename_variables,[],[3461])).
% 168.60/168.47 cnf(13121,plain,
% 168.60/168.47 (~P1(f315(f315(f317(x131211),x131212),f177(f909(x131211,a899))))),
% 168.60/168.47 inference(rename_variables,[],[4628])).
% 168.60/168.47 cnf(13124,plain,
% 168.60/168.47 (~P1(f315(f315(f317(x131241),x131242),f177(f909(x131241,a899))))),
% 168.60/168.47 inference(rename_variables,[],[4628])).
% 168.60/168.47 cnf(13129,plain,
% 168.60/168.47 (P1(f315(f315(f223(a901),x131291),x131291))),
% 168.60/168.47 inference(rename_variables,[],[3440])).
% 168.60/168.47 cnf(13137,plain,
% 168.60/168.47 (P1(f315(f315(f224(a901),x131371),f315(a101,x131371)))),
% 168.60/168.47 inference(rename_variables,[],[3507])).
% 168.60/168.47 cnf(13140,plain,
% 168.60/168.47 (P1(f315(f315(f223(a901),x131401),x131401))),
% 168.60/168.47 inference(rename_variables,[],[3440])).
% 168.60/168.47 cnf(13145,plain,
% 168.60/168.47 (P1(f315(f315(f223(a901),x131451),x131451))),
% 168.60/168.47 inference(rename_variables,[],[3440])).
% 168.60/168.47 cnf(13148,plain,
% 168.60/168.47 (P1(f315(f315(f223(a901),x131481),x131481))),
% 168.60/168.47 inference(rename_variables,[],[3440])).
% 168.60/168.47 cnf(13151,plain,
% 168.60/168.47 (P1(f315(f315(f223(a901),x131511),x131511))),
% 168.60/168.47 inference(rename_variables,[],[3440])).
% 168.60/168.47 cnf(13154,plain,
% 168.60/168.47 (E(f315(f315(f3(f909(x131541,a899)),f177(f909(x131541,a899))),x131542),f177(f909(x131541,a899)))),
% 168.60/168.47 inference(rename_variables,[],[3702])).
% 168.60/168.47 cnf(13155,plain,
% 168.60/168.47 (P1(f315(f54(x131551),f177(f909(x131551,a899))))),
% 168.60/168.47 inference(rename_variables,[],[3515])).
% 168.60/168.47 cnf(13158,plain,
% 168.60/168.47 (E(f315(f315(f3(f909(x131581,a899)),f177(f909(x131581,a899))),x131582),f177(f909(x131581,a899)))),
% 168.60/168.47 inference(rename_variables,[],[3702])).
% 168.60/168.47 cnf(13159,plain,
% 168.60/168.47 (P1(f315(f54(x131591),f177(f909(x131591,a899))))),
% 168.60/168.47 inference(rename_variables,[],[3515])).
% 168.60/168.47 cnf(13162,plain,
% 168.60/168.47 (E(f315(f315(f3(f909(x131621,a899)),f177(f909(x131621,a899))),x131622),f177(f909(x131621,a899)))),
% 168.60/168.47 inference(rename_variables,[],[3702])).
% 168.60/168.47 cnf(13163,plain,
% 168.60/168.47 (P1(f315(f54(x131631),f177(f909(x131631,a899))))),
% 168.60/168.47 inference(rename_variables,[],[3515])).
% 168.60/168.47 cnf(13166,plain,
% 168.60/168.47 (E(f315(f315(f3(f909(x131661,a899)),f177(f909(x131661,a899))),x131662),f177(f909(x131661,a899)))),
% 168.60/168.47 inference(rename_variables,[],[3702])).
% 168.60/168.47 cnf(13167,plain,
% 168.60/168.47 (P1(f315(f54(x131671),f177(f909(x131671,a899))))),
% 168.60/168.47 inference(rename_variables,[],[3515])).
% 168.60/168.47 cnf(13171,plain,
% 168.60/168.47 (E(f315(f272(x131711,x131711),f251(x131711,x131712)),x131712)),
% 168.60/168.47 inference(rename_variables,[],[3401])).
% 168.60/168.47 cnf(13176,plain,
% 168.60/168.47 (E(f315(f315(f3(f909(x131761,a899)),f177(f909(x131761,a899))),x131762),f177(f909(x131761,a899)))),
% 168.60/168.47 inference(rename_variables,[],[3702])).
% 168.60/168.47 cnf(13177,plain,
% 168.60/168.47 (P1(f315(f54(x131771),f177(f909(x131771,a899))))),
% 168.60/168.47 inference(rename_variables,[],[3515])).
% 168.60/168.47 cnf(13181,plain,
% 168.60/168.47 (P1(f315(f54(x131811),f177(f909(x131811,a899))))),
% 168.60/168.47 inference(rename_variables,[],[3515])).
% 168.60/168.47 cnf(13184,plain,
% 168.60/168.47 (P1(f315(f315(f223(a901),x131841),x131841))),
% 168.60/168.47 inference(rename_variables,[],[3440])).
% 168.60/168.47 cnf(13188,plain,
% 168.60/168.47 (P1(f315(f315(f223(a1),x131881),x131881))),
% 168.60/168.47 inference(rename_variables,[],[3441])).
% 168.60/168.47 cnf(13197,plain,
% 168.60/168.47 (P1(f315(f315(f223(a901),x131971),x131971))),
% 168.60/168.47 inference(rename_variables,[],[3440])).
% 168.60/168.47 cnf(13208,plain,
% 168.60/168.47 (P1(f315(f315(f223(a901),x132081),x132081))),
% 168.60/168.47 inference(rename_variables,[],[3440])).
% 168.60/168.47 cnf(13211,plain,
% 168.60/168.47 (P1(f315(f315(f223(a1),x132111),x132111))),
% 168.60/168.47 inference(rename_variables,[],[3441])).
% 168.60/168.47 cnf(13222,plain,
% 168.60/168.47 (~P1(f315(f315(f317(x132221),x132222),f177(f909(x132221,a899))))),
% 168.60/168.47 inference(rename_variables,[],[4628])).
% 168.60/168.47 cnf(13233,plain,
% 168.60/168.47 (P1(f315(f315(f317(x132331),x132332),f230(f909(x132331,a899))))),
% 168.60/168.47 inference(rename_variables,[],[3590])).
% 168.60/168.47 cnf(13234,plain,
% 168.60/168.47 (E(f315(f181(x132341,x132342),x132343),f110(x132341,x132342))),
% 168.60/168.47 inference(rename_variables,[],[3355])).
% 168.60/168.47 cnf(13237,plain,
% 168.60/168.47 (P1(f315(f315(f317(x132371),f315(x132372,x132373)),f315(f298(x132374,x132371,x132372),f230(f909(x132374,a899)))))),
% 168.60/168.47 inference(rename_variables,[],[4034])).
% 168.60/168.47 cnf(13241,plain,
% 168.60/168.47 (P1(f315(f315(f223(f909(x132411,a899)),x132412),f230(f909(x132411,a899))))),
% 168.60/168.47 inference(rename_variables,[],[3817])).
% 168.60/168.47 cnf(13244,plain,
% 168.60/168.47 (P1(f315(f315(f223(f909(x132441,a899)),x132442),x132442))),
% 168.60/168.47 inference(rename_variables,[],[3730])).
% 168.60/168.47 cnf(13250,plain,
% 168.60/168.47 (~P1(f315(f315(f224(a901),x132501),f2(a901)))),
% 168.60/168.47 inference(rename_variables,[],[4621])).
% 168.60/168.47 cnf(13251,plain,
% 168.60/168.47 (P1(f315(f315(f223(a1),x132511),x132511))),
% 168.60/168.47 inference(rename_variables,[],[3441])).
% 168.60/168.47 cnf(13255,plain,
% 168.60/168.47 (~P1(f315(f315(f224(a901),x132551),f2(a901)))),
% 168.60/168.47 inference(rename_variables,[],[4621])).
% 168.60/168.47 cnf(13256,plain,
% 168.60/168.47 (P1(f315(f315(f223(a1),x132561),x132561))),
% 168.60/168.47 inference(rename_variables,[],[3441])).
% 168.60/168.47 cnf(13261,plain,
% 168.60/168.47 (P1(f315(f315(f223(a901),x132611),x132611))),
% 168.60/168.47 inference(rename_variables,[],[3440])).
% 168.60/168.47 cnf(13262,plain,
% 168.60/168.47 (P1(f315(f54(a901),f291(a901,x132621,x132622)))),
% 168.60/168.47 inference(rename_variables,[],[3643])).
% 168.60/168.47 cnf(13269,plain,
% 168.60/168.47 (E(f315(f315(f18(x132691,x132692),x132693),x132694),x132693)),
% 168.60/168.47 inference(rename_variables,[],[3431])).
% 168.60/168.47 cnf(13272,plain,
% 168.60/168.47 (P1(f315(f315(f223(f909(x132721,a899)),f315(f161(x132721),f165(x132721,x132722,x132723))),f315(f161(x132721),x132722)))),
% 168.60/168.47 inference(rename_variables,[],[4124])).
% 168.60/168.47 cnf(13279,plain,
% 168.60/168.47 (~P1(f315(f315(f224(a901),x132791),f2(a901)))),
% 168.60/168.47 inference(rename_variables,[],[4621])).
% 168.60/168.47 cnf(13280,plain,
% 168.60/168.47 (P1(f315(f315(f223(a1),x132801),x132801))),
% 168.60/168.47 inference(rename_variables,[],[3441])).
% 168.60/168.47 cnf(13284,plain,
% 168.60/168.47 (~P1(f315(f315(f224(a901),x132841),f2(a901)))),
% 168.60/168.47 inference(rename_variables,[],[4621])).
% 168.60/168.47 cnf(13285,plain,
% 168.60/168.47 (P1(f315(f315(f223(a1),x132851),x132851))),
% 168.60/168.47 inference(rename_variables,[],[3441])).
% 168.60/168.47 cnf(13289,plain,
% 168.60/168.47 (~P1(f315(f315(f223(f909(a901,a899)),f291(a901,f315(a101,x132891),f315(a101,x132891))),f291(a901,x132892,x132891)))),
% 168.60/168.47 inference(scs_inference,[],[3783,4092,12728,12750,12872,12874,3674,11333,12394,12501,12504,12596,12638,12642,12650,12722,12863,3683,12468,12950,12952,3690,3410,12911,12913,12915,3411,12923,3377,12804,4603,4604,11974,4365,12957,3414,12919,3253,3309,12884,3310,12838,3311,3312,3313,12678,12890,4602,3732,4583,10413,10423,10436,10447,10519,10554,10557,10560,10662,10797,11110,11303,11306,11325,11328,11521,11622,11629,11643,11689,11692,11725,11740,11803,11862,11881,12175,12200,12216,12245,12251,12345,12464,12631,12692,3495,3459,12944,3642,12147,3361,4589,10646,10746,11213,11313,4595,3052,3053,3055,3056,3059,3060,3062,3063,3064,3070,3071,3075,3076,3077,3080,3081,3082,3086,3087,3091,3094,3097,3109,3115,3116,3123,3130,3133,3136,3137,3148,3156,3160,3161,3162,3174,3180,3181,3183,3186,3190,3191,3193,3194,3201,3202,3209,3212,3222,3231,3332,4580,3236,3308,4581,3772,3998,11912,3286,11619,3422,3398,3401,10482,10485,10581,10584,10900,11634,11637,11751,11790,11795,11865,11907,12366,12572,12782,12834,12836,12846,12851,12853,12880,12888,12897,12917,12968,3372,12663,12667,12671,3378,3387,3893,4194,3355,13234,3506,12725,12807,3276,3636,3984,11665,3494,3338,3272,3299,3752,3295,3403,4101,3992,3815,3281,3282,3263,3905,3319,3496,11060,11187,12465,12682,3371,4066,4597,10473,10643,11518,12623,12664,12668,4600,12635,3431,11994,11997,4024,4626,11239,11338,11574,11577,3834,3543,3758,3516,4606,3510,12909,12931,12933,3335,10546,10876,3336,3595,3327,3254,3357,11655,4208,12653,12794,4068,11259,11390,11449,12607,12613,12739,12742,12772,4644,11162,11403,11512,11538,11582,11588,12551,4645,11292,11406,11515,4646,11409,4647,11467,4648,3356,3634,12507,12548,12634,3799,3583,4479,4480,3655,4594,11648,3776,3734,3778,3948,3702,13154,13158,13162,13166,13176,3735,3994,12498,3620,3876,3507,10565,10685,10763,10836,10839,10879,10979,11229,11839,12091,12171,12238,12316,12357,12436,12439,12776,13034,13073,13076,13137,3886,11898,3424,3519,11724,3696,4621,10450,10453,10479,10606,10781,10987,11002,11120,11560,11658,11838,12062,12067,12292,12295,12378,12554,12657,12980,12999,13002,13026,13077,13250,13255,13279,4632,11767,11798,11835,11842,11878,13086,13090,3873,3643,13262,3645,13005,13008,13011,13014,13044,4016,3467,3469,3443,4618,3334,4591,3825,4130,3627,4633,4201,11535,3757,3479,12015,12018,12472,12576,12753,4624,10441,10444,10614,10709,10728,10735,10758,10766,10769,10786,10972,11216,11429,11718,11812,11963,12080,12083,4170,4129,12522,4077,11057,12164,12351,12532,4124,11265,12391,12471,12531,12575,3800,11846,12174,12323,12401,12455,4158,3817,10609,10706,11262,11343,11422,11486,12344,12348,12417,12687,12749,12769,12779,4636,11005,11414,3440,10574,10672,10822,10886,10961,11008,11011,11042,11068,11104,11142,11181,11966,12012,12144,12199,12219,12222,12225,12228,12410,12424,12427,12430,12433,12515,12579,12698,12745,13027,13050,13109,13129,13140,13145,13148,13151,13184,13197,13208,13261,3441,10601,10657,10891,10982,11107,11743,12045,12048,12059,12150,12161,12180,12185,12231,12254,12271,13041,13188,13211,13251,13256,13280,3442,12442,12445,3515,12383,13106,13155,13159,13163,13167,13177,13181,4617,10490,10522,11026,11071,11080,11926,11947,12118,12121,12124,12127,12215,12234,12237,12250,12304,12307,12310,12313,12483,12486,12582,12585,12691,12731,12816,3590,10751,10842,11115,11159,11393,11396,11475,11557,11728,11977,12630,12819,4628,11035,11045,11151,11172,11175,11242,11245,11256,11359,11367,11381,11417,11434,11443,11483,11524,11529,11532,11551,11554,11591,11596,11599,11602,11605,11845,11991,12024,12298,12301,12335,12384,12413,12560,12604,12610,12710,12713,12735,12793,12799,12810,12826,13105,13121,13124,3500,10873,10903,10912,10915,10918,11504,12732,12746,13087,13091,13094,13097,3539,3532,3952,3891,10525,11901,11929,13068,4625,10470,10861,10864,11362,11378,11861,11917,11951,11978,12077,12106,12109,12112,12115,12377,3461,10906,11065,11135,11930,12076,12276,12491,12516,3915,12021,13021,4249,3649,4622,3926,3960,4609,4612,4613,3417,3421,4611,4610,3747,4343,11750,4638,10772,10775,4643,11248,11251,11437,11548,11565,11611,4034,11608,11950,11954,12641,12649,12738,3881,11178,11184,11202,12196,12328,12416,3730,11318,11440,12448,12557,12567,12646,12701,12709,12823,4206,3883,10909,11281,11446,11480,11491,12645,3591,3697,10825,10828,10921,11091,3699,4641,11895,4637,12989,4642,10665,10778,12510,12519,12563,12763,4304,11048,12528,12543,4212,3914,12829,3859,3860,4639,10495,10498,10867,10870,11764,11955,12775,4640,11875,11960,3884,10831,11097,4144,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928,5930,5935,5943,5981,5996,6005,6008,6017,6021,6022,6023,6024,6025,6030,6035,6045,6051,6069,6073,6082,6112,6128,6154,6171,6172,6175,6190,6192,6194,6196,6211,6212,6215,6217,6220,6221,6238,6246,6247,6248,6250,6252,6290,6291,6296,6299,6305,6309,6343,6345,6347,6349,6359,6361,6364,6370,6372,6377,6380,6388,6396,6398,6399,6406,6429,6430,6431,6432,6433,6435,6442,6447,6481,6482,6485,6486,6487,6489,6490,6491,6492,6499,6535,6536,6545,6567,6568,6592,6594,6606,6607,6613,6643,6645,6660,6700,6703,6704,6760,6783,6826,6841,6849,6858,6859,6860,6861,6882,6883,6890,6902,6905,6907,6909,6910,6911,6913,6927,6938,6939,6940,6953,7008,7019,7021,7026,7045,7046,7082,7089,7096,7126,7157,7213,7242,7299,7320,7329,7332,7392,7402,7465,7467,7481,7490,7491,7492,7509,7513,7515,7562,7572,7575,7590,7638,7640,7643,7687,7688,7706,7776,7794,7818,7842,7854,7868,7879,7890,7891,7917,7919,7921,7931,7969,7980,8005,8032,8065,8096,8130,8169,8186,8188,8204,8205,8273,8284,8349,8373,8392,8419,8458,8459,8476,8516,8518,8520,8526,8542,8546,8561,8582,8590,8592,8602,8607,8611,8612,8613,8614,8615,8616,8635,8650,8651,8669,8671,8675,8676,8677,8678,8679,8697,8698,8699,8709,8722,8725,8736,8741,8743,8745,8746,8747,8754,8760,8768,8771,8788,8789,8798,8799,8807,8826,8839,8843,8864,8886,8887,8890,8891,8897,8906,8907,8930,8941,8951,8952,8953,8956,8979,8980,8991,9041,9051,9053,9069,9081,9082,9083,9094,9158,9189,9190,9191,9206,9223,9231,9259,9260,9329,9364,9370,9380,9381,9382,9391,9421,9437,9441,9445,9467,9468,9495,9559,9564,9567,9604,9605,9606,9634,9635,9651,9672,9678,9690,9715,9736,9745,9746,9747,9748,9763,9765,9770,9800,9801,9807,9808,9852,9853,9864,9865,9889,9907,9909,9910,9918,9923,9930,9954,9988,9990,9994,10044,10078,10088,10090,10094,10095,10097,10106,10107,10127,10132,10225,10317,10318,10319,10320,10379,10397,2,8,9,4668,4669,4687,4729,4731,4732,4755,4757,4758,4768,4813,4815,4863,4993,4994,5011,5035,5092,5093,5099,5100,5102,5104,5113,5116,5117,5125,5138,5139,5145,5166,5167,5185,5190,5191,5192,5193,5197,5205,5208,5215,5270,5275,5276,5281,5288,5319,5329,5334,5344,5362,5364,5371,5372,5374,5385,5403,5405,5406,5413,5420,5421,5433,5434,5435,5436,5438,5439,5444,5445,5446,5447,5478,5479,5480,5488,5489,5490,5491,5535,5540,5542,5578,5580,5581,5583,5584,5586,5587,5589,5598,5603,5605,5606,5607,5609,5611,5612,5613,5614,5615,5616,5625,5626,5636,5639,5650,5666,5667,5670,5681,5684,5685,5686,5713,5723,5738,5739,5748,5749,5751,5753,5758,5793,5798,5800,5859,5894,5895,5909,5915,5918,5919,5920,5921,5940,5944,5945,5954,5976,6009,6028,6029,6033,6034,6036,6059,6063,6066,6067,6068,6084,6096,6097,6130,6131,6135,6156,6159,6162,6184,6185,6213,6216,6225,6234,6236,6245,6249,6257,6258,6259,6260,6293,6310,6363,6400,6402,6403,6426,6427,6434,6438,6439,6443,6457,6473,6494,6495,6500,6512,6515,6528,6548,6555,6557,6572,6573,6576,6577,6579,6581,6582,6583,6585,6587,6593,6599,6600,6602,6603,6609,6611,6653,6659,6674,6678,6679,6680,6714,6719,6721,6726,6727,6737,6741,6755,6778,6779,6781,6782,6793,6799,6818,6821,6842,6862,6873,6876,6877,6878,6884,6898,6917,6919,6921,6923,6928,6934,6936,6950,6955,6956,6993,6994,6995,7010,7011,7013,7014,7035,7037,7052,7080,7104,7115,7117,7119,7121,7122,7154,7155,7156,7160,7161,7168,7169,7171,7173,7195,7204,7205,7216,7226,7266,7276,7282,7289,7300,7305,7307,7314,7322,7323,7336,7353,7374,7376,7395,7450,7451,7452,7454,7456,7460,7461,7466,7530,7558,7573,7578,7589,7620,7624,7631,7646,7671,7689,7692,7693,7703,7723,7725,7727,7729,7730,7731,7732,7733,7758,7784,7785,7817,7819,7820,7821,7827,7848,7865,7870,7876,7878,7886,7898,7899,7901,7922,7929,7950,8018,8019,8020,8068,8074,8075,8099,8100,8117,8118,8119,8177,8178,8207,8237,8247,8261,8276,8305,8309,8315,8327,8345,8350,8372,8417,8446,8460,8480,8483,8509,8535,8593,8594,8597,8598,8667,8701,8702,8703,8704,8731,8763,8792,8800,8801,8842,8863,8908,8924,8970,8973,8988,8995,9038,9077,9078,9096,9097,9111,9228,9233,9237,9257,9268,9291,9293,9296,9302,9304,9305,9316,9317,9336,9344,9355,9363,9407,9425,9480,9481,9487,9526,9551,9556,9596,9610,9614,9615,9619,9620,9633,9656,9671,9680,9681,9683,9685,9714,9834,9835,9884,9885,9924,9959,10069,10136,10291,10309,10314,3,2775,2779,2781,2782,2792,2793,2794,2798,2801,2802,2803,2813,2815,2818,2819,2821,2822,2823,2824,2825,2826,2827,2828,2829,2840,2841,2842,2843,2844,2850,2854,2856,2857,2858,2861,2862,2871,2872,2876,2885,2886,2887,2889,2891,2893,2894,2895,2901,2902,2903,2905,2915,2917,2924,2925,2926,2928,2929,2931,2932,2935,2936,2937,2939,2940,2941,2944,2945,2947,2952,2954,2955,2966,2987,2990,2991,2992,2993,2994,2998,3032,3039,5361,5402,5551,5552,5553,5637,5737,5767,5801,5817,5819,5825,5887,5888,5889,5890,5907,5942,6079,6119,6129,6153,6188,6226,6379,6384,6424,6425,6448,6450,6452,6459,6460,6461,6462,6463,6464,6465,6466,6550,6623,6624,6713,6750,6751,6790,6791,6935,6949,7005,7023,7024,7031,7053,7086,7088,7092,7137,7158,7159,7177,7178,7215,7260,7261,7360,7429,7430,7431,7432,7449,7482,7535,7536,7544,7549,7550,7561,7592,7593,7594,7595,7739,7740,7742,7744,7750,7751,7825,7956,7959,7965,7966,7977,8015,8016,8094,8135,8190,8212,8213,8291,8385,8456,8457,8461,8495,8531,8557,8558,8625,8643])).
% 168.60/168.47 cnf(13290,plain,
% 168.60/168.47 (P1(f315(f315(f223(a901),x132901),x132901))),
% 168.60/168.47 inference(rename_variables,[],[3440])).
% 168.60/168.47 cnf(13292,plain,
% 168.60/168.47 (~P1(f315(f315(f224(f909(a901,a899)),f291(a901,f315(a101,x132921),f315(a101,x132921))),f291(a901,x132922,x132921)))),
% 168.60/168.47 inference(scs_inference,[],[3783,4092,12728,12750,12872,12874,3674,11333,12394,12501,12504,12596,12638,12642,12650,12722,12863,3683,12468,12950,12952,3690,3410,12911,12913,12915,3411,12923,3377,12804,4603,4604,11974,4365,12957,3414,12919,3253,3309,12884,3310,12838,3311,3312,3313,12678,12890,4602,3732,4583,10413,10423,10436,10447,10519,10554,10557,10560,10662,10797,11110,11303,11306,11325,11328,11521,11622,11629,11643,11689,11692,11725,11740,11803,11862,11881,12175,12200,12216,12245,12251,12345,12464,12631,12692,3495,3459,12944,3642,12147,3361,4589,10646,10746,11213,11313,4595,3052,3053,3055,3056,3059,3060,3062,3063,3064,3070,3071,3075,3076,3077,3080,3081,3082,3086,3087,3091,3094,3097,3109,3115,3116,3123,3130,3133,3136,3137,3148,3156,3160,3161,3162,3174,3180,3181,3183,3186,3190,3191,3193,3194,3201,3202,3209,3212,3222,3231,3332,4580,3236,3308,4581,3772,3998,11912,3286,11619,3422,3398,3401,10482,10485,10581,10584,10900,11634,11637,11751,11790,11795,11865,11907,12366,12572,12782,12834,12836,12846,12851,12853,12880,12888,12897,12917,12968,3372,12663,12667,12671,3378,3387,3893,4194,3355,13234,3506,12725,12807,3276,3636,3984,11665,3494,3338,3272,3299,3752,3295,3403,4101,3992,3815,3281,3282,3263,3905,3319,3496,11060,11187,12465,12682,3371,4066,4597,10473,10643,11518,12623,12664,12668,4600,12635,3431,11994,11997,4024,4626,11239,11338,11574,11577,3834,3543,3758,3516,4606,3510,12909,12931,12933,3335,10546,10876,3336,3595,3327,3254,3357,11655,4208,12653,12794,4068,11259,11390,11449,12607,12613,12739,12742,12772,4644,11162,11403,11512,11538,11582,11588,12551,4645,11292,11406,11515,4646,11409,4647,11467,4648,3356,3634,12507,12548,12634,3799,3583,4479,4480,3655,4594,11648,3776,3734,3778,3948,3702,13154,13158,13162,13166,13176,3735,3994,12498,3620,3876,3507,10565,10685,10763,10836,10839,10879,10979,11229,11839,12091,12171,12238,12316,12357,12436,12439,12776,13034,13073,13076,13137,3886,11898,3424,3519,11724,3696,4621,10450,10453,10479,10606,10781,10987,11002,11120,11560,11658,11838,12062,12067,12292,12295,12378,12554,12657,12980,12999,13002,13026,13077,13250,13255,13279,4632,11767,11798,11835,11842,11878,13086,13090,3873,3643,13262,3645,13005,13008,13011,13014,13044,4016,3467,3469,3443,4618,3334,4591,3825,4130,3627,4633,4201,11535,3757,3479,12015,12018,12472,12576,12753,4624,10441,10444,10614,10709,10728,10735,10758,10766,10769,10786,10972,11216,11429,11718,11812,11963,12080,12083,4170,4129,12522,4077,11057,12164,12351,12532,4124,11265,12391,12471,12531,12575,3800,11846,12174,12323,12401,12455,4158,3817,10609,10706,11262,11343,11422,11486,12344,12348,12417,12687,12749,12769,12779,4636,11005,11414,3440,10574,10672,10822,10886,10961,11008,11011,11042,11068,11104,11142,11181,11966,12012,12144,12199,12219,12222,12225,12228,12410,12424,12427,12430,12433,12515,12579,12698,12745,13027,13050,13109,13129,13140,13145,13148,13151,13184,13197,13208,13261,13290,3441,10601,10657,10891,10982,11107,11743,12045,12048,12059,12150,12161,12180,12185,12231,12254,12271,13041,13188,13211,13251,13256,13280,3442,12442,12445,3515,12383,13106,13155,13159,13163,13167,13177,13181,4617,10490,10522,11026,11071,11080,11926,11947,12118,12121,12124,12127,12215,12234,12237,12250,12304,12307,12310,12313,12483,12486,12582,12585,12691,12731,12816,3590,10751,10842,11115,11159,11393,11396,11475,11557,11728,11977,12630,12819,4628,11035,11045,11151,11172,11175,11242,11245,11256,11359,11367,11381,11417,11434,11443,11483,11524,11529,11532,11551,11554,11591,11596,11599,11602,11605,11845,11991,12024,12298,12301,12335,12384,12413,12560,12604,12610,12710,12713,12735,12793,12799,12810,12826,13105,13121,13124,3500,10873,10903,10912,10915,10918,11504,12732,12746,13087,13091,13094,13097,3539,3532,3952,3891,10525,11901,11929,13068,4625,10470,10861,10864,11362,11378,11861,11917,11951,11978,12077,12106,12109,12112,12115,12377,3461,10906,11065,11135,11930,12076,12276,12491,12516,3915,12021,13021,4249,3649,4622,3926,3960,4609,4612,4613,3417,3421,4611,4610,3747,4343,11750,4638,10772,10775,4643,11248,11251,11437,11548,11565,11611,4034,11608,11950,11954,12641,12649,12738,3881,11178,11184,11202,12196,12328,12416,3730,11318,11440,12448,12557,12567,12646,12701,12709,12823,4206,3883,10909,11281,11446,11480,11491,12645,3591,3697,10825,10828,10921,11091,3699,4641,11895,4637,12989,4642,10665,10778,12510,12519,12563,12763,4304,11048,12528,12543,4212,3914,12829,3859,3860,4639,10495,10498,10867,10870,11764,11955,12775,4640,11875,11960,3884,10831,11097,4144,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928,5930,5935,5943,5981,5996,6005,6008,6017,6021,6022,6023,6024,6025,6030,6035,6045,6051,6069,6073,6082,6112,6128,6154,6171,6172,6175,6190,6192,6194,6196,6211,6212,6215,6217,6220,6221,6238,6246,6247,6248,6250,6252,6290,6291,6296,6299,6305,6309,6343,6345,6347,6349,6359,6361,6364,6370,6372,6377,6380,6388,6396,6398,6399,6406,6429,6430,6431,6432,6433,6435,6442,6447,6481,6482,6485,6486,6487,6489,6490,6491,6492,6499,6535,6536,6545,6567,6568,6592,6594,6606,6607,6613,6643,6645,6660,6700,6703,6704,6760,6783,6826,6841,6849,6858,6859,6860,6861,6882,6883,6890,6902,6905,6907,6909,6910,6911,6913,6927,6938,6939,6940,6953,7008,7019,7021,7026,7045,7046,7082,7089,7096,7126,7157,7213,7242,7299,7320,7329,7332,7392,7402,7465,7467,7481,7490,7491,7492,7509,7513,7515,7562,7572,7575,7590,7638,7640,7643,7687,7688,7706,7776,7794,7818,7842,7854,7868,7879,7890,7891,7917,7919,7921,7931,7969,7980,8005,8032,8065,8096,8130,8169,8186,8188,8204,8205,8273,8284,8349,8373,8392,8419,8458,8459,8476,8516,8518,8520,8526,8542,8546,8561,8582,8590,8592,8602,8607,8611,8612,8613,8614,8615,8616,8635,8650,8651,8669,8671,8675,8676,8677,8678,8679,8697,8698,8699,8709,8722,8725,8736,8741,8743,8745,8746,8747,8754,8760,8768,8771,8788,8789,8798,8799,8807,8826,8839,8843,8864,8886,8887,8890,8891,8897,8906,8907,8930,8941,8951,8952,8953,8956,8979,8980,8991,9041,9051,9053,9069,9081,9082,9083,9094,9158,9189,9190,9191,9206,9223,9231,9259,9260,9329,9364,9370,9380,9381,9382,9391,9421,9437,9441,9445,9467,9468,9495,9559,9564,9567,9604,9605,9606,9634,9635,9651,9672,9678,9690,9715,9736,9745,9746,9747,9748,9763,9765,9770,9800,9801,9807,9808,9852,9853,9864,9865,9889,9907,9909,9910,9918,9923,9930,9954,9988,9990,9994,10044,10078,10088,10090,10094,10095,10097,10106,10107,10127,10132,10225,10317,10318,10319,10320,10379,10397,2,8,9,4668,4669,4687,4729,4731,4732,4755,4757,4758,4768,4813,4815,4863,4993,4994,5011,5035,5092,5093,5099,5100,5102,5104,5113,5116,5117,5125,5138,5139,5145,5166,5167,5185,5190,5191,5192,5193,5197,5205,5208,5215,5270,5275,5276,5281,5288,5319,5329,5334,5344,5362,5364,5371,5372,5374,5385,5403,5405,5406,5413,5420,5421,5433,5434,5435,5436,5438,5439,5444,5445,5446,5447,5478,5479,5480,5488,5489,5490,5491,5535,5540,5542,5578,5580,5581,5583,5584,5586,5587,5589,5598,5603,5605,5606,5607,5609,5611,5612,5613,5614,5615,5616,5625,5626,5636,5639,5650,5666,5667,5670,5681,5684,5685,5686,5713,5723,5738,5739,5748,5749,5751,5753,5758,5793,5798,5800,5859,5894,5895,5909,5915,5918,5919,5920,5921,5940,5944,5945,5954,5976,6009,6028,6029,6033,6034,6036,6059,6063,6066,6067,6068,6084,6096,6097,6130,6131,6135,6156,6159,6162,6184,6185,6213,6216,6225,6234,6236,6245,6249,6257,6258,6259,6260,6293,6310,6363,6400,6402,6403,6426,6427,6434,6438,6439,6443,6457,6473,6494,6495,6500,6512,6515,6528,6548,6555,6557,6572,6573,6576,6577,6579,6581,6582,6583,6585,6587,6593,6599,6600,6602,6603,6609,6611,6653,6659,6674,6678,6679,6680,6714,6719,6721,6726,6727,6737,6741,6755,6778,6779,6781,6782,6793,6799,6818,6821,6842,6862,6873,6876,6877,6878,6884,6898,6917,6919,6921,6923,6928,6934,6936,6950,6955,6956,6993,6994,6995,7010,7011,7013,7014,7035,7037,7052,7080,7104,7115,7117,7119,7121,7122,7154,7155,7156,7160,7161,7168,7169,7171,7173,7195,7204,7205,7216,7226,7266,7276,7282,7289,7300,7305,7307,7314,7322,7323,7336,7353,7374,7376,7395,7450,7451,7452,7454,7456,7460,7461,7466,7530,7558,7573,7578,7589,7620,7624,7631,7646,7671,7689,7692,7693,7703,7723,7725,7727,7729,7730,7731,7732,7733,7758,7784,7785,7817,7819,7820,7821,7827,7848,7865,7870,7876,7878,7886,7898,7899,7901,7922,7929,7950,8018,8019,8020,8068,8074,8075,8099,8100,8117,8118,8119,8177,8178,8207,8237,8247,8261,8276,8305,8309,8315,8327,8345,8350,8372,8417,8446,8460,8480,8483,8509,8535,8593,8594,8597,8598,8667,8701,8702,8703,8704,8731,8763,8792,8800,8801,8842,8863,8908,8924,8970,8973,8988,8995,9038,9077,9078,9096,9097,9111,9228,9233,9237,9257,9268,9291,9293,9296,9302,9304,9305,9316,9317,9336,9344,9355,9363,9407,9425,9480,9481,9487,9526,9551,9556,9596,9610,9614,9615,9619,9620,9633,9656,9671,9680,9681,9683,9685,9714,9834,9835,9884,9885,9924,9959,10069,10136,10291,10309,10314,3,2775,2779,2781,2782,2792,2793,2794,2798,2801,2802,2803,2813,2815,2818,2819,2821,2822,2823,2824,2825,2826,2827,2828,2829,2840,2841,2842,2843,2844,2850,2854,2856,2857,2858,2861,2862,2871,2872,2876,2885,2886,2887,2889,2891,2893,2894,2895,2901,2902,2903,2905,2915,2917,2924,2925,2926,2928,2929,2931,2932,2935,2936,2937,2939,2940,2941,2944,2945,2947,2952,2954,2955,2966,2987,2990,2991,2992,2993,2994,2998,3032,3039,5361,5402,5551,5552,5553,5637,5737,5767,5801,5817,5819,5825,5887,5888,5889,5890,5907,5942,6079,6119,6129,6153,6188,6226,6379,6384,6424,6425,6448,6450,6452,6459,6460,6461,6462,6463,6464,6465,6466,6550,6623,6624,6713,6750,6751,6790,6791,6935,6949,7005,7023,7024,7031,7053,7086,7088,7092,7137,7158,7159,7177,7178,7215,7260,7261,7360,7429,7430,7431,7432,7449,7482,7535,7536,7544,7549,7550,7561,7592,7593,7594,7595,7739,7740,7742,7744,7750,7751,7825,7956,7959,7965,7966,7977,8015,8016,8094,8135,8190,8212,8213,8291,8385,8456,8457,8461,8495,8531,8557,8558,8625,8643,8644])).
% 168.60/168.47 cnf(13293,plain,
% 168.60/168.47 (P1(f315(f315(f223(a901),x132931),x132931))),
% 168.60/168.47 inference(rename_variables,[],[3440])).
% 168.60/168.47 cnf(13296,plain,
% 168.60/168.47 (~P1(f315(f315(f223(a901),f315(a101,x132961)),x132961))),
% 168.60/168.47 inference(rename_variables,[],[4625])).
% 168.60/168.47 cnf(13302,plain,
% 168.60/168.47 (P1(f315(f315(f317(x133021),f315(x133022,x133023)),f315(f298(x133024,x133021,x133022),f230(f909(x133024,a899)))))),
% 168.60/168.47 inference(rename_variables,[],[4034])).
% 168.60/168.47 cnf(13303,plain,
% 168.60/168.47 (P25(x133031,x133031,f7(x133031),x133032)),
% 168.60/168.47 inference(rename_variables,[],[3674])).
% 168.60/168.47 cnf(13307,plain,
% 168.60/168.47 (~P1(f315(f315(f317(x133071),x133072),f177(f909(x133071,a899))))),
% 168.60/168.47 inference(rename_variables,[],[4628])).
% 168.60/168.47 cnf(13311,plain,
% 168.60/168.47 (P1(f315(f315(f223(f909(x133111,a899)),x133112),f230(f909(x133111,a899))))),
% 168.60/168.47 inference(rename_variables,[],[3817])).
% 168.60/168.47 cnf(13312,plain,
% 168.60/168.47 (P25(x133121,x133121,f7(x133121),x133122)),
% 168.60/168.47 inference(rename_variables,[],[3674])).
% 168.60/168.47 cnf(13316,plain,
% 168.60/168.47 (P1(f315(f315(f223(f909(x133161,a899)),x133162),f230(f909(x133161,a899))))),
% 168.60/168.47 inference(rename_variables,[],[3817])).
% 168.60/168.47 cnf(13317,plain,
% 168.60/168.47 (P25(x133171,x133171,f7(x133171),x133172)),
% 168.60/168.47 inference(rename_variables,[],[3674])).
% 168.60/168.47 cnf(13321,plain,
% 168.60/168.47 (P25(x133211,x133211,f7(x133211),x133212)),
% 168.60/168.47 inference(rename_variables,[],[3674])).
% 168.60/168.47 cnf(13324,plain,
% 168.60/168.47 (~P1(f315(f315(f224(f909(x133241,a899)),x133242),f177(f909(x133241,a899))))),
% 168.60/168.47 inference(rename_variables,[],[4636])).
% 168.60/168.47 cnf(13327,plain,
% 168.60/168.47 (P25(x133271,x133271,f7(x133271),x133272)),
% 168.60/168.47 inference(rename_variables,[],[3674])).
% 168.60/168.47 cnf(13330,plain,
% 168.60/168.47 (P25(x133301,x133301,f7(x133301),x133302)),
% 168.60/168.47 inference(rename_variables,[],[3674])).
% 168.60/168.47 cnf(13333,plain,
% 168.60/168.47 (P1(f315(f315(f317(x133331),f315(x133332,x133333)),f315(f298(x133334,x133331,x133332),f230(f909(x133334,a899)))))),
% 168.60/168.47 inference(rename_variables,[],[4034])).
% 168.60/168.47 cnf(13339,plain,
% 168.60/168.47 (P1(f315(f315(f223(f909(x133391,a899)),x133392),f230(f909(x133391,a899))))),
% 168.60/168.47 inference(rename_variables,[],[3817])).
% 168.60/168.47 cnf(13344,plain,
% 168.60/168.47 (P1(f315(f315(f223(f909(x133441,a899)),f177(f909(x133441,a899))),x133442))),
% 168.60/168.47 inference(rename_variables,[],[3883])).
% 168.60/168.47 cnf(13348,plain,
% 168.60/168.47 (E(f315(f272(x133481,x133481),f251(x133481,x133482)),x133482)),
% 168.60/168.47 inference(rename_variables,[],[3401])).
% 168.60/168.47 cnf(13352,plain,
% 168.60/168.47 (~P1(f315(f315(f317(x133521),x133522),f177(f909(x133521,a899))))),
% 168.60/168.47 inference(rename_variables,[],[4628])).
% 168.60/168.47 cnf(13357,plain,
% 168.60/168.47 (P25(x133571,x133571,f7(x133571),x133572)),
% 168.60/168.47 inference(rename_variables,[],[3674])).
% 168.60/168.47 cnf(13360,plain,
% 168.60/168.47 (P1(f315(f315(f223(f909(x133601,a899)),x133602),f230(f909(x133601,a899))))),
% 168.60/168.47 inference(rename_variables,[],[3817])).
% 168.60/168.47 cnf(13368,plain,
% 168.60/168.47 (E(f315(f315(f18(x133681,x133682),x133683),x133684),x133683)),
% 168.60/168.47 inference(rename_variables,[],[3431])).
% 168.60/168.47 cnf(13371,plain,
% 168.60/168.47 (~P1(f315(f315(f317(x133711),x133712),f177(f909(x133711,a899))))),
% 168.60/168.47 inference(rename_variables,[],[4628])).
% 168.60/168.47 cnf(13374,plain,
% 168.60/168.47 (~P1(f315(f315(f317(x133741),x133742),f177(f909(x133741,a899))))),
% 168.60/168.47 inference(rename_variables,[],[4628])).
% 168.60/168.47 cnf(13379,plain,
% 168.60/168.47 (~E(f315(a101,x133791),x133791)),
% 168.60/168.47 inference(rename_variables,[],[4583])).
% 168.60/168.47 cnf(13382,plain,
% 168.60/168.47 (P1(f315(f315(f224(a901),x133821),f315(a101,x133821)))),
% 168.60/168.47 inference(rename_variables,[],[3507])).
% 168.60/168.47 cnf(13383,plain,
% 168.60/168.47 (~E(f315(a101,x133831),x133831)),
% 168.60/168.47 inference(rename_variables,[],[4583])).
% 168.60/168.47 cnf(13386,plain,
% 168.60/168.47 (P1(f315(f315(f224(a901),x133861),f315(a101,f315(f315(f73(a901),x133862),x133861))))),
% 168.60/168.47 inference(rename_variables,[],[3884])).
% 168.60/168.47 cnf(13387,plain,
% 168.60/168.47 (P1(f315(f315(f224(a901),x133871),f315(a101,x133871)))),
% 168.60/168.47 inference(rename_variables,[],[3507])).
% 168.60/168.47 cnf(13389,plain,
% 168.60/168.48 (~E(f315(f315(f74(a901),f315(a101,f2(a901))),f108(x133891)),f315(f315(f74(a901),f315(a101,f2(a901))),f115(x133891,x133892,x133893)))),
% 168.60/168.48 inference(scs_inference,[],[3783,4092,12728,12750,12872,12874,12876,3674,11333,12394,12501,12504,12596,12638,12642,12650,12722,12863,12865,13303,13312,13317,13321,13327,13330,3683,12468,12950,12952,3690,3410,12911,12913,12915,3411,12923,3377,12804,4603,4604,11974,4365,12957,3414,12919,3253,3309,12884,3310,12838,3311,3312,3313,12678,12890,4602,3732,4583,10413,10423,10436,10447,10519,10554,10557,10560,10662,10797,11110,11303,11306,11325,11328,11521,11622,11629,11643,11689,11692,11725,11740,11803,11862,11881,12175,12200,12216,12245,12251,12345,12464,12631,12692,12832,13379,13383,3495,3459,12944,3642,12147,3361,4589,10646,10746,11213,11313,4595,3052,3053,3055,3056,3059,3060,3062,3063,3064,3070,3071,3075,3076,3077,3080,3081,3082,3086,3087,3091,3094,3097,3109,3115,3116,3123,3130,3133,3136,3137,3148,3156,3160,3161,3162,3174,3180,3181,3183,3186,3190,3191,3193,3194,3201,3202,3209,3212,3222,3231,3332,4580,3236,3308,4581,3772,3998,11912,3286,11619,3422,3398,3401,10482,10485,10581,10584,10900,11634,11637,11751,11790,11795,11865,11907,12366,12572,12782,12834,12836,12846,12851,12853,12880,12888,12897,12917,12968,13171,3372,12663,12667,12671,3378,3387,3893,4194,3355,13234,3506,12725,12807,3275,3276,3636,3984,11665,3494,3338,3272,3299,3752,3295,3403,4101,3992,3815,3281,3282,3263,3905,3319,3496,11060,11187,12465,12682,3371,4066,4597,10473,10643,11518,12623,12664,12668,4600,12635,3431,11994,11997,13269,4024,4626,11239,11338,11574,11577,3406,3834,3428,3543,3758,3516,4606,3510,12909,12931,12933,3335,10546,10876,3336,4615,3595,3327,3254,3357,11655,4208,12653,12794,4068,11259,11390,11449,12607,12613,12739,12742,12772,4644,11162,11403,11512,11538,11582,11588,12551,4645,11292,11406,11515,4646,11409,11460,4647,11467,4648,3356,3634,12507,12548,12634,3799,3583,4479,4480,3655,4594,11648,3776,3734,3778,3948,3702,13154,13158,13162,13166,13176,3735,3994,12498,3620,3876,3507,10565,10685,10763,10836,10839,10879,10979,11229,11839,12091,12171,12238,12316,12357,12436,12439,12776,13034,13073,13076,13137,13382,3886,11898,3424,3519,11724,3696,4621,10450,10453,10479,10606,10781,10987,11002,11120,11560,11658,11838,12062,12067,12292,12295,12378,12554,12657,12980,12999,13002,13026,13077,13250,13255,13279,4632,11767,11798,11835,11842,11878,13086,13090,3873,3643,13262,3645,13005,13008,13011,13014,13044,4016,3467,3469,3443,4618,3334,4591,3825,4130,3627,4633,4201,11535,3757,3479,12015,12018,12472,12576,12753,4624,10441,10444,10614,10709,10728,10735,10758,10766,10769,10786,10972,11216,11429,11718,11812,11963,12080,12083,4170,4129,12522,4077,11057,12164,12351,12532,4124,11265,12391,12471,12531,12575,3800,11846,12174,12323,12401,12455,4158,3817,10609,10706,11262,11343,11422,11486,12344,12348,12417,12687,12749,12769,12779,13241,13311,13316,13339,4636,11005,11414,12535,13324,3440,10574,10672,10822,10886,10961,11008,11011,11042,11068,11104,11142,11181,11966,12012,12144,12199,12219,12222,12225,12228,12410,12424,12427,12430,12433,12515,12579,12698,12745,13027,13050,13109,13129,13140,13145,13148,13151,13184,13197,13208,13261,13290,13293,3441,10601,10657,10891,10982,11107,11743,12045,12048,12059,12150,12161,12180,12185,12231,12254,12271,13041,13188,13211,13251,13256,13280,3442,12442,12445,3515,12383,13106,13155,13159,13163,13167,13177,13181,4617,10490,10522,11026,11071,11080,11926,11947,12118,12121,12124,12127,12215,12234,12237,12250,12304,12307,12310,12313,12483,12486,12582,12585,12691,12731,12816,3590,10751,10842,11115,11159,11393,11396,11475,11557,11728,11977,12630,12819,13233,4628,11035,11045,11151,11172,11175,11242,11245,11256,11359,11367,11381,11417,11434,11443,11483,11524,11529,11532,11551,11554,11591,11596,11599,11602,11605,11845,11991,12024,12298,12301,12335,12384,12413,12560,12604,12610,12710,12713,12735,12793,12799,12810,12826,13105,13121,13124,13222,13307,13352,13371,3500,10873,10903,10912,10915,10918,11504,12732,12746,13087,13091,13094,13097,3539,3532,3952,3891,10525,11901,11929,13068,4625,10470,10861,10864,11362,11378,11861,11917,11951,11978,12077,12106,12109,12112,12115,12377,13296,3461,10906,11065,11135,11930,12076,12276,12491,12516,3915,12021,13021,4249,3649,4622,3926,3960,4609,4612,4613,3417,3421,4611,4610,3747,11894,4343,11750,4638,10772,10775,4643,11248,11251,11437,11548,11565,11611,4034,11608,11950,11954,12641,12649,12738,13237,13302,13333,3881,11178,11184,11202,12196,12328,12416,12706,3730,11318,11440,12448,12557,12567,12646,12701,12709,12823,4206,3883,10909,11281,11446,11480,11491,12645,12695,3591,3697,10825,10828,10921,11091,3699,4641,11895,4637,12989,4642,10665,10778,12510,12519,12563,12763,4304,11048,12528,12543,12566,4212,3914,12829,3859,3860,4639,10495,10498,10867,10870,11764,11955,12775,4640,11875,11960,3884,10831,11097,12090,4144,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928,5930,5935,5943,5981,5996,6005,6008,6017,6021,6022,6023,6024,6025,6030,6035,6045,6051,6069,6073,6082,6112,6128,6154,6171,6172,6175,6190,6192,6194,6196,6211,6212,6215,6217,6220,6221,6238,6246,6247,6248,6250,6252,6290,6291,6296,6299,6305,6309,6343,6345,6347,6349,6359,6361,6364,6370,6372,6377,6380,6388,6396,6398,6399,6406,6429,6430,6431,6432,6433,6435,6442,6447,6481,6482,6485,6486,6487,6489,6490,6491,6492,6499,6535,6536,6545,6567,6568,6592,6594,6606,6607,6613,6643,6645,6660,6700,6703,6704,6760,6783,6826,6841,6849,6858,6859,6860,6861,6882,6883,6890,6902,6905,6907,6909,6910,6911,6913,6927,6938,6939,6940,6953,7008,7019,7021,7026,7045,7046,7082,7089,7096,7126,7157,7213,7242,7299,7320,7329,7332,7392,7402,7465,7467,7481,7490,7491,7492,7509,7513,7515,7562,7572,7575,7590,7638,7640,7643,7687,7688,7706,7776,7794,7818,7842,7854,7868,7879,7890,7891,7917,7919,7921,7931,7969,7980,8005,8032,8065,8096,8130,8169,8186,8188,8204,8205,8273,8284,8349,8373,8392,8419,8458,8459,8476,8516,8518,8520,8526,8542,8546,8561,8582,8590,8592,8602,8607,8611,8612,8613,8614,8615,8616,8635,8650,8651,8669,8671,8675,8676,8677,8678,8679,8697,8698,8699,8709,8722,8725,8736,8741,8743,8745,8746,8747,8754,8760,8768,8771,8788,8789,8798,8799,8807,8826,8839,8843,8864,8886,8887,8890,8891,8897,8906,8907,8930,8941,8951,8952,8953,8956,8979,8980,8991,9041,9051,9053,9069,9081,9082,9083,9094,9158,9189,9190,9191,9206,9223,9231,9259,9260,9329,9364,9370,9380,9381,9382,9391,9421,9437,9441,9445,9467,9468,9495,9559,9564,9567,9604,9605,9606,9634,9635,9651,9672,9678,9690,9715,9736,9745,9746,9747,9748,9763,9765,9770,9800,9801,9807,9808,9852,9853,9864,9865,9889,9907,9909,9910,9918,9923,9930,9954,9988,9990,9994,10044,10078,10088,10090,10094,10095,10097,10106,10107,10127,10132,10225,10317,10318,10319,10320,10379,10397,2,8,9,4668,4669,4687,4729,4731,4732,4755,4757,4758,4768,4813,4815,4863,4993,4994,5011,5035,5092,5093,5099,5100,5102,5104,5113,5116,5117,5125,5138,5139,5145,5166,5167,5185,5190,5191,5192,5193,5197,5205,5208,5215,5270,5275,5276,5281,5288,5319,5329,5334,5344,5362,5364,5371,5372,5374,5385,5403,5405,5406,5413,5420,5421,5433,5434,5435,5436,5438,5439,5444,5445,5446,5447,5478,5479,5480,5488,5489,5490,5491,5535,5540,5542,5578,5580,5581,5583,5584,5586,5587,5589,5598,5603,5605,5606,5607,5609,5611,5612,5613,5614,5615,5616,5625,5626,5636,5639,5650,5666,5667,5670,5681,5684,5685,5686,5713,5723,5738,5739,5748,5749,5751,5753,5758,5793,5798,5800,5859,5894,5895,5909,5915,5918,5919,5920,5921,5940,5944,5945,5954,5976,6009,6028,6029,6033,6034,6036,6059,6063,6066,6067,6068,6084,6096,6097,6130,6131,6135,6156,6159,6162,6184,6185,6213,6216,6225,6234,6236,6245,6249,6257,6258,6259,6260,6293,6310,6363,6400,6402,6403,6426,6427,6434,6438,6439,6443,6457,6473,6494,6495,6500,6512,6515,6528,6548,6555,6557,6572,6573,6576,6577,6579,6581,6582,6583,6585,6587,6593,6599,6600,6602,6603,6609,6611,6653,6659,6674,6678,6679,6680,6714,6719,6721,6726,6727,6737,6741,6755,6778,6779,6781,6782,6793,6799,6818,6821,6842,6862,6873,6876,6877,6878,6884,6898,6917,6919,6921,6923,6928,6934,6936,6950,6955,6956,6993,6994,6995,7010,7011,7013,7014,7035,7037,7052,7080,7104,7115,7117,7119,7121,7122,7154,7155,7156,7160,7161,7168,7169,7171,7173,7195,7204,7205,7216,7226,7266,7276,7282,7289,7300,7305,7307,7314,7322,7323,7336,7353,7374,7376,7395,7450,7451,7452,7454,7456,7460,7461,7466,7530,7558,7573,7578,7589,7620,7624,7631,7646,7671,7689,7692,7693,7703,7723,7725,7727,7729,7730,7731,7732,7733,7758,7784,7785,7817,7819,7820,7821,7827,7848,7865,7870,7876,7878,7886,7898,7899,7901,7922,7929,7950,8018,8019,8020,8068,8074,8075,8099,8100,8117,8118,8119,8177,8178,8207,8237,8247,8261,8276,8305,8309,8315,8327,8345,8350,8372,8417,8446,8460,8480,8483,8509,8535,8593,8594,8597,8598,8667,8701,8702,8703,8704,8731,8763,8792,8800,8801,8842,8863,8908,8924,8970,8973,8988,8995,9038,9077,9078,9096,9097,9111,9228,9233,9237,9257,9268,9291,9293,9296,9302,9304,9305,9316,9317,9336,9344,9355,9363,9407,9425,9480,9481,9487,9526,9551,9556,9596,9610,9614,9615,9619,9620,9633,9656,9671,9680,9681,9683,9685,9714,9834,9835,9884,9885,9924,9959,10069,10136,10291,10309,10314,3,2775,2779,2781,2782,2792,2793,2794,2798,2801,2802,2803,2813,2815,2818,2819,2821,2822,2823,2824,2825,2826,2827,2828,2829,2840,2841,2842,2843,2844,2850,2854,2856,2857,2858,2861,2862,2871,2872,2876,2885,2886,2887,2889,2891,2893,2894,2895,2901,2902,2903,2905,2915,2917,2924,2925,2926,2928,2929,2931,2932,2935,2936,2937,2939,2940,2941,2944,2945,2947,2952,2954,2955,2966,2987,2990,2991,2992,2993,2994,2998,3032,3039,5361,5402,5551,5552,5553,5637,5737,5767,5801,5817,5819,5825,5887,5888,5889,5890,5907,5942,6079,6119,6129,6153,6188,6226,6379,6384,6424,6425,6448,6450,6452,6459,6460,6461,6462,6463,6464,6465,6466,6550,6623,6624,6713,6750,6751,6790,6791,6935,6949,7005,7023,7024,7031,7053,7086,7088,7092,7137,7158,7159,7177,7178,7215,7260,7261,7360,7429,7430,7431,7432,7449,7482,7535,7536,7544,7549,7550,7561,7592,7593,7594,7595,7739,7740,7742,7744,7750,7751,7825,7956,7959,7965,7966,7977,8015,8016,8094,8135,8190,8212,8213,8291,8385,8456,8457,8461,8495,8531,8557,8558,8625,8643,8644,8645,8646,8796,9031,9055,9056,9125,9139,9192,9193,9311,9313,9348,9375,9409,9450,9654,9777,9919,10105,10161,10163,5977,6533,6534,6626])).
% 168.60/168.48 cnf(13396,plain,
% 168.60/168.48 (P1(f315(f315(f223(a1),f2(a1)),f315(f89(a1),x133961)))),
% 168.60/168.48 inference(rename_variables,[],[3539])).
% 168.60/168.48 cnf(13399,plain,
% 168.60/168.48 (P1(f315(f315(f223(a901),f2(a901)),x133991))),
% 168.60/168.48 inference(rename_variables,[],[3461])).
% 168.60/168.48 cnf(13403,plain,
% 168.60/168.48 (~E(f315(a101,x134031),f2(a901))),
% 168.60/168.48 inference(rename_variables,[],[4589])).
% 168.60/168.48 cnf(13406,plain,
% 168.60/168.48 (P1(f315(f315(f223(a1),x134061),x134061))),
% 168.60/168.48 inference(rename_variables,[],[3441])).
% 168.60/168.48 cnf(13410,plain,
% 168.60/168.48 (P1(f315(f315(f223(f909(x134101,a899)),f315(f161(x134101),f165(x134101,x134102,x134103))),f315(f161(x134101),x134102)))),
% 168.60/168.48 inference(rename_variables,[],[4124])).
% 168.60/168.48 cnf(13415,plain,
% 168.60/168.48 (~P1(f315(f315(f317(x134151),x134152),f177(f909(x134151,a899))))),
% 168.60/168.48 inference(rename_variables,[],[4628])).
% 168.60/168.48 cnf(13418,plain,
% 168.60/168.48 (P1(f315(f54(a901),f293(a901,x134181,x134182)))),
% 168.60/168.48 inference(rename_variables,[],[3645])).
% 168.60/168.48 cnf(13419,plain,
% 168.60/168.48 (E(f315(f315(f221(a901),f315(a101,x134191)),f315(a101,x134192)),f315(a101,f315(f315(f221(a901),x134191),x134192)))),
% 168.60/168.48 inference(rename_variables,[],[3608])).
% 168.60/168.48 cnf(13422,plain,
% 168.60/168.48 (P1(f315(f54(a901),f293(a901,x134221,x134222)))),
% 168.60/168.48 inference(rename_variables,[],[3645])).
% 168.60/168.48 cnf(13423,plain,
% 168.60/168.48 (E(f315(f315(f222(a901),f315(a101,x134231)),f315(a101,x134232)),f315(a101,f315(f315(f222(a901),x134231),x134232)))),
% 168.60/168.48 inference(rename_variables,[],[3609])).
% 168.60/168.48 cnf(13426,plain,
% 168.60/168.48 (P1(f315(f54(a901),f293(a901,x134261,x134262)))),
% 168.60/168.48 inference(rename_variables,[],[3645])).
% 168.60/168.48 cnf(13435,plain,
% 168.60/168.48 (~P1(f315(f315(f317(x134351),x134352),f177(f909(x134351,a899))))),
% 168.60/168.48 inference(rename_variables,[],[4628])).
% 168.60/168.48 cnf(13436,plain,
% 168.60/168.48 (E(f315(f315(f18(x134361,x134362),x134363),x134364),x134363)),
% 168.60/168.48 inference(rename_variables,[],[3431])).
% 168.60/168.48 cnf(13439,plain,
% 168.60/168.48 (P1(f315(f315(f223(f909(x134391,a899)),f315(f161(x134391),f315(f125(x134391,x134392),x134393))),f315(f161(x134391),x134393)))),
% 168.60/168.48 inference(rename_variables,[],[4077])).
% 168.60/168.48 cnf(13440,plain,
% 168.60/168.48 (E(f315(f315(f18(x134401,x134402),x134403),x134404),x134403)),
% 168.60/168.48 inference(rename_variables,[],[3431])).
% 168.60/168.48 cnf(13443,plain,
% 168.60/168.48 (P1(f315(f315(f223(f909(x134431,a899)),f315(f161(x134431),f315(f315(f164(x134431),x134432),x134433))),f315(f161(x134431),x134433)))),
% 168.60/168.48 inference(rename_variables,[],[4119])).
% 168.60/168.48 cnf(13444,plain,
% 168.60/168.48 (E(f315(f315(f18(x134441,x134442),x134443),x134444),x134443)),
% 168.60/168.48 inference(rename_variables,[],[3431])).
% 168.60/168.48 cnf(13448,plain,
% 168.60/168.48 (E(f315(f315(f18(x134481,x134482),x134483),x134484),x134483)),
% 168.60/168.48 inference(rename_variables,[],[3431])).
% 168.60/168.48 cnf(13461,plain,
% 168.60/168.48 (P1(f315(f315(f223(a1),f2(a1)),f315(f89(a1),x134611)))),
% 168.60/168.48 inference(rename_variables,[],[3539])).
% 168.60/168.48 cnf(13466,plain,
% 168.60/168.48 (P25(x134661,x134661,f7(x134661),x134662)),
% 168.60/168.48 inference(rename_variables,[],[3674])).
% 168.60/168.48 cnf(13469,plain,
% 168.60/168.48 (~P1(f315(f315(f317(x134691),x134692),f177(f909(x134691,a899))))),
% 168.60/168.48 inference(rename_variables,[],[4628])).
% 168.60/168.48 cnf(13470,plain,
% 168.60/168.48 (E(f315(f272(x134701,x134701),f251(x134701,x134702)),x134702)),
% 168.60/168.48 inference(rename_variables,[],[3401])).
% 168.60/168.48 cnf(13471,plain,
% 168.60/168.48 (P25(x134711,x134711,f7(x134711),x134712)),
% 168.60/168.48 inference(rename_variables,[],[3674])).
% 168.60/168.48 cnf(13475,plain,
% 168.60/168.48 (E(f315(f272(x134751,x134751),f251(x134751,x134752)),x134752)),
% 168.60/168.48 inference(rename_variables,[],[3401])).
% 168.60/168.48 cnf(13489,plain,
% 168.60/168.48 (P1(f315(f315(f223(a901),f2(a901)),x134891))),
% 168.60/168.48 inference(rename_variables,[],[3461])).
% 168.60/168.48 cnf(13490,plain,
% 168.60/168.48 (P1(f315(f315(f224(a901),f2(a901)),f315(a101,x134901)))),
% 168.60/168.48 inference(rename_variables,[],[3519])).
% 168.60/168.48 cnf(13491,plain,
% 168.60/168.48 (E(f315(f272(x134911,x134911),f251(x134911,x134912)),x134912)),
% 168.60/168.48 inference(rename_variables,[],[3401])).
% 168.60/168.48 cnf(13576,plain,
% 168.60/168.48 (P1(f315(f315(f224(a1),f2(a1)),f315(f69(a1),f71(a1))))),
% 168.60/168.48 inference(scs_inference,[],[3783,4092,12728,12750,12872,12874,12876,3674,11333,12394,12501,12504,12596,12638,12642,12650,12722,12863,12865,13303,13312,13317,13321,13327,13330,13357,13466,13471,3683,12468,12950,12952,3690,3410,12911,12913,12915,3411,12923,3377,12804,4603,4604,11974,4365,12957,3414,12919,3253,3309,12884,3310,12838,3311,3312,3313,12678,12890,4602,3732,4583,10413,10423,10436,10447,10519,10554,10557,10560,10662,10797,11110,11303,11306,11325,11328,11521,11622,11629,11643,11689,11692,11725,11740,11803,11862,11881,12175,12200,12216,12245,12251,12345,12464,12631,12692,12832,13379,13383,3495,3459,12944,3642,12147,3361,4589,10646,10746,11213,11313,13051,13403,4595,3052,3053,3055,3056,3059,3060,3062,3063,3064,3070,3071,3075,3076,3077,3080,3081,3082,3086,3087,3091,3092,3094,3097,3109,3113,3115,3116,3123,3130,3133,3136,3137,3139,3148,3156,3157,3160,3161,3162,3174,3180,3181,3183,3186,3190,3191,3193,3194,3201,3202,3209,3212,3222,3231,3332,4580,3236,3308,4581,3772,3998,11912,3286,11619,3422,3398,3401,10482,10485,10581,10584,10900,11634,11637,11751,11790,11795,11865,11907,12366,12572,12782,12834,12836,12846,12851,12853,12880,12888,12897,12917,12968,13171,13348,13470,13475,13491,3372,12663,12667,12671,3378,3387,3893,4194,3355,13234,3506,12725,12807,3275,3276,3636,3984,11665,3494,3338,3272,3299,3752,3295,3403,4101,3992,3815,3281,3282,3263,3905,3319,3496,11060,11187,12465,12682,3371,4066,4597,10473,10643,11518,12623,12664,12668,4600,12635,3431,11994,11997,13269,13368,13436,13440,13444,13448,4024,4626,11239,11338,11574,11577,3406,3834,3428,3543,3758,3516,3535,4606,3510,12909,12931,12933,3335,10546,10876,3336,4615,3595,3327,3254,3357,11655,4208,12653,12794,4068,11259,11390,11449,12607,12613,12739,12742,12772,4644,11162,11403,11512,11538,11582,11588,12551,4645,11292,11406,11515,4646,11409,11460,4647,11467,4648,3356,3634,12507,12548,12634,3799,3583,4479,4480,3618,3655,4594,11648,3776,3734,3778,3948,3702,13154,13158,13162,13166,13176,3735,3994,12498,3620,3876,3507,10565,10685,10763,10836,10839,10879,10979,11229,11839,12091,12171,12238,12316,12357,12436,12439,12776,13034,13073,13076,13137,13382,13387,3886,11898,3424,3519,11724,12009,13490,3696,4621,10450,10453,10479,10606,10781,10987,11002,11120,11560,11658,11838,12062,12067,12292,12295,12378,12554,12657,12980,12999,13002,13026,13077,13250,13255,13279,13284,4632,11767,11798,11835,11842,11878,13086,13090,3873,3643,13262,3645,13005,13008,13011,13014,13044,13047,13418,13422,13426,3646,4016,3608,13419,3609,13423,3467,3469,3443,4618,3334,4591,3825,4130,3627,4633,4201,11535,3757,3479,12015,12018,12472,12576,12753,4624,10441,10444,10614,10709,10728,10735,10758,10766,10769,10786,10972,11216,11429,11718,11812,11963,12080,12083,4170,4129,12522,4077,11057,12164,12351,12532,12681,13439,4119,13443,4124,11265,12391,12471,12531,12575,13272,13410,4125,3800,11846,12174,12323,12401,12455,4158,3817,10609,10706,11262,11343,11422,11486,12344,12348,12417,12687,12749,12769,12779,13241,13311,13316,13339,13360,4636,11005,11414,12535,13324,3440,10574,10672,10822,10886,10961,11008,11011,11042,11068,11104,11142,11181,11966,12012,12144,12199,12219,12222,12225,12228,12410,12424,12427,12430,12433,12515,12579,12698,12745,13027,13050,13109,13129,13140,13145,13148,13151,13184,13197,13208,13261,13290,13293,3441,10601,10657,10891,10982,11107,11743,12045,12048,12059,12150,12161,12180,12185,12231,12254,12271,13041,13188,13211,13251,13256,13280,13285,13406,3442,12442,12445,3515,12383,13106,13155,13159,13163,13167,13177,13181,4617,10490,10522,11026,11071,11080,11926,11947,12118,12121,12124,12127,12215,12234,12237,12250,12304,12307,12310,12313,12483,12486,12582,12585,12691,12731,12816,3590,10751,10842,11115,11159,11393,11396,11475,11557,11728,11977,12630,12819,13233,4628,11035,11045,11151,11172,11175,11242,11245,11256,11359,11367,11381,11417,11434,11443,11483,11524,11529,11532,11551,11554,11591,11596,11599,11602,11605,11845,11991,12024,12298,12301,12335,12384,12413,12560,12604,12610,12710,12713,12735,12793,12799,12810,12826,13105,13121,13124,13222,13307,13352,13371,13374,13415,13435,13469,3500,10873,10903,10912,10915,10918,11504,12732,12746,13087,13091,13094,13097,3539,13396,13461,3532,3952,3891,10525,11901,11929,13068,4625,10470,10861,10864,11362,11378,11861,11917,11951,11978,12077,12106,12109,12112,12115,12377,13296,3461,10906,11065,11135,11930,12076,12276,12491,12516,13118,13399,13489,3915,12021,13021,4249,3649,4622,3926,3960,4609,4612,4613,3417,3421,4611,4610,4416,3747,11894,4343,11750,4638,10772,10775,4643,11248,11251,11437,11548,11565,11611,4034,11608,11950,11954,12641,12649,12738,13237,13302,13333,3881,11178,11184,11202,12196,12328,12416,12706,3730,11318,11440,12448,12557,12567,12646,12701,12709,12823,13244,4206,3883,10909,11281,11446,11480,11491,12645,12695,13344,3591,3697,10825,10828,10921,11091,3699,4641,11895,4637,12989,4642,10665,10778,12510,12519,12563,12763,4304,11048,12528,12543,12566,4212,3914,12829,3859,3860,4639,10495,10498,10867,10870,11764,11955,12775,4640,11875,11960,3884,10831,11097,12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,2872,2876,2885,2886,2887,2889,2891,2893,2894,2895,2901,2902,2903,2905,2915,2917,2924,2925,2926,2928,2929,2931,2932,2935,2936,2937,2939,2940,2941,2944,2945,2947,2952,2954,2955,2966,2987,2990,2991,2992,2993,2994,2998,3032,3039,5361,5402,5551,5552,5553,5637,5737,5767,5801,5817,5819,5825,5887,5888,5889,5890,5907,5942,6079,6119,6129,6153,6188,6226,6379,6384,6424,6425,6448,6450,6452,6459,6460,6461,6462,6463,6464,6465,6466,6550,6623,6624,6713,6750,6751,6790,6791,6935,6949,7005,7023,7024,7031,7053,7086,7088,7092,7137,7158,7159,7177,7178,7215,7260,7261,7360,7429,7430,7431,7432,7449,7482,7535,7536,7544,7549,7550,7561,7592,7593,7594,7595,7739,7740,7742,7744,7750,7751,7825,7956,7959,7965,7966,7977,8015,8016,8094,8135,8190,8212,8213,8291,8385,8456,8457,8461,8495,8531,8557,8558,8625,8643,8644,8645,8646,8796,9031,9055,9056,9125,9139,9192,9193,9311,9313,9348,9375,9409,9450,9654,9777,9919,10105,10161,10163,5977,6533,6534,6626,6646,6647,7077,7298,8443,8638,8717,8964,9150,9151,9219,9220,9404,9498,9499,9500,9501,9717,9982,9996,10365,10366,6608,8549,8550,9020,9039,9983,10364,4693,4702,4734,4735,4738,4780,4784,4789,4830,4927,4944,4974,4975,5006,5010,5069,5072,5132,5264,5304,5305,5307,5314,5315,5339,5379,5410,5432,5567,5642,5643,5644,5706,5763,5764])).
% 168.60/168.48 cnf(13590,plain,
% 168.60/168.48 (~P1(f315(f315(f224(a901),f315(a101,f315(f315(f73(a901),x135901),x135902))),f315(a101,x135901)))),
% 168.60/168.48 inference(scs_inference,[],[3783,4092,12728,12750,12872,12874,12876,3674,11333,12394,12501,12504,12596,12638,12642,12650,12722,12863,12865,13303,13312,13317,13321,13327,13330,13357,13466,13471,3683,12468,12950,12952,3690,3410,12911,12913,12915,3411,12923,3377,12804,4603,4604,11974,4365,12957,3414,12919,3253,3309,12884,3310,12838,3311,3312,3313,12678,12890,4602,3732,4583,10413,10423,10436,10447,10519,10554,10557,10560,10662,10797,11110,11303,11306,11325,11328,11521,11622,11629,11643,11689,11692,11725,11740,11803,11862,11881,12175,12200,12216,12245,12251,12345,12464,12631,12692,12832,13379,13383,3495,3459,12944,3642,12147,3361,4589,10646,10746,11213,11313,13051,13403,4595,3052,3053,3055,3056,3059,3060,3062,3063,3064,3070,3071,3075,3076,3077,3080,3081,3082,3086,3087,3091,3092,3094,3097,3109,3113,3115,3116,3123,3130,3133,3136,3137,3139,3148,3156,3157,3160,3161,3162,3174,3180,3181,3183,3186,3190,3191,3193,3194,3201,3202,3209,3212,3222,3231,3332,4580,3236,3308,4581,3772,3998,11912,3286,11619,3422,3398,3401,10482,10485,10581,10584,10900,11634,11637,11751,11790,11795,11865,11907,12366,12572,12782,12834,12836,12846,12851,12853,12880,12888,12897,12917,12968,13171,13348,13470,13475,13491,3372,12663,12667,12671,3378,3387,3893,4194,3355,13234,3506,12725,12807,3275,3276,3636,3984,11665,3494,3338,3272,3299,3752,3295,3403,4101,3992,3815,3281,3282,3263,3905,3319,3496,11060,11187,12465,12682,3371,4066,4597,10473,10643,11518,12623,12664,12668,4600,12635,3431,11994,11997,13269,13368,13436,13440,13444,13448,4024,4626,11239,11338,11574,11577,3406,3834,3428,3543,3758,3516,3535,4606,3510,12909,12931,12933,3335,10546,10876,3336,4615,3595,3327,3254,3357,11655,4208,12653,12794,4068,11259,11390,11449,12607,12613,12739,12742,12772,4644,11162,11403,11512,11538,11582,11588,12551,4645,11292,11406,11515,4646,11409,11460,4647,11467,4648,3356,3634,12507,12548,12634,3799,3583,4479,4480,3618,3655,4594,11648,3776,3734,3778,3948,3702,13154,13158,13162,13166,13176,3735,3994,12498,3620,3876,3507,10565,10685,10763,10836,10839,10879,10979,11229,11839,12091,12171,12238,12316,12357,12436,12439,12776,13034,13073,13076,13137,13382,13387,3886,11898,3424,3519,11724,12009,13490,3696,4621,10450,10453,10479,10606,10781,10987,11002,11120,11560,11658,11838,12062,12067,12292,12295,12378,12554,12657,12980,12999,13002,13026,13077,13250,13255,13279,13284,4632,11767,11798,11835,11842,11878,13086,13090,3873,3643,13262,3645,13005,13008,13011,13014,13044,13047,13418,13422,13426,3646,4016,3608,13419,3609,13423,3467,3469,3443,4618,3334,4591,3825,4130,3627,4633,4201,11535,3757,3479,12015,12018,12472,12576,12753,4624,10441,10444,10614,10709,10728,10735,10758,10766,10769,10786,10972,11216,11429,11718,11812,11963,12080,12083,4170,4129,12522,4077,11057,12164,12351,12532,12681,13439,4119,13443,4124,11265,12391,12471,12531,12575,13272,13410,4125,3800,11846,12174,12323,12401,12455,4158,3817,10609,10706,11262,11343,11422,11486,12344,12348,12417,12687,12749,12769,12779,13241,13311,13316,13339,13360,4636,11005,11414,12535,13324,3440,10574,10672,10822,10886,10961,11008,11011,11042,11068,11104,11142,11181,11966,12012,12144,12199,12219,12222,12225,12228,12410,12424,12427,12430,12433,12515,12579,12698,12745,13027,13050,13109,13129,13140,13145,13148,13151,13184,13197,13208,13261,13290,13293,3441,10601,10657,10891,10982,11107,11743,12045,12048,12059,12150,12161,12180,12185,12231,12254,12271,13041,13188,13211,13251,13256,13280,13285,13406,3442,12442,12445,3515,12383,13106,13155,13159,13163,13167,13177,13181,4617,10490,10522,11026,11071,11080,11926,11947,12118,12121,12124,12127,12215,12234,12237,12250,12304,12307,12310,12313,12483,12486,12582,12585,12691,12731,12816,3590,10751,10842,11115,11159,11393,11396,11475,11557,11728,11977,12630,12819,13233,4628,11035,11045,11151,11172,11175,11242,11245,11256,11359,11367,11381,11417,11434,11443,11483,11524,11529,11532,11551,11554,11591,11596,11599,11602,11605,11845,11991,12024,12298,12301,12335,12384,12413,12560,12604,12610,12710,12713,12735,12793,12799,12810,12826,13105,13121,13124,13222,13307,13352,13371,13374,13415,13435,13469,3500,10873,10903,10912,10915,10918,11504,12732,12746,13087,13091,13094,13097,3539,13396,13461,3532,3952,3891,10525,11901,11929,13068,4625,10470,10861,10864,11362,11378,11861,11917,11951,11978,12077,12106,12109,12112,12115,12377,13296,3461,10906,11065,11135,11930,12076,12276,12491,12516,13118,13399,13489,3915,12021,13021,4249,3649,4622,3926,3960,4609,4612,4613,3417,3421,4611,4610,4416,3747,11894,4343,11750,4638,10772,10775,4643,11248,11251,11437,11548,11565,11611,4034,11608,11950,11954,12641,12649,12738,13237,13302,13333,3881,11178,11184,11202,12196,12328,12416,12706,3730,11318,11440,12448,12557,12567,12646,12701,12709,12823,13244,4206,3883,10909,11281,11446,11480,11491,12645,12695,13344,3591,3697,10825,10828,10921,11091,3699,4641,11895,4637,12989,4642,10665,10778,12510,12519,12563,12763,4304,11048,12528,12543,12566,4212,3914,12829,3859,3860,4639,10495,10498,10867,10870,11764,11955,12775,4640,11875,11960,3884,10831,11097,12090,13386,4144,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928,5930,5935,5943,5981,5996,6005,6008,6017,6021,6022,6023,6024,6025,6030,6035,6045,6051,6069,6073,6082,6112,6128,6154,6171,6172,6175,6190,6192,6194,6196,6211,6212,6215,6217,6220,6221,6238,6246,6247,6248,6250,6252,6290,6291,6296,6299,6305,6309,6343,6345,6347,6349,6359,6361,6364,6370,6372,6377,6380,6388,6396,6398,6399,6406,6429,6430,6431,6432,6433,6435,6442,6447,6481,6482,6485,6486,6487,6489,6490,6491,6492,6499,6535,6536,6545,6567,6568,6592,6594,6606,6607,6613,6643,6645,6660,6700,6703,6704,6760,6783,6826,6841,6849,6858,6859,6860,6861,6882,6883,6890,6902,6905,6907,6909,6910,6911,6913,6927,6938,6939,6940,6953,7008,7019,7021,7026,7045,7046,7082,7089,7096,7126,7157,7213,7242,7299,7320,7329,7332,7392,7402,7465,7467,7481,7490,7491,7492,7509,7513,7515,7562,7572,7575,7590,7638,7640,7643,7687,7688,7706,7776,7794,7818,7842,7854,7868,7879,7890,7891,7917,7919,7921,7931,7969,7980,8005,8032,8065,8096,8130,8169,8186,8188,8204,8205,8273,8284,8349,8373,8392,8419,8458,8459,8476,8516,8518,8520,8526,8542,8546,8561,8582,8590,8592,8602,8607,8611,8612,8613,8614,8615,8616,8635,8650,8651,8669,8671,8675,8676,8677,8678,8679,8697,8698,8699,8709,8722,8725,8736,8741,8743,8745,8746,8747,8754,8760,8768,8771,8788,8789,8798,8799,8807,8826,8839,8843,8864,8886,8887,8890,8891,8897,8906,8907,8930,8941,8951,8952,8953,8956,8979,8980,8991,9041,9051,9053,9069,9081,9082,9083,9094,9158,9189,9190,9191,9206,9223,9231,9259,9260,9329,9364,9370,9380,9381,9382,9391,9421,9437,9441,9445,9467,9468,9495,9559,9564,9567,9604,9605,9606,9634,9635,9651,9672,9678,9690,9715,9736,9745,9746,9747,9748,9763,9765,9770,9800,9801,9807,9808,9852,9853,9864,9865,9889,9907,9909,9910,9918,9923,9930,9954,9988,9990,9994,10044,10078,10088,10090,10094,10095,10097,10106,10107,10127,10132,10225,10317,10318,10319,10320,10379,10397,2,8,9,4668,4669,4687,4729,4731,4732,4755,4757,4758,4768,4813,4815,4863,4993,4994,5011,5035,5092,5093,5099,5100,5102,5104,5113,5116,5117,5125,5138,5139,5145,5166,5167,5185,5190,5191,5192,5193,5197,5205,5208,5215,5270,5275,5276,5281,5288,5319,5329,5334,5344,5362,5364,5371,5372,5374,5385,5403,5405,5406,5413,5420,5421,5433,5434,5435,5436,5438,5439,5444,5445,5446,5447,5478,5479,5480,5488,5489,5490,5491,5535,5540,5542,5578,5580,5581,5583,5584,5586,5587,5589,5598,5603,5605,5606,5607,5609,5611,5612,5613,5614,5615,5616,5625,5626,5636,5639,5650,5666,5667,5670,5681,5684,5685,5686,5713,5723,5738,5739,5748,5749,5751,5753,5758,5793,5798,5800,5859,5894,5895,5909,5915,5918,5919,5920,5921,5940,5944,5945,5954,5976,6009,6028,6029,6033,6034,6036,6059,6063,6066,6067,6068,6084,6096,6097,6130,6131,6135,6156,6159,6162,6184,6185,6213,6216,6225,6234,6236,6245,6249,6257,6258,6259,6260,6293,6310,6363,6400,6402,6403,6426,6427,6434,6438,6439,6443,6457,6473,6494,6495,6500,6512,6515,6528,6548,6555,6557,6572,6573,6576,6577,6579,6581,6582,6583,6585,6587,6593,6599,6600,6602,6603,6609,6611,6653,6659,6674,6678,6679,6680,6714,6719,6721,6726,6727,6737,6741,6755,6778,6779,6781,6782,6793,6799,6818,6821,6842,6862,6873,6876,6877,6878,6884,6898,6917,6919,6921,6923,6928,6934,6936,6950,6955,6956,6993,6994,6995,7010,7011,7013,7014,7035,7037,7052,7080,7104,7115,7117,7119,7121,7122,7154,7155,7156,7160,7161,7168,7169,7171,7173,7195,7204,7205,7216,7226,7266,7276,7282,7289,7300,7305,7307,7314,7322,7323,7336,7353,7374,7376,7395,7450,7451,7452,7454,7456,7460,7461,7466,7530,7558,7573,7578,7589,7620,7624,7631,7646,7671,7689,7692,7693,7703,7723,7725,7727,7729,7730,7731,7732,7733,7758,7784,7785,7817,7819,7820,7821,7827,7848,7865,7870,7876,7878,7886,7898,7899,7901,7922,7929,7950,8018,8019,8020,8068,8074,8075,8099,8100,8117,8118,8119,8177,8178,8207,8237,8247,8261,8276,8305,8309,8315,8327,8345,8350,8372,8417,8446,8460,8480,8483,8509,8535,8593,8594,8597,8598,8667,8701,8702,8703,8704,8731,8763,8792,8800,8801,8842,8863,8908,8924,8970,8973,8988,8995,9038,9077,9078,9096,9097,9111,9228,9233,9237,9257,9268,9291,9293,9296,9302,9304,9305,9316,9317,9336,9344,9355,9363,9407,9425,9480,9481,9487,9526,9551,9556,9596,9610,9614,9615,9619,9620,9633,9656,9671,9680,9681,9683,9685,9714,9834,9835,9884,9885,9924,9959,10069,10136,10291,10309,10314,3,2775,2779,2781,2782,2792,2793,2794,2798,2801,2802,2803,2813,2815,2818,2819,2821,2822,2823,2824,2825,2826,2827,2828,2829,2840,2841,2842,2843,2844,2850,2854,2856,2857,2858,2861,2862,2871,2872,2876,2885,2886,2887,2889,2891,2893,2894,2895,2901,2902,2903,2905,2915,2917,2924,2925,2926,2928,2929,2931,2932,2935,2936,2937,2939,2940,2941,2944,2945,2947,2952,2954,2955,2966,2987,2990,2991,2992,2993,2994,2998,3032,3039,5361,5402,5551,5552,5553,5637,5737,5767,5801,5817,5819,5825,5887,5888,5889,5890,5907,5942,6079,6119,6129,6153,6188,6226,6379,6384,6424,6425,6448,6450,6452,6459,6460,6461,6462,6463,6464,6465,6466,6550,6623,6624,6713,6750,6751,6790,6791,6935,6949,7005,7023,7024,7031,7053,7086,7088,7092,7137,7158,7159,7177,7178,7215,7260,7261,7360,7429,7430,7431,7432,7449,7482,7535,7536,7544,7549,7550,7561,7592,7593,7594,7595,7739,7740,7742,7744,7750,7751,7825,7956,7959,7965,7966,7977,8015,8016,8094,8135,8190,8212,8213,8291,8385,8456,8457,8461,8495,8531,8557,8558,8625,8643,8644,8645,8646,8796,9031,9055,9056,9125,9139,9192,9193,9311,9313,9348,9375,9409,9450,9654,9777,9919,10105,10161,10163,5977,6533,6534,6626,6646,6647,7077,7298,8443,8638,8717,8964,9150,9151,9219,9220,9404,9498,9499,9500,9501,9717,9982,9996,10365,10366,6608,8549,8550,9020,9039,9983,10364,4693,4702,4734,4735,4738,4780,4784,4789,4830,4927,4944,4974,4975,5006,5010,5069,5072,5132,5264,5304,5305,5307,5314,5315,5339,5379,5410,5432,5567,5642,5643,5644,5706,5763,5764,5790,5794,5853,5855,5864,5870,5958])).
% 168.60/168.48 cnf(13600,plain,
% 168.60/168.48 (~P1(f315(f54(x136001),f30(f909(x136001,a899),f230(f909(f909(x136001,a899),a899)))))),
% 168.60/168.48 inference(scs_inference,[],[3783,4092,12728,12750,12872,12874,12876,3674,11333,12394,12501,12504,12596,12638,12642,12650,12722,12863,12865,13303,13312,13317,13321,13327,13330,13357,13466,13471,3683,12468,12950,12952,3690,3410,12911,12913,12915,3411,12923,3377,12804,4603,4604,11974,4365,12957,3414,12919,3253,3309,12884,3310,12838,3311,3312,3313,12678,12890,4602,3732,4583,10413,10423,10436,10447,10519,10554,10557,10560,10662,10797,11110,11303,11306,11325,11328,11521,11622,11629,11643,11689,11692,11725,11740,11803,11862,11881,12175,12200,12216,12245,12251,12345,12464,12631,12692,12832,13379,13383,3495,3459,12944,3642,12147,3361,4589,10646,10746,11213,11313,13051,13403,4595,3052,3053,3055,3056,3059,3060,3062,3063,3064,3070,3071,3075,3076,3077,3080,3081,3082,3086,3087,3091,3092,3094,3097,3109,3113,3115,3116,3123,3130,3133,3136,3137,3139,3148,3156,3157,3160,3161,3162,3174,3180,3181,3183,3186,3190,3191,3193,3194,3201,3202,3209,3212,3222,3231,3332,4580,3236,3308,4581,3772,3998,11912,3286,11619,3422,3398,3401,10482,10485,10581,10584,10900,11634,11637,11751,11790,11795,11865,11907,12366,12572,12782,12834,12836,12846,12851,12853,12880,12888,12897,12917,12968,13171,13348,13470,13475,13491,3372,12663,12667,12671,3378,3387,3893,4194,3355,13234,3506,12725,12807,3275,3276,3636,3984,11665,3494,3338,3272,3299,3752,3295,3403,4101,3992,3815,3281,3282,3263,3905,3319,3496,11060,11187,12465,12682,3371,4066,4597,10473,10643,11518,12623,12664,12668,4600,12635,3431,11994,11997,13269,13368,13436,13440,13444,13448,4024,4626,11239,11338,11574,11577,3406,3834,3428,3543,3758,3516,3535,4606,3510,12909,12931,12933,3335,10546,10876,3336,4615,3595,3327,3254,3357,11655,4208,12653,12794,4068,11259,11390,11449,12607,12613,12739,12742,12772,4644,11162,11403,11512,11538,11582,11588,12551,4645,11292,11406,11515,4646,11409,11460,4647,11467,4648,3356,3634,12507,12548,12634,3799,3583,4479,4480,3618,3655,4594,11648,3776,3734,3778,3948,3702,13154,13158,13162,13166,13176,3735,3994,12498,3620,3876,3507,10565,10685,10763,10836,10839,10879,10979,11229,11839,12091,12171,12238,12316,12357,12436,12439,12776,13034,13073,13076,13137,13382,13387,3886,11898,3424,3519,11724,12009,13490,3696,4621,10450,10453,10479,10606,10781,10987,11002,11120,11560,11658,11838,12062,12067,12292,12295,12378,12554,12657,12980,12999,13002,13026,13077,13250,13255,13279,13284,4632,11767,11798,11835,11842,11878,13086,13090,3873,3643,13262,3645,13005,13008,13011,13014,13044,13047,13418,13422,13426,3646,4016,3608,13419,3609,13423,3467,3469,3443,4618,3334,4591,3825,4130,3627,4633,4201,11535,3757,3479,12015,12018,12472,12576,12753,4624,10441,10444,10614,10709,10728,10735,10758,10766,10769,10786,10972,11216,11429,11718,11812,11963,12080,12083,4170,4129,12522,4077,11057,12164,12351,12532,12681,13439,4119,13443,4124,11265,12391,12471,12531,12575,13272,13410,4125,3800,11846,12174,12323,12401,12455,4158,3817,10609,10706,11262,11343,11422,11486,12344,12348,12417,12687,12749,12769,12779,13241,13311,13316,13339,13360,4636,11005,11414,12535,13324,3440,10574,10672,10822,10886,10961,11008,11011,11042,11068,11104,11142,11181,11966,12012,12144,12199,12219,12222,12225,12228,12410,12424,12427,12430,12433,12515,12579,12698,12745,13027,13050,13109,13129,13140,13145,13148,13151,13184,13197,13208,13261,13290,13293,3441,10601,10657,10891,10982,11107,11743,12045,12048,12059,12150,12161,12180,12185,12231,12254,12271,13041,13188,13211,13251,13256,13280,13285,13406,3442,12442,12445,3515,12383,13106,13155,13159,13163,13167,13177,13181,4617,10490,10522,11026,11071,11080,11926,11947,12118,12121,12124,12127,12215,12234,12237,12250,12304,12307,12310,12313,12483,12486,12582,12585,12691,12731,12816,3590,10751,10842,11115,11159,11393,11396,11475,11557,11728,11977,12630,12819,13233,4628,11035,11045,11151,11172,11175,11242,11245,11256,11359,11367,11381,11417,11434,11443,11483,11524,11529,11532,11551,11554,11591,11596,11599,11602,11605,11845,11991,12024,12298,12301,12335,12384,12413,12560,12604,12610,12710,12713,12735,12793,12799,12810,12826,13105,13121,13124,13222,13307,13352,13371,13374,13415,13435,13469,3500,10873,10903,10912,10915,10918,11504,12732,12746,13087,13091,13094,13097,3539,13396,13461,3532,3952,3891,10525,11901,11929,13068,4625,10470,10861,10864,11362,11378,11861,11917,11951,11978,12077,12106,12109,12112,12115,12377,13296,3461,10906,11065,11135,11930,12076,12276,12491,12516,13118,13399,13489,3915,12021,13021,4249,3649,4622,3926,3960,4609,4612,4613,3417,3421,4611,4610,4416,3747,11894,4343,11750,4638,10772,10775,4643,11248,11251,11437,11548,11565,11611,4034,11608,11950,11954,12641,12649,12738,13237,13302,13333,3881,11178,11184,11202,12196,12328,12416,12706,3730,11318,11440,12448,12557,12567,12646,12701,12709,12823,13244,4206,3883,10909,11281,11446,11480,11491,12645,12695,13344,3591,3697,10825,10828,10921,11091,3699,4641,11895,4637,12989,4642,10665,10778,12510,12519,12563,12763,4304,11048,12528,12543,12566,4212,3914,12829,3859,3860,4639,10495,10498,10867,10870,11764,11955,12775,4640,11875,11960,3884,10831,11097,12090,13386,4144,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928,5930,5935,5943,5981,5996,6005,6008,6017,6021,6022,6023,6024,6025,6030,6035,6045,6051,6069,6073,6082,6112,6128,6154,6171,6172,6175,6190,6192,6194,6196,6211,6212,6215,6217,6220,6221,6238,6246,6247,6248,6250,6252,6290,6291,6296,6299,6305,6309,6343,6345,6347,6349,6359,6361,6364,6370,6372,6377,6380,6388,6396,6398,6399,6406,6429,6430,6431,6432,6433,6435,6442,6447,6481,6482,6485,6486,6487,6489,6490,6491,6492,6499,6535,6536,6545,6567,6568,6592,6594,6606,6607,6613,6643,6645,6660,6700,6703,6704,6760,6783,6826,6841,6849,6858,6859,6860,6861,6882,6883,6890,6902,6905,6907,6909,6910,6911,6913,6927,6938,6939,6940,6953,7008,7019,7021,7026,7045,7046,7082,7089,7096,7126,7157,7213,7242,7299,7320,7329,7332,7392,7402,7465,7467,7481,7490,7491,7492,7509,7513,7515,7562,7572,7575,7590,7638,7640,7643,7687,7688,7706,7776,7794,7818,7842,7854,7868,7879,7890,7891,7917,7919,7921,7931,7969,7980,8005,8032,8065,8096,8130,8169,8186,8188,8204,8205,8273,8284,8349,8373,8392,8419,8458,8459,8476,8516,8518,8520,8526,8542,8546,8561,8582,8590,8592,8602,8607,8611,8612,8613,8614,8615,8616,8635,8650,8651,8669,8671,8675,8676,8677,8678,8679,8697,8698,8699,8709,8722,8725,8736,8741,8743,8745,8746,8747,8754,8760,8768,8771,8788,8789,8798,8799,8807,8826,8839,8843,8864,8886,8887,8890,8891,8897,8906,8907,8930,8941,8951,8952,8953,8956,8979,8980,8991,9041,9051,9053,9069,9081,9082,9083,9094,9158,9189,9190,9191,9206,9223,9231,9259,9260,9329,9364,9370,9380,9381,9382,9391,9421,9437,9441,9445,9467,9468,9495,9559,9564,9567,9604,9605,9606,9634,9635,9651,9672,9678,9690,9715,9736,9745,9746,9747,9748,9763,9765,9770,9800,9801,9807,9808,9852,9853,9864,9865,9889,9907,9909,9910,9918,9923,9930,9954,9988,9990,9994,10044,10078,10088,10090,10094,10095,10097,10106,10107,10127,10132,10225,10317,10318,10319,10320,10379,10397,2,8,9,4668,4669,4687,4729,4731,4732,4755,4757,4758,4768,4813,4815,4863,4993,4994,5011,5035,5092,5093,5099,5100,5102,5104,5113,5116,5117,5125,5138,5139,5145,5166,5167,5185,5190,5191,5192,5193,5197,5205,5208,5215,5270,5275,5276,5281,5288,5319,5329,5334,5344,5362,5364,5371,5372,5374,5385,5403,5405,5406,5413,5420,5421,5433,5434,5435,5436,5438,5439,5444,5445,5446,5447,5478,5479,5480,5488,5489,5490,5491,5535,5540,5542,5578,5580,5581,5583,5584,5586,5587,5589,5598,5603,5605,5606,5607,5609,5611,5612,5613,5614,5615,5616,5625,5626,5636,5639,5650,5666,5667,5670,5681,5684,5685,5686,5713,5723,5738,5739,5748,5749,5751,5753,5758,5793,5798,5800,5859,5894,5895,5909,5915,5918,5919,5920,5921,5940,5944,5945,5954,5976,6009,6028,6029,6033,6034,6036,6059,6063,6066,6067,6068,6084,6096,6097,6130,6131,6135,6156,6159,6162,6184,6185,6213,6216,6225,6234,6236,6245,6249,6257,6258,6259,6260,6293,6310,6363,6400,6402,6403,6426,6427,6434,6438,6439,6443,6457,6473,6494,6495,6500,6512,6515,6528,6548,6555,6557,6572,6573,6576,6577,6579,6581,6582,6583,6585,6587,6593,6599,6600,6602,6603,6609,6611,6653,6659,6674,6678,6679,6680,6714,6719,6721,6726,6727,6737,6741,6755,6778,6779,6781,6782,6793,6799,6818,6821,6842,6862,6873,6876,6877,6878,6884,6898,6917,6919,6921,6923,6928,6934,6936,6950,6955,6956,6993,6994,6995,7010,7011,7013,7014,7035,7037,7052,7080,7104,7115,7117,7119,7121,7122,7154,7155,7156,7160,7161,7168,7169,7171,7173,7195,7204,7205,7216,7226,7266,7276,7282,7289,7300,7305,7307,7314,7322,7323,7336,7353,7374,7376,7395,7450,7451,7452,7454,7456,7460,7461,7466,7530,7558,7573,7578,7589,7620,7624,7631,7646,7671,7689,7692,7693,7703,7723,7725,7727,7729,7730,7731,7732,7733,7758,7784,7785,7817,7819,7820,7821,7827,7848,7865,7870,7876,7878,7886,7898,7899,7901,7922,7929,7950,8018,8019,8020,8068,8074,8075,8099,8100,8117,8118,8119,8177,8178,8207,8237,8247,8261,8276,8305,8309,8315,8327,8345,8350,8372,8417,8446,8460,8480,8483,8509,8535,8593,8594,8597,8598,8667,8701,8702,8703,8704,8731,8763,8792,8800,8801,8842,8863,8908,8924,8970,8973,8988,8995,9038,9077,9078,9096,9097,9111,9228,9233,9237,9257,9268,9291,9293,9296,9302,9304,9305,9316,9317,9336,9344,9355,9363,9407,9425,9480,9481,9487,9526,9551,9556,9596,9610,9614,9615,9619,9620,9633,9656,9671,9680,9681,9683,9685,9714,9834,9835,9884,9885,9924,9959,10069,10136,10291,10309,10314,3,2775,2779,2781,2782,2792,2793,2794,2798,2801,2802,2803,2813,2815,2818,2819,2821,2822,2823,2824,2825,2826,2827,2828,2829,2840,2841,2842,2843,2844,2850,2854,2856,2857,2858,2861,2862,2871,2872,2876,2885,2886,2887,2889,2891,2893,2894,2895,2901,2902,2903,2905,2915,2917,2924,2925,2926,2928,2929,2931,2932,2935,2936,2937,2939,2940,2941,2944,2945,2947,2952,2954,2955,2966,2987,2990,2991,2992,2993,2994,2998,3032,3039,5361,5402,5551,5552,5553,5637,5737,5767,5801,5817,5819,5825,5887,5888,5889,5890,5907,5942,6079,6119,6129,6153,6188,6226,6379,6384,6424,6425,6448,6450,6452,6459,6460,6461,6462,6463,6464,6465,6466,6550,6623,6624,6713,6750,6751,6790,6791,6935,6949,7005,7023,7024,7031,7053,7086,7088,7092,7137,7158,7159,7177,7178,7215,7260,7261,7360,7429,7430,7431,7432,7449,7482,7535,7536,7544,7549,7550,7561,7592,7593,7594,7595,7739,7740,7742,7744,7750,7751,7825,7956,7959,7965,7966,7977,8015,8016,8094,8135,8190,8212,8213,8291,8385,8456,8457,8461,8495,8531,8557,8558,8625,8643,8644,8645,8646,8796,9031,9055,9056,9125,9139,9192,9193,9311,9313,9348,9375,9409,9450,9654,9777,9919,10105,10161,10163,5977,6533,6534,6626,6646,6647,7077,7298,8443,8638,8717,8964,9150,9151,9219,9220,9404,9498,9499,9500,9501,9717,9982,9996,10365,10366,6608,8549,8550,9020,9039,9983,10364,4693,4702,4734,4735,4738,4780,4784,4789,4830,4927,4944,4974,4975,5006,5010,5069,5072,5132,5264,5304,5305,5307,5314,5315,5339,5379,5410,5432,5567,5642,5643,5644,5706,5763,5764,5790,5794,5853,5855,5864,5870,5958,6043,6151,6195,6253,6366])).
% 168.60/168.48 cnf(13628,plain,
% 168.60/168.48 (~P25(x136281,x136282,f315(f66(x136283,x136282,x136281,f181(x136284,x136285)),f315(f140(x136286),x136287)),f230(f909(x136281,a899)))),
% 168.60/168.48 inference(scs_inference,[],[3783,4092,12728,12750,12872,12874,12876,3674,11333,12394,12501,12504,12596,12638,12642,12650,12722,12863,12865,13303,13312,13317,13321,13327,13330,13357,13466,13471,3683,12468,12950,12952,3690,3410,12911,12913,12915,3411,12923,3377,12804,4603,4604,11974,4365,12957,3414,12919,3253,3309,12884,3310,12838,3311,3312,3313,12678,12890,4602,3732,4583,10413,10423,10436,10447,10519,10554,10557,10560,10662,10797,11110,11303,11306,11325,11328,11521,11622,11629,11643,11689,11692,11725,11740,11803,11862,11881,12175,12200,12216,12245,12251,12345,12464,12631,12692,12832,13379,13383,3495,3459,12944,3642,12147,3361,4589,10646,10746,11213,11313,13051,13403,4595,3052,3053,3055,3056,3059,3060,3062,3063,3064,3070,3071,3075,3076,3077,3080,3081,3082,3086,3087,3091,3092,3094,3097,3109,3113,3115,3116,3123,3130,3133,3136,3137,3139,3148,3156,3157,3160,3161,3162,3174,3180,3181,3183,3186,3190,3191,3193,3194,3201,3202,3209,3212,3222,3231,3332,4580,3236,3308,4581,3772,3998,11912,3286,11619,3422,3398,3401,10482,10485,10581,10584,10900,11634,11637,11751,11790,11795,11865,11907,12366,12572,12782,12834,12836,12846,12851,12853,12880,12888,12897,12917,12968,13171,13348,13470,13475,13491,3372,12663,12667,12671,3378,3387,3893,4194,3355,13234,3506,12725,12807,3275,3276,3636,3984,11665,3494,3338,3272,3299,3752,3295,3403,4101,3992,3815,3281,3282,3263,3905,3319,3496,11060,11187,12465,12682,3371,4066,4597,10473,10643,11518,12623,12664,12668,4600,12635,3431,11994,11997,13269,13368,13436,13440,13444,13448,4024,4626,11239,11338,11574,11577,3406,3834,3428,3543,3758,3516,3535,4606,3510,12909,12931,12933,3335,10546,10876,3336,4615,3595,3327,3254,3357,11655,4208,12653,12794,4068,11259,11390,11449,12607,12613,12739,12742,12772,4644,11162,11403,11512,11538,11582,11588,12551,4645,11292,11406,11515,4646,11409,11460,4647,11467,4648,3356,3634,12507,12548,12634,3799,3583,4479,4480,3618,3655,4594,11648,3776,3734,3778,3948,3702,13154,13158,13162,13166,13176,3735,3994,12498,3620,3876,3507,10565,10685,10763,10836,10839,10879,10979,11229,11839,12091,12171,12238,12316,12357,12436,12439,12776,13034,13073,13076,13137,13382,13387,3886,11898,3424,3519,11724,12009,13490,3696,4621,10450,10453,10479,10606,10781,10987,11002,11120,11560,11658,11838,12062,12067,12292,12295,12378,12554,12657,12980,12999,13002,13026,13077,13250,13255,13279,13284,4632,11767,11798,11835,11842,11878,13086,13090,3873,3643,13262,3645,13005,13008,13011,13014,13044,13047,13418,13422,13426,3646,4016,3608,13419,3609,13423,3467,3469,3443,4618,3334,4591,3825,4130,3627,4633,4201,11535,3757,3479,12015,12018,12472,12576,12753,4624,10441,10444,10614,10709,10728,10735,10758,10766,10769,10786,10972,11216,11429,11718,11812,11963,12080,12083,4170,4129,12522,4077,11057,12164,12351,12532,12681,13439,4119,13443,4124,11265,12391,12471,12531,12575,13272,13410,4125,3800,11846,12174,12323,12401,12455,4158,3817,10609,10706,11262,11343,11422,11486,12344,12348,12417,12687,12749,12769,12779,13241,13311,13316,13339,13360,4636,11005,11414,12535,13324,3440,10574,10672,10822,10886,10961,11008,11011,11042,11068,11104,11142,11181,11966,12012,12144,12199,12219,12222,12225,12228,12410,12424,12427,12430,12433,12515,12579,12698,12745,13027,13050,13109,13129,13140,13145,13148,13151,13184,13197,13208,13261,13290,13293,3441,10601,10657,10891,10982,11107,11743,12045,12048,12059,12150,12161,12180,12185,12231,12254,12271,13041,13188,13211,13251,13256,13280,13285,13406,3442,12442,12445,3515,12383,13106,13155,13159,13163,13167,13177,13181,4617,10490,10522,11026,11071,11080,11926,11947,12118,12121,12124,12127,12215,12234,12237,12250,12304,12307,12310,12313,12483,12486,12582,12585,12691,12731,12816,3590,10751,10842,11115,11159,11393,11396,11475,11557,11728,11977,12630,12819,13233,4628,11035,11045,11151,11172,11175,11242,11245,11256,11359,11367,11381,11417,11434,11443,11483,11524,11529,11532,11551,11554,11591,11596,11599,11602,11605,11845,11991,12024,12298,12301,12335,12384,12413,12560,12604,12610,12710,12713,12735,12793,12799,12810,12826,13105,13121,13124,13222,13307,13352,13371,13374,13415,13435,13469,3500,10873,10903,10912,10915,10918,11504,12732,12746,13087,13091,13094,13097,3539,13396,13461,3532,3952,3891,10525,11901,11929,13068,4625,10470,10861,10864,11362,11378,11861,11917,11951,11978,12077,12106,12109,12112,12115,12377,13296,3461,10906,11065,11135,11930,12076,12276,12491,12516,13118,13399,13489,3915,12021,13021,4249,3649,4622,3926,3960,4609,4612,4613,3417,3421,4611,4610,4416,3747,11894,4343,11750,4638,10772,10775,4643,11248,11251,11437,11548,11565,11611,4034,11608,11950,11954,12641,12649,12738,13237,13302,13333,3881,11178,11184,11202,12196,12328,12416,12706,3730,11318,11440,12448,12557,12567,12646,12701,12709,12823,13244,4206,3883,10909,11281,11446,11480,11491,12645,12695,13344,3591,3697,10825,10828,10921,11091,3699,4641,11895,4637,12989,4642,10665,10778,12510,12519,12563,12763,4304,11048,12528,12543,12566,4212,3914,12829,3859,3860,4639,10495,10498,10867,10870,11764,11955,12775,4640,11875,11960,3884,10831,11097,12090,13386,4144,4655,4681,4736,4740,4764,4779,4786,4788,4824,4829,4858,4864,4950,4976,4977,4992,5046,5047,5070,5071,5085,5089,5114,5120,5136,5140,5141,5142,5147,5148,5171,5196,5198,5199,5209,5214,5220,5256,5257,5265,5273,5277,5279,5282,5294,5297,5303,5308,5309,5322,5328,5331,5332,5336,5365,5380,5389,5391,5392,5395,5396,5397,5407,5409,5415,5416,5417,5423,5427,5428,5429,5437,5441,5442,5448,5461,5469,5482,5484,5492,5494,5495,5498,5502,5529,5543,5544,5559,5571,5593,5599,5623,5624,5628,5647,5655,5656,5661,5662,5672,5674,5688,5692,5701,5702,5704,5705,5721,5726,5735,5736,5747,5754,5768,5772,5775,5781,5782,5783,5786,5791,5827,5828,5831,5833,5835,5837,5838,5839,5841,5843,5845,5850,5857,5872,5886,5892,5893,5905,5916,5917,5924,5928,5930,5935,5943,5981,5996,6005,6008,6017,6021,6022,6023,6024,6025,6030,6035,6045,6051,6069,6073,6082,6112,6128,6154,6171,6172,6175,6190,6192,6194,6196,6211,6212,6215,6217,6220,6221,6238,6246,6247,6248,6250,6252,6290,6291,6296,6299,6305,6309,6343,6345,6347,6349,6359,6361,6364,6370,6372,6377,6380,6388,6396,6398,6399,6406,6429,6430,6431,6432,6433,6435,6442,6447,6481,6482,6485,6486,6487,6489,6490,6491,6492,6499,6535,6536,6545,6567,6568,6592,6594,6606,6607,6613,6643,6645,6660,6700,6703,6704,6760,6783,6826,6841,6849,6858,6859,6860,6861,6882,6883,6890,6902,6905,6907,6909,6910,6911,6913,6927,6938,6939,6940,6953,7008,7019,7021,7026,7045,7046,7082,7089,7096,7126,7157,7213,7242,7299,7320,7329,7332,7392,7402,7465,7467,7481,7490,7491,7492,7509,7513,7515,7562,7572,7575,7590,7638,7640,7643,7687,7688,7706,7776,7794,7818,7842,7854,7868,7879,7890,7891,7917,7919,7921,7931,7969,7980,8005,8032,8065,8096,8130,8169,8186,8188,8204,8205,8273,8284,8349,8373,8392,8419,8458,8459,8476,8516,8518,8520,8526,8542,8546,8561,8582,8590,8592,8602,8607,8611,8612,8613,8614,8615,8616,8635,8650,8651,8669,8671,8675,8676,8677,8678,8679,8697,8698,8699,8709,8722,8725,8736,8741,8743,8745,8746,8747,8754,8760,8768,8771,8788,8789,8798,8799,8807,8826,8839,8843,8864,8886,8887,8890,8891,8897,8906,8907,8930,8941,8951,8952,8953,8956,8979,8980,8991,9041,9051,9053,9069,9081,9082,9083,9094,9158,9189,9190,9191,9206,9223,9231,9259,9260,9329,9364,9370,9380,9381,9382,9391,9421,9437,9441,9445,9467,9468,9495,9559,9564,9567,9604,9605,9606,9634,9635,9651,9672,9678,9690,9715,9736,9745,9746,9747,9748,9763,9765,9770,9800,9801,9807,9808,9852,9853,9864,9865,9889,9907,9909,9910,9918,9923,9930,9954,9988,9990,9994,10044,10078,10088,10090,10094,10095,10097,10106,10107,10127,10132,10225,10317,10318,10319,10320,10379,10397,2,8,9,4668,4669,4687,4729,4731,4732,4755,4757,4758,4768,4813,4815,4863,4993,4994,5011,5035,5092,5093,5099,5100,5102,5104,5113,5116,5117,5125,5138,5139,5145,5166,5167,5185,5190,5191,5192,5193,5197,5205,5208,5215,5270,5275,5276,5281,5288,5319,5329,5334,5344,5362,5364,5371,5372,5374,5385,5403,5405,5406,5413,5420,5421,5433,5434,5435,5436,5438,5439,5444,5445,5446,5447,5478,5479,5480,5488,5489,5490,5491,5535,5540,5542,5578,5580,5581,5583,5584,5586,5587,5589,5598,5603,5605,5606,5607,5609,5611,5612,5613,5614,5615,5616,5625,5626,5636,5639,5650,5666,5667,5670,5681,5684,5685,5686,5713,5723,5738,5739,5748,5749,5751,5753,5758,5793,5798,5800,5859,5894,5895,5909,5915,5918,5919,5920,5921,5940,5944,5945,5954,5976,6009,6028,6029,6033,6034,6036,6059,6063,6066,6067,6068,6084,6096,6097,6130,6131,6135,6156,6159,6162,6184,6185,6213,6216,6225,6234,6236,6245,6249,6257,6258,6259,6260,6293,6310,6363,6400,6402,6403,6426,6427,6434,6438,6439,6443,6457,6473,6494,6495,6500,6512,6515,6528,6548,6555,6557,6572,6573,6576,6577,6579,6581,6582,6583,6585,6587,6593,6599,6600,6602,6603,6609,6611,6653,6659,6674,6678,6679,6680,6714,6719,6721,6726,6727,6737,6741,6755,6778,6779,6781,6782,6793,6799,6818,6821,6842,6862,6873,6876,6877,6878,6884,6898,6917,6919,6921,6923,6928,6934,6936,6950,6955,6956,6993,6994,6995,7010,7011,7013,7014,7035,7037,7052,7080,7104,7115,7117,7119,7121,7122,7154,7155,7156,7160,7161,7168,7169,7171,7173,7195,7204,7205,7216,7226,7266,7276,7282,7289,7300,7305,7307,7314,7322,7323,7336,7353,7374,7376,7395,7450,7451,7452,7454,7456,7460,7461,7466,7530,7558,7573,7578,7589,7620,7624,7631,7646,7671,7689,7692,7693,7703,7723,7725,7727,7729,7730,7731,7732,7733,7758,7784,7785,7817,7819,7820,7821,7827,7848,7865,7870,7876,7878,7886,7898,7899,7901,7922,7929,7950,8018,8019,8020,8068,8074,8075,8099,8100,8117,8118,8119,8177,8178,8207,8237,8247,8261,8276,8305,8309,8315,8327,8345,8350,8372,8417,8446,8460,8480,8483,8509,8535,8593,8594,8597,8598,8667,8701,8702,8703,8704,8731,8763,8792,8800,8801,8842,8863,8908,8924,8970,8973,8988,8995,9038,9077,9078,9096,9097,9111,9228,9233,9237,9257,9268,9291,9293,9296,9302,9304,9305,9316,9317,9336,9344,9355,9363,9407,9425,9480,9481,9487,9526,9551,9556,9596,9610,9614,9615,9619,9620,9633,9656,9671,9680,9681,9683,9685,9714,9834,9835,9884,9885,9924,9959,10069,10136,10291,10309,10314,3,2775,2779,2781,2782,2792,2793,2794,2798,2801,2802,2803,2813,2815,2818,2819,2821,2822,2823,2824,2825,2826,2827,2828,2829,2840,2841,2842,2843,2844,2850,2854,2856,2857,2858,2861,2862,2871,2872,2876,2885,2886,2887,2889,2891,2893,2894,2895,2901,2902,2903,2905,2915,2917,2924,2925,2926,2928,2929,2931,2932,2935,2936,2937,2939,2940,2941,2944,2945,2947,2952,2954,2955,2966,2987,2990,2991,2992,2993,2994,2998,3032,3039,5361,5402,5551,5552,5553,5637,5737,5767,5801,5817,5819,5825,5887,5888,5889,5890,5907,5942,6079,6119,6129,6153,6188,6226,6379,6384,6424,6425,6448,6450,6452,6459,6460,6461,6462,6463,6464,6465,6466,6550,6623,6624,6713,6750,6751,6790,6791,6935,6949,7005,7023,7024,7031,7053,7086,7088,7092,7137,7158,7159,7177,7178,7215,7260,7261,7360,7429,7430,7431,7432,7449,7482,7535,7536,7544,7549,7550,7561,7592,7593,7594,7595,7739,7740,7742,7744,7750,7751,7825,7956,7959,7965,7966,7977,8015,8016,8094,8135,8190,8212,8213,8291,8385,8456,8457,8461,8495,8531,8557,8558,8625,8643,8644,8645,8646,8796,9031,9055,9056,9125,9139,9192,9193,9311,9313,9348,9375,9409,9450,9654,9777,9919,10105,10161,10163,5977,6533,6534,6626,6646,6647,7077,7298,8443,8638,8717,8964,9150,9151,9219,9220,9404,9498,9499,9500,9501,9717,9982,9996,10365,10366,6608,8549,8550,9020,9039,9983,10364,4693,4702,4734,4735,4738,4780,4784,4789,4830,4927,4944,4974,4975,5006,5010,5069,5072,5132,5264,5304,5305,5307,5314,5315,5339,5379,5410,5432,5567,5642,5643,5644,5706,5763,5764,5790,5794,5853,5855,5864,5870,5958,6043,6151,6195,6253,6366,6493,6657,6695,6870,7132,7303,7537,7599,7936,7937,8187,8193,8889,9018])).
% 168.60/168.48 cnf(13733,plain,
% 168.60/168.48 (P1(f315(f315(f223(f909(x137331,a899)),x137332),x137332))),
% 168.60/168.48 inference(rename_variables,[],[3730])).
% 168.60/168.48 cnf(13736,plain,
% 168.60/168.48 (~P1(f315(f315(f224(a901),f315(f315(f73(a901),x137361),x137362)),x137361))),
% 168.60/168.48 inference(rename_variables,[],[4640])).
% 168.60/168.48 cnf(13739,plain,
% 168.60/168.48 (~P1(f315(f315(f317(f908(f902(x137391),f902(x137391))),f315(f315(f240(f902(x137391),f902(x137391)),f102(x137391)),x137392)),f146(x137391,x137393)))),
% 168.60/168.48 inference(rename_variables,[],[4648])).
% 168.60/168.48 cnf(13745,plain,
% 168.60/168.48 (~P1(f315(f315(f224(a901),x137451),x137451))),
% 168.60/168.48 inference(rename_variables,[],[4617])).
% 168.60/168.48 cnf(13748,plain,
% 168.60/168.48 (E(f315(f272(x137481,x137481),f251(x137481,x137482)),x137482)),
% 168.60/168.48 inference(rename_variables,[],[3401])).
% 168.60/168.48 cnf(13773,plain,
% 168.60/168.48 (~P1(f315(f315(f317(a901),x137731),f315(f270(a901),f2(a901))))),
% 168.60/168.48 inference(rename_variables,[],[12042])).
% 168.60/168.48 cnf(13778,plain,
% 168.60/168.48 (~P1(f315(f315(f317(a901),x137781),f315(f270(a901),f2(a901))))),
% 168.60/168.48 inference(rename_variables,[],[12042])).
% 168.60/168.48 cnf(13793,plain,
% 168.60/168.48 (~P1(f315(f315(f317(f908(x137931,x137931)),x137932),f251(x137931,f177(f909(x137931,a899)))))),
% 168.60/168.48 inference(rename_variables,[],[11171])).
% 168.60/168.48 cnf(13796,plain,
% 168.60/168.48 (P1(f315(f315(f223(a901),x137961),f315(f315(f73(a901),x137961),x137962)))),
% 168.60/168.48 inference(rename_variables,[],[3699])).
% 168.60/168.48 cnf(13803,plain,
% 168.60/168.48 (E(f315(f272(x138031,x138031),f251(x138031,x138032)),x138032)),
% 168.60/168.48 inference(rename_variables,[],[3401])).
% 168.60/168.48 cnf(13822,plain,
% 168.60/168.48 (P1(f315(f315(f223(a901),f2(a901)),x138221))),
% 168.60/168.48 inference(rename_variables,[],[3461])).
% 168.60/168.48 cnf(13861,plain,
% 168.60/168.48 (~E(f315(f315(f140(x138611),x138612),x138613),x138613)),
% 168.60/168.48 inference(rename_variables,[],[4597])).
% 168.60/168.48 cnf(13870,plain,
% 168.60/168.48 (~E(f315(f315(f90(a901),f315(a101,x138701)),x138701),f315(a101,x138701))),
% 168.60/168.48 inference(rename_variables,[],[11783])).
% 168.60/168.48 cnf(13873,plain,
% 168.60/168.48 (~P1(f315(f55(x138731,x138732,f177(f909(x138731,a899))),x138733))),
% 168.60/168.48 inference(rename_variables,[],[4638])).
% 168.60/168.48 cnf(13898,plain,
% 168.60/168.48 (P36(x138981,x138982,x138983,f315(f315(f143(x138984,x138981),x138985),f103(x138984,f102(x138984))),f102(x138982))),
% 168.60/168.48 inference(rename_variables,[],[11455])).
% 168.60/168.48 cnf(13903,plain,
% 168.60/168.48 (E(f315(f315(f123(x139031),x139032),f102(x139031)),x139032)),
% 168.60/168.48 inference(rename_variables,[],[3372])).
% 168.60/168.48 cnf(13906,plain,
% 168.60/168.48 (~P1(f315(f315(f224(a901),f315(f315(f73(a901),x139061),x139062)),x139061))),
% 168.60/168.48 inference(rename_variables,[],[4640])).
% 168.60/168.48 cnf(13909,plain,
% 168.60/168.48 (~P1(f315(f315(f317(f908(x139091,x139091)),x139092),f251(x139091,f177(f909(x139091,a899)))))),
% 168.60/168.48 inference(rename_variables,[],[11171])).
% 168.60/168.48 cnf(13915,plain,
% 168.60/168.48 (~E(f315(f315(f140(x139151),x139152),x139153),x139153)),
% 168.60/168.48 inference(rename_variables,[],[4597])).
% 168.60/168.48 cnf(13932,plain,
% 168.60/168.48 (~P1(f315(f315(f317(f908(x139321,x139321)),x139322),f251(x139321,f177(f909(x139321,a899)))))),
% 168.60/168.48 inference(rename_variables,[],[11171])).
% 168.60/168.48 cnf(13970,plain,
% 168.60/168.48 (P1(f315(f315(f224(a1),f315(f315(f3(a1),x139701),f71(a1))),x139701))),
% 168.60/168.48 inference(rename_variables,[],[10981])).
% 168.60/168.48 cnf(13977,plain,
% 168.60/168.48 (E(f315(f272(x139771,x139771),f251(x139771,x139772)),x139772)),
% 168.60/168.48 inference(rename_variables,[],[3401])).
% 168.60/168.48 cnf(14002,plain,
% 168.60/168.48 (~E(f315(f315(f140(x140021),x140022),x140023),f102(x140021))),
% 168.60/168.48 inference(rename_variables,[],[4600])).
% 168.60/168.48 cnf(14014,plain,
% 168.60/168.48 (P1(f315(f315(f223(f909(x140141,a899)),f177(f909(x140141,a899))),x140142))),
% 168.60/168.48 inference(rename_variables,[],[3883])).
% 168.60/168.48 cnf(14021,plain,
% 168.60/168.48 (P1(f315(f315(f223(f909(x140211,a899)),f315(f161(x140211),f165(x140211,x140212,x140213))),f315(f161(x140211),x140212)))),
% 168.60/168.48 inference(rename_variables,[],[4124])).
% 168.60/168.48 cnf(14059,plain,
% 168.60/168.48 (~P1(f315(f55(x140591,x140592,f177(f909(x140591,a899))),x140593))),
% 168.60/168.48 inference(rename_variables,[],[4638])).
% 168.60/168.48 cnf(14127,plain,
% 168.60/168.48 ($false),
% 168.60/168.48 inference(scs_inference,[],[3783,3467,3469,4016,3236,3442,4208,4641,4618,3515,4611,3532,3886,4644,4068,4034,4628,4124,14021,3914,4597,13861,13915,4600,14002,4606,3424,3519,3440,3441,3891,3461,13822,3730,13733,3883,14014,3697,3699,13796,4304,3884,3401,13748,13803,13977,3372,13903,3282,3396,4648,13739,4617,13745,4638,13873,14059,4637,4642,4639,4640,13736,13906,11783,13870,13389,10796,10562,12103,11593,13576,10755,12518,13036,11310,12760,10981,13970,11153,11490,11445,11315,11542,10743,3497,3472,3386,11387,13289,13292,13590,10930,12450,12556,13038,12040,12042,13773,13778,10938,11377,12163,11171,13793,13909,13932,11493,10920,11610,12721,13600,13628,11189,11455,13898,12625,11330,11424,3078,3985,9,2,8,4788,8130,5199,9765,6025,6005,8204,5409,6345,6361,8771,8889,5864,5482,5674,7157,7575,8930,8699,8953,5336,8032,5332,7329,8590,10320,7491,6703,8373,8669,9069,5623,5141,5857,6594,6907,7980,6433,5315,8671,5850,6290,6490,6861,5309,5642,6250,6366,5828,7126,7842,9747,6291,8789,5567,8798,5314,7213,8607,4977,6657,6783,8458,9748,9807,9865,5841,9364,6364,8736,5492,5429,5209,9930,5692,6112,6211,6447,7537,5148,6890,7688,5643,7891,5495,9053,5835,5264,5257,9329,6826,6217,5461,6430,5417,5831,4693,5396,5593,5781,6704,8205,4655,5529,5827,6021,6909,9994,4740,6486,6022,8516,8193,5308,6172,10379,6432,5322,6030,8520,8839,8768,9391,8096,8907,5071,5120,5432,7045,8419,8956,8526,9468,5279,5494,5559,5905,6535,8476,9259,7089,6349,8677,6190,6073,8760,9690,5790,5656,9441,5427,5837,10094,5644,9559,9954,5783,6212,8561,5304,4786,5916,9606,9746,4764]),
% 168.60/168.48 ['proof']).
% 168.60/168.48 % SZS output end Proof
% 168.60/168.48 % Total time :142.200000s
%------------------------------------------------------------------------------